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arXiv · 1709.01947

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

Giorgos Mamakoukas·Malcolm A. MacIver·Todd D. Murphey
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Abstract

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.

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Giorgos Mamakoukas, Malcolm A. MacIver, Todd D. Murphey. 2017-09-06. Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions. https://doi.org/10.15607/rss.2017.xiii.066

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