robotics
A Standard IK Solver Gained the Gradients It Never Exposed
The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.
Summary
The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.
Most analytic inverse-kinematics functions come from meta-solvers such as IKFast and are difficult to rewrite for gradient-based trajectory optimization. The proposed method recovers gradients of their local solution charts from the ordinary forward-kinematic Jacobian through the inverse function theorem. A least-squares extension preserves useful gradient signal outside the reachable workspace, while an explicit reachability description constrains optimization. Numerical experiments and a hardware demonstration had an RB-Y1 pick up a box and place it on a table. The approach applies where the local chart and selected Jacobian remain regular.
Why it matters
The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.
Limits and context
- The approach applies where the local chart and selected Jacobian remain regular.
Key claims
The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.
Qualification: The approach applies where the local chart and selected Jacobian remain regular.
Evidence: source-2026-09-13-008
Sources
- arXiv preprint 2609.10905arXiv · primary research
Corrections
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