接触暗黙的動作計画における逐次凸最適化の驚くべきロバスト性
On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning
接触を暗黙的な相補性制約として扱う動作計画問題に対し、主問題のみを解く逐次凸計画法CRISPを提案し、その収束条件を示すとともに、ゼロ初期化でも解ける高いロバスト性を実証した。
著者: Yulin Li, Haoyu Han, Shucheng Kang, Jun Ma, Heng Yang
分類: math.OC, cs.RO
原文アブストラクト
Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization, being an instance of Mathematical Programming with Complementary Constraints, fails the classical constraint qualifications that are crucial for the convergence of popular numerical solvers. We present robust contact-implicit motion planning with sequential convex programming (CRISP), a solver that departs from the usual primal-dual algorithmic framework but instead only focuses on the primal problem. CRISP solves a convex quadratic program with an adaptive trust region radius at each iteration, and its convergence is evaluated by a merit function using weighted penalty. We (i) provide sufficient conditions on CRISP's convergence to first-order stationary points of the merit function; (ii) release a high-performance C++ implementation of CRISP with a generic nonlinear programming interface; and (iii) demonstrate CRISP's surprising robustness in solving contact-implicit planning with naive initialization. In fact, CRISP solves several contact-implicit problems with all-zero initialization.
