Using a closed-form inverse kinematics solution for motion planning has many advantages compared to traditional numerical approaches, most notably much faster computation times and better suitability for real-time applications. Steady progress has been made to develop an analytic inverse kinematics solution for seven degrees of freedom (DoF) manipulators without joint offsets. Redundancy resolutions have been proposed to push the individual joint angles away from their limits. However, no further objectives are considered in these closed-form solutions. We propose a multi-objective real-time optimization approach that is able to minimize joint velocities and accelerations, while still avoiding joint limits. A closed-form solution to the optimization is derived, which only requires a single intuitive tuning parameter. We provide a free and open-source software implementation of the full kinematics algorithm that covers the complete solution space. The null-space motion resulting from our method is evaluated, achieving faster motion times and smoother arm motions along Cartesian paths in comparison to the state-of-the-art approach. Finally, experimental results with a KUKA iiwa robot are reported.

中文翻译：

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一种用于七自由度串行机械手的实时闭式多目标冗余解决方案

与传统数值方法相比，使用闭式逆运动学解决方案进行运动规划具有许多优势，最显着的是更快的计算时间和更好的实时应用适用性。在为无关节偏移的七自由度 (DoF) 操纵器开发解析逆运动学解决方案方面取得了稳步进展。已经提出了冗余解决方案以将各个关节角度推离其极限。然而，在这些封闭形式的解决方案中没有考虑进一步的目标。我们提出了一种多目标实时优化方法，能够最小化关节速度和加速度，同时仍然避免关节限制。推导出优化的封闭形式解决方案，它只需要一个直观的调整参数。我们提供涵盖完整解决方案空间的完整运动学算法的免费开源软件实现。评估由我们的方法产生的零空间运动，与最先进的方法相比，沿着笛卡尔路径实现更快的运动时间和更平滑的手臂运动。最后，报告了 KUKA iiwa 机器人的实验结果。