Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions
| Title: | Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions |
|---|---|
| Publication Type: | Conference Paper |
| Year of Publication: | 2017 |
| Authors: | G.Mamakoukas, M. A.MacIver, and T. D.Murphey |
| Conference Name: | Robotics Science and Systems |
| Google Scholar: | Access article in Google Scholar |
| 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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