Motion Planning for Planar Closed-Chains with Obstacles

Problem statement:

Given start and goal configurations of a closed polygonal chain in the plane among obstacles, determine a trajectory connecting the start to the goal.

We have developed a complete algorithm for solving this problem in the plane for arbitrary numbers of links and point obstacles. You can see one of our solutions for a 6-bar closed chain with two point obstacles (below).

Here is a related paper: RSS 2005.

Another type of obstacle arises when one connects multiple closed chains to form more complicated robots. We have developed a complete motion planner for “star-shaped” robots. This robot in the figure below is a star-shaped robot with four legs. It can be constructed by joining two closed-chains at the joints labeled “A.”

Click on the two images below to play videos showing plans for two different three-legged star-shaped manipulators. One has three joints per leg, the other has five. Both plans are discussed in detail in the link below, labeled “journal submission.”

Here are some related papers: ICRA 2006, journal submission.