Trajectory Planning with Homotopy Constraints
Specifying topological constraints for either trajectory generation for mobile robots, or for searching for a periodic walking gait in a specific region of the state-space would be extremely useful. However, a topological constraint, such as homotopy of a trajectory, has a gradient of zero almost everywhere, making standard gradient decent algorithms infeasible for searching for trajectories that respect the specified topological constraint. We formulate the problem as a constrained mixed-integer quadratic program, that is easily solved by a convex optimizer.
Optimal trajectory generation under homology class constraints. In IEEE Conference on Decision and Control (CDC), pages 3157–3164, Maui, HI, December 2012. pdf | Details
Trajectory planning for systems with homotopy class constraints. In Latest Advances in Robot Kinematics (ARK), pages 83–90, Innsbruck, Austria, June 2012. Springer, Netherlands. pdf | Details