├── Example_1_Illustrative ├── Compare_MC.fig ├── Compare_MC_Opt.fig ├── README.md ├── genpow.m ├── main_1.m ├── main_2_compare_MonteCarlo.m ├── main_3_compare_Analytic.m └── main_4_compare_ConvexOpt.m ├── Example_2_Illustrative ├── README.md └── main_1.m ├── Example_3_Illustrative ├── README.md ├── RRT-SOS │ ├── README.md │ ├── Results.txt │ └── main_RRT_SOS.m ├── Standard-SOS │ ├── Piece-wise-Linear_Traj │ │ ├── README.md │ │ ├── Results.txt │ │ ├── main_1_Coeffs_RiskContour_traj1.m │ │ ├── main_1_Coeffs_RiskContour_traj2.m │ │ └── main_2_GloptiPoly.m │ ├── Polynomial_Traj │ │ ├── README.md │ │ ├── Results.txt │ │ ├── main_1_Coeffs_RiskContour.m │ │ └── main_2_GloptiPoly.m │ └── README.md └── Time-Varying-SOS │ ├── README.md │ ├── Results.txt │ ├── func_PathPlanningSOS.jl │ ├── main.jl │ └── main_plot_traj.m ├── Example_4_Illustrative ├── README.md ├── RRT-SOS │ ├── README.md │ ├── Results.txt │ └── main_RRT_SOS.m └── Time-Varying-SOS │ ├── README.md │ ├── Results.png │ ├── Results.txt │ ├── func_PathPlanningSOS.jl │ ├── main.jl │ └── main_plot_traj.m ├── Example_5_SOS-Safety ├── Example_1 │ ├── README.md │ ├── func_sos_spot.m │ └── main_sos_safety.m ├── Example_2 │ ├── README.md │ ├── main_linear.m │ ├── sosOnK.m │ ├── verify_all_line_segments.m │ └── verify_line_segment.m └── README.md ├── Example_A ├── 2D │ ├── Compare_MC.fig │ ├── README.md │ ├── main_0_obstacle.m │ ├── main_1.m │ ├── main_2_compare_MonteCarlo.m │ └── main_3_compare_Analytic.m └── 3D │ ├── README.md │ ├── main_0_obstacle.m │ └── main_1.m ├── Example_B ├── README.md ├── RRT-SOS │ ├── README.md │ ├── Results.txt │ ├── main_1_RiskContours_vehicle1.m │ ├── main_2_RiskContours_vehicle2.m │ └── main_RRT_SOS.m └── Time-Varying-SOS │ ├── README.md │ ├── Results.txt │ ├── func_PathPlanningSOS.jl │ ├── main.jl │ ├── main_1_RiskContours_vehicle1.m │ ├── main_2_RiskContours_vehicle2.m │ └── main_plot_traj.m ├── Example_C ├── README.md ├── RRT-SOS │ ├── README.md │ ├── Results.txt │ ├── main_1_RiskContours_obs1.m │ ├── main_2_RiskContours_obs2.m │ ├── main_3_RiskContours_obs3.m │ └── main_RRT_SOS.m └── Time-Varying-SOS │ ├── README.md │ ├── Results.txt │ ├── func_PathPlanningSOS.jl │ ├── main.jl │ ├── main_1_RiskContours_obs1.m │ ├── main_2_RiskContours_obs2.m │ ├── main_3_RiskContours_obs3.m │ └── main_plot_traj.m ├── Example_D ├── 2D │ ├── README.md │ ├── Results.txt │ └── main_RRT_SOS.m ├── 3D │ ├── README.md │ ├── Results.txt │ ├── main_1_RiskContours.m │ └── main_RRT_SOS.m └── README.md ├── README.md ├── RRT_Tools ├── PriorityQueue.m ├── README.md ├── README.txt ├── RRT_SOS_Dynamic.m ├── RRT_SOS_Static.m ├── find_nearest_tree_point.m ├── iterative_widening_sampling.m ├── iterative_widening_sampling_3D.m ├── iterative_widening_sampling_TVRRT.m ├── iterative_widening_sampling_TVRRT_3D.m ├── momball.m ├── sosOnK.m ├── verify_all_line_segments.m ├── verify_all_line_segments_3D.m ├── verify_all_line_segments_TVRRT.m ├── verify_all_line_segments_TVRRT_3D.m ├── 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