Control design along trajectories with sums of squares programming
international conference on robotics and automation(2013)
摘要
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.
更多查看译文
关键词
Lyapunov methods,control system synthesis,feedback,mathematical programming,nonlinear control systems,path planning,pendulums,robot dynamics,stability,time-varying systems,trajectory control,uncertain systems,Acrobot,Lyapunov inequalities,control design procedure,controller safety,dynamics uncertainty,formal guarantee,input saturation,invariance certificate,invariant funnel size maximization,polynomial controllers,robot control task,semidefinite optimization,severely torque limited underactuated double pendulum,space-filling feedback motion planning algorithm,stability,state uncertainty,sums of squares programming,sums of squares proof,time-varying dynamics,trajectories,trajectory tracking
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要