測地凸集合グラフによる非ユークリッド運動計画
Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets
リーマン多様体上の配置空間を測地凸集合のグラフで表現し、混合整数凸最適化に帰着させることで、移動ロボットや連続回転関節を含む系の衝突回避軌道を大域最適に近い形で計画する手法を提案した。
著者: Thomas Cohn, Mark Petersen, Max Simchowitz, Russ Tedrake
分類: cs.RO
原文アブストラクト
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent nonconvexities in the optimization landscape. The use of mixed-integer programming to encapsulate these nonconvexities and find globally optimal trajectories has recently shown great promise, thanks in part to tight convex relaxations and efficient approximation strategies that greatly reduce runtimes. These approaches were previously limited to Euclidean configuration spaces, precluding their use with mobile bases or continuous revolute joints. In this paper, we handle such scenarios by modeling configuration spaces as Riemannian manifolds, and we describe a reduction procedure for the zero-curvature case to a mixed-integer convex optimization problem. We demonstrate our results on various robot platforms, including producing efficient collision-free trajectories for a PR2 bimanual mobile manipulator.
