CS 326A: Motion Planningai.stanford.edu/~latombe/cs326/2007/index.htm

Motion Planning for Legged Robots

Coordination for Multiple Robots (Notes for HW#2)

n robots R1, …, Rn, with configuration spaces C1, …, Cn, sharing the same workspace

Problem: Plan coordinated motion so that each robot achieves its own goal configuration.

Centralized planning: Plan the coordinated motion in C1xC2x…xCn (but very high dimensional space)

Decoupled planning: Plan the motion of each robot ignoring the other robots; then coordinate their motions so that no two robots collide

Prioritized planning: Plan the motion of one robot ignoring the other robots; then plan the trajectory of a second robot in its configurationxtime space treating the first robot as a moving obstacle; then plan the trajectory of a third robot …

Coordination Space 2 robots R1 and R2 2 paths: i : si [0,1] Ci (i=1,2) 2-D coordination space

Generalize to n robots n-D coordination space

0 1

1

s1

s2

Variants of Decoupled Planning

#1: Coordinate the n paths in n-D coordination space

#2:Coordinate paths of R1 and R2 in a 2-D coordination diagram ( path of “R1-R2”) , then coordinate paths of R1-R2 and R3 in 2-D coordination diagram, etc…

s1

Today’s Papers Footstep planning for a humanoid robot:

J. Kuffner, K. Nishiwaki, S. Kagami, M. Inaba, and H. Inoue. Footstep Planning Among Obstacles for Biped Robots. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), 2001.

Motion planning for a climbing robot:T. Bretl. Motion Planning of Multi-Limbed Robots Subject to Equilibrium Constraints: The Free-Climbing Robot Problem. International Journal of Robotics Research, 25(4):317-342, Apr 2006.  

Some New Ideas

Equilibrium constraint

Footstep planning: Where to make contact?

Stance (+ configuration space at a stance)

Multi-step planning