We propose a representation for the set of forces a robot can counteract using full system dynamics: the residual force polytope. Given the nominal torques required by a dynamic motion, this representation models the forces which can be sustained without interfering with that motion. The residual force polytope can be used to analyze and compare the set of admissible forces of different trajectories, but it can also be used to define metrics for solving optimization problems, such as in trajectory optimization or system design. We demonstrate how such a metric can be applied to trajectory optimization and compare it against other objective functions typically used. Our results show that the trajectories computed by optimizing objectives defined as functions of the residual force polytope are more robust to unknown external disturbances. The computational cost of these metrics is relatively high and not compatible with the short planning times required by online methods, but they are acceptable for planning motions offline.
翻译:我们为机器人用整个系统动态来抵消的一组力量提出一个代表:残余力量聚变。根据动态运动所需的名义托盘,这种代表模式可以代表能够持续而不会干扰该运动的力量。残余力量聚变可以用来分析和比较不同轨迹的一组可接受力量,但也可以用来确定解决优化问题的衡量标准,例如轨道优化或系统设计。我们证明如何将这种衡量标准应用于轨道优化,并将其与其他通常使用的目标功能进行比较。我们的结果显示,通过优化作为残余力量聚变功能的目标而计算的轨迹对于未知的外部扰动更为强大。这些计量的计算成本相对较高,与在线方法所需的短期规划时间不相容,但用于规划离线运动是可以接受的。