17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper TuP07.5

Nishimura, Yuki (Hokkaido Univ.), Yamashita, Yuh (Hokkaido Univ.)

Stabilization Problem of 1-Input Underactuated Mechanics

Scheduled for presentation during the Regular Session "Control of Mechanical Systems" (TuP07), Tuesday, July 25, 2006, 17:00−17:25, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 15, 2024

Keywords Non-holonomic systems, Optimal control

Abstract

A horizontal two-link underactuated robot arm is an example of 1-input underactuated mechanics. The arm has a nonholonomic constraint and does not conform to the continuous asymptotically stabilizing control law. The system has no effective pure feedback law because although it is a simple model, it has a complicated nonholonomic structure. We show the existence of a subset on which the state of the system converges to the origin. We deal with the system as an optimal regulation problem. We use the viscosity solutions to this problem as weak solutions of a Hamilton-Jacobi-Bellman equation that determines an optimal feedback law. We obtained a feedback law of the system that moves the state neighborhood of the origin using finite-difference numerical approximations.