区分アフィン系の近似最適制御のためのサンプリングベース多面体木
Sampling-based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems
接触を伴うロボットの非線形ダイナミクスを表す区分アフィン系に対し、混合整数凸計画を用いてフィードバック制御則と到達可能初期状態を木構造で構築し、目標多面体へ最適コストで収束させる手法を提案した。
著者: Sadra Sadraddini, Russ Tedrake
分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
Piecewise affine (PWA) systems are widely used to model highly nonlinear behaviors such as contact dynamics in robot locomotion and manipulation. Existing control techniques for PWA systems have computational drawbacks, both in offline design and online implementation. In this paper, we introduce a method to obtain feedback control policies and a corresponding set of admissible initial conditions for discrete-time PWA systems such that all the closed-loop trajectories reach a goal polytope, while a cost function is optimized. The idea is conceptually similar to LQR-trees \cite{tedrake2010lqr}, which consists of 3 steps: (1) open-loop trajectory optimization, (2) feedback control for computation of "funnels" of states around trajectories, and (3) repeating (1) and (2) in a way that the funnels are grown backward from the goal in a tree fashion and fill the state-space as much as possible. We show PWA dynamics can be exploited to combine step (1) and (2) into a single step that is tackled using mixed-integer convex programming, which makes the method suitable for dealing with hard constraints. Illustrative examples on contact-based dynamics are presented.
