Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum
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.
Keywords
Cite
@article{arxiv.1710.10932,
title = {Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum},
author = {Karmvir Singh Phogat and Ravi Banavar and Debasish Chatterjee},
journal= {arXiv preprint arXiv:1710.10932},
year = {2017}
}