REDUCED DYNAMIC INVERSION FOR PLANAR AND SPATIAL VEHICLES

This paper addresses the dynamic inversion problem for planar and spatial vehicles having as configuration space the Lie groups SE(2) and SE(3), respectively. For vehicles whose dynamics is invariant with respect to the group action and satisfy suitable conditions, we show that the dynamic inversion problem can be reduced and studied in the Lie algebra of the group. We outline a procedure to solve the reduced dynamic inversion problem, showing that one need to find, at each instant of time, the input value that satisfies a set of nonlinear constraints depending on current state and desired maneuver. Simulation examples of a two-wheel vehicle and a neutrally buoyant autonomous underwater vehicle (AUV) are provided to show effectiveness of the method.