Abstract
This study proposes a time-optimal control method for a wheeled inverted pendulum (WIP) vehicle under specified paths. Firstly, the given path is described with a parametric form, and the kinematic model, velocity constraint and acceleration constraint are all parameterized with a same parameter as the geometric path. Meanwhile, the stabilization constraint of vehicle body is also formulated through the kinematic coupling relationship to take the underactuated characteristic into full consideration. Next, the time-optimal trajectory is constructed by a sequence of minimum acceleration and maximum acceleration trajectories based on phase-plane analysis, and the optimality is illustrated through rigorous analysis. Finally, a time-optimal trajectory tracking controller is designed for the WIP vehicle to realize the minimum-time motion, and numerical simulation results validate the effectiveness of the proposed method.
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