aiqbench analysis
This research advances robot motion planning by enabling gradient-based optimization through differentiable analytic inverse kinematics, addressing the limitations of standard automated solvers like IKFast. By leveraging the inverse function theorem to recover gradients from forward kinematic Jacobians, the method allows for efficient trajectory generation on constrained manifolds without sacrificing reachability outside the workspace. The approach is validated via numerical experiments and a hardware demonstration of a robotic arm performing pick-and-place tasks.
Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers
arXiv:2609.10905v1 Announce Type: new 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/
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: this https URL
8 pages, 4 figures, 3 tables. Under review. Project website: this https URL
Robotics (cs.RO)
arXiv:2609.10905 [cs.RO]
(or arXiv:2609.10905v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.10905 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 270 words
