微分動的計画法におけるマルチプルシューティングの統一的理解
A Unified Perspective on Multiple Shooting In Differential Dynamic Programming
微分動的計画法(DDP)をマルチプルシューティングに拡張し、初期推定へのロバスト性を高める新たな導出法を提案。ペナルティ法や適応的メリット関数で収束性能を改善し、四足ロボットの動的跳躍MPCなどで有効性を示した。
著者: He Li, Wenhao Yu, Tingnan Zhang, Patrick M. Wensing
分類: cs.RO
原文アブストラクト
Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work considers the extension of DDP to multiple shooting (MS), improving its robustness to initial guesses. A novel derivation is proposed that accounts for the defect between shooting segments during the DDP backward pass, while still maintaining quadratic convergence locally. The derivation enables unifying multiple previous MS algorithms, and opens the door to many smaller algorithmic improvements. A penalty method is introduced to strategically control the step size, further improving the convergence performance. An adaptive merit function and a more reliable acceptance condition are employed for globalization. The effects of these improvements are benchmarked for trajectory optimization with a quadrotor, an acrobot, and a manipulator. MS-DDP is also demonstrated for use in Model Predictive Control (MPC) for dynamic jumping with a quadruped robot, showing its benefits over a single shooting approach.
