Trajectory planning is a crucial aspect of macro-micro robotic systems (MMRSs), especially when the system has high degrees of freedom (DOFs). In the field of robotic polishing, the MMRS is usually composed of an industrial robot and an end-effector, which is responsible for polishing force control. Therefore, the compliance of the macro-robot can be minimized by trajectory planning to reduce its impact on the micro-robot. This study proposes a trajectory planning strategy based on Gauss pseudospectral method for a 9-DOF MMRS. Different from traditional sequential solution strategies, it can be used to obtain an approximate global optimal trajectory. Firstly, the velocity-level kinematics model of MMRS is built, which comprehensively considers the workpiece placement pose and task redundancy. Secondly, an optimal control model for trajectory planning is developed through an effective variable allocation. On the premise of considering traditional trajectory smoothness constraints, a constraint on manipulability is additionally analyzed to avoid reaching a singular configuration during compliance optimization. Thirdly, a Gauss pseudospectral framework based on the optimal control model is proposed, and the costate mapping theorem is proved. The latter provides a theoretical basis for the efficiency and accuracy of the proposed method. Finally, comparison results demonstrate the effectiveness of the proposed method.

中文翻译：

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使用高斯伪谱框架的宏观-微观机器人系统的直接轨迹优化

轨迹规划是宏观-微观机器人系统 (MMRS) 的一个重要方面，特别是当系统具有高自由度 (DOF) 时。在机器人抛光领域，MMRS通常由工业机器人和末端执行器组成，负责抛光力控制。因此，可以通过轨迹规划来最小化宏机器人的柔顺性，以减少其对微型机器人的影响。本研究提出了一种基于高斯伪谱方法的 9 自由度 MMRS 轨迹规划策略。与传统的顺序求解策略不同，它可以用来获得近似的全局最优轨迹。首先，建立MMRS速度级运动学模型，综合考虑工件放置位姿和任务冗余。其次，通过有效的变量分配开发轨迹规划的最优控制模型。在考虑传统轨迹平滑约束的前提下，额外分析可操纵性约束，以避免柔度优化时达到奇异配置。再次，提出了基于最优控制模型的高斯伪谱框架，并证明了共态映射定理。后者为该方法的效率和准确性提供了理论基础。最后，比较结果证明了该方法的有效性。