Control design along trajectories with sums of squares programming

Research output: Chapter in Book/Report/Conference proceedingConference contribution

63 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Robotics and Automation, ICRA 2013
Pages4054-4061
Number of pages8
DOIs
StatePublished - Nov 14 2013
Externally publishedYes
Event2013 IEEE International Conference on Robotics and Automation, ICRA 2013 - Karlsruhe, Germany
Duration: May 6 2013May 10 2013

Publication series

NameProceedings - IEEE International Conference on Robotics and Automation
ISSN (Print)1050-4729

Other

Other2013 IEEE International Conference on Robotics and Automation, ICRA 2013
CountryGermany
CityKarlsruhe
Period5/6/135/10/13

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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    Majumdar, A., Ahmadi, A. A., & Tedrake, R. (2013). Control design along trajectories with sums of squares programming. In 2013 IEEE International Conference on Robotics and Automation, ICRA 2013 (pp. 4054-4061). [6631149] (Proceedings - IEEE International Conference on Robotics and Automation). https://doi.org/10.1109/ICRA.2013.6631149