In this paper, we review and compare several velocity-level and acceleration-level Pseudo-Inverse-based Path Planning (PPP) and Pseudo-Inverse-based Repetitive Motion Planning (PRMP) schemes based on the kinematic model of robotic manipulators. We show that without unit consistency in the pseudo-inverse computation, path planning of incommensurate robotic manipulators will fail. Also, we investigated the robustness and noise tolerance of six PPP and PRMP schemes in the literature against various noise types (i.e. zero, constant, time-varying and random noises). We compared the simulated results using two redundant robotic manipulators: a 3DoF (2RP), and a 7DoF (2RP4R). These experimental results demonstrate that the improper Generalized Inverse (GI) with arbitrary selection of unit and/or in the presence of noise can lead to unexpected behavior of the robot, while producing wrong instantaneous outputs in the task space, which results in distortions and/or failures in the execution of the planned path. Finally, we propose and demonstrate the efficacy of the Mixed Inverse (MX) as the proper GI to achieve unit-consistency in path planning.

翻译：本文回顾并比较了基于机器人操作器运动学模型的几种速度级和加速度级伪逆路径规划（PPP）及伪逆重复运动规划（PRMP）方案。我们证明，若伪逆计算中缺乏单位一致性，非公度机器人操作器的路径规划将失败。此外，我们研究了文献中六种PPP与PRMP方案在多种噪声类型（即零噪声、恒定噪声、时变噪声和随机噪声）下的鲁棒性与噪声容忍度。我们利用两个冗余机器人操作器（一个3自由度2RP型，一个7自由度2RP4R型）对仿真结果进行了比较。实验结果表明，单位选择不当或存在噪声时的广义逆（GI）会导致机器人出现意外行为，同时在任务空间中产生错误的瞬时输出，进而造成规划路径执行中的畸变或失败。最后，我们提出混合逆（MX）作为实现路径规划单位一致性的适当广义逆，并验证了其有效性。