Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum
This work addresses optimal control for nonholonomic, underactuated mechanical systems with constraints, but the approach is incremental as it applies existing methods (geometric mechanics, discrete maximum principle) to a specific system.
The authors developed an energy-optimal control law for point-to-point state transfer of a wheeled inverted pendulum (Segway) using geometric mechanics and a discrete-time maximum principle, incorporating state and momentum constraints. Numerical experiments on a prototype-based model showed highly encouraging results.
The Wheeled Inverted Pendulum (WIP) is a nonholonomic, underactuated mechanical system, and has been popularized commercially as the {\it Segway}. Designing optimal control laws for point-to-point state-transfer for this autonomous mechanical system, while respecting momentum and torque constraints as well as the underlying manifold, continues to pose challenging problems. In this article we present a successful effort in this direction: We employ geometric mechanics to obtain a discrete-time model of the system, followed by the synthesis of an energy-optimal control based on a discrete-time maximum principle applicable to mechanical systems whose configuration manifold is a Lie group. Moreover, we incorporate state and momentum constraints into the discrete-time control directly at the synthesis stage. The control is implemented on a WIP with parameters obtained from an existing prototype; the results are highly encouraging, as demonstrated by numerical experiments.