Coordination of Multiple Car-like Robots

Project Description

The goal of this project is to plan paths for multiple (here, 3) car-like robots in a 2-d polygonal environment. All the polygons are assumed to be simple and convex. The car-like robots have turning radius constraints but are allowed to reverse.

The project was written in 5 parts. A description of each part, including algorithms is included below:

1. C-Obstacle Region Formation

   In this part the C-Obstacle region of the robot (which can translate and rotate) was computed, using a layering technique. First, an algorithm was developed using normals (the one discussed in class) to find the C-Obstacle region of a robot that can translate only. This algorithm was invoked repeatedly for various orientations of the robot in the range [0, 360), giving a layer of C-obstacle regions at discrete orientations. Finally, a C-sentence for each layer was produced to be used in later parts.

2. 3-D Bitmap Formation

   A grid was layed over the 2d environment, and a 3-d bitmap representation of the C-obstacle region was computed and stored in this grid. The resolution of the grid varied from 20 x 20 x 36 for testing to 50 x 50 x 36 for solution generation.

3. Potential Function Calculation

   A potential function was developed to be stored in the grid. Initially I used NF1 but later shifted to NF2 which produced better results. Note that this potential function was developed on the 3-d grid, not on the 2-d workspace.

4. Holonomic Path Planning

   A best first search algorithm was used to trace a path from the initial configuration to the goal configuration in the 3-d grid. The path of steepest potential change was followed.

5. Nonoholonomic Path Planning

   The holonomic path generated above was transformed using Reeds-Shepp curves into a nonholonomic one. In cases where the resolution was not fine enough to produce a feasible path, a linear interpolation between successive configurations of the input path was performed and then passed back to the Nonholonomic path planner.

6. Coordination of Multiple Robots

   I used the path coordination technique described in Latombe's Robot Motion Planning to coordinate 2 robots. However, instead of using the scheduling algorithm, I performed a graph search to allow for the 3 robot case. Currently, this has not been tested since the time taken for even a simple world is enormous.

Project Problems

• Problems with Nonholonomic Planner

  Some of the paths returned by the Reeds Shepp curves are found to be infeasible by my bitmap. This is because :

  (i) I linearly interpolate between the input (holonomic) path configurations to produce a larger input path.

  (ii) Since I use the same bitmap to check feasibility of the nonholonomic path, many configurations that are actually feasible map to a grid cell which has been deemed infeasible.

  I could solve this by using a new resolution for my grid for the nonholonomic planner, or even by checking my nonholonomic path configurations individually to ascertain feasibility.

• Problems with Coordination

  There are two main problems with the coordination space technique I used:

  (i) Slow speed: The coordination increased the running time of my planner by around 2000%. This is because my nonholonomic path is very large (around 2000 configurations for some robots) and every pair of configurations is checked to prevent collisions.

  (ii) Bugs: I do a grid search to find a coordinated path. I chose this over the scheduling algorithm in the book because it seemed easier to extend to 3 or more robots. Currently there is a problem with my outputting the path between two grid cells -- when a robot is stationary, the same path gets outputted repeatedly so the robot appears to jump back and forth between two configurations. I thought I had fixed it by using flags to prevent a visited cell from having its configurations from being outputted, but it still seemed to appear in some places.

Motion Planning Examples

Sample worlds

1. The car12.jmv file: This file contains coordination of 2 robots in a very simple world.
2. The car2.mv file: This file displays nonholonomic planning for 2 robots (uncoordinated) in a more complex world. This file shows one bug I have that I forgot to fix -- keeping my cars from going outside the world.
3. The car3.mv file: This file is the same as the car2.mv but here I prevent my cars from going outside the world by adding thin polygons around the boundary (these thus get automatically incorporated into my bitmap).

Source Code

• README (please)
• Planner source code: planner.tar
• Movie file 1
• Movie file 2
• Movie file 3