Underactuated Robot Control: Comparing LQR, Subspace Stabilization, and Combined Error Metric Approaches

• Published in: IEEE transactions on industrial electronics (1982) Vol. 55; no. 10; pp. 3724 - 3730
• Main Authors: Marton, L., Hodel, A.S., Lantos, B., Hung, J.Y.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive systems; Beams (radiation); Design engineering; Error correction; Friction; Friction compensation; linear quadratic regulator (LQR); Lyapunov methods; Nonlinearity; Programmable control; Regulators; Robot control; Robots; Robust control; Settling; sliding mode control; Stability; Stabilization; subspace stabilization; Subspaces; Testing; linear-quadratic control; subspace stabilization; sliding mode control; friction compensation; Lyapunov methods
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2008.923285

In this paper, three techniques for robust control of underactuated robots are experimentally compared on the classical ball and beam system. An adaptive tracking controller is first designed and implemented to identify the nominal friction characteristic. Then, designs for a linear quadratic regulator (LQR), subspace stabilization controller, and combined error metric controller are presented. Step response tests confirm that both nonlinear approaches exhibit better stability properties than the standard LQR design. In addition, the subspace stabilization approach permits a much more aggressive beam motion, resulting in shorter settling time with excellent control of overshoot.