Robot motion planning improved with gradient-friendly inverse kinematics
Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers
Robotics
Summary
Planning robot arm movements gets tricky when the arm must follow exact rules, because the possible positions form a tiny set in a huge space. The authors found a way to calculate how to adjust robot arm positions smoothly using math called gradients, even when using common inverse kinematics tools that weren't designed for that. They do this by cleverly using the forward movement formulas backwards, allowing robots to plan better and reach tricky positions more reliably. This method was tested in simulations and real robot tasks like picking up and placing boxes.
What this means in practice
- •For robotics engineers: Plan smooth, precise movements for robot arms operating under strict joint constraints using general-purpose inverse kinematics tools.
- •For automation system developers: Improve pick-and-place robot performance in manufacturing by enabling gradient-friendly IK solutions without custom analytic code.
Authors
Thomas Cohn, Seiji Shaw, Harel Biggie, Travis Manderson, Nicholas Roy, Russ Tedrake
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/