二乗和計画法による軌道に沿った制御設計
Control Design along Trajectories with Sums of Squares Programming
二乗和計画法を用いて、目標集合へ導く不変な「ファネル」を最大化する制御器を設計し、トルク制限付きアクロボットで検証した論文。
著者: Anirudha Majumdar, Amir Ali Ahmadi, Russ Tedrake
分類: cs.RO, cs.SY, eess.SY, math.OC
原文アブストラクト
Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant "funnel" that leads to a predefined goal set. Our certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities. These certificates, together with our proposed polynomial controllers, can be efficiently obtained via semidefinite optimization. Our approach can handle time-varying dynamics resulting from tracking a given trajectory, input saturations (e.g. torque limits), and can be extended to deal with uncertainty in the dynamics and state. The resulting controllers can be used by space-filling feedback motion planning algorithms to fill up the space with significantly fewer trajectories. We demonstrate our approach on a severely torque limited underactuated double pendulum (Acrobot) and provide extensive simulation and hardware validation.
