Motion Planning for Closed-Chain Mechanisms

Problem statement:

Given start (purple) and goal (red) configurations of a closed polygonal chain, determine an optimal trajectory connecting the start to the goal.

We have developed a low-order polynomial-time complete algorithm for solving this problem; if a solution exists, it will be found; if not, nonexistence will be reported. We ignore link-link collisions and assume no joint limits. You can see some of our initial solutions in action by clicking on the images below. Here are some related papers: theory, algorithm description, conference version of algorithm description.

Future Plans:
We are now extending this work to allow point obstacles in the work space. Techniques from homology theory are being used to count components of the configuration space and to determine if the start and goal configurations are in the space component.