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

• URL: http://arxiv.org/abs/2609.10905v1
• Date: Wed, 09 Sep 2026 23:22:03 GMT
• Title: Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers
• Abstract summary: Planning trajectories for robot manipulators under kinematic equality constraints restricts feasible motions to a measure-zero submanifold of the configuration space.<n>A promising strategy is parametrizing the set of feasible using analytic inverse kinematics (IK)<n>We present a new approach for computing gradients of analytic IK parameterizations.
• Score: 29.871447775096808
• License: http://creativecommons.org/licenses/by/4.0/
• 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/

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