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.

我们提出了机器人可以使用完整系统动力学来抵消的一组力的表示：残余力多面体. 给定动态运动所需的标称扭矩，该表示模拟了在不干扰该运动的情况下可以承受的力。残余力多面体可用于分析和比较不同轨迹的一组容许力，但也可用于定义解决优化问题的度量，例如在轨迹优化或系统设计中。我们演示了如何将此类度量应用于轨迹优化，并将其与通常使用的其他目标函数进行比较。我们的结果表明，通过优化定义为残余力多面体函数的目标计算出的轨迹对未知的外部干扰更加鲁棒。这些指标的计算成本相对较高，与在线方法所需的短规划时间不兼容，