Trajectory Planning with Homotopy Constraints

Homotopy

Homotopy

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.

Publications

  1. Optimal Trajectory Generation Under Homology Class Constraints. Soonkyum Kim, Koushil Sreenath, Subhrajit Bhattacharya, and Vijay Kumar. IEEE Conference on Decision and Control (CDC), pages 3157--3164, Maui, HI, December 2012. pdf
    @conference{ CDC2012,
    author={ Soonkyum Kim and Koushil Sreenath and Subhrajit Bhattacharya and Vijay Kumar },
    title={ Optimal Trajectory Generation Under Homology Class Constraints },
    booktitle={ IEEE Conference on Decision and Control (CDC) },
    pages={ 3157--3164 },
    month={ December },
    year={ 2012 },
    address={ Maui, HI },
    }
  2. Trajectory Planning for Systems with Homotopy Class Constraints. Soonkyum Kim, Koushil Sreenath, Subhrajit Bhattacharya, and Vijay Kumar. Latest Advances in Robot Kinematics (ARK), pages 83--90, Innsbruck, Austria, June 2012. pdf
    @conference{ ARK2012,
    author={ Soonkyum Kim and Koushil Sreenath and Subhrajit Bhattacharya and Vijay Kumar },
    title={ Trajectory Planning for Systems with Homotopy Class Constraints },
    booktitle={ Latest Advances in Robot Kinematics (ARK) },
    pages={ 83--90 },
    month={ June },
    year={ 2012 },
    address={ Innsbruck, Austria },
    }