ガウスの最小拘束原理に基づく等価LQR定式化による効率的な拘束動力学アルゴリズム
Efficient Constrained Dynamics Algorithms based on an Equivalent LQR Formulation using Gauss' Principle of Least Constraint
ガウスの最小拘束原理を用いて拘束動力学を等価なLQR問題として定式化し、動的計画法で解くことで、従来のO(nd^2 + m^2d + d^2m)より高速なO(n + m)の新アルゴリズムを導出した。
著者: Ajay Suresha Sathya, Herman Bruyninckx, Wilm Decre, Goele Pipeleers
分類: cs.RO
原文アブストラクト
We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss principle of least constraint and solving it using dynamic programming. Our approach builds upon the pioneering (but largely unknown) O(n + m^2d + m^3) solver by Popov and Vereshchagin (PV), where n, m and d are the number of joints, number of constraints and the kinematic tree depth respectively. We provide an expository derivation for the original PV solver and extend it to floating-base kinematic trees with constraints allowed on any link. We make new connections between the LQR's dual Hessian and the inverse operational space inertia matrix (OSIM), permitting efficient OSIM computation, which we further accelerate using matrix inversion lemma. By generalizing the elimination ordering and accounting for MUJOCO-type soft constraints, we derive two original O(n + m) complexity solvers. Our numerical results indicate that significant simulation speed-up can be achieved for high dimensional robots like quadrupeds and humanoids using our algorithms as they scale better than the widely used O(nd^2 + m^2d + d^2m) LTL algorithm of Featherstone. The derivation through the LQR-constrained dynamics connection can make our algorithm accessible to a wider audience and enable cross-fertilization of software and research results between the fields
