基于通用逆运动学求解器的约束流形可微图规划
Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers
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中文总结 AI 辅助
针对运动学约束下机器人轨迹规划难题，提出利用反函数定理从正向运动学雅可比矩阵计算解析IK参数化梯度，并扩展域以保留梯度信号，经实验验证有效。
中文摘要 AI 辅助
在运动学等式约束下规划机器人操纵器的轨迹，将可行运动限制在配置空间的零测度子流形上，这需要特殊的算法处理。一种有前景的策略是利用解析逆运动学（IK）对可行配置集进行参数化。定制的解析IK函数可以写成可微的，这是基于梯度的轨迹优化所必需的属性。然而，绝大多数IK函数是由IKFast等自动化元求解器计算的，难以修改以实现可微性。我们提出了一种计算解析IK参数化梯度的新方法：利用反函数定理从普通的前向运动学雅可比矩阵中恢复所需梯度。此外，我们提出了一种最小二乘域扩展和可达性约束的优化友好描述，该描述在可达工作空间之外保留梯度信号。我们通过数值实验和下游任务证明了我们方法的有效性，包括RB-Y1拾取盒子并将其放置在桌子上的硬件演示。项目网站：此https URL。
英文摘要
Planning trajectories for robot manipulators under kinematic equality constraints restricts feasible motions to a measure-zero submanifold of the configuration space, requiring special algorithmic treatment. A promising strategy is parametrizing the set of feasible configurations using analytic inverse kinematics (IK). Bespoke analytic IK functions can be written to be differentiable, a necessary property for gradient-based trajectory optimization. But the vast majority of IK functions are computed by automated meta-solvers like IKFast, and are difficult to modify for differentiability. We present a new approach for computing gradients of analytic IK parameterizations: we leverage the inverse function theorem to recover the desired gradients from the ordinary forward kinematic Jacobian. Furthermore, we present a least-squares domain extension and an optimization-amenable description of the reachability constraint, which preserves gradient signal outside the reachable workspace. We demonstrate the efficacy of our approach through numerical experiments and downstream tasks, including a hardware demonstration of an RB-Y1 picking up a box and placing it on a table. Project website: https://cohnt.github.io/inverse-function-theorem-parameterization/
发表机构
- Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。
