Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum

TL;DR

This paper develops a geometric, structure-preserving discrete-time optimal control method for a wheeled inverted pendulum, effectively handling constraints and respecting the system's manifold, demonstrated through numerical experiments.

Contribution

It introduces a novel geometric, discrete-time optimal control approach for WIP systems that incorporates constraints directly into the control synthesis.

Findings

Control laws respect the system's manifold structure.

Numerical experiments show promising performance.

Constraints are effectively integrated into the control design.

Abstract

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.