In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality constraints in the configuration space, which are difficult for trajectory optimizers. In addition, the set of feasible configurations becomes a measure zero set, which presents a challenge to sampling-based motion planners. We leverage an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure. We describe how to use this parametrization with existing motion planning algorithms, including sampling-based approaches, trajectory optimizers, and techniques that plan through convex inner-approximations of collision-free space.

翻译：为让双臂机器人操控由两只手共同持有的物体，必须构建运动规划，使得两末端执行器之间的变换保持固定。这相当于在构型空间中引入复杂的非线性等式约束，对轨迹优化器而言极具挑战性。此外，可行构型集成为零测度集，给基于采样的运动规划器带来难题。我们利用逆运动学问题的解析解对构型空间进行参数化，得到具有正测度有效构型集的低维表示。本文阐述了如何将该参数化方法应用于现有运动规划算法，包括基于采样的方法、轨迹优化器以及通过碰撞自由空间凸内部近似进行规划的技术。