Accelerated Reeds-Shepp Planning

Solves the Reeds-Shepp path planning problem 15x faster on average than OMPL's implementation.

Paper attachment TBD.

Reduces set of cases to consider down to 20 and introduces a new partition that speeds up the computation of the shortest path.

Requires SFML & OMPL. It has a demo in main.cpp that computes and draws paths between randomly generated start/end configurations.

Also contains an implemntation of "An efficient algorithm to find a shortest path for a car-like robot".

Benchmarking Results

This table presents sample benchmarking results of our proposed planner against OMPL's implementation of the original Reeds-Shepp algorithm and against our implementation of Desaulniers1995.

Performed on idle Linux Intel i9-13980HX.

Method	Average Time per State (µs)	Time Ratio to OMPL	Maximum Path Length Error	Average Path Length Error
Proposed	0.0827	15.12	9.82e-15	3.28e-16
Desaulniers1995	0.216	5.79	5.82e-15	2.77e-16
OMPL	1.25	1	-	-

Table: Benchmarking results of our proposed planner against OMPL's implementation of the original Reeds-Shepp algorithm and against our implementation of Desaulniers1995.

Sample partition in 3D

3D partition of regions in the configuration space. Each color refers to a unique region (out of 20) where one identified path type is certainly the shortest. 1 million configurations $p_{f}$ spanning $\big[ [-100,100,], [-100,100], [-\pi,\pi)\big]$ for $p_{0} = (0,0,0)$ and $r = 20$. Red axis = $x$ axis, blue axis = $y$ axis, yellow axis = $\theta$ axis.

Variability Based on Types

1e8 final configuration samples spanning $\big[ [-1000,1000,], [-1000,1000], [-\pi,\pi)\big]$ for $p_{0} = (0,0,0)$ and $r = 400$. Computing those speedups for each path type incurs an overhead that makes the speedups slightly slower. This is only to show that the speedup is not uniform across all path types. The weighted average speedup is around 11.87.

Type	Occurrences	Speedup
1	6829417	11.5399
2	8684623	13.1266
3	9879506	12.3335
4	7630623	13.4698
5	6732552	12.8536
6	6683699	11.8223
7	791193	11.4474
8	2287070	11.8638
9	554434	11.7778
10	2529318	11.9787
11	1985832	10.639
12	11555	10.8744
13	7494149	10.3889
14	8013981	11.3507
15	7714423	9.52923
16	9776168	11.3254
17	1118135	10.2761
18	9897533	11.0233
19	138503	9.18825
20	1247286	8.42923

How to Use (to be completed)

Set compiler path if needed. Make sure SFML:
sudo apt install libsfml-dev
and OMPL libraries:
https://ompl.kavrakilab.org/installation.html
are installed, then:
sudo apt install cmake
sudo apt install g++
mkdir build && cd build
cmake ..
make

Troubleshooting build issues with OMPL:
By default, OMPL installs in /usr/local/include/ompl-1.6/ompl. Create a symbolic link so that it can be properly located:
sudo ln -s /usr/local/include/ompl-1.6/ompl /usr/local/include/ompl
Similarly, create Eigen symbolic links so that required files can be found by OMPL: cd /usr/include
sudo ln -sf eigen3/Eigen Eigen
sudo ln -sf eigen3/unsupported unsupported
After making any changes to the library paths or creating symbolic links, run the ldconfig command to update the system's cache of shared libraries:
sudo ldconfig
After building, you can verify that the required libraries have been properly found using ldd, for example:
ldd ./acceleratedRSPlanner

To use this project, follow these simple steps: