Integral control on Lie groups |
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Affiliation: | 1. Department of electronic technology, Engineering Technical College-Baghdad, Middle Technical University (MTU) Baghdad, Iraq;1. Department of Electrical and Computer Engineering, University of Western Ontario, London, Ontario, Canada, N6A 3K7;2. Department of Electrical Engineering, Lakehead University, Thunder Bay, Ontario, Canada, P7B 5E1 |
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Abstract: | 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. |
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Keywords: | PID control Riemannian manifolds Lie groups Bias rejection |
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