├── .gitattributes ├── .gitignore ├── Code_Generation ├── EvilPlotting.py ├── GFOLD_Generate.py └── GFOLD_Generate_Parms.py ├── LICENSE ├── README.md └── Static_Solution ├── EvilPlotting.py ├── GFOLD_Static.py └── GFOLD_Static_Parms.py /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | *.egg-info/ 24 | .installed.cfg 25 | *.egg 26 | 27 | # PyInstaller 28 | # Usually these files are written by a python script from a template 29 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 30 | *.manifest 31 | *.spec 32 | 33 | # Installer logs 34 | pip-log.txt 35 | pip-delete-this-directory.txt 36 | 37 | # Unit test / coverage reports 38 | htmlcov/ 39 | .tox/ 40 | .coverage 41 | .coverage.* 42 | .cache 43 | nosetests.xml 44 | coverage.xml 45 | *.cover 46 | .hypothesis/ 47 | 48 | # Translations 49 | *.mo 50 | *.pot 51 | 52 | # Django stuff: 53 | *.log 54 | local_settings.py 55 | 56 | # Flask stuff: 57 | instance/ 58 | .webassets-cache 59 | 60 | # Scrapy stuff: 61 | .scrapy 62 | 63 | # Sphinx documentation 64 | docs/_build/ 65 | 66 | # PyBuilder 67 | target/ 68 | 69 | # Jupyter Notebook 70 | .ipynb_checkpoints 71 | 72 | # pyenv 73 | .python-version 74 | 75 | # celery beat schedule file 76 | celerybeat-schedule 77 | 78 | # SageMath parsed files 79 | *.sage.py 80 | 81 | # Environments 82 | .env 83 | .venv 84 | env/ 85 | venv/ 86 | ENV/ 87 | 88 | # Spyder project settings 89 | .spyderproject 90 | .spyproject 91 | 92 | # Rope project settings 93 | .ropeproject 94 | 95 | # mkdocs documentation 96 | /site 97 | 98 | # mypy 99 | .mypy_cache/ 100 | -------------------------------------------------------------------------------- /Code_Generation/EvilPlotting.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import matplotlib as mpl 3 | from mpl_toolkits.mplot3d import Axes3D 4 | import numpy as np 5 | import GFOLD_parms_static as p 6 | 7 | def plot_run2D(t, r, v, u, m): 8 | ''' 9 | print('r =',r) 10 | print('v =',v) 11 | print('u =',u) 12 | print('m =',m) 13 | print('s =',s) 14 | ''' 15 | r = np.array(r.value) 16 | v = np.array(v.value) 17 | u = np.array(u.value) 18 | T_val = [np.linalg.norm(u[:,i])*m[i] for i in range(len(v.T))] 19 | vnorm = [np.linalg.norm(vel) for vel in v.T] 20 | 21 | #u_dirs = 90 - np.degrees(np.atan2(u[1,:], u[0,:])) 22 | #T_vals = np.multiply(u_norms , m) 23 | 24 | traj = plt.figure() 25 | 26 | #plt.subplot(4,1,1) 27 | plt.plot(r[0,:],r[1,:]) 28 | M =str(np.tan(np.radians(p.slope))) 29 | nM=str(-float(M)) 30 | bx=str(p.r_d[0]) 31 | by=str(p.r_d[1]) 32 | x=np.array(range(0,int(max(r[0,:])))) 33 | plt.plot(x,eval(M+'*(x-'+bx+')+'+by)) 34 | x=np.array(range(int(min(r[0,:])),0)) 35 | plt.plot(x,eval(nM+'*(x-'+bx+')+'+by)) 36 | plt.title('Position (m)') 37 | 38 | f = plt.figure() 39 | ax = f.add_subplot(411) 40 | 41 | plt.plot(t,vnorm) 42 | by=str(p.V_max) 43 | x=np.array(range(0,int(max(t)))) 44 | plt.plot(x,eval(by)) 45 | plt.xlabel(r"$t$", fontsize=16) 46 | plt.title('Velocity Magnitude (m/s)') 47 | 48 | plt.subplot(4,1,2) 49 | plt.plot(t,r[1,:]) 50 | plt.xlabel(r"$t$", fontsize=16) 51 | plt.title('Altitude (m)') 52 | 53 | plt.subplot(4,1,3) 54 | plt.plot(t,m) 55 | plt.title('Mass (kg)') 56 | 57 | plt.subplot(4,1,4) 58 | plt.plot(t,T_val) 59 | by=str(p.T_max) 60 | x=np.array(range(0,int(max(t)))) 61 | plt.plot(x,eval(by)) 62 | plt.title('Thrust (N)') 63 | 64 | plt.tight_layout() 65 | plt.subplots_adjust(hspace=0) 66 | plt.show() 67 | 68 | def plot_run3D(tf, x, u, m, s, z): 69 | 70 | print('tf',tf) 71 | t = np.linspace(0,tf,num=len(m)) 72 | 73 | r = np.array(x[0:3,:]) 74 | v = np.array(x[3:6,:]) 75 | z = np.array(z) 76 | s = np.array(s) 77 | u = np.array(u) 78 | 79 | print('t',t.shape) 80 | print('r',r.shape) 81 | print('v',v.shape) 82 | print('u',u.shape) 83 | print('m',len(m)) 84 | print('s',s.shape) 85 | print('z',z.shape) 86 | 87 | if t.shape==() or r.shape==() or v.shape==() or u.shape==(): 88 | print('data actually empty') 89 | return 90 | 91 | Th= [np.linalg.norm(u[:,i])*m[i] for i in range(len(v.T))] 92 | vnorm = [np.linalg.norm(vel) for vel in v.T] 93 | 94 | #u_dirs_1 = [90 - np.degrees(np.atan2(u[0,n], u[1,n])) for n in range(p.N)] 95 | #u_dirs_2 = [90 - np.degrees(np.atan2(u[0,n], u[2,n])) for n in range(p.N)] 96 | 97 | traj = plt.figure() 98 | ax = traj.gca(projection='3d') 99 | ax.set_aspect('equal') 100 | 101 | r_= np.linspace(0, max(max(r[1,:]),max(r[2,:])), 7) 102 | a_= np.linspace(0, 2*np.pi, 20) 103 | R, P = np.meshgrid(r_, a_) 104 | X, Y, Z = R*np.cos(P), R*np.sin(P), R*(np.tan(p.y_gs)) 105 | #X,Y,Z=R*np.cos(P), R*np.sin(P),((R**2 - 1)**2) 106 | 107 | #ax.plot(x(t),y(t),z(t),label='Flight Path') 108 | ax.plot(r[1,:],r[2,:],r[0,:],label='Flight Path') 109 | ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r) 110 | 111 | # Tweak the limits and add latex math labels. 112 | 113 | ax.set_xlabel(r'$x{1}$') 114 | ax.set_ylabel(r'$x{2}$') 115 | ax.set_zlabel(r'$x{0}$') 116 | 117 | ax.legend() 118 | 119 | f = plt.figure() 120 | ax = f.add_subplot(511) 121 | 122 | plt.plot(t,vnorm) 123 | y=str(p.V_max) 124 | x=np.array(range(0,int(max(t)))) 125 | plt.plot(x,eval('0*x+'+y)) 126 | plt.title('Velocity Magnitude (m/s)') 127 | 128 | plt.subplot(5,1,2) 129 | plt.plot(t,r[0,:]) 130 | plt.title('Altitude (m)') 131 | 132 | plt.subplot(5,1,3) 133 | plt.plot(t,m) 134 | plt.title('Mass (kg)') 135 | 136 | plt.subplot(5,1,4) 137 | plt.plot(t,Th) 138 | y=str(p.T_max) 139 | x=np.array(range(0,int(max(t)))) 140 | plt.plot(x,eval('0*x+'+y)) 141 | plt.title('Thrust (N)') 142 | 143 | z0_term = (p.m_wet - p.alpha * p.r2) # see ref [2], eq 34,35,36 144 | z1_term = (p.m_wet - p.alpha * p.r1) 145 | lim=[] 146 | lim2=[] 147 | n=0 148 | z=z.flatten() 149 | for t_ in t: 150 | if t_ > 0: 151 | try: 152 | v = p.r2/(z0_term*t_) * (1 - (z[n] - np.log(z0_term*t_))) 153 | except ZeroDivisionError: 154 | v = 0 155 | lim.append( v ) 156 | try: 157 | v = p.r1/(z1_term*t_) *(1 - (z[n] - np.log(z0_term*t_)) + (1/2)*(z[n] - np.log(z0_term*t_))**2 ) 158 | except ZeroDivisionError: 159 | v = 0 160 | lim2.append( v ) 161 | else: 162 | lim.append(0) 163 | lim2.append(0) 164 | n+=1 165 | lim = np.array(lim).flatten() 166 | plt.subplot(5,1,5) 167 | plt.plot(t,lim) 168 | plt.plot(t,lim2) 169 | s = s.flatten() 170 | if s.shape == (1,65): 171 | s.reshape((65,)) 172 | print('reshape',s) 173 | print('s',s) 174 | plt.plot(t,s) 175 | plt.title('Sigma Slack') 176 | 177 | plt.tight_layout() 178 | plt.subplots_adjust(hspace=0) 179 | plt.show() 180 | -------------------------------------------------------------------------------- /Code_Generation/GFOLD_Generate.py: -------------------------------------------------------------------------------- 1 | # GFOLD_static_p3p4_gen_precalcz 2 | 3 | import numpy as np 4 | import GFOLD_parms_static_gen as parameters 5 | from EvilPlotting import * 6 | 7 | ''' 8 | 9 | This code can do both static runs (tests) AND initialize code gen. 10 | If doing code generation, you must still compile the generated code. 11 | 12 | PROBLEM 1: Minimum Landing Error (tf roughly solved) 13 | MINIMIZE : norm of landing error vector 14 | SUBJ TO : 15 | 0) initial conditions satisfied (position, velocity) 16 | 1) final conditions satisfied (altitude, velocity) 17 | 2) dynamics always satisfied 18 | 3) x stays in cone at all times 19 | 4) relaxed convexified mass and thrust constraints 20 | 5) thrust pointing constraint 21 | 6) sub-surface flight constraint 22 | 23 | PROBLEM 2: Minimum Fuel Use 24 | MAXIMIZE : landing mass, opt variables are dynamical and 25 | SUBJ TO : 26 | 0) same constraints as p1, plus: 27 | 1) landing point must be equal or better than that found by p1 28 | ''' 29 | 30 | VERSION = 1.0 31 | 32 | test = 1 # are we doing a static run or a generation run? 33 | 34 | if test: 35 | from cvxpy import * 36 | else: 37 | from cvxpy_codegen import * 38 | 39 | def GFOLD_C_GEN(prog_flag,_s_,_v_): # PRIMARY GFOLD SOLVER 40 | 41 | N_tf=250 # MUST BE FIXED FOR CODE GEN TO WORK 42 | 43 | sk,vk=parameters.Sk,parameters.Vk 44 | if not test: 45 | dt=Parameter(1,1,name='dt') # determines tf implicitly dt = tf/N, tf = dt*N(const) 46 | S=Parameter(1,17,name='S') # contains all parms_static scalar variables 47 | V=Parameter(3,9,name='V') # contains all parms_static vect variables 48 | z0=Parameter(N_tf,name='z0') 49 | z1=Parameter(N_tf,name='z1') 50 | mu_1=Parameter(N_tf,name='mu_1') 51 | mu_2=Parameter(N_tf,name='mu_2') 52 | z0_term=Parameter(N_tf,name='z0_term') 53 | z1_term=Parameter(N_tf,name='z1_term') 54 | 55 | else: 56 | V=_v_ # for cvxpy testing 57 | S=_s_ # for cvxpy testing 58 | 59 | dt=Parameter(1,1,name='dt') # determines tf implicitly dt = tf/N, 60 | # tf = dt*N(const) 61 | 62 | dt.value = float(S[0,sk['tf']])/(N_tf) 63 | 64 | # Precalculate Z limits, then pass in as a PARAMETER 65 | 66 | z0=Parameter(N_tf,name='z0') 67 | z1=Parameter(N_tf,name='z1') 68 | mu_1=Parameter(N_tf,name='mu_1') 69 | mu_2=Parameter(N_tf,name='mu_2') 70 | z0_term=Parameter(N_tf,name='z0_term') 71 | z1_term=Parameter(N_tf,name='z1_term') 72 | 73 | z0_term_, z1_term_ = np.zeros(N_tf),np.zeros(N_tf) 74 | z0_, z1_ = np.zeros(N_tf),np.zeros(N_tf) 75 | mu_1_, mu_2_ = np.zeros(N_tf),np.zeros(N_tf) 76 | 77 | for n in range(0,N_tf-1): 78 | z0_term_[n] = S[0,sk['m_wet']] - S[0,sk['alpha']] * S[0,sk['r2']] * (n) * dt.value # see ref [2], eq 34,35,36 79 | z1_term_[n] = S[0,sk['m_wet']] - S[0,sk['alpha']] * S[0,sk['r1']] * (n) * dt.value 80 | z0_[n] = np.log( z0_term_[n] ) 81 | z1_[n] = np.log( z1_term_[n] ) 82 | mu_1_[n] = S[0,sk['r1']]/(z1_term_[n]) 83 | mu_2_[n] = S[0,sk['r2']]/(z0_term_[n]) 84 | 85 | z0_term.value = z0_term_ 86 | z1_term.value = z1_term_ 87 | z0.value = z0_ 88 | z1.value = z1_ 89 | mu_1.value = mu_1_ 90 | mu_2.value = mu_2_ 91 | 92 | # new variables here for brevity in the dynamics equations 93 | c=vk['c'] 94 | g=vk['g'] 95 | rf=vk['rf'] 96 | alpha=sk['alpha'] 97 | #print(c,g,rf,alpha) 98 | 99 | if prog_flag=='p3': 100 | program = 3 101 | elif prog_flag=='p4': 102 | program = 4 103 | 104 | x = Variable(6,N_tf,name='x') # state vector (3position,3velocity) 105 | u = Variable(3,N_tf,name='u') # u = Tc/mass because Tc[:,n]/m[n] is not allowed by DCP 106 | z = Variable(1,N_tf,name='z') # z = ln(mass) 107 | s = Variable(1,N_tf,name='s') # thrust slack parameter 108 | 109 | con = [] 110 | 111 | con += [x[0:3,0] == V[:,vk['r0']]] 112 | con += [x[3:6,0] == V[:,vk['v0']]] 113 | con += [x[3:6,N_tf-1]==V[:,vk['vf']]] # don't forget to slow down, buddy! 114 | 115 | con += [s[N_tf-1] == 0] # thrust at the end must be zero 116 | con += [u[:,0] == s[0]*np.array([1,0,0]) ] # thrust direction starts straight 117 | con += [u[:,N_tf-1] == s[N_tf-1]*np.array([1,0,0]) ] # and ends straight 118 | con += [z[0] == S[0,sk['z0']]] # convexified (7) 119 | 120 | if program==3: 121 | con += [x[0,N_tf-1] == 0] # end altitude 122 | 123 | elif program==4: 124 | 125 | # force landing point equal to found program 3 point 126 | con += [x[0:3,N_tf-1] == V[:,vk['rf3']]] 127 | 128 | for n in range(0,N_tf-1): # any t in [0,tf] maps to any n in [0,N-1] 129 | 130 | # Leapfrog Integration Method 131 | # accurate +/- sqrt( (dt*df/dr)**2 + 1) 132 | # https://goo.gl/jssWkB 133 | # https://en.wikipedia.org/wiki/Leapfrog_integration 134 | 135 | con += [x[3:6,n+1] == x[3:6,n] + (dt*0.5)*((u[:,n]+V[:,g]) + (u[:,n+1]+V[:,g]))] 136 | con += [x[0:3,n+1] == x[0:3,n] + (dt*0.5)*(x[3:6,n+1]+x[3:6,n])] 137 | 138 | con += [ norm((x[0:3,n]-V[:,rf])[0:2] ) - V[0,c]*(x[0,n]-V[0,rf]) <= 0 ] # glideslope constraint 139 | con += [ norm(x[3:6,n]) <= S[0,sk['V_max']] ] # velocity 140 | 141 | con += [z[n+1] == z[n] - (S[0,alpha]*dt*0.5)*(s[n] + s[n+1])] # mass decreases 142 | con += [norm(u[:,n]) <= s[n]] # limit thrust magnitude & also therefore, mass 143 | 144 | # Thrust pointing constraint 145 | con += [ u[0,n] >= S[0,sk['p_cs']]*s[n] ] 146 | if n > 0: 147 | # lower thrust bound 148 | #con += [s[n] >= mu_1 * (1 - (z[:,n] - z0) + (1/2)*square(z[:,n] - z0))] 149 | con += [s[n] <= mu_2[n]* (1 - (z[:,n] - z0[n]))] # upper thrust bound 150 | con += [z[n] >= z0[n]] # Ensures physical bounds on z are never violated 151 | con += [z[n] <= z1[n]] 152 | 153 | con += [x[0,0:N_tf-1] >= 0] # no, this is not the Boring Company! 154 | 155 | if program == 3: 156 | print('-----------------------------') 157 | if test: 158 | 159 | objective=Minimize(norm(x[0:3,N_tf-1]-V[:,rf])) 160 | problem=Problem(objective,con) 161 | obj_opt=problem.solve(solver=ECOS,verbose=True) 162 | print(obj_opt) 163 | 164 | else: 165 | 166 | objective=Minimize(norm(x[0:3,N_tf-1]-V[:,rf])) 167 | problem=Problem(objective,con) 168 | obj_opt=problem.codegen('GFOLD_'+prog_flag+'_') 169 | 170 | print('-----------------------------') 171 | 172 | 173 | elif program == 4: 174 | print('-----------------------------') 175 | if test: 176 | 177 | objective=Minimize(z[N_tf-1]) 178 | problem=Problem(objective,con) 179 | obj_opt=problem.solve(solver=ECOS,verbose=True) 180 | print(obj_opt) 181 | 182 | else: 183 | 184 | objective=Maximize(z[N_tf-1]) 185 | problem=Problem(objective,con) 186 | obj_opt=problem.codegen('GFOLD_'+prog_flag) 187 | print('-----------------------------') 188 | 189 | if __name__ == '__main__': 190 | 191 | PROGRAM_TO_COMPILE = 'p3' 192 | GFOLD_C_GEN(PROGRAM_TO_COMPILE, parameters.S, parameters.V) 193 | -------------------------------------------------------------------------------- /Code_Generation/GFOLD_Generate_Parms.py: -------------------------------------------------------------------------------- 1 | # GFOLD_parms_static_gen 2 | 3 | import numpy as np 4 | 5 | def e(i): # create a specific basis vector 6 | if i==0: 7 | return [1,0,0] 8 | if i==1: 9 | return [0,1,0] 10 | if i==2: 11 | return [0,0,1] 12 | 13 | def S_mat(_w_): # _w_ to distinguish from our global namespace's w! 14 | return np.matrix([[0,-_w_[2],+_w_[1]], 15 | [_w_[2],0, -_w_[0]], 16 | [-_w_[1],_w_[0],0]]) 17 | 18 | def A(w): 19 | _A_ = np.empty([6,6]) 20 | np.copyto(_A_[0:3,0:3] , np.zeros((3,3)) ) # top left 21 | np.copyto(_A_[0:3,3:6] , np.eye(3) ) # top right 22 | np.copyto(_A_[3:6,0:3] , -np.square(S(w)) ) # bottom left 23 | np.copyto(_A_[3:6,3:6] , np.multiply(-1,S(w))) # bottom right 24 | return _A_ 25 | 26 | ''' Numerical Example 1 ''' 27 | s = [ # scalars 28 | #'N' : 100, # Deprecated, replaced by N_tf, static 29 | ['tf' , 90], 30 | ['g0' , 9.80665], # standard gravity [m/s**2] 31 | ['m_dry' , (2)*1e3], # dry mass kg 32 | ['m_fuel', (0.3)*1e3], # fuel in tons 33 | ['T_max' , 24000], # thrust max 34 | ['tmin' , 0.2], # throttle ability 35 | ['tmax' , 0.8], 36 | ['G_max' , 3], # maximum allowable structural Gs 37 | ['Isp' , 203.94 ], # fuel efficiency (specific impulse) 38 | ['V_max' , 90 ] , # velocity max 39 | ['y_gs' , np.radians(30)], # glide slope cone, must be 0 < Degrees < 90 40 | ['p_cs' , np.cos(np.radians(45))], # thrust pointing constraint 41 | ] 42 | v = [ # vectors 43 | 44 | ['g' , np.array([-3.71,0,0])], # gravity 45 | ['w' , np.array([2.53*1e-5, 0, 6.62*1e-5])] , # planetary angular velocity 46 | ['nh', np.array([1,0,0]) ], # thrust vector reference direction 47 | 48 | ['r0' , np.array([2400, 2000, 0]) ], # initial position 49 | ['v0' , np.array([-40, 30, 0]) ], # initial velocity 50 | #['v0' , np.array([0, 0, 0]) ], # initial velocity 51 | #['r0' , np.array([2400, 0, 0]) ], # initial position 52 | #['v0' , np.array([-40, 0, 0]) ], # initial velocity 53 | 54 | ['rf3', np.array([0,0,0]) ] , # final position target for p4 55 | ['rf' , np.array([0,0,0]) ] , # final position target 56 | ['vf' , np.array([0,0,0]) ] # final velocity target 57 | ] 58 | 59 | sk = [k[0] for k in s] 60 | sv = [n[1] for n in s] 61 | # derived values: 62 | s += [ 63 | ['alpha' , 1/(sv[sk.index('Isp')]*sv[sk.index('g0')]) ], # fuel consumption parameter 64 | ['m_wet' , (sv[sk.index('m_dry')]+sv[sk.index('m_fuel')])], # wet mass kg 65 | ['r1' , sv[sk.index('tmin')]*sv[sk.index('T_max')] ], # lower thrust bound 66 | ['r2' , sv[sk.index('tmax')]*sv[sk.index('T_max')] ], # upper thrust bound 67 | #['z0' , np.log(sv[sk.index('m_dry')]+sv[sk.index('m_fuel')])] # initial log(mass) constraint 68 | ['z0' , np.log(sv[sk.index('m_dry')]+sv[sk.index('m_fuel')])] # initial log(mass) constraint 69 | ] 70 | v += [ 71 | ['c' , np.divide(e(0),np.tan(sv[sk.index('y_gs')]))], 72 | ] 73 | S,Sk,n=[],{},0 74 | for loople in (s): # 'loople' = a list who wants to be a tuple, but wants assignment too :) 75 | key = loople[0] 76 | value=loople[1] 77 | Sk[key] = n 78 | S.append( value) 79 | n+=1 80 | S=np.matrix(S) 81 | 82 | V,Vk,n=[],{},0 83 | for loople in (v): 84 | key = loople[0] 85 | value=loople[1] 86 | Vk[key] = n 87 | V.append( value) 88 | n+=1 89 | 90 | V = np.matrix(V).transpose() # 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EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) 2018 {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | G-FOLD-Python Copyright (C) 2018 jonnyhyman 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | Falcon Heavy Demo Mission 3 | 4 | # G-FOLD Python 5 | ### Guidance for Fuel Optimal Landing Diverts (GFOLD) 6 | 7 | This code reimplements GFOLD algorithm in Python with use of the fantastic cvxpy utility. The algorithm was defined by a number of papers, but chiefly [this paper by Ackimese, Carson, and Blackmore at JPL.](http://www.larsblackmore.com/iee_tcst13.pdf) 8 | 9 | ### What you can do with GFOLD-Python 10 | 11 | - Calculate fuel optimal spacecraft landing trajectories 12 | - Generate embeddable C code for real-time trajectory calculation (~0.3 second calculation time 1x 2.4GHz) 13 | - [Autonomous landing of Kerbal Space Program rockets](https://www.youtube.com/watch?v=7skZHu9i7Fg) 14 | 15 | ### What you can't do with GFOLD-Python 16 | 17 | - Attitude control 18 | - Robust control 19 | - Control of any kind (this is a guidance algorithm!) 20 | 21 | ### How to use it 22 | 23 | - If you wish to do a static calculation (not generating C code) 24 | 1. Define your vehicle and environment in GFOLD_Static_Parms 25 | - All notation follows conventions laid out in the [original paper](http://www.larsblackmore.com/iee_tcst13.pdf) 26 | 2. Comment / Uncomment the constraints you wish to have in GFOLD_Static 27 | 3. Run `python GFOLD_Static.py` *(requires scipy)* 28 | 4. View the "evil" plots *(this name is just a joke btw)* 29 | 30 | 31 | - If you wish to do C code generation 32 | 1. Set `test = 0` at the top of `GFOLD_Generate.py` 33 | 3. Run `python GFOLD_Generate.py` *(requires cvxpy_codegen)* 34 | 3. Fix some of the known-bugs cvxpy_codegen creates 35 | - See issues page of the repo 36 | - Attempt to compile, and solve each error as they come 37 | 4. Compile the generated C code 38 | 5. *(Optional:)* Install the compiled CPython code into your Python distribution with setup.py if you wish to use the compiled code from Python 39 | - Be aware that the Python2.7 Windows Compiler provided by Microsoft will not work because it has a pathetically tiny stack heap size. Recommend using MinGW on Windows! 40 | 41 | ### Documentation 42 | 43 | - Since this is a pre-alpha research project, the main documentation is found in `#code comments`, and in the content of the [paper](http://www.larsblackmore.com/iee_tcst13.pdf) itself. 44 | 45 | ### Requirements 46 | 47 | - Python 2.7 *(I'm sorry about still using python 2, Mr. Guido, but cvxpy_codegen is the constraint here...)* 48 | - scipy (for static solutions) 49 | - cvxpy (for static solutions) 50 | - cvxpy_codegen (for code generation) 51 | 52 | ### License 53 | GPLv3, copyleft license. 54 | 55 | Chose this license because I spent way too many late nights and heartbeats working on this - and want to see what people do with it and have changes propagated forward! 56 | -------------------------------------------------------------------------------- /Static_Solution/EvilPlotting.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import matplotlib as mpl 3 | from mpl_toolkits.mplot3d import Axes3D 4 | import numpy as np 5 | import GFOLD_parms_static as p 6 | 7 | def plot_run2D(t, r, v, u, m): 8 | ''' 9 | print('r =',r) 10 | print('v =',v) 11 | print('u =',u) 12 | print('m =',m) 13 | print('s =',s) 14 | ''' 15 | r = np.array(r.value) 16 | v = np.array(v.value) 17 | u = np.array(u.value) 18 | T_val = [np.linalg.norm(u[:,i])*m[i] for i in range(len(v.T))] 19 | vnorm = [np.linalg.norm(vel) for vel in v.T] 20 | 21 | #u_dirs = 90 - np.degrees(np.atan2(u[1,:], u[0,:])) 22 | #T_vals = np.multiply(u_norms , m) 23 | 24 | traj = plt.figure() 25 | 26 | #plt.subplot(4,1,1) 27 | plt.plot(r[0,:],r[1,:]) 28 | M =str(np.tan(np.radians(p.slope))) 29 | nM=str(-float(M)) 30 | bx=str(p.r_d[0]) 31 | by=str(p.r_d[1]) 32 | x=np.array(range(0,int(max(r[0,:])))) 33 | plt.plot(x,eval(M+'*(x-'+bx+')+'+by)) 34 | x=np.array(range(int(min(r[0,:])),0)) 35 | plt.plot(x,eval(nM+'*(x-'+bx+')+'+by)) 36 | plt.title('Position (m)') 37 | 38 | f = plt.figure() 39 | ax = f.add_subplot(411) 40 | 41 | plt.plot(t,vnorm) 42 | by=str(p.V_max) 43 | x=np.array(range(0,int(max(t)))) 44 | plt.plot(x,eval(by)) 45 | plt.xlabel(r"$t$", fontsize=16) 46 | plt.title('Velocity Magnitude (m/s)') 47 | 48 | plt.subplot(4,1,2) 49 | plt.plot(t,r[1,:]) 50 | plt.xlabel(r"$t$", fontsize=16) 51 | plt.title('Altitude (m)') 52 | 53 | plt.subplot(4,1,3) 54 | plt.plot(t,m) 55 | plt.title('Mass (kg)') 56 | 57 | plt.subplot(4,1,4) 58 | plt.plot(t,T_val) 59 | by=str(p.T_max) 60 | x=np.array(range(0,int(max(t)))) 61 | plt.plot(x,eval(by)) 62 | plt.title('Thrust (N)') 63 | 64 | plt.tight_layout() 65 | plt.subplots_adjust(hspace=0) 66 | plt.show() 67 | 68 | def plot_run3D(tf, x, u, m, s, z): 69 | 70 | print('tf',tf) 71 | t = np.linspace(0,tf,num=len(m)) 72 | 73 | r = np.array(x[0:3,:]) 74 | v = np.array(x[3:6,:]) 75 | z = np.array(z) 76 | s = np.array(s) 77 | u = np.array(u) 78 | 79 | print('t',t.shape) 80 | print('r',r.shape) 81 | print('v',v.shape) 82 | print('u',u.shape) 83 | print('m',len(m)) 84 | print('s',s.shape) 85 | print('z',z.shape) 86 | 87 | if t.shape==() or r.shape==() or v.shape==() or u.shape==(): 88 | print('data actually empty') 89 | return 90 | 91 | Th= [np.linalg.norm(u[:,i])*m[i] for i in range(len(v.T))] 92 | vnorm = [np.linalg.norm(vel) for vel in v.T] 93 | 94 | #u_dirs_1 = [90 - np.degrees(np.atan2(u[0,n], u[1,n])) for n in range(p.N)] 95 | #u_dirs_2 = [90 - np.degrees(np.atan2(u[0,n], u[2,n])) for n in range(p.N)] 96 | 97 | traj = plt.figure() 98 | ax = traj.gca(projection='3d') 99 | ax.set_aspect('equal') 100 | 101 | r_= np.linspace(0, max(max(r[1,:]),max(r[2,:])), 7) 102 | a_= np.linspace(0, 2*np.pi, 20) 103 | R, P = np.meshgrid(r_, a_) 104 | X, Y, Z = R*np.cos(P), R*np.sin(P), R*(np.tan(p.y_gs)) 105 | #X,Y,Z=R*np.cos(P), R*np.sin(P),((R**2 - 1)**2) 106 | 107 | #ax.plot(x(t),y(t),z(t),label='Flight Path') 108 | ax.plot(r[1,:],r[2,:],r[0,:],label='Flight Path') 109 | ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r) 110 | 111 | # Tweak the limits and add latex math labels. 112 | 113 | ax.set_xlabel(r'$x{1}$') 114 | ax.set_ylabel(r'$x{2}$') 115 | ax.set_zlabel(r'$x{0}$') 116 | 117 | ax.legend() 118 | 119 | f = plt.figure() 120 | ax = f.add_subplot(511) 121 | 122 | plt.plot(t,vnorm) 123 | y=str(p.V_max) 124 | x=np.array(range(0,int(max(t)))) 125 | plt.plot(x,eval('0*x+'+y)) 126 | plt.title('Velocity Magnitude (m/s)') 127 | 128 | plt.subplot(5,1,2) 129 | plt.plot(t,r[0,:]) 130 | plt.title('Altitude (m)') 131 | 132 | plt.subplot(5,1,3) 133 | plt.plot(t,m) 134 | plt.title('Mass (kg)') 135 | 136 | plt.subplot(5,1,4) 137 | plt.plot(t,Th) 138 | y=str(p.T_max) 139 | x=np.array(range(0,int(max(t)))) 140 | plt.plot(x,eval('0*x+'+y)) 141 | plt.title('Thrust (N)') 142 | 143 | z0_term = (p.m_wet - p.alpha * p.r2) # see ref [2], eq 34,35,36 144 | z1_term = (p.m_wet - p.alpha * p.r1) 145 | lim=[] 146 | lim2=[] 147 | n=0 148 | z=z.flatten() 149 | for t_ in t: 150 | if t_ > 0: 151 | try: 152 | v = p.r2/(z0_term*t_) * (1 - (z[n] - np.log(z0_term*t_))) 153 | except ZeroDivisionError: 154 | v = 0 155 | lim.append( v ) 156 | try: 157 | v = p.r1/(z1_term*t_) *(1 - (z[n] - np.log(z0_term*t_)) + (1/2)*(z[n] - np.log(z0_term*t_))**2 ) 158 | except ZeroDivisionError: 159 | v = 0 160 | lim2.append( v ) 161 | else: 162 | lim.append(0) 163 | lim2.append(0) 164 | n+=1 165 | lim = np.array(lim).flatten() 166 | plt.subplot(5,1,5) 167 | plt.plot(t,lim) 168 | plt.plot(t,lim2) 169 | s = s.flatten() 170 | if s.shape == (1,65): 171 | s.reshape((65,)) 172 | print('reshape',s) 173 | print('s',s) 174 | plt.plot(t,s) 175 | plt.title('Sigma Slack') 176 | 177 | plt.tight_layout() 178 | plt.subplots_adjust(hspace=0) 179 | plt.show() 180 | -------------------------------------------------------------------------------- /Static_Solution/GFOLD_Static.py: -------------------------------------------------------------------------------- 1 | # GFOLD_static_p3p4 2 | 3 | from cvxpy import * 4 | from time import time 5 | import numpy as np 6 | from GFOLD_parms_static import * 7 | from EvilPlotting import * 8 | 9 | ''' As defined in the paper... 10 | 11 | PROBLEM 3: Minimum Landing Error (tf roughly solved) 12 | MINIMIZE : norm of landing error vector 13 | SUBJ TO : 14 | 0) initial conditions satisfied (position, velocity) 15 | 1) final conditions satisfied (altitude, velocity) 16 | 2) dynamics always satisfied 17 | 3) x stays in cone at all times 18 | 4) relaxed convexified mass and thrust constraints 19 | 5) thrust pointing constraint 20 | 6) sub-surface flight constraint 21 | 22 | PROBLEM 4: Minimum Fuel Use 23 | MAXIMIZE : landing mass, opt variables are dynamical and 24 | SUBJ TO : 25 | 0) same constraints as p1, plus: 26 | 1) landing point must be equal or better than that found by p1 27 | 28 | ''' 29 | 30 | def GFOLD(inputs): # PRIMARY GFOLD SOLVER 31 | 32 | #dt = 0.24 #1e0 # dynamics precision ----> BEWARE OF MEMORY OVERFLOW! 33 | 34 | if inputs[-1]=='p3': 35 | program = 3 36 | tf_,r0,prog_flag = inputs 37 | elif inputs[-1]=='p4': 38 | program = 4 39 | tf_,r0,rf_,prog_flag=inputs 40 | #N =int(tf_/dt) 41 | 42 | N = 250 # Need not be fixed in STATIC runs, MUST be fixed in code-gen 43 | dt = 4.5 # Integration dt 44 | 45 | print('N = ',N) 46 | print('dt= ',dt) 47 | 48 | x0=Parameter() 49 | x0=np.array([r0[0],r0[1],r0[2],v0[0],v0[1],v0[2]]) 50 | 51 | x =Variable(6,N) # state vector (3position,3velocity) 52 | u =Variable(3,N) # u = Tc/mass because Tc[:,n]/m[n] is not allowed by DCP 53 | z= Variable(1,N) # z = ln(mass) 54 | s= Variable(1,N) # thrust slack parameter 55 | 56 | con = [] # CONSTRAINTS LIST 57 | 58 | con += [x[0:3:1,0] == x0[0:3:1]] 59 | con += [x[3:6,0] == x0[3:6]] 60 | con += [x[3:6,N-1]== vf] # don't forget to slow down, buddy! 61 | 62 | con += [s[N-1] == 0] # thrust at the end must be zero 63 | con += [u[:,0] == s[0]*np.array([1,0,0]) ] # thrust direction starts straight 64 | con += [u[:,N-1] == s[N-1]*np.array([1,0,0]) ] # and ends straight 65 | con += [z[0] == log(m_wet)] # convexified (7) 66 | 67 | if program==3: 68 | #con += [np.multiply(e(0).T,r[:,N-1]) == rf] # end altitude (fully general) 69 | con += [x[0,N-1] == 0] 70 | 71 | elif program==4: 72 | con += [x[0:3,N-1] == rf_] # force landing point equal to found p1 pt 73 | #con += [norm(E*(x[0:3,N-1]-rf))<=norm(rf_-rf)] # CONVEX <= CONVEX (?) 74 | 75 | for n in range(0,N-1): # any t in [0,tf] maps to any n in [0,N-1] 76 | 77 | # Leapfrog Integration Method 78 | # accurate +/- sqrt( (dt*df/dr)**2 + 1) 79 | # https://goo.gl/jssWkB 80 | # https://en.wikipedia.org/wiki/Leapfrog_integration 81 | 82 | # Dynamics --> v = A(w)*x + B*(g + u) 83 | 84 | con += [x[3:6,n+1] == x[3:6,n] + (dt/2)*((u[:,n]+g) + (u[:,n+1]+g))] 85 | con += [x[0:3,n+1] == x[0:3,n] + (dt/2)*(x[3:6,n+1]+x[3:6,n])] 86 | 87 | #con += [ norm(E*(x[0:3,n]-rf)) - c.T*(x[0:3,n]-rf) <= 0 ] # glideslope, full generality # (5) 88 | con += [ norm( (x[0:3,n]-rf)[0:2] ) - c.T[0]*(x[0,n]-rf[0]) <= 0 ] # specific, but faster 89 | 90 | con += [ norm(x[3:6,n]) <= V_max ] # velocity 91 | con += [z[n+1] == z[n] - (alpha*dt/2)*(s[n] + s[n+1])] # mass decreases 92 | con += [norm(u[:,n]) <= s[n]] # limit thrust magnitude & also therefore, mass 93 | 94 | # Thrust pointing constraint 95 | #con += [ nh.T*u[:,n] >= np.cos(p_cs)*G[n] ] # full generality 96 | con += [ u[0,n] >= np.cos(p_cs)*s[n] ] 97 | 98 | if n > 0: 99 | z0_term = m_wet - alpha * r2 * (n) * dt # see ref [2], eq 34,35,36 100 | z1_term = m_wet - alpha * r1 * (n) * dt 101 | z0 = log( z0_term ) 102 | z1 = log( z1_term ) 103 | mu_1 = r1/(z1_term) 104 | mu_2 = r2/(z0_term) 105 | 106 | # lower thrust bound 107 | con += [s[n] <= mu_2 * (1 - (z[:,n] - z0))] # upper thrust bound 108 | con += [z[n] >= z0] # Ensures physical bounds on z are never violated 109 | con += [z[n] <= z1] 110 | 111 | 112 | con += [x[0,0:N-1] >= 0] # no, this is not the Boring Company! 113 | 114 | if program == 3: 115 | print('-----------------------------') 116 | objective=Minimize(norm(x[0:3,N-1]-rf)) 117 | problem=Problem(objective,con) 118 | obj_opt=problem.solve(solver=ECOS,verbose=True,feastol=5e-20)#solver=SCS,max_iters=5000,verbose=True,use_indirect=False) 119 | print('-----------------------------') 120 | elif program == 4: 121 | print('-----------------------------') 122 | objective=Maximize(z[N-1]) 123 | problem=Problem(objective,con) 124 | obj_opt=problem.solve(solver=ECOS,verbose=True)#solver=SCS,max_iters=5000,verbose=True,use_indirect=False,warm_start=True) # OK to warm start b/c p1 gave us a decent answer probably 125 | print('-----------------------------') 126 | 127 | if program == 3: 128 | #return obj_opt,(N/dt),x[0:3,N-1] 129 | if z.value is not None: 130 | m = map(np.exp,z.value.tolist()[0]) # make a mass iterable fm z 131 | return obj_opt,x,u,m,(N/dt),s,z # N/dt is tf 132 | else: 133 | return obj_opt,None,None,None,(N/dt),None,None # 134 | elif program == 4: 135 | if z.value is not None: 136 | m = map(np.exp,z.value.tolist()[0]) # make a mass iterable fm z 137 | return obj_opt,x,u,m,(N/dt),s,z # N/dt is tf 138 | else: 139 | return obj_opt,None,None,None,None,(N/dt),None,None 140 | 141 | def P3_P4(r0=r_): 142 | 143 | start_ = time() 144 | 145 | tf_min = (m_dry*np.linalg.norm(v0/r2)) 146 | tf_max = (m_wet-m_dry)/(alpha*r1) 147 | print 'min tf :%f max tf: %f' % (tf_min,tf_max) 148 | 149 | t = [60,60] 150 | 151 | obj,x,u,m,tf,s,z = GFOLD((t,r0,'p3')) # EXECUTE PROBLEM 3 152 | print 'p3 object :%f after %f sec' % (obj,time()-start_) 153 | print 'tf : %f' % (tf) 154 | print 'rf :' 155 | if x is None: # Better luck next time! :) 156 | print(' '+str(None)) 157 | return None 158 | for r in x[0:3,-1].value: 159 | print(' '+str(r)) 160 | print 161 | 162 | ''' 163 | obj,x,u,m,tf,s,z = GFOLD((tf,r0,rf,'p4')) # EXECUTE PROBLEM 4 164 | print 'p4 object :%f after %f sec' % (obj,time()-start_) 165 | print 'tf : %f' % (tf) 166 | print 'rf :' 167 | for r in x[0:3,-1].value: 168 | print(' '+str(r)) 169 | print 170 | 171 | print 'gfold took: %f sec'%(time()-start_) 172 | ''' 173 | 174 | # Debugging stuff: 175 | 176 | #obj,r,v,u,m = yielded[[vector[0] for vector in yielded].index(min(tf_yield))] 177 | #tf_opt = tf_array[[vector[0] for vector in yielded].index(min(tf_yield))] 178 | 179 | #for var in (tf,r,v,u,m): 180 | # print('var =',var) 181 | # print(' ') 182 | # print('varval =',var.value) 183 | 184 | x=x.value 185 | u=u.value 186 | s=s.value 187 | z=z.value 188 | plot_run3D(tf,x,u,m,s,z) 189 | return obj,x,u,m,tf 190 | 191 | if __name__ == '__main__': 192 | P3_P4(r_) 193 | -------------------------------------------------------------------------------- /Static_Solution/GFOLD_Static_Parms.py: -------------------------------------------------------------------------------- 1 | # GFOLD_parms_static 2 | 3 | import numpy as np 4 | from scipy import signal 5 | 6 | def e(i): 7 | return signal.unit_impulse(3,i) # create a specific basis vector 8 | 9 | def S(_w_): # _w_ to distinguish from our global namespace's w! 10 | return np.matrix([[0,-_w_[2],+_w_[1]], 11 | [_w_[2],0, -_w_[0]], 12 | [-_w_[1],_w_[0],0]]) 13 | 14 | '''------------------------ Numerical Example 1 -------------------------- ''' 15 | # These are the numbers from the original paper 16 | 17 | g0 = 9.80665 # standard gravity [m/s**2] 18 | m_dry = (2)*1e3 # dry mass kg 19 | m_fuel= (0.3)*1e3 # fuel in tons 20 | T_max = 24000 # thrust max 21 | throt = [0.2,0.8] # throttle ability 22 | G_max = 3 # maximum allowable structural Gs 23 | Isp = 203.94 # fuel efficiency (specific impulse) 24 | V_max = 90 # velocity max 25 | y_gs = np.radians(30)# glide slope cone, must be 0 < Degrees < 90 26 | p_cs = np.radians(45) # thrust pointing constraint 27 | alpha = 1/(Isp*g0) # fuel consumption parameter 28 | m_wet = (m_dry+m_fuel) # wet mass kg 29 | r1 = throt[0]*T_max # lower thrust bound 30 | r2 = throt[1]*T_max # upper thrust bound 31 | 32 | g = np.array([-3.71,0,0]) # gravity 33 | w = np.array([2.53*1e-5, 0, 6.62*1e-5]) # planetary angular velocity 34 | nh= np.array([1,0,0]) # thrust vector reference direction 35 | 36 | r_ = np.array([2400, 2000, 0]) # initial position 37 | v0 = np.array([-40, 30, 0]) # initial velocity 38 | 39 | rf = np.array([0,0,0]) # final position target 40 | vf = np.array([0,0,0]) # final velocity target 41 | 42 | c = np.divide(e(0),np.tan(y_gs)) 43 | E = np.array( [ [e(0).T],[e(1).T] ] ) 44 | 45 | A = np.empty([6,6]) 46 | np.copyto(A[0:3,0:3] , np.zeros((3,3)) ) # top left 47 | np.copyto(A[0:3,3:6] , np.eye(3) ) # top right 48 | np.copyto(A[3:6,0:3] , -np.square(S(w)) ) # bottom left 49 | np.copyto(A[3:6,3:6] , np.multiply(-1,S(w))) # bottom right 50 | B = np.array([[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,1,0],[0,0,1]]) # 0vect and I 51 | 52 | 53 | ''' ------------------------ Masten Lander ---------------------------- ''' 54 | ''' 55 | g0 = 9.80665 # standard gravity [m/s**2] 56 | m_dry = (3.725)*1e3 # dry mass kg 57 | m_fuel= (6.2)*1e3 # fuel in tons 58 | T_max = 13000 # thrust max 59 | throt = [0.1,0.8] # throttle ability 60 | G_max = 3 # maximum allowable structural Gs 61 | Isp = 295 # fuel efficiency (specific impulse) 62 | V_max = 330 # velocity max 63 | y_gs = np.radians(0.1)# glide slope cone, must be 0 < Degrees < 90 64 | p_cs = np.radians(45) # thrust pointing constraint 65 | alpha = 1/(Isp*g0) # fuel consumption parameter 66 | m_wet = (m_dry+m_fuel) # wet mass kg 67 | r1 = throt[0]*T_max # lower thrust bound 68 | r2 = throt[1]*T_max # upper thrust bound 69 | 70 | g = np.array([-9.81,0,0]) # gravity 71 | w = np.array([2.53*1e-5, 0, 6.62*1e-5]) # planetary angular velocity 72 | nh= np.array([1,0,0]) # thrust vector reference direction 73 | 74 | r_ = np.array([160, 0, 0]) # initial position 75 | v0 = np.array([-1, 0, 0 ]) # initial velocity 76 | 77 | rf = np.array([0,0,0]) # final position target 78 | vf = np.array([0,0,0]) # final velocity target 79 | 80 | c = np.divide(e(0),np.tan(y_gs)) 81 | E = np.array( [ [e(0).T],[e(1).T] ] ) 82 | 83 | A = np.empty([6,6]) 84 | np.copyto(A[0:3,0:3] , np.zeros((3,3)) ) # top left 85 | np.copyto(A[0:3,3:6] , np.eye(3) ) # top right 86 | np.copyto(A[3:6,0:3] , -np.square(S(w)) ) # bottom left 87 | np.copyto(A[3:6,3:6] , np.multiply(-1,S(w))) # bottom right 88 | B = np.array([[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,1,0],[0,0,1]]) # 0vect and I 89 | ''' 90 | 91 | ''' ------------------------------ Falcon 9 ---------------------------------''' 92 | ''' 93 | N = 50 # nodes in discretization (more --> more accurate) 94 | g0= 9.80665 # standard gravity [m/s**2] 95 | m_dry = (22.2)*1e3 # dry mass kg 96 | m_fuel= (13.4)*1e3 # fuel in tons 97 | T_max = 845000*3 # thrust max 98 | throt = [0.4,1.0] # throttle ability 99 | G_max = 3 # maximum allowable structural Gs 100 | Isp = 282 # fuel efficiency (specific impulse) 101 | V_max = 1300 # velocity max 102 | y_gs = np.radians(1) # glide slope cone, must be 0 < Degrees < 90 103 | p_cs = np.radians(120) # thrust pointing constraint 104 | alpha = 1/(Isp*g0) # fuel consumption parameter 105 | m_wet = (m_dry+m_fuel) # wet mass kg 106 | r1 = throt[0]*T_max # lower thrust bound 107 | r2 = throt[1]*T_max # upper thrust bound 108 | 109 | g = np.array([-g0,0,0]) # gravity 110 | w = np.array([2.91*1e-5, 0, 6.68*1e-5]) # planetary angular velocity 111 | nh= np.array([1,0,0]) # thrust vector reference direction 112 | 113 | r_ = np.array([20000, 10, 5]) # initial position 114 | v0 = np.array([-500,-100,-200]) # initial velocity 115 | 116 | rf = np.array([0,0,0]) # final position target 117 | vf = np.array([0,0,0]) # final velocity target 118 | 119 | c = np.divide(e(0),np.tan(y_gs)) 120 | E = np.array( [ [e(0).T],[e(1).T] ] ) 121 | ''' 122 | ''' 123 | A = np.empty([6,6]) 124 | np.copyto(A[0:3,0:3] , np.zeros((3,3)) ) # top left 125 | np.copyto(A[0:3,3:6] , np.eye(3) ) # top right 126 | np.copyto(A[3:6,0:3] , -np.square(S(w)) ) # bottom left 127 | np.copyto(A[3:6,3:6] , np.multiply(-1,S(w))) # bottom right 128 | B = np.array([[0,0,0],[0,0,0],[0,0,0],[1,0,0],[0,1,0],[0,0,1]]) # 0vect and I 129 | ''' 130 | --------------------------------------------------------------------------------