Feedback Synthesis For Underactuated Systems Using Sequential Second-Order Needle Variations

• DOI: 10.48550/arxiv.1804.09559
• Publication Date: 2018-01-01
• Authors: Giorgos Mamakoukas; Malcolm A. MacIver; Todd Murphey
• Keywords: Underactuation

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