Integral control on Lie groups

• DOI: 10.1016/j.sysconle.2015.02.009
• Publication Date: 2015-04-18T18:07:34Z
• Authors: Zhifei Zhang; Alain Sarlette; Zhihao Ling
• Keywords: 0209 industrial biotechnology; [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]; Systems and Control (eess.SY); 02 engineering and technology; 16. Peace & justice; Electrical Engineering and Systems Science - Systems and Control; [SPI.AUTO]Engineering Sciences [physics]/Automatic; 004; 620; [SPI.AUTO] Engineering Sciences [physics]/Automatic; FOS: Electrical engineering, electronic engineering, information engineering; 0202 electrical engineering, electronic engineering, information engineering; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; 93Bxx, 93Cxx

Resubmitted to Systems and Control Letters, February 2015<br/>In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of "integral action" for proportional(-derivative)-controlled systems whose configuration evolves on a nonlinear space, where configuration errors cannot be simply added up to compute a definite integral. We then prove that the proposed integral control allows to cancel the drift induced by a constant bias in both first order (velocity) and second order (torque) control inputs for fully actuated systems evolving on abstract Lie groups. We illustrate the approach by 3-dimensional motion control applications.<br/>