用李群理论统一规划移动机械臂运动，实现平滑精准控制。
Lie Theory Based Optimization for Unified State Planning of Mobile Manipulators
- 基于螺旋坐标将运动学模型在李群与向量间转换，统一建模
- 通过优化求解整体关节状态，生成协调的运动轨迹
- 适用于高自由度移动机械臂，适合工业自动化场景
移动机械臂在众多实际应用中日益普及。当前主要挑战源于移动基座带来的庞大状态空间，以及高自由度系统的建模困难。亟需快速准确的算法来生成平滑的运动规划。现有方法多将基座与机械臂运动分开处理。本文提出基于李理论的方法，通过螺旋坐标将运动学模型在李群与向量表示间转换，推导逆运动学约束，并设计优化函数求解整个移动机械臂的期望关节状态。该方法可协同规划基座与机械臂运动，生成平滑精确的轨迹。所提状态规划器在模拟移动机械臂上通过解析实验验证有效。求解器代码及推导细节详见 https://github.com/peleito/slithers。
原文摘要 · Abstract (English)
Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is critical to devise fast and accurate algorithms that generate smooth motion plans for such mobile manipulators. Existing techniques attempt to solve this problem but focus on separating the motion of the base and manipulator. We propose an approach using Lie theory to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation. An optimization function is devised to solve for the desired joint states of the entire mobile manipulator. This allows the motion of the mobile base and manipulator to be planned and applied in unison resulting in a smooth and accurate motion plan. The performance of the proposed state planner is validated on simulated mobile manipulators in an analytical experiment. Our solver is available with further derivations and results at https://github.com/peleito/slithers.
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