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arXiv · 1710.10932

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

Karmvir Singh Phogat·Ravi Banavar·Debasish Chatterjee
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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.

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Karmvir Singh Phogat, Ravi Banavar, Debasish Chatterjee. 2017-10-30. Structure-preserving discrete-time optimal maneuvers of a wheeled inverted pendulum. https://arxiv.org/abs/1710.10932

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