基於黎曼運動決策的機器人多優先級控制與規劃

Abstract

面對越來越複雜和多變的環境和人機協作的需求，現在的服務型機 器人需要動態地對環境做出回應， 這本質上是一個多優先級的問題。 傳統使用雅可比的零空間的解析解和使用最佳化和約束的數值解法並 不能有效地對每個任務的優先級進行判斷從而給出最合理的結果。本論文提出一套完整的處理機器人多任務控制和規劃的方法。基於黎曼運動決策的數學工具和高效的計算圖數據結構，機器人可以快速地在每個時間點規劃出運動。另外，本文中所有對機器人的運動學的分析都基於螺旋理論和一些基本的微分幾何理論，它們為本論文的其他部分提供了扎實的基礎。

Facing more and more complicated and dynamic environments as well as the requirements of human-robot interaction, modern robots may need to handle multiple tasks simultaneously and react dynamically to the environment. Analytic approaches using null space of Jacobian matrix and numerical approaches using optimization with constraints failed to provide a proper solution in some cases due to the absence of the consideration of task priorities. This article aims to solve this problem. Based on the mathematical tool of Riemannian Motion Policies with an efficient computational graph, the robot can rapidly plan its motion at each time step. In addition, the kinematic analysis of robots in this thesis is based on screw theory and some basic results of differential geometry, which form the fundamental basis.