Planar time-optimal paths for asymmetric vehicles in constant flows

Abstract

This paper introduces a new kinematic model to describe the planar motion of an autonomous underwater vehicle moving in constant current flows. The vehicle is modeled as a rigid body moving at maximum attainable forward velocity with symmetric bounds on the control input for the steering rate. The model approximates the effect a flow will induce on the steering rate of the vehicle due to the asymmetric geometry of the vehicle. By imposing restrictions on the magnitude of the flow, the model is then used to characterize and construct the minimum-time paths that guide the vehicle from a given initial to a final configuration in the plane. Algorithms for the time-optimal path synthesis problem are also introduced, along with several simulations to validate the proposed method. Lastly, insights into how one would approach the energy-optimal problem are given, highlighting the fundamental differences in formulation and methods used to solve for the optimal paths.