Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers

2026-09-09

AI Summary

本文提出一种新方法，通过逆函数定理计算解析IK参数化的梯度，以解决机器人在运动学约束下的轨迹规划问题。

Abstract

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/

Problem

• trajectory planning
• kinematic constraints
• differentiable inverse kinematics
• configuration space

Innovation

• inverse function theorem
• differentiable IK
• trajectory optimization
• reachability constraint