制約多様体の微分可能チャートに沿った計画：汎用IKソルバーを用いて
Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers
IKFastなどの汎用逆運動学ソルバーが出力する解析的IKを微分可能に扱うため、逆関数定理を用いて勾配を計算する手法を提案し、マニピュレータの制約付き軌道計画に応用した。
著者: Thomas Cohn, Seiji Shaw, Harel Biggie, Travis Manderson, Nicholas Roy, Russ Tedrake
分類: cs.RO
原文アブストラクト
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/