2012/10/02 by Majumdar, Anirudha, Ahmadi, Amir Ali, Tedrake, Russ · 2 citations
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1210.0888
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.