1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2004 Coordination of Multiple Robots

2. Two Main Approaches Decoupled Planning: - Plan for each robot independently - Coordinate them later  Several possible schemes Centralized Planning: Plan the motion of the robots in their “composite” configuration space

3. Decoupled Planning  Velocity tuning: (1) Separately plan a path of each robot to avoid collision with obstacles (2) Compute the relative velocities of the robots to avoid inter-robot collision (e.g., coordination or task-completion diagram) - Pairwise coordination - Global coordination

4. Decoupled Planning  Velocity tuning:  Robot prioritization: (1) Plan path of a first robot in its C-space (2) Loop: Plan trajectory of ith robot assuming that robots 1,…,i-1 are moving obstacles

5. Planning with Moving Obstacles  trajectory , a path indexed by time  is a continuous curve in configuration x time space tx y Obstacles map as forbidden regions in CT-space. Tangents to  project positively along the time axis Constraints on velocity constrain tangents to  Constraints on acceleration constrain curvature of 

6. Centralized Planning  Plan collision-free path  in composite configuration C 1 x C 2 x…x C p space of the p robots  Forbidden regions in composite C-space are all configurations where either a robot collide with an obstacle or two robots collide with each other  The projection of  into C i is the path of the ith robot

7. Pros and Cons Assume p robots with n degrees of freedom each. Worst-case complexity of centralized planning is ~ e np Worst-case complexity of decoupled planning is ~ pe n << e np But decoupled planning is incomplete