├── DualMultWS.jl ├── LICENSE ├── ParkingConstraints.jl ├── ParkingSignedDist.jl ├── README.md ├── a_star.jl ├── collision_check.jl ├── hybrid_a_star.jl ├── images ├── TrajParallelHOBCA.gif └── TrajReverseHOBCA.gif ├── main.jl ├── obstHrep.jl ├── plotTraj.jl ├── reeds_shepp.jl ├── setup.jl └── veloSmooth.jl /DualMultWS.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # DualMultWS.jl: computes warm starting points for dual multipliers lambda and mu 28 | ############### 29 | # 30 | function DualMultWS(N,nOb,vOb, A, b,rx,ry,ryaw) 31 | 32 | x = zeros(3,N+1) 33 | x[1,:] = rx 34 | x[2,:] = ry 35 | x[3,:] = ryaw 36 | 37 | m = Model(solver=IpoptSolver(hessian_approximation="exact",mumps_pivtol=1e-5, 38 | max_iter=100,tol=1e-5, print_level=3, suppress_all_output="yes")) 39 | 40 | W_ev = ego[2]+ego[4] 41 | L_ev = ego[1]+ego[3] 42 | 43 | g = [L_ev/2,W_ev/2,L_ev/2,W_ev/2] 44 | 45 | # ofset from X-Y to the center of the ego set 46 | offset = (ego[1]+ego[3])/2 - ego[3] 47 | 48 | 49 | @variable(m, l[1:sum(vOb),1:(N+1)]) # dual multiplier associated with obstacleShape 50 | @variable(m, n[1:nOb*4,1:(N+1)]) # dual multiplier associated with carShape 51 | @variable(m, d[1:nOb,1:(N+1)]) 52 | 53 | @NLobjective(m, Max,sum(sum(d[i,k] for k=1:N+1) for i=1:nOb )) 54 | 55 | @constraint(m, l .>= 0 ) 56 | @constraint(m, n .>= 0) 57 | 58 | for i in 1:N+1 # iterate over time steps 59 | for j = 1 : nOb # iterate over obstacles 60 | Aj = A[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract obstacle matrix associated with j-th obstacle 61 | lj = l[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract lambda dual variables associate j-th obstacle 62 | nj = n[(j-1)*4+1:j*4 ,:] # extract mu dual variables associated with j-th obstacle 63 | bj = b[sum(vOb[1:j-1])+1 : sum(vOb[1:j])] # extract obstacle matrix associated with j-th obstacle 64 | 65 | # norm(A'*lambda) <= 1 66 | @constraint(m, (sum(Aj[k,1]*lj[k,i] for k = 1 : vOb[j]))^2 + (sum(Aj[k,2]*lj[k,i] for k = 1 : vOb[j]))^2 <= 1 ) 67 | 68 | # G'*mu + R'*A*lambda = 0 69 | @constraint(m, (nj[1,i] - nj[3,i]) + cos(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + sin(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j]) == 0 ) 70 | @constraint(m, (nj[2,i] - nj[4,i]) - sin(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + cos(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j]) == 0 ) 71 | 72 | # -g'*mu + (A*t - b)*lambda > 0 73 | @constraint(m, d[j,i] == -sum(g[k]*nj[k,i] for k = 1:4) + (x[1,i]+cos(x[3,i])*offset)*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) 74 | + (x[2,i]+sin(x[3,i])*offset)*sum(Aj[k,2]*lj[k,i] for k=1:vOb[j]) - sum(bj[k]*lj[k,i] for k=1:vOb[j])) 75 | end 76 | end 77 | tic() 78 | solve(m; suppress_warnings=true) 79 | time = toq(); 80 | # print("Auxillery problem time (to warm start dual variables) = ",time," s \n") 81 | 82 | 83 | lp = getvalue(l)' 84 | np = getvalue(n)' 85 | 86 | return lp,np 87 | 88 | end -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /ParkingConstraints.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # checks if the path provided by IPOPT is feasible 28 | # useful when Restoration Failure is reported by IPOPT 29 | ############### 30 | 31 | 32 | function ParkingConstraints(x0,xF,N,Ts,L,ego,XYbounds,nOb,vOb, A, b,x,u,l,n,timeScale,fixTime,sd) 33 | 34 | 35 | # desired safety distance 36 | dmin = 0.05 # anything bigger than 0, e.g. 0.05 37 | 38 | c0 = zeros(5,1) 39 | c1 = zeros(4,1) 40 | c2 = zeros(4,1) 41 | c3 = zeros(4,N) 42 | c4 = zeros(1,1) 43 | c5 = zeros(1,1) 44 | c6 = zeros(4,N+1) 45 | 46 | e = zeros(7,1) 47 | 48 | c0[1] = maximum(abs(u[1,:]))-0.6 49 | c0[2] = maximum(abs(u[2,:]))-0.4 50 | 51 | 52 | c0[3] = maximum(abs(timeScale-1))-0.2 53 | 54 | c0[4] = -minimum(l) 55 | c0[5] = -minimum(n) 56 | 57 | print(c0,"\n") 58 | 59 | 60 | #starting point 61 | c1[1] = abs(x[1,1] - x0[1]) 62 | c1[2] = abs(x[2,1] - x0[2]) 63 | c1[3] = abs(x[3,1] - x0[3]) 64 | c1[4] = abs(x[4,1] - x0[4]) 65 | 66 | #end point 67 | c2[1] = abs(x[1,N+1] - xF[1]) 68 | c2[2] = abs(x[2,N+1] - xF[2]) 69 | c2[3] = abs(x[3,N+1] - xF[3]) 70 | c2[4] = abs(x[4,N+1] - xF[4]) 71 | 72 | ############################## 73 | # dynamics of the car 74 | ############################## 75 | # - unicycle dynamic with euler forward 76 | # - sampling time scaling, is identical over the horizon 77 | 78 | for i in 1:N 79 | 80 | if fixTime == 1 81 | c3[1,i] = x[1,i+1] - (x[1,i] + Ts*(x[4,i] + Ts/2*u[2,i])*cos((x[3,i] + Ts/2*x[4,i]*tan(u[1,i])/L))) 82 | c3[2,i] = x[2,i+1] - (x[2,i] + Ts*(x[4,i] + Ts/2*u[2,i])*sin((x[3,i] + Ts/2*x[4,i]*tan(u[1,i])/L))) 83 | c3[3,i] = x[3,i+1] - (x[3,i] + Ts*(x[4,i] + Ts/2*u[2,i])*tan(u[1,i])/L) 84 | c3[4,i] = x[4,i+1] - (x[4,i] + Ts*u[2,i]) 85 | else 86 | c3[1,i] = x[1,i+1] - (x[1,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*cos((x[3,i] + timeScale[i]*Ts/2*x[4,i]*tan(u[1,i])/L))) 87 | c3[1,i] = x[2,i+1] - (x[2,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*sin((x[3,i] + timeScale[i]*Ts/2*x[4,i]*tan(u[1,i])/L))) 88 | c3[1,i] = x[3,i+1] - (x[3,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*tan(u[1,i])/L) 89 | c3[1,i] = x[4,i+1] - (x[4,i] + timeScale[i]*Ts*u[2,i]) 90 | 91 | end 92 | 93 | end 94 | 95 | u0 = [0,0] 96 | 97 | 98 | if fixTime == 1 99 | 100 | # print(diff([0. u[1,:]']'),"\n") 101 | # print(abs(diff([0. u[1,:]']'))/Ts,"\n") 102 | c5 = maximum(abs(diff([0. u[1,:]']'))/Ts) - 0.6 103 | c4 = 0 104 | else 105 | c4 = maximum(abs(diff(timeScale))) 106 | c5 = maximum(abs(diff([0 u[1,:]']'))/(timeScale[1]*Ts)) - 0.6 107 | end 108 | 109 | 110 | ############################## 111 | # obstacle avoidance constraints 112 | ############################## 113 | 114 | # width and length of ego set 115 | W_ev = ego[2]+ego[4] 116 | L_ev = ego[1]+ego[3] 117 | 118 | g = [L_ev/2,W_ev/2,L_ev/2,W_ev/2] 119 | 120 | # ofset from X-Y to the center of the ego set 121 | offset = (ego[1]+ego[3])/2 - ego[3] 122 | 123 | 124 | for i in 1:N+1 # iterate over time steps 125 | for j = 1 : nOb # iterate over obstacles 126 | Aj = A[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract obstacle matrix associated with j-th obstacle 127 | lj = l[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract lambda dual variables associate j-th obstacle 128 | nj = n[(j-1)*4+1:j*4 ,:] # extract mu dual variables associated with j-th obstacle 129 | bj = b[sum(vOb[1:j-1])+1 : sum(vOb[1:j])] # extract obstacle matrix associated with j-th obstacle 130 | 131 | # norm(A'*lambda) <= 1 132 | if sd == 1 133 | c6[1,i] = abs((sum(Aj[k,1]*lj[k,i] for k = 1 : vOb[j]))^2 + (sum(Aj[k,2]*lj[k,i] for k = 1 : vOb[j]))^2) - 1 134 | else 135 | c6[1,i] = (sum(Aj[k,1]*lj[k,i] for k = 1 : vOb[j]))^2 + (sum(Aj[k,2]*lj[k,i] for k = 1 : vOb[j]))^2 - 1 136 | end 137 | 138 | # G'*mu + R'*A*lambda = 0 139 | c6[2,i] = abs((nj[1,i] - nj[3,i]) + cos(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + sin(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j])) 140 | c6[3,i] = abs((nj[2,i] - nj[4,i]) - sin(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + cos(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j])) 141 | 142 | # -g'*mu + (A*t - b)*lambda > 0 143 | c6[4,i] = -(-sum(g[k]*nj[k,i] for k = 1:4) + (x[1,i]+cos(x[3,i])*offset)*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) 144 | + (x[2,i]+sin(x[3,i])*offset)*sum(Aj[k,2]*lj[k,i] for k=1:vOb[j]) - sum(bj[k]*lj[k,i] for k=1:vOb[j])) + dmin 145 | end 146 | 147 | end 148 | 149 | e[1] = maximum(c0)<= 5e-5 150 | e[2] = maximum(c1)<= 5e-5 151 | e[3] = maximum(c2)<= 5e-5 152 | e[4] = maximum(abs(c3))<= 5e-5 153 | e[5] = c4 <= 5e-5 154 | e[6] = c5 <= 5e-5 155 | e[7] = maximum(c6)<= 5e-5 156 | 157 | # print(e,"\n") 158 | 159 | if sum(e) == 7 160 | return 1 161 | else 162 | return 0 163 | end 164 | 165 | end 166 | -------------------------------------------------------------------------------- /ParkingSignedDist.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # computes collision-free trajectory by appropriately reformulating the distance function 28 | ############### 29 | 30 | 31 | function ParkingSignedDist(x0,xF,N,Ts,L,ego,XYbounds,nOb,vOb, A, b,fixTime,xWS,uWS) 32 | 33 | 34 | # desired safety distance 35 | dmin = 0.05 # anything bigger than 0, e.g. 0.05 36 | 37 | ############################## 38 | # Define JuMP file 39 | ############################## 40 | # Define IPOPT as solver and well as solver settings 41 | ############################## 42 | # seems to work best 43 | m = Model(solver=IpoptSolver(hessian_approximation="exact",mumps_pivtol=1e-6,alpha_for_y="min",recalc_y="yes", 44 | mumps_mem_percent=6000,max_iter=200,tol=1e-5, print_level=0, 45 | min_hessian_perturbation=1e-12,jacobian_regularization_value=1e-7))#,nlp_scaling_method="none" 46 | 47 | ############################## 48 | # defining optimization variables 49 | ############################## 50 | #state 51 | @variable(m, x[1:4,1:(N+1)]) 52 | #scaling on sampling time 53 | if fixTime == 0 54 | @variable(m, timeScale[1:N+1]) 55 | end 56 | # timeScale = ones(1,N+1) 57 | #control 58 | @variable(m, u[1:2,1:(N)]) 59 | # lagrange multipliers for dual dist function 60 | @variable(m, l[1:sum(vOb),1:(N+1)]) # dual multiplier associated with obstacleShape 61 | @variable(m, n[1:nOb*4,1:(N+1)]) # dual multiplier associated with carShape 62 | 63 | 64 | # regularization parameter to improve numerical stability 65 | reg = 1e-7; 66 | ############################## 67 | # cost function 68 | ############################## 69 | # (min control inputs)+ 70 | # (min input rate) 71 | # (min time)+ 72 | # (regularization wrt HA* traj) 73 | ############################## 74 | 75 | u0 = [0,0] 76 | #fix time objective 77 | if fixTime == 1 78 | @NLobjective(m, Min,sum(0.01*u[1,i]^2 + 0.5*u[2,i]^2 for i = 1:N) + 79 | sum(0.1*((u[1,i+1]-u[1,i])/Ts)^2 + 0.1*((u[2,i+1]-u[2,i])/Ts)^2 for i = 1:N-1)+ 80 | (0.1*((u[1,1]-u0[1])/(Ts))^2 + 0.1*((u[2,1]-u0[2])/(Ts))^2) + 81 | sum(0.001*(x[1,i]-xWS[i,1])^2 + 0.001*(x[2,i]-xWS[i,2])^2 + 0.0001*(x[3,i]-xWS[i,3])^2 for i=1:N+1)) 82 | else 83 | #varo time objective 84 | @NLobjective(m, Min,sum(0.01*u[1,i]^2 + 0.1*u[2,i]^2 for i = 1:N) + 85 | sum(0.1*((u[1,i+1]-u[1,i])/(timeScale[i]*Ts))^2 + 0.1*((u[2,i+1]-u[2,i])/(timeScale[i]*Ts))^2 for i = 1:N-1) + 86 | (0.1*((u[1,1]-u0[1]) /(timeScale[1]*Ts))^2 + 0.1*((u[2,1]-u0[2]) /(timeScale[1]*Ts))^2) + 87 | sum(0.5*timeScale[i] + 1*timeScale[i]^2 for i = 1:N+1)+ 88 | sum(0.001*(x[1,i]-xWS[i,1])^2 + 0.001*(x[2,i]-xWS[i,2])^2 + 0.0001*(x[3,i]-xWS[i,3])^2 for i=1:N+1)) 89 | end 90 | 91 | ############################## 92 | # bounds on states, inputs, 93 | # and dual multipliers. 94 | ############################## 95 | #input constraints 96 | @constraint(m, [i=1:N], -0.6 <= u[1,i] <= 0.6) 97 | @constraint(m, [i=1:N], -0.4 <= u[2,i] <= 0.4) 98 | 99 | #state constraints 100 | @constraint(m, [i=1:N+1], XYbounds[1] <= x[1,i] <= XYbounds[2]) 101 | @constraint(m, [i=1:N+1], XYbounds[3] <= x[2,i] <= XYbounds[4]) 102 | 103 | @constraint(m, [i=1:N+1], -1 <= x[4,i] <= 2) 104 | 105 | # bounds on time scaling 106 | if fixTime == 0 107 | @constraint(m, 0.8 .<= timeScale .<= 1.2) 108 | end 109 | 110 | 111 | # positivity constraints on dual multipliers 112 | @constraint(m, l .>= 0) 113 | @constraint(m, n .>= 0) 114 | 115 | ############################## 116 | # start and finish point 117 | ############################## 118 | 119 | #starting point 120 | @constraint(m, x[1,1] == x0[1]) 121 | @constraint(m, x[2,1] == x0[2]) 122 | @constraint(m, x[3,1] == x0[3]) 123 | @constraint(m, x[4,1] == x0[4]) 124 | 125 | #end point 126 | @constraint(m, x[1,N+1] == xF[1]) 127 | @constraint(m, x[2,N+1] == xF[2]) 128 | @constraint(m, x[3,N+1] == xF[3]) 129 | @constraint(m, x[4,N+1] == xF[4]) 130 | 131 | ############################## 132 | # dynamics of the car 133 | ############################## 134 | # - unicycle dynamic with euler forward 135 | # - sampling time scaling, is identical over the horizon 136 | 137 | for i in 1:N 138 | 139 | if fixTime == 1 # sampling time is fixed 140 | @NLconstraint(m, x[1,i+1] == x[1,i] + Ts*(x[4,i] + Ts/2*u[2,i])*cos((x[3,i] + Ts/2*x[4,i]*tan(u[1,i])/L))) 141 | @NLconstraint(m, x[2,i+1] == x[2,i] + Ts*(x[4,i] + Ts/2*u[2,i])*sin((x[3,i] + Ts/2*x[4,i]*tan(u[1,i])/L))) 142 | @NLconstraint(m, x[3,i+1] == x[3,i] + Ts*(x[4,i] + Ts/2*u[2,i])*tan(u[1,i])/L) 143 | @NLconstraint(m, x[4,i+1] == x[4,i] + Ts*u[2,i]) 144 | else # sampling time is variable 145 | @NLconstraint(m, x[1,i+1] == x[1,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*cos((x[3,i] + timeScale[i]*Ts/2*x[4,i]*tan(u[1,i])/L))) 146 | @NLconstraint(m, x[2,i+1] == x[2,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*sin((x[3,i] + timeScale[i]*Ts/2*x[4,i]*tan(u[1,i])/L))) 147 | @NLconstraint(m, x[3,i+1] == x[3,i] + timeScale[i]*Ts*(x[4,i] + timeScale[i]*Ts/2*u[2,i])*tan(u[1,i])/L) 148 | @NLconstraint(m, x[4,i+1] == x[4,i] + timeScale[i]*Ts*u[2,i]) 149 | end 150 | 151 | if fixTime == 0 152 | @constraint(m, timeScale[i] == timeScale[i+1]) 153 | end 154 | 155 | end 156 | 157 | u0 = [0,0] 158 | if fixTime == 1 159 | for i in 1:N 160 | if i==1 161 | @constraint(m,-0.6<=(u0[1]-u[1,i])/Ts <= 0.6) 162 | else 163 | @constraint(m,-0.6<=(u[1,i-1]-u[1,i])/Ts <= 0.6) 164 | end 165 | end 166 | else 167 | for i in 1:N 168 | if i==1 169 | @NLconstraint(m,-0.6<=(u0[1]-u[1,i])/(timeScale[i]*Ts) <= 0.6) 170 | else 171 | @NLconstraint(m,-0.6<=(u[1,i-1]-u[1,i])/(timeScale[i]*Ts) <= 0.6) 172 | end 173 | end 174 | end 175 | 176 | 177 | ############################## 178 | # obstacle avoidance constraints 179 | ############################## 180 | 181 | # width and length of ego set 182 | W_ev = ego[2]+ego[4] 183 | L_ev = ego[1]+ego[3] 184 | 185 | g = [L_ev/2,W_ev/2,L_ev/2,W_ev/2] 186 | 187 | # ofset from X-Y to the center of the ego set 188 | offset = (ego[1]+ego[3])/2 - ego[3] 189 | 190 | 191 | for i in 1:N+1 # iterate over time steps 192 | for j = 1 : nOb # iterate over obstacles 193 | Aj = A[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract obstacle matrix associated with j-th obstacle 194 | lj = l[sum(vOb[1:j-1])+1 : sum(vOb[1:j]) ,:] # extract lambda dual variables associate j-th obstacle 195 | nj = n[(j-1)*4+1:j*4 ,:] # extract mu dual variables associated with j-th obstacle 196 | bj = b[sum(vOb[1:j-1])+1 : sum(vOb[1:j])] # extract obstacle matrix associated with j-th obstacle 197 | 198 | # norm(A'*lambda) = 1 199 | @NLconstraint(m, (sum(Aj[k,1]*lj[k,i] for k = 1 : vOb[j]))^2 + (sum(Aj[k,2]*lj[k,i] for k = 1 : vOb[j]))^2 == 1 ) 200 | 201 | # G'*mu + R'*A*lambda = 0 202 | @NLconstraint(m, (nj[1,i] - nj[3,i]) + cos(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + sin(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j]) == 0 ) 203 | @NLconstraint(m, (nj[2,i] - nj[4,i]) - sin(x[3,i])*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) + cos(x[3,i])*sum(Aj[k,2]lj[k,i] for k = 1:vOb[j]) == 0 ) 204 | 205 | # -g'*mu + (A*t - b)*lambda > 0 206 | @NLconstraint(m, (-sum(g[k]*nj[k,i] for k = 1:4) + (x[1,i]+cos(x[3,i])*offset)*sum(Aj[k,1]*lj[k,i] for k = 1:vOb[j]) 207 | + (x[2,i]+sin(x[3,i])*offset)*sum(Aj[k,2]*lj[k,i] for k=1:vOb[j]) - sum(bj[k]*lj[k,i] for k=1:vOb[j])) >= dmin ) 208 | end 209 | end 210 | 211 | ############################## 212 | # set initial guesses 213 | ############################## 214 | 215 | if fixTime == 0 216 | setvalue(timeScale,1*ones(N+1,1)) 217 | end 218 | setvalue(x,xWS') 219 | setvalue(u,uWS[1:N,:]') 220 | 221 | lWS,nWS = DualMultWS(N,nOb,vOb, A, b,xWS[:,1],xWS[:,2],xWS[:,3]) 222 | 223 | setvalue(l,lWS') 224 | setvalue(n,nWS') 225 | 226 | ############################## 227 | # solve problem 228 | ############################## 229 | # ipopt has sometimes problems in the restoration phase, 230 | # it turns out that restarting ipopt with the previous solution 231 | # as an initial guess works well to achieve a high success rate. 232 | # 233 | # if restoration failure is reported by IPOPT, solution should be checked manually as it can still be feasible 234 | ############################## 235 | 236 | # at most three attempts considered 237 | time1 = 0 238 | time2 = 0 239 | 240 | exitflag = 0 241 | 242 | tic() 243 | status = solve(m; suppress_warnings=true) 244 | time1 = toq(); 245 | 246 | if status == :Optimal 247 | exitflag = 1 248 | elseif status ==:Error || status ==:UserLimit 249 | 250 | Feasible = 0 251 | if Feasible == 0 252 | tic() 253 | status = solve(m; suppress_warnings=true) 254 | time2 = toq(); 255 | 256 | if status == :Optimal 257 | exitflag = 1 258 | elseif status ==:Error || status ==:UserLimit 259 | xp = getvalue(x) 260 | up = getvalue(u) 261 | if fixTime == 1 262 | timeScalep = ones(1,N+1) 263 | else 264 | timeScalep = getvalue(timeScale) 265 | end 266 | lp = getvalue(l) 267 | np = getvalue(n) 268 | Feasible = 0 269 | Feasible = ParkingConstraints(x0,xF,N,Ts,L,ego,XYbounds,nOb,vOb, A, b,xp,up,lp,np,timeScalep,fixTime,1) 270 | 271 | if Feasible == 1 272 | exitflag = 1 273 | else 274 | exitflag = 0 275 | end 276 | end 277 | else 278 | exitflag = 1 279 | end 280 | else 281 | exitflag = 0 282 | end 283 | 284 | ############################## 285 | # return values 286 | ############################## 287 | 288 | # computation times is the sum of all trials 289 | time = time1+time2 290 | # print(" elapsed time: ") 291 | # print(time) 292 | # println(" seconds") 293 | 294 | xp = getvalue(x) 295 | up = getvalue(u) 296 | if fixTime == 1 297 | timeScalep = ones(1,N+1) 298 | else 299 | timeScalep = getvalue(timeScale) 300 | end 301 | 302 | lp = getvalue(l) 303 | np = getvalue(n) 304 | 305 | return xp, up, timeScalep, exitflag, time, lp, np 306 | 307 | end 308 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # H-OBCA 2 | Hierarchical Optimization-Based Collision Avoidance - An algorithm for generating dynamically feasible parking trajectories 3 | 4 | Paper describing the theory can be found [here](http://arxiv.org/abs/1711.03449). 5 | 6 | ## Short Description 7 | H-OBCA is an optimization-based approach for autonomous parking. It builds on [OBCA](https://github.com/XiaojingGeorgeZhang/OBCA), which is a recent method for generating obstacle-free trajectories using optimal control. 8 | 9 | H-OBCA is able to generate high-quality *kino-dynamically feasible obstacle-free* trajectories. These trajectories are smooth, and can be accurately tracked by simple low-level path following controllers. A [Julia](https://julialang.org/)-based implementation is provided. 10 | 11 | 12 | ## Examples 13 | 14 | ### H-OBCA for Reverse Parking 15 | 16 | 17 | ### H-OBCA for Parallel Parking 18 | 19 | 20 | 21 | ## How to run the Parking code: 22 | 23 | ### First steps 24 | 25 | 1. Change to the directory 26 | 27 | 2. Install Julia from https://julialang.org/downloads/ (code tested on version 0.5.1 and 0.6.0) 28 | 29 | 3. Open Julia in terminal 30 | 31 | 4. Install Julia package JuMP using Pkg.add("JuMP") 32 | 33 | 5. Install Julia package Ipopt using Pkg.add("Ipopt") 34 | 35 | 6. Install Julia package PyPlot using Pkg.add("PyPlot") 36 | 37 | 7. Install Julia package NearestNeighbors using Pkg.add("NearestNeighbors") 38 | 39 | 8. Install Julia package ControlSystems using Pkg.add("ControlSystems") 40 | 41 | 42 | ### Running the parking example 43 | 44 | 1. Start Julia in terminal 45 | 46 | 2. Type in terminal: include("setup.jl") 47 | 48 | 3. Type in terminal: include("main.jl") 49 | 50 | 51 | ### modifying the code 52 | 53 | 1. To play with start points, change x0 in main.jl and run 54 | the code by: include("main.jl") 55 | 56 | 2. If you change anything in one of the collision avoidance 57 | problems, you need to activate the changes by running: 58 | include("setup.jl") 59 | 60 | 3. If you change the size of the car in main.jl, the change 61 | also need to be made in collision_check.jl 62 | 63 | ### Note 64 | 1. this code has been tested on Julia 0.5.1 and 0.6.0, and might not run on any other Julia versions 65 | 66 | 2. For best results, run code in Julia terminal 67 | -------------------------------------------------------------------------------- /a_star.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 5 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 6 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # Grid based A* shorest path planning 28 | ############### 29 | 30 | 31 | module a_star 32 | 33 | using PyPlot 34 | using NearestNeighbors 35 | using DataStructures 36 | 37 | const VEHICLE_RADIUS = 5.0 #[m] 38 | const GRID_RESOLUTION = 1.0 #[m] 39 | 40 | 41 | type Node 42 | x::Int64 #x index 43 | y::Int64 #y index 44 | cost::Float64 # cost 45 | pind::Int64 # parent index 46 | end 47 | 48 | 49 | function calc_dist_policy(gx::Float64, gy::Float64, 50 | ox::Array{Float64}, oy::Array{Float64}, 51 | reso::Float64, vr::Float64) 52 | """ 53 | gx: goal x position [m] 54 | gx: goal x position [m] 55 | ox: x position list of Obstacles [m] 56 | oy: y position list of Obstacles [m] 57 | reso: grid resolution [m] 58 | vr: vehicle radius[m] 59 | """ 60 | 61 | ngoal = Node(round(Int64, gx/reso),round(Int64, gy/reso),0.0, -1) 62 | 63 | ox = [iox/reso for iox in ox] 64 | oy = [ioy/reso for ioy in oy] 65 | 66 | obmap, minx, miny, maxx, maxy, xw, yw = calc_obstacle_map(ox, oy, reso, vr) 67 | 68 | #open, closed set 69 | open, closed = Dict{Int64, Node}(), Dict{Int64, Node}() 70 | open[calc_index(ngoal, xw, minx, miny)] = ngoal 71 | 72 | motion = get_motion_model() 73 | nmotion = length(motion[:,1]) 74 | pq = PriorityQueue() 75 | enqueue!(pq, calc_index(ngoal, xw, minx, miny), ngoal.cost) 76 | 77 | while true 78 | if length(open) == 0 79 | # println("Finish Search") 80 | break 81 | end 82 | 83 | c_id = dequeue!(pq) 84 | current = open[c_id] 85 | 86 | delete!(open, c_id) 87 | closed[c_id] = current 88 | 89 | for i in 1:nmotion # expand search grid based on motion model 90 | node = Node(current.x+motion[i,1], current.y+motion[i,2], current.cost+motion[i,3], c_id) 91 | 92 | if !verify_node(node, minx, miny, xw, yw, obmap) 93 | continue 94 | end 95 | 96 | node_ind = calc_index(node, xw, minx, miny) 97 | 98 | # If it is already in the closed set, skip it 99 | if haskey(closed,node_ind) continue end 100 | 101 | if haskey(open, node_ind) 102 | if open[node_ind].cost > node.cost 103 | # If so, update the node to have a new parent 104 | open[node_ind].cost = node.cost 105 | open[node_ind].pind = c_id 106 | end 107 | else # add to open set 108 | open[node_ind] = node 109 | enqueue!(pq, calc_index(node, xw, minx, miny), node.cost) 110 | end 111 | end 112 | end 113 | 114 | pmap = calc_policy_map(closed, xw, yw, minx, miny) 115 | 116 | return pmap 117 | end 118 | 119 | 120 | function calc_policy_map(closed, xw, yw, minx, miny) 121 | 122 | pmap = fill(Inf, (xw,yw)) 123 | 124 | for n in values(closed) 125 | pmap[n.x-minx, n.y-miny] = n.cost 126 | end 127 | # println(pmap) 128 | 129 | return pmap 130 | end 131 | 132 | 133 | function calc_astar_path(sx::Float64, sy::Float64, gx::Float64, gy::Float64, 134 | ox::Array{Float64}, oy::Array{Float64}, reso::Float64, vr::Float64) 135 | """ 136 | sx: start x position [m] 137 | sy: start y position [m] 138 | gx: goal x position [m] 139 | gx: goal x position [m] 140 | ox: x position list of Obstacles [m] 141 | oy: y position list of Obstacles [m] 142 | reso: grid resolution [m] 143 | """ 144 | 145 | nstart = Node(round(Int64,sx/reso),round(Int64, sy/reso),0.0, -1) 146 | ngoal = Node(round(Int64, gx/reso),round(Int64, gy/reso),0.0, -1) 147 | 148 | ox = [iox/reso for iox in ox] 149 | oy = [ioy/reso for ioy in oy] 150 | 151 | obmap, minx, miny, maxx, maxy, xw, yw = calc_obstacle_map(ox, oy, reso, vr) 152 | 153 | #open, closed set 154 | open, closed = Dict{Int64, Node}(), Dict{Int64, Node}() 155 | open[calc_index(nstart, xw, minx, miny)] = nstart 156 | 157 | motion = get_motion_model() 158 | nmotion = length(motion[:,1]) 159 | pq = PriorityQueue() 160 | enqueue!(pq, calc_index(nstart, xw, minx, miny), calc_cost(nstart, ngoal)) 161 | 162 | while true 163 | if length(open) == 0;println("Error: No open set");break;end 164 | 165 | c_id = dequeue!(pq) 166 | current = open[c_id] 167 | 168 | if current.x == ngoal.x && current.y == ngoal.y # check goal 169 | println("Goal!!") 170 | closed[c_id] = current 171 | break 172 | end 173 | 174 | delete!(open, c_id) 175 | closed[c_id] = current 176 | 177 | for i in 1:nmotion # expand search grid based on motion model 178 | node = Node(current.x+motion[i,1], current.y+motion[i,2], current.cost+motion[i,3], c_id) 179 | 180 | if !verify_node(node, minx, miny, xw, yw, obmap) 181 | continue 182 | end 183 | 184 | node_ind = calc_index(node, xw, minx, miny) 185 | 186 | # If it is already in the closed set, skip it 187 | if haskey(closed,node_ind) continue end 188 | 189 | if haskey(open, node_ind) 190 | if open[node_ind].cost > node.cost 191 | # If so, update the node to have a new parent 192 | open[node_ind].cost = node.cost 193 | open[node_ind].pind = c_id 194 | end 195 | else # add to open set 196 | open[node_ind] = node 197 | enqueue!(pq, calc_index(node, xw, minx, miny), calc_cost(node, ngoal)) 198 | end 199 | end 200 | end 201 | 202 | rx, ry = get_final_path(closed, ngoal, nstart, xw, minx, miny, reso) 203 | 204 | return rx, ry 205 | end 206 | 207 | 208 | function verify_node(node::Node, minx::Int64, miny::Int64, xw::Int64, yw::Int64, obmap::Array{Bool,2}) 209 | 210 | if (node.x - minx) >= xw 211 | return false 212 | elseif (node.x - minx) <= 0 213 | return false 214 | end 215 | if (node.y - miny) >= yw 216 | return false 217 | elseif (node.y - miny) <= 0 218 | return false 219 | end 220 | 221 | #collision check 222 | if obmap[node.x-minx, node.y-miny] 223 | return false 224 | end 225 | 226 | return true 227 | end 228 | 229 | 230 | function calc_cost(n::Node, ngoal::Node) 231 | return (n.cost + h(n.x - ngoal.x, n.y - ngoal.y)) 232 | end 233 | 234 | 235 | function get_motion_model() 236 | # dx, dy, cost 237 | motion=[1 0 1; 238 | 0 1 1; 239 | -1 0 1; 240 | 0 -1 1; 241 | -1 -1 sqrt(2); 242 | -1 1 sqrt(2); 243 | 1 -1 sqrt(2); 244 | 1 1 sqrt(2);] 245 | 246 | return motion 247 | end 248 | 249 | 250 | function calc_index(node::Node, xwidth::Int64, xmin::Int64, ymin::Int64) 251 | return (node.y - ymin)*xwidth + (node.x - xmin) 252 | end 253 | 254 | 255 | function calc_obstacle_map(ox::Array{Float64}, oy::Array{Float64}, reso::Float64, vr::Float64) 256 | 257 | minx = round(Int64, minimum(ox)) 258 | miny = round(Int64, minimum(oy)) 259 | maxx = round(Int64, maximum(ox)) 260 | maxy = round(Int64, maximum(oy)) 261 | # println("minx:", minx) 262 | # println("miny:", miny) 263 | # println("maxx:", maxx) 264 | # println("maxy:", maxy) 265 | 266 | xwidth = round(Int64, maxx - minx) 267 | ywidth = round(Int64, maxy - miny) 268 | # println("xwidth:", xwidth) 269 | # println("ywidth:", ywidth) 270 | 271 | obmap = fill(false, (xwidth,ywidth)) 272 | 273 | kdtree = KDTree(hcat(ox, oy)') 274 | for ix in 1:xwidth 275 | x = ix + minx 276 | for iy in 1:ywidth 277 | y = iy + miny 278 | idxs, onedist = knn(kdtree, [x, y] , 1) 279 | if onedist[1] <= vr/reso 280 | obmap[ix,iy] = true 281 | end 282 | end 283 | end 284 | 285 | # println(" calc_obstacle_map done") 286 | 287 | return obmap, minx, miny, maxx, maxy, xwidth, ywidth 288 | end 289 | 290 | 291 | function get_final_path(closed::Dict{Int64, Node}, 292 | ngoal::Node, 293 | nstart::Node, 294 | xw::Int64, 295 | minx::Int64, 296 | miny::Int64, 297 | reso::Float64) 298 | 299 | rx, ry = [ngoal.x],[ngoal.y] 300 | nid = calc_index(ngoal, xw, minx, miny) 301 | while true 302 | n = closed[nid] 303 | push!(rx, n.x) 304 | push!(ry, n.y) 305 | nid = n.pind 306 | 307 | if rx[end] == nstart.x && ry[end] == nstart.y 308 | # println("done") 309 | break 310 | end 311 | end 312 | 313 | rx = reverse(rx) .* reso 314 | ry = reverse(ry) .* reso 315 | 316 | return rx, ry 317 | end 318 | 319 | 320 | function search_min_cost_node(open::Dict{Int64, Node}, ngoal::Node) 321 | mnode = nothing 322 | mcost = Inf 323 | for n in values(open) 324 | # println(n) 325 | cost = n.cost + h(n.x - ngoal.x, n.y - ngoal.y) 326 | if mcost > cost 327 | mnode = n 328 | mcost = cost 329 | end 330 | end 331 | # println("minnode:", mnode) 332 | 333 | return mnode 334 | end 335 | 336 | 337 | function h(x::Int64, y::Int64) 338 | """ 339 | Heuristic cost function 340 | """ 341 | return sqrt(x^2+y^2); 342 | end 343 | 344 | 345 | function main() 346 | println(PROGRAM_FILE," start!!") 347 | 348 | sx = 10.0 # [m] 349 | sy = 10.0 # [m] 350 | gx = 50.0 # [m] 351 | gy = 50.0 # [m] 352 | 353 | ox = Float64[] 354 | oy = Float64[] 355 | 356 | for i in 0:60 357 | push!(ox, Float64(i)) 358 | push!(oy, 0.0) 359 | end 360 | for i in 0:60 361 | push!(ox, 60.0) 362 | push!(oy, Float64(i)) 363 | end 364 | for i in 0:60 365 | push!(ox, Float64(i)) 366 | push!(oy, 60.0) 367 | end 368 | for i in 0:60 369 | push!(ox, 0.0) 370 | push!(oy, Float64(i)) 371 | end 372 | for i in 0:40 373 | push!(ox, 20.0) 374 | push!(oy, Float64(i)) 375 | end 376 | for i in 0:40 377 | push!(ox, 40.0) 378 | push!(oy, 60.0-Float64(i)) 379 | end 380 | 381 | @time rx, ry = calc_astar_path(sx, sy, gx, gy, ox, oy, GRID_RESOLUTION, VEHICLE_RADIUS) 382 | 383 | plot(ox, oy, ".k",label="obstacles") 384 | plot(sx, sy, "xr",label="start") 385 | plot(gx, gy, "xb",label="goal") 386 | plot(rx, ry, "-r",label="A* path") 387 | legend() 388 | grid(true) 389 | axis("equal") 390 | show() 391 | 392 | println(PROGRAM_FILE," Done!!") 393 | end 394 | 395 | 396 | if length(PROGRAM_FILE)!=0 && 397 | contains(@__FILE__, PROGRAM_FILE) 398 | 399 | main() 400 | end 401 | 402 | 403 | end #module 404 | 405 | -------------------------------------------------------------------------------- /collision_check.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 5 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 6 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | module collision_check 27 | 28 | using NearestNeighbors 29 | using PyPlot 30 | 31 | const B = 1.0 #[m] distance from rear to vehicle back end 32 | const C = 3.7 #[m] distance from rear to vehicle front end 33 | const I = 2.0 #[m] width of vehicle 34 | const WBUBBLE_DIST = (B+C)/2.0-B #[m] distance from rear and the center of whole bubble 35 | const WBUBBLE_R = (B+C)/2.0 #[m] whole bubble radius 36 | 37 | const vrx = [C, C, -B, -B, C ] 38 | const vry = [-I/2.0, I/2.0, I/2.0, -I/2.0, -I/2.0] 39 | 40 | function check_collision(x, y, yaw, kdtree, ox, oy) 41 | 42 | for (ix, iy, iyaw) in zip(x, y, yaw) 43 | cx = ix + WBUBBLE_DIST*cos(iyaw) 44 | cy = iy + WBUBBLE_DIST*sin(iyaw) 45 | 46 | # Whole bubble check 47 | ids = inrange(kdtree, [cx, cy], WBUBBLE_R, true) 48 | if length(ids) == 0 continue end 49 | 50 | if !rect_check(ix, iy, iyaw, ox[ids], oy[ids]) 51 | return false #collision 52 | end 53 | end 54 | 55 | return true #OK 56 | 57 | end 58 | 59 | 60 | function rect_check(ix, iy, iyaw, ox, oy) 61 | 62 | c = cos(-iyaw) 63 | s = sin(-iyaw) 64 | 65 | for (iox, ioy) in zip(ox, oy) 66 | tx = iox - ix 67 | ty = ioy - iy 68 | lx = (c*tx - s*ty) 69 | ly = (s*tx + c*ty) 70 | 71 | sumangle = 0.0 72 | for i in 1:length(vrx)-1 73 | x1 = vrx[i] - lx 74 | y1 = vry[i] - ly 75 | x2 = vrx[i+1] - lx 76 | y2 = vry[i+1] - ly 77 | d1 = hypot(x1,y1) 78 | d2 = hypot(x2,y2) 79 | theta1 = atan2(y1,x1) 80 | tty = (-sin(theta1)*x2 + cos(theta1)*y2) 81 | 82 | tmp = (x1*x2+y1*y2)/(d1*d2) 83 | if tmp >= 1.0 tmp = 1.0 end 84 | 85 | if tty >= 0.0 86 | sumangle += acos(tmp) 87 | else 88 | sumangle -= acos(tmp) 89 | end 90 | end 91 | 92 | if sumangle >= pi 93 | return false 94 | end 95 | end 96 | 97 | return true #OK 98 | end 99 | 100 | 101 | function main() 102 | 103 | ox = rand(3)*30.0 - 30.0/2.0 104 | oy = rand(3)*30.0 - 30.0/2.0 105 | 106 | kdtree = KDTree(hcat(ox, oy)') 107 | 108 | x = [10.0, 5.0] 109 | y = [10.0, 5.0] 110 | yaw = [deg2rad(10.0), deg2rad(0.0)] 111 | 112 | flag = check_collision(x, y, yaw, kdtree, ox, oy) 113 | if flag 114 | println("OK") 115 | else 116 | println("Collision") 117 | end 118 | 119 | plot(ox, oy, ".r") 120 | grid(true) 121 | axis("equal") 122 | show() 123 | 124 | end 125 | 126 | 127 | if length(PROGRAM_FILE)!=0 && 128 | contains(@__FILE__, PROGRAM_FILE) 129 | 130 | @time main() 131 | end 132 | 133 | 134 | end #module 135 | 136 | 137 | -------------------------------------------------------------------------------- /hybrid_a_star.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 5 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 6 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # Hybrid A star: Julia implementation of Hybrid A* algorithm 28 | ############### 29 | 30 | module hybrid_a_star 31 | 32 | using PyPlot 33 | using DataFrames 34 | using NearestNeighbors 35 | using DataStructures 36 | 37 | include("./reeds_shepp.jl") 38 | include("./a_star.jl") 39 | include("./collision_check.jl") 40 | 41 | 42 | const VEHICLE_RADIUS = 1.0 #[m]; radius of rear ball; 43 | const BUBBLE_DIST = 1.7 #[m]; distance to "forward bubble"; 44 | 45 | ##### Fast Comp Time values from Alex Liniger ###### 46 | const OB_MAP_RESOLUTION = 0.1 #[m]; obstacle resolution 47 | const YAW_GRID_RESOLUTION = deg2rad(5.0) #[m]; 10.0 /// 5.0 48 | const N_STEER = 5.0 # number of steer command; 10.0 seems OK /// 5 49 | ## For Backwards Parking 50 | const XY_GRID_RESOLUTION = 0.3 #[m]; 51 | const MOTION_RESOLUTION = 0.1 #[m]; 52 | ################################################### 53 | 54 | const USE_HOLONOMIC_WITH_OBSTACLE_HEURISTIC = true 55 | const USE_NONHOLONOMIC_WITHOUT_OBSTACLE_HEURISTIC = false 56 | 57 | const SB_COST = 10.0 # switch back penalty cost 58 | const BACK_COST = 0.0 # backward penalty cost 59 | const STEER_CHANGE_COST = 10.0 # steer angle change penalty cost 60 | const STEER_COST = 0.0 # steer angle penalty cost 61 | const H_COST = 1. # Heuristic cost; higher -> heuristic; 1.0 62 | 63 | const WB = 2.7 #[m]; 7.0 64 | const MAX_STEER = 0.6 #[rad] 65 | 66 | type Node 67 | xind::Int64 #x index 68 | yind::Int64 #y index 69 | yawind::Int64 #yaw index 70 | direction::Bool # moving direction forword:true, backword:false 71 | x::Array{Float64} # x position [m] 72 | y::Array{Float64} # y position [m] 73 | yaw::Array{Float64} # yaw angle [rad] 74 | steer::Float64 # steer input 75 | cost::Float64 # cost 76 | pind::Int64 # parent index 77 | end 78 | 79 | type Config 80 | minx::Int64 81 | miny::Int64 82 | minyaw::Int64 83 | maxx::Int64 84 | maxy::Int64 85 | maxyaw::Int64 86 | xw::Int64 87 | yw::Int64 88 | yaww::Int64 89 | xyreso::Float64 90 | yawreso::Float64 91 | obminx::Int64 92 | obminy::Int64 93 | obmaxx::Int64 94 | obmaxy::Int64 95 | obxw::Int64 96 | obyw::Int64 97 | obreso::Float64 98 | end 99 | 100 | 101 | function calc_hybrid_astar_path(sx::Float64, sy::Float64, syaw::Float64, 102 | gx::Float64, gy::Float64, gyaw::Float64, 103 | ox::Array{Float64}, oy::Array{Float64}, 104 | xyreso::Float64, yawreso::Float64, 105 | obreso::Float64) 106 | """ 107 | Calc hybrid astar path 108 | sx: start x position [m] 109 | sy: start y position [m] 110 | gx: goal x position [m] 111 | gx: goal x position [m] 112 | ox: x position list of Obstacles [m] 113 | oy: y position list of Obstacles [m] 114 | xyreso: grid resolution [m] 115 | yawreso: yaw angle resolution [rad] 116 | """ 117 | 118 | syaw, gyaw = pi_2_pi(syaw), pi_2_pi(gyaw) 119 | 120 | const c = calc_config(ox, oy, xyreso, yawreso, obreso) 121 | kdtree = KDTree(hcat(ox, oy)') 122 | obmap, gkdtree = calc_obstacle_map(ox, oy, c) 123 | nstart = Node(round(Int64,sx/xyreso), round(Int64,sy/xyreso), round(Int64, syaw/yawreso),true,[sx],[sy],[syaw],0.0,0.0, -1) 124 | ngoal = Node(round(Int64,gx/xyreso), round(Int64,gy/xyreso), round(Int64,gyaw/yawreso),true,[gx],[gy],[gyaw],0.0,0.0, -1) 125 | 126 | if USE_HOLONOMIC_WITH_OBSTACLE_HEURISTIC 127 | h_dp = calc_holonomic_with_obstacle_heuristic(ngoal, ox, oy, xyreso) 128 | else 129 | h_dp = Array{Float64}() 130 | end 131 | if USE_NONHOLONOMIC_WITHOUT_OBSTACLE_HEURISTIC 132 | h_rs = calc_nonholonomic_without_obstacle_heuristic(ngoal, c) 133 | else 134 | h_rs = Array{Float64}() 135 | end 136 | 137 | open, closed = Dict{Int64, Node}(), Dict{Int64, Node}() 138 | open[calc_index(nstart, c)] = nstart 139 | pq = PriorityQueue() 140 | enqueue!(pq, calc_index(nstart, c), calc_cost(nstart, h_rs, h_dp, ngoal, c)) 141 | 142 | u, d = calc_motion_inputs() 143 | nmotion = length(u) 144 | 145 | while true 146 | if length(open) == 0 147 | println("Error: Cannot find path, No open set") 148 | return nothing, nothing, nothing 149 | end 150 | 151 | c_id = dequeue!(pq) 152 | current = open[c_id] 153 | 154 | isupdated, current = update_node_with_analystic_expantion(current, ngoal, obmap, c, kdtree, ox, oy) 155 | if isupdated 156 | closed[calc_index(ngoal, c)] = current 157 | break #goal 158 | end 159 | 160 | #move current node from open to closed 161 | delete!(open, c_id) 162 | closed[c_id] = current 163 | 164 | for i in 1:nmotion 165 | node = calc_next_node(current, c_id, u[i], d[i], c, gkdtree) 166 | 167 | if !verify_index(node, obmap, c, kdtree, ox, oy) continue end 168 | 169 | node_ind = calc_index(node, c) 170 | 171 | # If it is already in the closed set, skip it 172 | if haskey(closed, node_ind) continue end 173 | 174 | if !haskey(open, node_ind) 175 | open[node_ind] = node 176 | enqueue!(pq, calc_index(node, c), calc_cost(node, h_rs, h_dp, ngoal, c)) 177 | end 178 | end 179 | 180 | end 181 | 182 | # println("final expand node:", length(open) + length(closed)) 183 | 184 | rx, ry, ryaw = get_final_path(closed, ngoal, nstart, c) 185 | 186 | return rx, ry, ryaw 187 | end 188 | 189 | 190 | function update_node_with_analystic_expantion(current::Node, 191 | ngoal::Node, 192 | obmap::Array{Bool,2}, 193 | c::Config, 194 | kdtree::NearestNeighbors.KDTree, 195 | ox::Array{Float64}, 196 | oy::Array{Float64} 197 | ) 198 | 199 | apath = analystic_expantion(current, ngoal, obmap, c, kdtree, ox, oy) 200 | if apath != nothing 201 | # println("Find path! with analystic_expantion") 202 | current.x = vcat(current.x, apath.x[2:end-1]) 203 | current.y = vcat(current.y, apath.y[2:end-1]) 204 | current.yaw = vcat(current.yaw, apath.yaw[2:end-1]) 205 | current.cost += calc_rs_path_cost(apath) 206 | return true, current 207 | end 208 | 209 | return false, current #no update 210 | end 211 | 212 | 213 | function calc_rs_path_cost(rspath::hybrid_a_star.reeds_shepp.Path) 214 | 215 | cost = 0.0 216 | for l in rspath.lengths 217 | if l >= 0 # forward 218 | cost += l 219 | else # back 220 | cost += abs(l) * BACK_COST 221 | end 222 | end 223 | 224 | # swich back penalty 225 | for i in 1:length(rspath.lengths) - 1 226 | if rspath.lengths[i] * rspath.lengths[i+1] < 0.0 # switch back 227 | cost += SB_COST 228 | end 229 | end 230 | 231 | # steer penalyty 232 | for ctype in rspath.ctypes 233 | if ctype != "S" # curve 234 | cost += STEER_COST*abs(MAX_STEER) 235 | end 236 | end 237 | 238 | # ==steer change penalty 239 | # calc steer profile 240 | nctypes = length(rspath.ctypes) 241 | ulist = fill(0.0, nctypes) 242 | for i in 1:nctypes 243 | if rspath.ctypes[i] == "R" 244 | ulist[i] = - MAX_STEER 245 | elseif rspath.ctypes[i] == "L" 246 | ulist[i] = MAX_STEER 247 | end 248 | end 249 | 250 | for i in 1:length(rspath.ctypes) - 1 251 | cost += STEER_CHANGE_COST*abs(ulist[i+1] - ulist[i]) 252 | end 253 | 254 | # println("RS cost is ", cost) 255 | return cost 256 | end 257 | 258 | 259 | function analystic_expantion(n::Node, ngoal::Node, obmap::Array{Bool,2}, c::Config, 260 | kdtree::NearestNeighbors.KDTree, 261 | ox::Array{Float64}, 262 | oy::Array{Float64} 263 | ) 264 | 265 | sx = n.x[end] 266 | sy = n.y[end] 267 | syaw = n.yaw[end] 268 | 269 | max_curvature = tan(MAX_STEER)/WB 270 | path = reeds_shepp.calc_shortest_path(sx, sy, syaw, 271 | ngoal.x[end], ngoal.y[end], ngoal.yaw[end], 272 | max_curvature, step_size=MOTION_RESOLUTION) 273 | 274 | if path == nothing 275 | return nothing 276 | end 277 | 278 | if !collision_check.check_collision(path.x, path.y, path.yaw, kdtree, ox, oy) 279 | return nothing 280 | end 281 | 282 | # println(paths) 283 | return path # find good path 284 | end 285 | 286 | 287 | function calc_motion_inputs() 288 | 289 | up = [i for i in MAX_STEER/N_STEER:MAX_STEER/N_STEER:MAX_STEER] 290 | u = vcat([0.0], [i for i in up], [-i for i in up]) 291 | d = vcat([1.0 for i in 1:length(u)], [-1.0 for i in 1:length(u)]) 292 | u = vcat(u,u) 293 | 294 | return u, d 295 | end 296 | 297 | 298 | function verify_index(node::Node, obmap::Array{Bool,2}, c::Config, 299 | kdtree::NearestNeighbors.KDTree, 300 | ox::Array{Float64}, 301 | oy::Array{Float64} 302 | )::Bool 303 | 304 | # overflow map 305 | if (node.xind - c.minx) >= c.xw 306 | return false 307 | elseif (node.xind - c.minx) <= 0 308 | return false 309 | end 310 | if (node.yind - c.miny) >= c.yw 311 | return false 312 | elseif (node.yind - c.miny) <= 0 313 | return false 314 | end 315 | 316 | # check collisiton 317 | # rectangle check 318 | if !collision_check.check_collision(node.x, node.y,node.yaw, kdtree, ox, oy) 319 | return false 320 | end 321 | 322 | return true #index is ok" 323 | end 324 | 325 | 326 | function pi_2_pi(iangle::Float64) 327 | while (iangle > pi) 328 | iangle -= 2.0 * pi 329 | end 330 | while (iangle < -pi) 331 | iangle += 2.0 * pi 332 | end 333 | 334 | return iangle 335 | end 336 | 337 | 338 | function calc_next_node(current::Node, c_id::Int64, 339 | u::Float64, d::Float64, 340 | c::Config, 341 | gkdtree::NearestNeighbors.KDTree) 342 | 343 | 344 | arc_l = XY_GRID_RESOLUTION 345 | 346 | nlist = round(Int64, arc_l/MOTION_RESOLUTION)+1 347 | xlist = fill(0.0, nlist) 348 | ylist = fill(0.0, nlist) 349 | yawlist = fill(0.0, nlist) 350 | xlist[1] = current.x[end] + d * MOTION_RESOLUTION*cos(current.yaw[end]) 351 | ylist[1] = current.y[end] + d * MOTION_RESOLUTION*sin(current.yaw[end]) 352 | yawlist[1] = pi_2_pi(current.yaw[end] + d*MOTION_RESOLUTION/WB * tan(u)) 353 | 354 | 355 | for i in 1:(nlist - 1) 356 | xlist[i+1] = xlist[i] + d * MOTION_RESOLUTION*cos(yawlist[i]) 357 | ylist[i+1] = ylist[i] + d * MOTION_RESOLUTION*sin(yawlist[i]) 358 | yawlist[i+1] = pi_2_pi(yawlist[i] + d*MOTION_RESOLUTION/WB * tan(u)) 359 | end 360 | 361 | xind = round(Int64, xlist[end]/c.xyreso) 362 | yind = round(Int64, ylist[end]/c.xyreso) 363 | yawind = round(Int64, yawlist[end]/c.yawreso) 364 | 365 | addedcost = 0.0 366 | if d > 0 367 | direction = true 368 | addedcost += abs(arc_l) 369 | else 370 | direction = false 371 | addedcost += abs(arc_l) * BACK_COST 372 | end 373 | 374 | # swich back penalty 375 | if direction != current.direction # switch back penalty 376 | addedcost += SB_COST 377 | end 378 | 379 | # steer penalyty 380 | addedcost += STEER_COST*abs(u) 381 | 382 | # steer change penalty 383 | addedcost += STEER_CHANGE_COST*abs(current.steer - u) 384 | 385 | cost = current.cost + addedcost 386 | node = Node(xind, yind, yawind, direction, xlist, ylist, yawlist, u, cost, c_id) 387 | # println(node) 388 | 389 | return node 390 | end 391 | 392 | 393 | function is_same_grid(node1::Node,node2::Node) 394 | 395 | if node1.xind != node2.xind 396 | return false 397 | end 398 | if node1.yind != node2.yind 399 | return false 400 | end 401 | if node1.yawind != node2.yawind 402 | return false 403 | end 404 | 405 | return true 406 | 407 | end 408 | 409 | 410 | function calc_index(node::Node, c::Config) 411 | ind = (node.yawind - c.minyaw)*c.xw*c.yw+(node.yind - c.miny)*c.xw + (node.xind - c.minx) 412 | if ind <= 0 413 | println("Error(calc_index):", ind) 414 | end 415 | return ind 416 | end 417 | 418 | 419 | function calc_holonomic_with_obstacle_heuristic(gnode::Node, ox::Array{Float64}, oy::Array{Float64}, xyreso::Float64) 420 | # println("Calc distance policy") 421 | h_dp = a_star.calc_dist_policy(gnode.x[end], gnode.y[end], ox, oy, xyreso, VEHICLE_RADIUS) 422 | return h_dp 423 | end 424 | 425 | 426 | function calc_nonholonomic_without_obstacle_heuristic(ngoal::Node, 427 | c::Config) 428 | 429 | h_rs = fill(0.0, (c.xw,c.yw,c.yaww)) 430 | max_curvature = tan(MAX_STEER)/WB 431 | 432 | for ix in 1:c.xw 433 | for iy in 1:c.yw 434 | for iyaw in 1:c.yaww 435 | sx = (ix + c.minx)*c.xyreso 436 | sy = (iy + c.miny)*c.xyreso 437 | syaw = pi_2_pi((iyaw + c.minyaw)*c.yawreso) 438 | L = reeds_shepp.calc_shortest_path_length(sx, sy, syaw, 439 | ngoal.x[end], ngoal.y[end], ngoal.yaw[end], 440 | max_curvature, step_size=MOTION_RESOLUTION) 441 | h_rs[ix, iy, iyaw] = L 442 | end 443 | end 444 | end 445 | 446 | # println(h_rs[:,:,1]) 447 | 448 | return h_rs 449 | end 450 | 451 | 452 | function calc_config(ox::Array{Float64}, oy::Array{Float64}, xyreso::Float64, yawreso::Float64, obreso::Float64) 453 | minx = round(Int64, minimum(ox)/xyreso) 454 | miny = round(Int64, minimum(oy)/xyreso) 455 | maxx = round(Int64, maximum(ox)/xyreso) 456 | maxy = round(Int64, maximum(oy)/xyreso) 457 | obminx = round(Int64, minimum(ox)/obreso) 458 | obminy = round(Int64, minimum(oy)/obreso) 459 | obmaxx = round(Int64, maximum(ox)/obreso) 460 | obmaxy = round(Int64, maximum(oy)/obreso) 461 | # println("minx:", minx) 462 | # println("miny:", miny) 463 | # println("maxx:", maxx) 464 | # println("maxy:", maxy) 465 | 466 | xw = round(Int64,(maxx - minx)) 467 | yw = round(Int64,(maxy - miny)) 468 | obxw = round(Int64,(obmaxx - obminx)) 469 | obyw = round(Int64,(obmaxy - obminy)) 470 | 471 | minyaw = round(Int64, - pi/yawreso) - 1 472 | maxyaw = round(Int64, pi/yawreso) 473 | yaww = round(Int64,(maxyaw - minyaw)) 474 | 475 | config = Config(minx, miny, minyaw, maxx, maxy, maxyaw, xw, yw, yaww, 476 | xyreso, yawreso, obminx, obminy, obmaxx, obmaxy, obxw, obyw, obreso) 477 | 478 | return config 479 | end 480 | 481 | 482 | function calc_obstacle_map(ox::Array{Float64}, 483 | oy::Array{Float64}, 484 | c::Config) 485 | 486 | ox = [iox/c.obreso for iox in ox] 487 | oy = [ioy/c.obreso for ioy in oy] 488 | 489 | obmap = fill(false, (c.obxw, c.obyw)) 490 | 491 | gkdtree = KDTree(hcat(ox, oy)') 492 | for ix in 1:c.obxw 493 | x = ix + c.obminx 494 | for iy in 1:c.obyw 495 | y = iy + c.obminy 496 | idxs, onedist = knn(gkdtree, [x, y] , 1) 497 | if onedist[1] <= VEHICLE_RADIUS/c.obreso 498 | obmap[ix,iy] = true 499 | end 500 | end 501 | end 502 | 503 | return obmap, gkdtree 504 | end 505 | 506 | 507 | function get_final_path(closed::Dict{Int64, Node}, 508 | ngoal::Node, 509 | nstart::Node, 510 | c::Config) 511 | 512 | rx, ry, ryaw = Array{Float64}(ngoal.x),Array{Float64}(ngoal.y),Array{Float64}(ngoal.yaw) 513 | nid = calc_index(ngoal, c) 514 | # println("Final cost is ", closed[nid].cost) 515 | while true 516 | n = closed[nid] 517 | rx = vcat(rx, reverse(n.x)) 518 | ry = vcat(ry, reverse(n.y)) 519 | ryaw = vcat(ryaw, reverse(n.yaw)) 520 | nid = n.pind 521 | if is_same_grid(n, nstart) 522 | # println("done") 523 | break 524 | end 525 | end 526 | 527 | rx = reverse(rx) 528 | ry = reverse(ry) 529 | ryaw = reverse(ryaw) 530 | 531 | dist = sum([sqrt(idx^2+idy^2) for (idx,idy) in zip(diff(rx), diff(ry))]) 532 | # println("Final path distance is ", dist) 533 | 534 | return rx, ry, ryaw 535 | end 536 | 537 | 538 | function calc_cost(n::Node, h_rs::Array{Float64}, h_dp::Array{Float64}, ngoal::Node, c::Config) 539 | 540 | if length(h_rs) > 1 && length(h_dp) > 1 # Both heuristic cost are activated 541 | c_h_dp = h_dp[n.xind - c.minx, n.yind - c.miny] 542 | c_h_rs = h_rs[n.xind - c.minx, n.yind - c.miny, n.yawind - c.minyaw] 543 | return (n.cost + H_COST*max(c_h_dp, c_h_rs)) 544 | elseif length(h_dp) > 1 # Distance policy heuristics is activated 545 | return (n.cost + H_COST*h_dp[n.xind - c.minx, n.yind - c.miny]) 546 | elseif length(h_rs) > 1 # Reed Sheep path heuristics is activated 547 | return (n.cost + H_COST*h_rs[n.xind - c.minx, n.yind - c.miny, n.yawind - c.minyaw]) 548 | end 549 | 550 | return (n.cost + H_COST*calc_euclid_dist(n.x[end] - ngoal.x[end],n.y[end] - ngoal.y[end], n.yaw[end] - ngoal.yaw[end])) 551 | end 552 | 553 | 554 | function calc_euclid_dist(x::Float64, y::Float64, yaw::Float64) 555 | """ 556 | Heuristic cost function 557 | """ 558 | if yaw >= pi 559 | yaw -= pi 560 | else yaw <= -pi 561 | yaw += pi 562 | end 563 | return sqrt(x^2+y^2+yaw^2) 564 | end 565 | 566 | 567 | function main() 568 | println(PROGRAM_FILE," start!!") 569 | 570 | sx = 20.0 # [m] 571 | sy = 20.0 # [m] 572 | syaw = deg2rad(90.0) 573 | gx = 180.0 # [m] 574 | gy = 100.0 # [m] 575 | gyaw = deg2rad(-90.0) 576 | 577 | ox = Float64[] 578 | oy = Float64[] 579 | 580 | for i in 0:200 581 | push!(ox, Float64(i)) 582 | push!(oy, 0.0) 583 | end 584 | for i in 0:120 585 | push!(ox, 200.0) 586 | push!(oy, Float64(i)) 587 | end 588 | for i in 0:200 589 | push!(ox, Float64(i)) 590 | push!(oy, 120.0) 591 | end 592 | for i in 0:120 593 | push!(ox, 0.0) 594 | push!(oy, Float64(i)) 595 | end 596 | for i in 0:80 597 | push!(ox, 40.0) 598 | push!(oy, Float64(i)) 599 | end 600 | for i in 0:80 601 | push!(ox, 80.0) 602 | push!(oy, 120.0-Float64(i)) 603 | end 604 | for i in 0:40 605 | push!(ox, 120.0) 606 | push!(oy, 120.0-Float64(i)) 607 | push!(ox, 120.0) 608 | push!(oy, Float64(i)) 609 | end 610 | for i in 0:80 611 | push!(ox, 160.0) 612 | push!(oy, 120.0-Float64(i)) 613 | end 614 | 615 | @time rx, ry, ryaw = calc_hybrid_astar_path(sx, sy, syaw, gx, gy, gyaw, ox, oy, XY_GRID_RESOLUTION, YAW_GRID_RESOLUTION, OB_MAP_RESOLUTION) 616 | 617 | plot(ox, oy, ".k",label="obstacles") 618 | if rx != nothing 619 | plot(rx, ry, "-r",label="Hybrid A* path") 620 | end 621 | 622 | legend() 623 | grid(true) 624 | axis("equal") 625 | 626 | show() 627 | 628 | println(PROGRAM_FILE," Done!!") 629 | end 630 | 631 | 632 | if length(PROGRAM_FILE)!=0 && 633 | contains(@__FILE__, PROGRAM_FILE) 634 | 635 | main() 636 | end 637 | 638 | 639 | end #module 640 | 641 | -------------------------------------------------------------------------------- /images/TrajParallelHOBCA.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/XiaojingGeorgeZhang/H-OBCA/72503586429f81a4fd397edc5391db2f0308b8ed/images/TrajParallelHOBCA.gif -------------------------------------------------------------------------------- /images/TrajReverseHOBCA.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/XiaojingGeorgeZhang/H-OBCA/72503586429f81a4fd397edc5391db2f0308b8ed/images/TrajReverseHOBCA.gif -------------------------------------------------------------------------------- /main.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # Main file: computes Collision-Free and Minimum-Penetration trajectories for parking 28 | ############### 29 | 30 | # function defined in setup.jl 31 | clear() 32 | using PyCall 33 | 34 | close("all") 35 | ################################################## 36 | 37 | # define scenarios 38 | # scenario = "parallel" 39 | scenario = "backwards" 40 | 41 | # fixed or variable sampling time 1/0 42 | fixTime = 0 # default: 0 (variable time steps) 43 | 44 | #### problem parameters #### 45 | TsPF = 0.05 46 | if scenario == "backwards" 47 | # nominal sampling time 48 | sampleN = 3 # down-sampling from Hybrid A* to OBCA 49 | if fixTime == 1 # 50 | Ts = 0.65/3*sampleN # 0.65/3 must be compatible with motion resolution of Hybrid A* algorithm 51 | else 52 | Ts = 0.6/3*sampleN # 0.6/3 must be compatible with motion resolution of Hybrid A* algorithm 53 | end 54 | else 55 | sampleN = 3 56 | if fixTime == 1 57 | Ts = 0.95/3*sampleN # 0.95/3 must be compatible with motion resolution of Hybrid A* algorithm 58 | else 59 | Ts = 0.9/3*sampleN # 0.9/3 must be compatible with motion resolution of Hybrid A* algorithm 60 | end 61 | end 62 | 63 | # wheelbase 64 | L = 2.7 65 | 66 | motionStep = 0.1 # step length of Hybrid A*", 67 | 68 | # "nominal" shape of ego/controlled car, ego object is later rotated around the car center 69 | # center of rear wheel axis is reference point 70 | # size of car is: (x_upper + x_lower) + (y_upper + y_lower) 71 | # [x_upper, y_upper, -x_lower, -y_lower ] 72 | ego = [ 3.7 , 1 , 1 , 1 ] 73 | 74 | ##### define obstacles; for simplicity, only polyhedral obstacles are supported at this point 75 | # obstacles are defined by vertices, which are assumed to be enumerated in clock-wise direction 76 | # the first vertex must appear at the end of the list 77 | 78 | # for plotting 79 | nObPlot = 3 # number of obstacles 80 | vObPlot = [4 4 4] # number of vertices of each obstacle, vector of dimenion nOb 81 | 82 | # obstacle representation for optimization problem 83 | nOb = 3 # number of obstacles 84 | vOb = [3 3 2] # number of vertices of each obstacle, vector of dimenion nOb 85 | vObMPC = vOb-1 # adjustment for optimizaton problem 86 | 87 | if scenario == "backwards" 88 | println("Start Reverse Parking") 89 | elseif scenario == "parallel" 90 | println("Start Parallel Parking") 91 | else 92 | println("ERROR: please specify parking scenario") 93 | end 94 | 95 | # build environment 96 | if scenario == "backwards" 97 | # obstacles for backwards 98 | # [ [[obst1_x1;obst1_y1],[obst1_x2;obst1_y2],[obst1_x3;obst1_y4],...,[obst1_x1;obst1_y1]] , [[obst2_x1;obst2_y1],[obst2_x2;obst2_y2],[obst2_x3;obst2_y4],...,[obst2_x1;obst2_y1]] , ... ] 99 | lObPlot = [ [ [-20;5], [-1.3;5], [-1.3;-5], [-20;-5], [-20;5] ] , 100 | [ [1.3;5], [20;5], [20;-5], [1.3;-5], [1.3;5] ] , 101 | [ [-20;15], [20;15], [20;11], [-20,11], [-20;15] ] ] #vetices given in CLOCK-WISE direction 102 | 103 | # for optimization problem 104 | lOb = [ [ [-20;5], [-1.3;5], [-1.3;-5]] , 105 | [ [1.3;-5] , [1.3;5] , [20;5] ] , 106 | [ [20;11], [-20;11]] ] #vetices given in CLOCK-WISE direction 107 | 108 | # final state 109 | xF = [ 0 1.3 pi/2 0] 110 | 111 | # build obstacles for Hybrid A* algorithm 112 | ox = Float64[] 113 | oy = Float64[] 114 | # obstacle 1 115 | for i = -12:0.1:-1.3 116 | push!(ox, Float64(i)) 117 | push!(oy, 5.0) 118 | end 119 | for i in -2:5 120 | push!(ox, -1.3) 121 | push!(oy, Float64(i)) 122 | end 123 | # obstacle 2 124 | for i in -2:5 125 | push!(ox, 1.3) 126 | push!(oy, Float64(i)) 127 | end 128 | for i = 1.3:0.1:12 129 | push!(ox, Float64(i)) 130 | push!(oy, 5.0) 131 | end 132 | # obstacle 3 133 | for i = -12:12 134 | push!(ox, Float64(i)) 135 | push!(oy, 11.0) 136 | end 137 | 138 | elseif scenario == "parallel" 139 | # obstacles for backwards 140 | # [ [[obst1_x1;obst1_y1],[obst1_x2;obst1_y2],[obst1_x3;obst1_y4],...,[obst1_x1;obst1_y1]] , [[obst2_x1;obst2_y1],[obst2_x2;obst2_y2],[obst2_x3;obst2_y4],...,[obst2_x1;obst2_y1]] , ... ] 141 | lObPlot = [ [ [-15;5], [-3;5], [-3;0], [-15;0], [-15;5] ] , 142 | [ [3;5], [15;5], [15;0], [3;0], [3;5] ] , 143 | [ [-3;0], [-3;2.5], [3;2.5], [3,0], [-3;0] ] ] #vetices given in CLOCK-WISE direction 144 | # obstacle representation for optimization problem 145 | lOb = [ [ [-20;5], [-3.;5], [-3.;0]] , 146 | [ [3.;0] , [3.;5] , [20;5] ] , 147 | [ [-3;2.5], [ 3;2.5]]] #vetices given in CLOCK-WISE direction 148 | 149 | 150 | # final state 151 | xF = [-L/2 4 0 0] 152 | 153 | # obstacles for Hybrid A* algorithms 154 | ox = Float64[] 155 | oy = Float64[] 156 | # obstacle 1 157 | for i in -12:0.1: -3. 158 | push!(ox,Float64(i)) 159 | push!(oy,5.0) 160 | end 161 | for i in -2 : 5 162 | push!(ox,-3.0) 163 | push!(oy,Float64(i)) 164 | end 165 | # obstacle 2 166 | for i in -3 : 3 167 | push!(ox,Float64(i)) 168 | push!(oy,2.5) 169 | end 170 | # obstacle 3 171 | for i in -2 : 5 172 | push!(ox,3.0) 173 | push!(oy,Float64(i)) 174 | end 175 | for i in 3 :0.1: 12 176 | push!(ox,Float64(i)) 177 | push!(oy,5.0) 178 | end 179 | # obstacle 4 180 | for i in -12 : 12 181 | push!(ox,Float64(i)) 182 | push!(oy,11.0) 183 | end 184 | end 185 | 186 | # [x_lower, x_upper, -y_lower, y_upper ] 187 | XYbounds = [ -15 , 15 , 1 , 10 ] 188 | 189 | # set initial state 190 | x0 = [-6 9.5 0.0 0.0] 191 | # x0 = [9 7 0.0 0.0] 192 | 193 | # call Hybrid A* 194 | tic() 195 | rx, ry, ryaw = hybrid_a_star.calc_hybrid_astar_path(x0[1], x0[2], x0[3], xF[1], xF[2], xF[3], ox, oy, hybrid_a_star.XY_GRID_RESOLUTION, hybrid_a_star.YAW_GRID_RESOLUTION, hybrid_a_star.OB_MAP_RESOLUTION) 196 | timeHybAstar = toq(); 197 | 198 | 199 | ### extract (smooth) velocity profile from Hybrid A* solution #### 200 | rv = zeros(length(rx),1) 201 | for i=1:length(rx) 202 | if i < length(rx) 203 | rv[i] = (rx[i+1] - rx[i])/(Ts/sampleN)*cos(ryaw[i]) + (ry[i+1]-ry[i])/(Ts/sampleN)*sin(ryaw[i]) 204 | else 205 | rv[i] = 0 206 | end 207 | end 208 | ### Smoothen velocity 0.3 m/s^2 max acceleration ### 209 | v,a = veloSmooth(rv,0.3,Ts/sampleN) 210 | ### compute steering angle ### 211 | delta = atan(diff(ryaw)*L/motionStep.*sign(v[1:end-1])); 212 | 213 | ### Down-sample for Warmstart ########## 214 | rx_sampled = rx[1:sampleN:end] 215 | ry_sampled = ry[1:sampleN:end] 216 | ryaw_sampled = ryaw[1:sampleN:end] 217 | v_sampled = v[1:sampleN:end] 218 | 219 | a_sampled = a[1:sampleN:end] 220 | delta_sampled = delta[1:sampleN:end] 221 | 222 | ## initialize warm start solution 223 | xWS = [rx_sampled ry_sampled ryaw_sampled v_sampled] 224 | uWS = [delta_sampled a_sampled] 225 | 226 | ### solve OBCA step ### 227 | N = length(rx_sampled)-1 228 | AOb, bOb = obstHrep(nOb, vOb, lOb) # obtain H-representation of obstacles 229 | xp10, up10, scaleTime10, exitflag10, time10, lp10, np10 = ParkingSignedDist(x0,xF,N,Ts,L,ego,XYbounds,nOb,vObMPC,AOb,bOb,fixTime,xWS,uWS) 230 | 231 | 232 | ### plot H-OBCA solution ### 233 | if exitflag10==1 234 | println("H-OBCA successfully completed.") 235 | figure(1) 236 | hold(1) 237 | plot(xp10[1,:],xp10[2,:],"b") 238 | 239 | plotTraj(xp10',up10',length(rx_sampled)-1,ego,L,nObPlot,vObPlot,lObPlot,"Trajectory generated by H-OBCA",1) 240 | else 241 | println(" WARNING: Problem could not be solved.") 242 | end 243 | 244 | ### comparison with Hybrid A* ### 245 | figure(2) 246 | title("Trajectory Comparison") 247 | hold(1) 248 | for j = 1 : nObPlot # plot obstacles 249 | for k = 1 : vObPlot[j] 250 | plot([lObPlot[j][k][1],lObPlot[j][k+1][1]] , [lObPlot[j][k][2],lObPlot[j][k+1][2]] ,"k") 251 | end 252 | end 253 | plot(xp10[1,:],xp10[2,:], "-b", label="H-OBCA") 254 | plot(rx, ry, "--r", label="Hybrid A*") 255 | plot(x0[1],x0[2],"ob") 256 | plot(xF[1],xF[2],"ob") 257 | legend() 258 | axis("equal") 259 | 260 | totTime = timeHybAstar+time10 # total execution time of H-OBCA 261 | println("Total run time: " , totTime, " s") 262 | println(" Hybrid A* time: ", timeHybAstar, " s") 263 | println(" optimization (OBCA) time: ", time10, " s") -------------------------------------------------------------------------------- /obstHrep.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # Function computes H-representation for obstacles given their vertices 28 | # it is assumed that the vertices are given in CLOCK-WISE, and that the first vertex is repeated at the end of the vertex list 29 | ############### 30 | 31 | 32 | 33 | function obstHrep(nOb, vOb, lOb) 34 | 35 | # do simple checks 36 | if nOb != length(lOb) 37 | println("ERROR in number of obstacles") 38 | end 39 | 40 | # these matrices contain the H-rep 41 | A_all = zeros(sum(vOb)-nOb,2) 42 | b_all = zeros(sum(vOb)-nOb,1) 43 | 44 | # counter for lazy people 45 | lazyCounter = 1; 46 | 47 | for i = 1 : nOb # building H-rep 48 | 49 | A_i = zeros(vOb[i]-1,2) 50 | b_i = zeros(vOb[i]-1,1) 51 | 52 | # take two subsequent vertices, and compute hyperplane 53 | for j = 1 : vOb[i]-1 54 | 55 | # extract two vertices 56 | v1 = lOb[i][j] # vertex 1 57 | v2 = lOb[i][j+1] # vertex 2 58 | 59 | # find hyperplane passing through v1 and v2 60 | if v1[1] == v2[1] # perpendicular hyperplane, not captured by general formula 61 | if v2[2] < v1[2] # line goes "down" 62 | A_tmp = [1 0] 63 | b_tmp = v1[1] 64 | else 65 | A_tmp = [-1 0] 66 | b_tmp = -v1[1] 67 | end 68 | elseif v1[2] == v2[2] # horizontal hyperplane, captured by general formula but included for numerical stability 69 | if v1[1] < v2[1] 70 | A_tmp = [0 1] 71 | b_tmp = v1[2] 72 | else 73 | A_tmp = [0 -1] 74 | b_tmp = -v1[2] 75 | end 76 | else # general formula for non-horizontal and non-vertical hyperplanes 77 | ab = [v1[1] 1 ; v2[1] 1] \ [v1[2] ; v2[2]] 78 | a = ab[1] 79 | b = ab[2] 80 | 81 | if v1[1] < v2[1] # v1 --> v2 (line moves right) 82 | A_tmp = [-a 1] 83 | b_tmp = b 84 | else # v2 <-- v1 (line moves left) 85 | A_tmp = [a -1] 86 | b_tmp = -b 87 | 88 | end 89 | end 90 | # store vertices 91 | A_i[j,:] = A_tmp 92 | b_i[j] = b_tmp 93 | end 94 | 95 | # store everything 96 | A_all[lazyCounter : lazyCounter+vOb[i]-2,:] = A_i 97 | b_all[lazyCounter : lazyCounter+vOb[i]-2] = b_i 98 | 99 | # update counter 100 | lazyCounter = lazyCounter + vOb[i]-1 101 | end 102 | 103 | return A_all, b_all 104 | 105 | end 106 | -------------------------------------------------------------------------------- /plotTraj.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # function plots trajectory 28 | ############### 29 | 30 | 31 | function plotTraj(xp,up,N,ego,L,nOb,vOb,lOb,disp_title,plotNumb) 32 | 33 | # obcenter1 = [(ob1[1]+ob1[3])/2-ob1[3]; 34 | # (ob1[2]+ob1[4])/2-ob1[4]] 35 | # 36 | # obcenter2 = [(ob2[1]+ob2[3])/2-ob2[3]; 37 | # (ob2[2]+ob2[4])/2-ob2[4]] 38 | # 39 | # obcenter3 = [(ob3[1]+ob3[3])/2-ob3[3]; 40 | # (ob3[2]+ob3[4])/2-ob3[4]] 41 | 42 | W_ev = ego[2]+ego[4] 43 | L_ev = ego[1]+ego[3] 44 | 45 | # W_tv1 = ob1[2]+ob1[4] 46 | # L_tv1 = ob1[1]+ob1[3] 47 | # 48 | # W_tv2 = ob2[2]+ob2[4] 49 | # L_tv2 = ob2[1]+ob2[3] 50 | # 51 | # W_tv3 = ob3[2]+ob3[4] 52 | # L_tv3 = ob3[1]+ob3[3] 53 | 54 | up = [up ; zeros(1,2)] # final position no input 55 | 56 | w = W_ev/2; 57 | offset = L_ev/2 - ego[3] 58 | 59 | # initial state 60 | x0_s = xp[1,:] 61 | Rot0 = [cos(x0_s[3]) -sin(x0_s[3]); sin(x0_s[3]) cos(x0_s[3])] 62 | x0 = [x0_s[1]; x0_s[2]] 63 | centerCar0 = x0 + Rot0*[offset;0] 64 | 65 | # end state 66 | xF_s = xp[end,:] 67 | RotF = [cos(xF_s[3]) -sin(xF_s[3]); sin(xF_s[3]) cos(xF_s[3])] 68 | xF = [xF_s[1]; xF_s[2]] 69 | centerCarF = xF + RotF*[offset;0] 70 | 71 | for i = 1:1:N+1 72 | 73 | figure(plotNumb) 74 | plot(xp[1:i,1],xp[1:i,2],"b") # plot trajectory so far 75 | title(disp_title) 76 | hold(1) 77 | 78 | # plot trajectory 79 | for j = 1 : nOb 80 | for k = 1 : vOb[j] 81 | plot([lOb[j][k][1],lOb[j][k+1][1]] , [lOb[j][k][2],lOb[j][k+1][2]] ,"k") 82 | end 83 | end 84 | 85 | Rot = [cos(xp[i,3]) -sin(xp[i,3]);sin(xp[i,3]) cos(xp[i,3])] 86 | 87 | x_cur = [xp[i,1]; 88 | xp[i,2]] 89 | 90 | centerCar = x_cur + Rot*[offset;0] 91 | 92 | carBox(centerCar,xp[i,3],W_ev/2,L_ev/2) 93 | carBox(x_cur + (Rot*[L;w-0.15]), xp[i,3] + up[i,1],0.15,0.3) 94 | carBox(x_cur + (Rot*[L;-w+0.15]),xp[i,3] + up[i,1],0.15,0.3) 95 | carBox(x_cur + (Rot*[0; w-0.15]) ,xp[i,3],0.15,0.3) 96 | carBox(x_cur + (Rot*[0;-w+0.15]) ,xp[i,3],0.15,0.3) 97 | 98 | # plot start position 99 | plot(x0[1],x0[2],"ob") 100 | carBox(centerCar0,x0_s[3],W_ev/2,L_ev/2) 101 | carBox(x0 + (Rot0*[L;w-0.15]) ,x0_s[3],0.15,0.3) 102 | carBox(x0 + (Rot0*[L;-w+0.15]) ,x0_s[3],0.15,0.3) 103 | carBox(x0 + (Rot0*[0; w-0.15]) ,x0_s[3], 0.15,0.3) 104 | carBox(x0 + (Rot0*[0;-w+0.15]) ,x0_s[3], 0.15,0.3) 105 | 106 | # plot end position 107 | carBox_dashed(centerCarF,xF_s[3],W_ev/2,L_ev/2) 108 | carBox_dashed(xF + (RotF*[L;w-0.15]) ,xF_s[3],0.15,0.3) 109 | carBox_dashed(xF + (RotF*[L;-w+0.15]) ,xF_s[3],0.15,0.3) 110 | carBox_dashed(xF + (RotF*[0; w-0.15]) ,xF_s[3], 0.15,0.3) 111 | carBox_dashed(xF + (RotF*[0;-w+0.15]) ,xF_s[3], 0.15,0.3) 112 | if i == N+1 113 | plot(xF[1],xF[2],"ob") 114 | end 115 | 116 | axis("equal") 117 | 118 | hold(0) 119 | 120 | sleep(0.05) 121 | end 122 | end 123 | 124 | # plot cars 125 | function carBox(x0,phi,w,l) 126 | car1 = x0[1:2] + [cos(phi)*l;sin(phi)*l] + [sin(phi)*w;-cos(phi)*w]; 127 | car2 = x0[1:2] + [cos(phi)*l;sin(phi)*l] - [sin(phi)*w;-cos(phi)*w]; 128 | car3 = x0[1:2] - [cos(phi)*l;sin(phi)*l] + [sin(phi)*w;-cos(phi)*w]; 129 | car4 = x0[1:2] - [cos(phi)*l;sin(phi)*l] - [sin(phi)*w;-cos(phi)*w]; 130 | plot([car1[1],car2[1],car4[1],car3[1],car1[1]],[car1[2],car2[2],car4[2],car3[2],car1[2]],"k") 131 | end 132 | 133 | # plot cars 134 | function carBox_dashed(x0,phi,w,l) 135 | car1 = x0[1:2] + [cos(phi)*l;sin(phi)*l] + [sin(phi)*w;-cos(phi)*w]; 136 | car2 = x0[1:2] + [cos(phi)*l;sin(phi)*l] - [sin(phi)*w;-cos(phi)*w]; 137 | car3 = x0[1:2] - [cos(phi)*l;sin(phi)*l] + [sin(phi)*w;-cos(phi)*w]; 138 | car4 = x0[1:2] - [cos(phi)*l;sin(phi)*l] - [sin(phi)*w;-cos(phi)*w]; 139 | plot([car1[1],car2[1],car4[1],car3[1],car1[1]],[car1[2],car2[2],car4[2],car3[2],car1[2]],":k") 140 | end 141 | -------------------------------------------------------------------------------- /reeds_shepp.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 5 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 6 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # Reeds Shepp path planner 28 | ############### 29 | 30 | 31 | module reeds_shepp 32 | 33 | using PyPlot 34 | 35 | const STEP_SIZE = 0.1 36 | 37 | type Path 38 | lengths::Array{Float64} #lengths of each part of the path +: forward, -: backward 39 | ctypes::Array{String} # type of each part of the path 40 | L::Float64 # total path length 41 | x::Array{Float64} # final x positions [m] 42 | y::Array{Float64} # final y positions [m] 43 | yaw::Array{Float64} # final yaw angles [rad] 44 | directions::Array{Int8} # forward:1, backward:-1 45 | end 46 | 47 | function pi_2_pi(iangle::Float64)::Float64 48 | while (iangle > pi) 49 | iangle -= 2.0 * pi 50 | end 51 | while (iangle < -pi) 52 | iangle += 2.0 * pi 53 | end 54 | 55 | return iangle 56 | end 57 | 58 | 59 | function calc_shortest_path(sx::Float64, sy::Float64, syaw::Float64, 60 | gx::Float64, gy::Float64, gyaw::Float64, 61 | maxc::Float64; 62 | step_size::Float64 = STEP_SIZE) 63 | # println("Find Shortest Path") 64 | paths = calc_paths(sx,sy,syaw,gx,gy,gyaw,maxc,step_size=step_size) 65 | 66 | minL = Inf 67 | best_path_index = -1 68 | for i in 1:length(paths) 69 | if paths[i].L <= minL 70 | minL = paths[i].L 71 | best_path_index = i 72 | end 73 | end 74 | 75 | return paths[best_path_index] 76 | end 77 | 78 | 79 | function calc_shortest_path_length(sx::Float64, sy::Float64, syaw::Float64, 80 | gx::Float64, gy::Float64, gyaw::Float64, 81 | maxc::Float64; 82 | step_size::Float64 = STEP_SIZE) 83 | q0 = [sx, sy, syaw] 84 | q1 = [gx, gy, gyaw] 85 | paths = generate_path(q0, q1, maxc) 86 | 87 | minL = Inf 88 | for i in 1:length(paths) 89 | L = paths[i].L/maxc 90 | if L <= minL 91 | minL = L 92 | end 93 | end 94 | 95 | return minL 96 | end 97 | 98 | 99 | function calc_paths(sx::Float64, sy::Float64, syaw::Float64, 100 | gx::Float64, gy::Float64, gyaw::Float64, 101 | maxc::Float64; step_size::Float64 = STEP_SIZE)::Array{Path} 102 | q0 = [sx, sy, syaw] 103 | q1 = [gx, gy, gyaw] 104 | 105 | paths = generate_path(q0, q1, maxc) 106 | for path in paths 107 | x, y, yaw, directions = generate_local_course(path.L, path.lengths, path.ctypes, maxc, step_size*maxc) 108 | 109 | # convert global coordinate 110 | path.x = [cos(-q0[3]) * ix + sin(-q0[3]) * iy + q0[1] for (ix, iy) in zip(x, y)] 111 | path.y = [-sin(-q0[3]) * ix + cos(-q0[3]) * iy + q0[2] for (ix, iy) in zip(x, y)] 112 | path.yaw = pi_2_pi.([iyaw + q0[3] for iyaw in yaw]) 113 | path.directions = directions 114 | path.lengths = [l/maxc for l in path.lengths] 115 | path.L = path.L/maxc 116 | 117 | end 118 | 119 | return paths 120 | end 121 | 122 | 123 | function get_label(path::Path) 124 | label ="" 125 | 126 | for (m,l) in zip(path.ctypes, path.lengths) 127 | label = string(label, m) 128 | if l > 0.0 129 | label = string(label, "+") 130 | else 131 | label = string(label, "-") 132 | end 133 | end 134 | 135 | return label 136 | end 137 | 138 | 139 | function polar(x::Float64, y::Float64) 140 | r = sqrt(x^2+y^2) 141 | theta = atan2(y, x) 142 | return r, theta 143 | end 144 | 145 | 146 | function mod2pi(x::Float64) 147 | v = mod(x, 2.0*pi) 148 | if v < -pi 149 | v += 2.0*pi; 150 | else 151 | if v > pi 152 | v -= 2.0*pi 153 | end 154 | end 155 | return v 156 | end 157 | 158 | 159 | function LSL(x::Float64, y::Float64, phi::Float64) 160 | u, t = polar(x - sin(phi), y - 1.0 + cos(phi)) 161 | if t >= 0.0 162 | v = mod2pi(phi - t) 163 | if (v >= 0.0) 164 | return true, t, u, v 165 | end 166 | end 167 | 168 | return false, 0.0, 0.0, 0.0 169 | end 170 | 171 | 172 | function LSR(x::Float64, y::Float64, phi::Float64) 173 | u1, t1 = polar(x + sin(phi), y - 1.0 - cos(phi)) 174 | u1 = u1^2; 175 | if u1 >= 4.0 176 | u = sqrt(u1 - 4.0) 177 | theta = atan2(2.0, u) 178 | t = mod2pi(t1 + theta) 179 | v = mod2pi(t - phi) 180 | 181 | if t >= 0.0 && v >= 0.0 182 | return true, t, u, v 183 | end 184 | end 185 | 186 | return false, 0.0, 0.0, 0.0 187 | end 188 | 189 | 190 | function LRL(x::Float64, y::Float64, phi::Float64) 191 | u1, t1 = polar(x - sin(phi), y - 1.0 + cos(phi)) 192 | 193 | if u1 <= 4.0 194 | u = -2.0*asin(0.25 * u1) 195 | t = mod2pi(t1 + 0.5 * u + pi); 196 | v = mod2pi(phi - t + u); 197 | 198 | if t >= 0.0 && u <= 0.0 199 | return true, t, u, v 200 | end 201 | end 202 | 203 | return false, 0.0, 0.0, 0.0 204 | end 205 | 206 | 207 | function set_path(paths::Array{Path}, lengths::Array{Float64}, ctypes::Array{String}) 208 | 209 | path = Path([],[],0.0,[],[],[],[]) 210 | path.ctypes = ctypes 211 | path.lengths = lengths 212 | 213 | # check same path exist 214 | for tpath in paths 215 | typeissame = (tpath.ctypes == path.ctypes) 216 | if typeissame 217 | if sum(tpath.lengths - path.lengths) <= 0.01 218 | return paths # not insert path 219 | end 220 | end 221 | end 222 | 223 | path.L = sum([abs(i) for i in lengths]) 224 | 225 | Base.Test.@test path.L >= 0.01 226 | 227 | push!(paths, path) 228 | 229 | return paths 230 | end 231 | 232 | 233 | function SCS(x::Float64, y::Float64, phi::Float64, paths::Array{Path})::Array{Path} 234 | flag, t, u, v = SLS(x, y, phi) 235 | if flag 236 | # println("SCS1") 237 | paths = set_path(paths, [t, u, v], ["S","L","S"]) 238 | end 239 | flag, t, u, v = SLS(x, -y, -phi) 240 | if flag 241 | # println("SCS2") 242 | paths = set_path(paths, [t, u, v], ["S","R","S"]) 243 | end 244 | 245 | return paths 246 | end 247 | 248 | 249 | function SLS(x::Float64, y::Float64, phi::Float64) 250 | # println(x,",", y,",", phi, ",", mod2pi(phi)) 251 | phi = mod2pi(phi) 252 | if y > 0.0 && phi > 0.0 && phi < pi*0.99 253 | xd = - y/tan(phi) + x 254 | t = xd - tan(phi/2.0) 255 | u = phi 256 | v = sqrt((x-xd)^2+y^2)-tan(phi/2.0) 257 | # println("1,",t,",",u,",",v) 258 | return true, t, u, v 259 | elseif y < 0.0 && phi > 0.0 && phi < pi*0.99 260 | xd = - y/tan(phi) + x 261 | t = xd - tan(phi/2.0) 262 | u = phi 263 | v = -sqrt((x-xd)^2+y^2)-tan(phi/2.0) 264 | # println("2,",t,",",u,",",v) 265 | return true, t, u, v 266 | end 267 | 268 | return false, 0.0, 0.0, 0.0 269 | end 270 | 271 | 272 | function CSC(x::Float64, y::Float64, phi::Float64, paths::Array{Path}) 273 | flag, t, u, v = LSL(x, y, phi) 274 | if flag 275 | # println("CSC1") 276 | paths = set_path(paths, [t, u, v], ["L","S","L"]) 277 | end 278 | flag, t, u, v = LSL(-x, y, -phi) 279 | if flag 280 | # println("CSC2") 281 | paths = set_path(paths, [-t, -u, -v], ["L","S","L"]) 282 | end 283 | flag, t, u, v = LSL(x, -y, -phi) 284 | if flag 285 | # println("CSC3") 286 | paths = set_path(paths, [t, u, v], ["R","S","R"]) 287 | end 288 | flag, t, u, v = LSL(-x, -y, phi) 289 | if flag 290 | # println("CSC4") 291 | paths = set_path(paths, [-t, -u, -v], ["R","S","R"]) 292 | end 293 | flag, t, u, v = LSR(x, y, phi) 294 | if flag 295 | # println("CSC5") 296 | paths = set_path(paths, [t, u, v], ["L","S","R"]) 297 | end 298 | flag, t, u, v = LSR(-x, y, -phi) 299 | if flag 300 | # println("CSC6") 301 | paths = set_path(paths, [-t, -u, -v], ["L","S","R"]) 302 | end 303 | flag, t, u, v = LSR(x, -y, -phi) 304 | if flag 305 | # println("CSC7") 306 | paths = set_path(paths, [t, u, v], ["R","S","L"]) 307 | end 308 | flag, t, u, v = LSR(-x, -y, phi) 309 | if flag 310 | # println("CSC8") 311 | paths = set_path(paths, [-t, -u, -v], ["R","S","L"]) 312 | end 313 | 314 | return paths 315 | end 316 | 317 | 318 | function CCC(x::Float64, y::Float64, phi::Float64, paths::Array{Path}) 319 | 320 | flag, t, u, v = LRL(x, y, phi) 321 | if flag 322 | # println("CCC1") 323 | paths = set_path(paths, [t, u, v], ["L","R","L"]) 324 | end 325 | flag, t, u, v = LRL(-x, y, -phi) 326 | if flag 327 | # println("CCC2") 328 | paths = set_path(paths, [-t, -u, -v], ["L","R","L"]) 329 | end 330 | flag, t, u, v = LRL(x, -y, -phi) 331 | if flag 332 | # println("CCC3") 333 | paths = set_path(paths, [t, u, v], ["R","L","R"]) 334 | end 335 | flag, t, u, v = LRL(-x, -y, phi) 336 | if flag 337 | # println("CCC4") 338 | paths = set_path(paths, [-t, -u, -v], ["R","L","R"]) 339 | end 340 | 341 | # backwards 342 | xb = x*cos(phi) + y*sin(phi) 343 | yb = x*sin(phi) - y*cos(phi) 344 | # println(xb, ",", yb,",",x,",",y) 345 | 346 | flag, t, u, v = LRL(xb, yb, phi) 347 | if flag 348 | # println("CCC5") 349 | paths = set_path(paths, [v, u, t], ["L","R","L"]) 350 | end 351 | flag, t, u, v = LRL(-xb, yb, -phi) 352 | if flag 353 | # println("CCC6") 354 | paths = set_path(paths, [-v, -u, -t], ["L","R","L"]) 355 | end 356 | flag, t, u, v = LRL(xb, -yb, -phi) 357 | if flag 358 | # println("CCC7") 359 | paths = set_path(paths, [v, u, t], ["R","L","R"]) 360 | end 361 | flag, t, u, v = LRL(-xb, -yb, phi) 362 | if flag 363 | # println("CCC8") 364 | paths = set_path(paths, [-v, -u, -t], ["R","L","R"]) 365 | end 366 | 367 | return paths 368 | end 369 | 370 | 371 | function calc_tauOmega(u::Float64, v::Float64, xi::Float64, eta::Float64, phi::Float64) 372 | delta = mod2pi(u-v) 373 | A = sin(u) - sin(delta) 374 | B = cos(u) - cos(delta) - 1.0 375 | 376 | t1 = atan2(eta*A - xi*B, xi*A + eta*B) 377 | t2 = 2.0 * (cos(delta) - cos(v) - cos(u)) + 3.0; 378 | 379 | if t2 < 0 380 | tau = mod2pi(t1+pi) 381 | else 382 | tau = mod2pi(t1) 383 | end 384 | omega = mod2pi(tau - u + v - phi) 385 | 386 | return tau, omega 387 | end 388 | 389 | 390 | function LRLRn(x::Float64, y::Float64, phi::Float64) 391 | xi = x + sin(phi) 392 | eta = y - 1.0 - cos(phi) 393 | rho = 0.25 * (2.0 + sqrt(xi*xi + eta*eta)) 394 | 395 | if rho <= 1.0 396 | u = acos(rho) 397 | t, v = calc_tauOmega(u, -u, xi, eta, phi); 398 | if t >= 0.0 && v <= 0.0 399 | return true, t, u, v 400 | end 401 | end 402 | 403 | return false, 0.0, 0.0, 0.0 404 | end 405 | 406 | 407 | function LRLRp(x::Float64, y::Float64, phi::Float64) 408 | xi = x + sin(phi) 409 | eta = y - 1.0 - cos(phi) 410 | rho = (20.0 - xi*xi - eta*eta) / 16.0; 411 | # println(xi,",",eta,",",rho) 412 | 413 | if (rho>=0.0 && rho<=1.0) 414 | u = -acos(rho); 415 | if (u >= -0.5 * pi) 416 | t, v = calc_tauOmega(u, u, xi, eta, phi); 417 | if t >= 0.0 && v >= 0.0 418 | return true, t, u, v 419 | end 420 | end 421 | end 422 | 423 | return false, 0.0, 0.0, 0.0 424 | end 425 | 426 | 427 | function CCCC(x::Float64, y::Float64, phi::Float64, paths::Array{Path}) 428 | 429 | flag, t, u, v = LRLRn(x, y, phi) 430 | if flag 431 | # println("CCCC1") 432 | paths = set_path(paths, [t, u, -u, v], ["L","R","L","R"]) 433 | end 434 | 435 | flag, t, u, v = LRLRn(-x, y, -phi) 436 | if flag 437 | # println("CCCC2") 438 | paths = set_path(paths, [-t, -u, u, -v], ["L","R","L","R"]) 439 | end 440 | 441 | flag, t, u, v = LRLRn(x, -y, -phi) 442 | if flag 443 | # println("CCCC3") 444 | paths = set_path(paths, [t, u, -u, v], ["R","L","R","L"]) 445 | end 446 | 447 | flag, t, u, v = LRLRn(-x, -y, phi) 448 | if flag 449 | # println("CCCC4") 450 | paths = set_path(paths, [-t, -u, u, -v], ["R","L","R","L"]) 451 | end 452 | 453 | flag, t, u, v = LRLRp(x, y, phi) 454 | if flag 455 | # println("CCCC5") 456 | paths = set_path(paths, [t, u, u, v], ["L","R","L","R"]) 457 | end 458 | 459 | flag, t, u, v = LRLRp(-x, y, -phi) 460 | if flag 461 | # println("CCCC6") 462 | paths = set_path(paths, [-t, -u, -u, -v], ["L","R","L","R"]) 463 | end 464 | 465 | flag, t, u, v = LRLRp(x, -y, -phi) 466 | if flag 467 | # println("CCCC7") 468 | paths = set_path(paths, [t, u, u, v], ["R","L","R","L"]) 469 | end 470 | 471 | flag, t, u, v = LRLRp(-x, -y, phi) 472 | if flag 473 | # println("CCCC8") 474 | paths = set_path(paths, [-t, -u, -u, -v], ["R","L","R","L"]) 475 | end 476 | 477 | return paths 478 | end 479 | 480 | 481 | function LRSR(x::Float64, y::Float64, phi::Float64) 482 | 483 | xi = x + sin(phi) 484 | eta = y - 1.0 - cos(phi) 485 | rho, theta = polar(-eta, xi) 486 | 487 | if rho >= 2.0 488 | t = theta 489 | u = 2.0 - rho 490 | v = mod2pi(t + 0.5*pi - phi) 491 | if t >= 0.0 && u <= 0.0 && v <=0.0 492 | return true, t, u, v 493 | end 494 | end 495 | 496 | return false, 0.0, 0.0, 0.0 497 | end 498 | 499 | 500 | function LRSL(x::Float64, y::Float64, phi::Float64) 501 | xi = x - sin(phi) 502 | eta = y - 1.0 + cos(phi) 503 | rho, theta = polar(xi, eta) 504 | 505 | if rho >= 2.0 506 | r = sqrt(rho*rho - 4.0); 507 | u = 2.0 - r; 508 | t = mod2pi(theta + atan2(r, -2.0)); 509 | v = mod2pi(phi - 0.5*pi - t); 510 | if t >= 0.0 && u<=0.0 && v<=0.0 511 | return true, t, u, v 512 | end 513 | end 514 | 515 | return false, 0.0, 0.0, 0.0 516 | end 517 | 518 | 519 | function CCSC(x::Float64, y::Float64, phi::Float64, paths::Array{Path}) 520 | 521 | flag, t, u, v = LRSL(x, y, phi) 522 | if flag 523 | # println("CCSC1") 524 | paths = set_path(paths, [t, -0.5*pi, u, v], ["L","R","S","L"]) 525 | end 526 | 527 | flag, t, u, v = LRSL(-x, y, -phi) 528 | if flag 529 | # println("CCSC2") 530 | paths = set_path(paths, [-t, 0.5*pi, -u, -v], ["L","R","S","L"]) 531 | end 532 | 533 | flag, t, u, v = LRSL(x, -y, -phi) 534 | if flag 535 | # println("CCSC3") 536 | paths = set_path(paths, [t, -0.5*pi, u, v], ["R","L","S","R"]) 537 | end 538 | 539 | flag, t, u, v = LRSL(-x, -y, phi) 540 | if flag 541 | # println("CCSC4") 542 | paths = set_path(paths, [-t, 0.5*pi, -u, -v], ["R","L","S","R"]) 543 | end 544 | 545 | flag, t, u, v = LRSR(x, y, phi) 546 | if flag 547 | # println("CCSC5") 548 | paths = set_path(paths, [t, -0.5*pi, u, v], ["L","R","S","R"]) 549 | end 550 | 551 | flag, t, u, v = LRSR(-x, y, -phi) 552 | if flag 553 | # println("CCSC6") 554 | paths = set_path(paths, [-t, 0.5*pi, -u, -v], ["L","R","S","R"]) 555 | end 556 | 557 | flag, t, u, v = LRSR(x, -y, -phi) 558 | if flag 559 | # println("CCSC7") 560 | paths = set_path(paths, [t, -0.5*pi, u, v], ["R","L","S","L"]) 561 | end 562 | 563 | flag, t, u, v = LRSR(-x, -y, phi) 564 | if flag 565 | # println("CCSC8") 566 | paths = set_path(paths, [-t, 0.5*pi, -u, -v], ["R","L","S","L"]) 567 | end 568 | 569 | # backwards 570 | xb = x*cos(phi) + y*sin(phi) 571 | yb = x*sin(phi) - y*cos(phi) 572 | flag, t, u, v = LRSL(xb, yb, phi) 573 | if flag 574 | # println("CCSC9") 575 | paths = set_path(paths, [v, u, -0.5*pi, t], ["L","S","R","L"]) 576 | end 577 | 578 | flag, t, u, v = LRSL(-xb, yb, -phi) 579 | if flag 580 | # println("CCSC10") 581 | paths = set_path(paths, [-v, -u, 0.5*pi, -t], ["L","S","R","L"]) 582 | end 583 | 584 | flag, t, u, v = LRSL(xb, -yb, -phi) 585 | if flag 586 | # println("CCSC11") 587 | paths = set_path(paths, [v, u, -0.5*pi, t], ["R","S","L","R"]) 588 | end 589 | 590 | flag, t, u, v = LRSL(-xb, -yb, phi) 591 | if flag 592 | # println("CCSC12") 593 | paths = set_path(paths, [-v, -u, 0.5*pi, -t], ["R","S","L","R"]) 594 | end 595 | 596 | flag, t, u, v = LRSR(xb, yb, phi) 597 | if flag 598 | # println("CCSC13") 599 | paths = set_path(paths, [v, u, -0.5*pi, t], ["R","S","R","L"]) 600 | end 601 | 602 | flag, t, u, v = LRSR(-xb, yb, -phi) 603 | if flag 604 | # println("CCSC14") 605 | paths = set_path(paths, [-v, -u, 0.5*pi, -t], ["R","S","R","L"]) 606 | end 607 | 608 | flag, t, u, v = LRSR(xb, -yb, -phi) 609 | if flag 610 | # println("CCSC15") 611 | paths = set_path(paths, [v, u, -0.5*pi, t], ["L","S","L","R"]) 612 | end 613 | 614 | flag, t, u, v = LRSR(-xb, -yb, phi) 615 | if flag 616 | # println("CCSC16") 617 | paths = set_path(paths, [-v, -u, 0.5*pi, -t], ["L","S","L","R"]) 618 | end 619 | 620 | return paths 621 | end 622 | 623 | 624 | function LRSLR(x::Float64, y::Float64, phi::Float64) 625 | # formula 8.11 *** TYPO IN PAPER *** 626 | xi = x + sin(phi) 627 | eta = y - 1.0 - cos(phi) 628 | rho, theta = polar(xi, eta) 629 | if rho >= 2.0 630 | u = 4.0 - sqrt(rho*rho - 4.0) 631 | if u <= 0.0 632 | t = mod2pi(atan2((4.0-u)*xi -2.0*eta, -2.0*xi + (u-4.0)*eta)); 633 | v = mod2pi(t - phi); 634 | 635 | if t >= 0.0 && v >=0.0 636 | return true, t, u, v 637 | end 638 | end 639 | end 640 | 641 | return false, 0.0, 0.0, 0.0 642 | end 643 | 644 | 645 | function CCSCC(x::Float64, y::Float64, phi::Float64, paths::Array{Path}) 646 | flag, t, u, v = LRSLR(x, y, phi) 647 | if flag 648 | # println("CCSCC1") 649 | paths = set_path(paths, [t, -0.5*pi, u, -0.5*pi, v], ["L","R","S","L","R"]) 650 | end 651 | flag, t, u, v = LRSLR(-x, y, -phi) 652 | if flag 653 | # println("CCSCC2") 654 | paths = set_path(paths, [-t, 0.5*pi, -u, 0.5*pi, -v], ["L","R","S","L","R"]) 655 | end 656 | 657 | flag, t, u, v = LRSLR(x, -y, -phi) 658 | if flag 659 | # println("CCSCC3") 660 | paths = set_path(paths, [t, -0.5*pi, u, -0.5*pi, v], ["R","L","S","R","L"]) 661 | end 662 | 663 | flag, t, u, v = LRSLR(-x, -y, phi) 664 | if flag 665 | # println("CCSCC4") 666 | paths = set_path(paths, [-t, 0.5*pi, -u, 0.5*pi, -v], ["R","L","S","R","L"]) 667 | end 668 | 669 | return paths 670 | end 671 | 672 | 673 | function generate_local_course(L::Float64, 674 | lengths::Array{Float64}, 675 | mode::Array{String}, 676 | maxc::Float64, 677 | step_size::Float64) 678 | npoint = trunc(Int64, L/step_size) + length(lengths)+3 679 | # println(npoint, ",", L, ",", step_size, ",", L/step_size) 680 | 681 | px = fill(0.0, npoint) 682 | py = fill(0.0, npoint) 683 | pyaw = fill(0.0, npoint) 684 | directions = fill(0, npoint) 685 | ind = 2 686 | 687 | if lengths[1] > 0.0 688 | directions[1] = 1 689 | else 690 | directions[1] = -1 691 | end 692 | 693 | if lengths[1] > 0.0 694 | d = step_size 695 | else 696 | d = -step_size 697 | end 698 | 699 | pd = d 700 | ll = 0.0 701 | 702 | for (m, l, i) in zip(mode, lengths, 1:length(mode)) 703 | 704 | if l > 0.0 705 | d = step_size 706 | else 707 | d = -step_size 708 | end 709 | 710 | # set prigin state 711 | ox, oy, oyaw = px[ind], py[ind], pyaw[ind] 712 | 713 | ind -= 1 714 | if i >= 2 && (lengths[i-1]*lengths[i])>0 715 | pd = - d - ll 716 | else 717 | pd = d - ll 718 | end 719 | 720 | while abs(pd) <= abs(l) 721 | ind += 1 722 | px, py, pyaw, directions = interpolate(ind, pd, m, maxc, ox, oy, oyaw, px, py, pyaw, directions) 723 | pd += d 724 | end 725 | 726 | ll = l - pd - d # calc remain length 727 | 728 | ind += 1 729 | px, py, pyaw, directions = interpolate(ind, l, m, maxc, ox, oy, oyaw, px, py, pyaw, directions) 730 | end 731 | 732 | #remove unused data 733 | while px[end] == 0.0 734 | pop!(px) 735 | pop!(py) 736 | pop!(pyaw) 737 | pop!(directions) 738 | end 739 | 740 | return px, py, pyaw, directions 741 | end 742 | 743 | 744 | function interpolate(ind::Int64, l::Float64, m::String, maxc::Float64, 745 | ox::Float64, oy::Float64, oyaw::Float64, 746 | px::Array{Float64}, py::Array{Float64}, pyaw::Array{Float64}, 747 | directions::Array{Int64}) 748 | 749 | if m == "S" 750 | px[ind] = ox + l / maxc * cos(oyaw) 751 | py[ind] = oy + l / maxc * sin(oyaw) 752 | pyaw[ind] = oyaw 753 | else # curve 754 | ldx = sin(l) / maxc 755 | if m == "L" # left turn 756 | ldy = (1.0 - cos(l)) / maxc 757 | elseif m == "R" # right turn 758 | ldy = (1.0 - cos(l)) / -maxc 759 | end 760 | gdx = cos(-oyaw) * ldx + sin(-oyaw) * ldy 761 | gdy = -sin(-oyaw) * ldx + cos(-oyaw) * ldy 762 | px[ind] = ox + gdx 763 | py[ind] = oy + gdy 764 | end 765 | 766 | if m == "L" # left turn 767 | pyaw[ind] = oyaw + l 768 | elseif m == "R" # right turn 769 | pyaw[ind] = oyaw - l 770 | end 771 | 772 | if l > 0.0 773 | directions[ind] = 1 774 | else 775 | directions[ind] = -1 776 | end 777 | 778 | return px, py, pyaw, directions 779 | end 780 | 781 | 782 | function generate_path(q0::Array{Float64}, q1::Array{Float64}, maxc::Float64)::Array{Path} 783 | dx = q1[1] - q0[1] 784 | dy = q1[2] - q0[2] 785 | dth = q1[3] - q0[3] 786 | c = cos(q0[3]) 787 | s = sin(q0[3]); 788 | x = (c*dx + s*dy)*maxc 789 | y = (-s*dx + c*dy)*maxc 790 | 791 | paths = Path[] 792 | paths = SCS(x, y, dth, paths) 793 | paths = CSC(x, y, dth, paths) 794 | paths = CCC(x, y, dth, paths) 795 | paths = CCCC(x, y, dth, paths) 796 | paths = CCSC(x, y, dth, paths) 797 | paths = CCSCC(x, y, dth, paths) 798 | 799 | return paths 800 | end 801 | 802 | 803 | function calc_curvature(x,y,yaw, directions) 804 | 805 | c = Float64[] 806 | ds = Float64[] 807 | 808 | for i in 2:length(x)-1 809 | dxn = x[i]-x[i-1] 810 | dxp = x[i+1]-x[i] 811 | dyn = y[i]-y[i-1] 812 | dyp = y[i+1]-y[i] 813 | dn =sqrt(dxn^2.0+dyn^2.0) 814 | dp =sqrt(dxp^2.0+dyp^2.0) 815 | dx = 1.0/(dn+dp)*(dp/dn*dxn+dn/dp*dxp) 816 | ddx = 2.0/(dn+dp)*(dxp/dp-dxn/dn) 817 | dy = 1.0/(dn+dp)*(dp/dn*dyn+dn/dp*dyp) 818 | ddy = 2.0/(dn+dp)*(dyp/dp-dyn/dn) 819 | curvature = (ddy*dx-ddx*dy)/(dx^2+dy^2) 820 | d = (dn+dp)/2.0 821 | 822 | if isnan(curvature) 823 | curvature = 0.0 824 | end 825 | 826 | if directions[i] <= 0.0 827 | curvature = -curvature 828 | end 829 | 830 | if length(c) == 0 831 | push!(ds, d) 832 | push!(c, curvature) 833 | end 834 | 835 | push!(ds, d) 836 | push!(c, curvature) 837 | end 838 | 839 | push!(ds, ds[end]) 840 | push!(c, c[end] ) 841 | 842 | return c, ds 843 | end 844 | 845 | 846 | function check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 847 | # println("Test") 848 | # println(start_x,",", start_y, "," ,start_yaw, ",", max_curvature) 849 | paths = calc_paths(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 850 | 851 | Base.Test.@test length(paths) >= 1 852 | 853 | for path in paths 854 | Base.Test.@test abs(path.x[1] - start_x) <= 0.01 855 | Base.Test.@test abs(path.y[1] - start_y) <= 0.01 856 | Base.Test.@test abs(path.yaw[1] - start_yaw) <= 0.01 857 | Base.Test.@test abs(path.x[end] - end_x) <= 0.01 858 | Base.Test.@test abs(path.y[end] - end_y) <= 0.01 859 | Base.Test.@test abs(path.yaw[end] - end_yaw) <= 0.01 860 | 861 | #course distance check 862 | d = [sqrt(dx^2+dy^2) for (dx, dy) in zip(diff(path.x[1:end-1]), diff(path.y[1:end-1]))] 863 | 864 | for i in length(d) 865 | Base.Test.@test abs(d[i] - STEP_SIZE) <= 0.001 866 | end 867 | end 868 | 869 | end 870 | 871 | function test() 872 | println("Test1") 873 | start_x = 0.0 # [m] 874 | start_y = 0.0 # [m] 875 | start_yaw = deg2rad(10.0) # [rad] 876 | end_x = 7.0 # [m] 877 | end_y = -8.0 # [m] 878 | end_yaw = deg2rad(50.0) # [rad] 879 | max_curvature = 2.0 880 | 881 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 882 | 883 | start_x = 0.0 # [m] 884 | start_y = 0.0 # [m] 885 | start_yaw = deg2rad(10.0) # [rad] 886 | end_x = 7.0 # [m] 887 | end_y = -8.0 # [m] 888 | end_yaw = deg2rad(-50.0) # [rad] 889 | max_curvature = 2.0 890 | 891 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 892 | 893 | start_x = 0.0 # [m] 894 | start_y = 10.0 # [m] 895 | start_yaw = deg2rad(-10.0) # [rad] 896 | end_x = -7.0 # [m] 897 | end_y = -8.0 # [m] 898 | end_yaw = deg2rad(-50.0) # [rad] 899 | max_curvature = 2.0 900 | 901 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 902 | 903 | start_x = 0.0 # [m] 904 | start_y = 10.0 # [m] 905 | start_yaw = deg2rad(-10.0) # [rad] 906 | end_x = -7.0 # [m] 907 | end_y = -8.0 # [m] 908 | end_yaw = deg2rad(150.0) # [rad] 909 | max_curvature = 1.0 910 | 911 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 912 | 913 | start_x = 0.0 # [m] 914 | start_y = 10.0 # [m] 915 | start_yaw = deg2rad(-10.0) # [rad] 916 | end_x = 7.0 # [m] 917 | end_y = 8.0 # [m] 918 | end_yaw = deg2rad(150.0) # [rad] 919 | max_curvature = 2.0 920 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 921 | 922 | start_x = -40.0 # [m] 923 | start_y = 549.0 # [m] 924 | start_yaw = 2.44346 # [rad] 925 | end_x = 36.0 # [m] 926 | end_y = 446.0 # [m] 927 | end_yaw = -0.698132 928 | max_curvature = 0.05890904077226434 929 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 930 | 931 | # Random test 932 | for i in 1:100 933 | start_x = rand()*100.0 - 50.0 934 | start_y = rand()*100.0 - 50.0 935 | start_yaw = deg2rad(rand()*360.0 - 180.0) 936 | end_x = rand()*100.0 - 50.0 937 | end_y = rand()*100.0 - 50.0 938 | end_yaw = deg2rad(rand()*360.0 - 180.0) 939 | max_curvature = rand()/10.0 940 | # println(i, ",", start_x, ",", start_y,",", start_yaw,",",end_x,",",end_y,",", end_yaw) 941 | check_path(start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 942 | end 943 | end 944 | 945 | 946 | function main() 947 | println(PROGRAM_FILE," start!!") 948 | test() 949 | 950 | start_x = 3.0 # [m] 951 | start_y = 10.0 # [m] 952 | start_yaw = deg2rad(40.0) # [rad] 953 | end_x = 0.0 # [m] 954 | end_y = 1.0 # [m] 955 | end_yaw = deg2rad(0.0) # [rad] 956 | max_curvature = 0.1 957 | 958 | @time bpath = calc_shortest_path( 959 | start_x, start_y, start_yaw, end_x, end_y, end_yaw, max_curvature) 960 | 961 | rc, rds = calc_curvature(bpath.x, bpath.y, bpath.yaw, bpath.directions) 962 | 963 | subplots(1) 964 | plot(bpath.x, bpath.y,"-r", label=get_label(bpath)) 965 | 966 | plot(start_x, start_y) 967 | plot(end_x, end_y) 968 | 969 | legend() 970 | grid(true) 971 | axis("equal") 972 | 973 | subplots(1) 974 | plot(rc, ".r", label="reeds shepp") 975 | grid(true) 976 | title("Curvature") 977 | 978 | show() 979 | 980 | println(PROGRAM_FILE," Done!!") 981 | end 982 | 983 | 984 | if length(PROGRAM_FILE)!=0 && 985 | contains(@__FILE__, PROGRAM_FILE) 986 | 987 | main() 988 | end 989 | 990 | end #module 991 | 992 | -------------------------------------------------------------------------------- /setup.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # setup.jl: run this file before running main.jl 28 | ############### 29 | 30 | ############################## 31 | # include JuMP -> Optimization modeling tool 32 | # include IPOPT -> Interior point based nonlinear solver 33 | # include PyPlot -> Ploting library (matplotlib python) 34 | ############################## 35 | using JuMP, Ipopt, PyPlot, NearestNeighbors, ControlSystems 36 | ############################## 37 | # register warm start function 38 | ############################## 39 | # register Distance and Signeddistance 40 | # parking optimal control problems 41 | 42 | include("ParkingSignedDist.jl") 43 | include("ParkingConstraints.jl") 44 | ############################## 45 | # register polytope converter 46 | include("obstHrep.jl") 47 | ############################## 48 | # register ploting function 49 | include("plotTraj.jl") 50 | include("hybrid_a_star.jl") 51 | ############################## 52 | include("DualMultWS.jl") 53 | include("veloSmooth.jl") 54 | 55 | # function that clears terminal output 56 | clear() = run(@static is_unix() ? `clear` : `cmd /c cls`) 57 | 58 | -------------------------------------------------------------------------------- /veloSmooth.jl: -------------------------------------------------------------------------------- 1 | ############### 2 | # H-OBCA: Hierarchical Optimization-based Collision Avoidance - a path planner for autonomous parking 3 | # Copyright (C) 2018 4 | # Alexander LINIGER [liniger@control.ee.ethz.ch; Automatic Control Lab, ETH Zurich] 5 | # Xiaojing ZHANG [xiaojing.zhang@berkeley.edu; MPC Lab, UC Berkeley] 6 | # Atsushi SAKAI [atsushisakai@global.komatsu; Komatsu Ltd / MPC Lab] 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # 13 | # This program is distributed in the hope that it will be useful, 14 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 15 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 | # GNU General Public License for more details. 17 | # 18 | # You should have received a copy of the GNU General Public License 19 | # along with this program. If not, see . 20 | ############### 21 | # The paper describing the theory can be found here: 22 | # X. Zhang, A. Liniger and F. Borrelli; "Optimization-Based Collision Avoidance"; Technical Report, 2017, [https://arxiv.org/abs/1711.03449] 23 | # X. Zhang, A. Liniger, A. Sakai and F. Borrelli; "Autonomous Parking using Optimization-Based Collision Avoidance"; Technical Report, 2018 [add URL] 24 | ############### 25 | 26 | ############### 27 | # veloSmooth: a velocity smoother 28 | ############### 29 | 30 | 31 | function veloSmooth(v,amax,Ts) 32 | v_ex = zeros(length(v)+40,1) 33 | v_bar = zeros(4,length(v)+40) 34 | v_bar2 = zeros(4,length(v)+40) 35 | v_barMM = zeros(1,length(v)) 36 | 37 | for i = 1:length(v) 38 | for j = 1:4 39 | v_bar[j,i+19] = v[i]; 40 | v_ex[i+19] = v[i]; 41 | end 42 | end 43 | 44 | v_cut1 = 0.25*abs(v[1]) 45 | v_cut2 = 0.25*abs(v[1])+abs(v[1]) 46 | 47 | accPhase = Int(round(abs(v[1])/amax/Ts)) 48 | 49 | index1 = find((diff(v_ex).>v_cut1) & (diff(v_ex).v_cut2) 51 | 52 | index3 = find((diff(v_ex).<-v_cut1) & (diff(v_ex).>-v_cut2)) 53 | index4 = find(diff(v_ex).<-v_cut2) 54 | 55 | if length(index1) >=1 && index1[1]==19 56 | index1[1] = index1[1]+1 57 | end 58 | if length(index3) >=1 && index3[1]==19 59 | index3[1] = index3[1]+1 60 | end 61 | 62 | 63 | for j = 1:length(index1) 64 | if v_ex[index1[j]] > v_cut1 || v_ex[index1[j]+1] > v_cut1 65 | v_bar[1,index1[j]:index1[j]+accPhase] = linspace(0,abs(v[1]),accPhase+1)'' 66 | elseif v_ex[index1[j]] < -v_cut1 || v_ex[index1[j]+1] < -v_cut1 67 | v_bar[1,index1[j]-accPhase+1:index1[j]+1] = linspace(-abs(v[1]),0,accPhase+1)'' 68 | end 69 | end 70 | 71 | for j = 1:length(index3) 72 | if v_ex[index3[j]] > v_cut1 || v_ex[index3[j]+1] > v_cut1 73 | v_bar[2,index3[j]-accPhase+1:index3[j]+1] = linspace(abs(v[1]),0,accPhase+1)'' 74 | elseif v_ex[index3[j]] < -v_cut1 || v_ex[index3[j]+1] < -v_cut1 75 | v_bar[2,index3[j]:index3[j]+accPhase] = linspace(0,-abs(v[1]),accPhase+1)'' 76 | end 77 | end 78 | 79 | for j = 1:length(index2) 80 | v_bar[3,index2[j]-accPhase:index2[j]+accPhase] = linspace(-abs(v[1]),abs(v[1]),2*accPhase+1)'' 81 | end 82 | 83 | for j = 1:length(index4) 84 | v_bar[4,index4[j]-accPhase:index4[j]+accPhase] = linspace(abs(v[1]),-abs(v[1]),2*accPhase+1)'' 85 | end 86 | 87 | for i = 20:length(v)+19 88 | for j = 1:4 89 | if v_bar[j,i] == 0 90 | v_bar2[j,i] = v_bar[j,i] 91 | elseif sign(v_ex[i]) != sign(v_bar[j,i]) 92 | v_bar2[j,i] = v_ex[i] 93 | else 94 | v_bar2[j,i] = v_bar[j,i] 95 | end 96 | end 97 | end 98 | 99 | for i = 20:length(v)+19 100 | if v_ex[i] > 0 101 | v_barMM[i-19] = minimum(v_bar2[:,i]) 102 | else 103 | v_barMM[i-19] = maximum(v_bar2[:,i]) 104 | end 105 | end 106 | 107 | a = diff(v_barMM')./Ts 108 | 109 | return v_barMM', a 110 | 111 | end 112 | --------------------------------------------------------------------------------