两台凸对称机器人如何以最短路径协同避障移动
Minimum-Length Coordinated Motions For Two Convex Centrally-Symmetric Robots
- 用闵可夫斯基和边界构造六段以内路径，总长可闭式求解
- 路径总长仅由初始与目标状态决定，最优路径存在且可精确刻画
- 支持单机运动或姿态单调变化，适合实时控制场景
研究在无障碍平面中，两个任意凸中心对称（CCS）机器人在避免碰撞前提下，使两机器人中心轨迹总长度最小的协同运动问题。以两机器人中心轨迹总长度为度量标准，本文给出了所有初始与目标配置下最短路径的精确刻画（不唯一）。路径由至多六段凸曲线组成，总长度可表示为仅依赖于初始与目标配置的闭式积分。路径片段为直线段或两机器人闵可夫斯基和边界的弧段（圆形机器人时为圆弧）。此外，路径可参数化为：(i) 任意时刻仅一个机器人运动（解耦运动），或 (ii) 机器人构型姿态单调变化。
原文摘要 · Abstract (English)
We study the problem of determining coordinated motions, of minimum total length, for two arbitrary convex centrally-symmetric (CCS) robots in an otherwise obstacle-free plane. Using the total path length traced by the two robot centres as a measure of distance, we give an exact characterization of a (not necessarily unique) shortest collision-avoiding motion for all initial and goal configurations of the robots. The individual paths are composed of at most six convex pieces, and their total length can be expressed as a simple integral with a closed form solution depending only on the initial and goal configuration of the robots. The path pieces are either straight segments or segments of the boundary of the Minkowski sum of the two robots (circular arcs, in the special case of disc robots). Furthermore, the paths can be parameterized in such a way that (i) only one robot is moving at any given time (decoupled motion), or (ii) the orientation of the robot configuration changes monotonically.
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