Control design along trajectories with sums of squares programming
Name
Tedrake_Control design.pdf
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1.93 MB
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Adobe PDF
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Author(s)
Majumdar, Anirudha
Ahmadi, Amir Ali
Tedrake, Russell Louis
Date Issued
May 2013
Journal
Proceedings of the 2013 IEEE International Conference on Robotics and Automation
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Majumdar, Anirudha, Amir Ali Ahmadi, and Russ Tedrake. “Control Design Along Trajectories with Sums of Squares Programming.” 2013 IEEE International Conference on Robotics and Automation (May 2013).
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ICRA.2013.6631149
