Transactions of the Society of Instrument and Control Engineers
Online ISSN : 1883-8189
Print ISSN : 0453-4654
ISSN-L : 0453-4654
Paper
Path-following Control for a Four-forked Steering Walker Based on the Lyapunov's Stability Theory and Its Verification
Takahiro SATOHiroaki YAMAGUCHINaoaki YONEZAWAAtsushi KAWAKAMI
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2019 Volume 55 Issue 9 Pages 559-572

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Abstract

This paper presents a novel path-following feedback control method for a four-forked steering walker based on the Lyapunov's stability theory. The locomotor has a square base on which objects to be carried can be loaded. Links are connected through joints at each corner of the base, and a steering system is attached at the endpoint of each link. The locomotor is an undulatory locomotor which transforms the periodic driving of its four joints into its motion through the periodic operation of its four steering systems. Since all the wheels of the locomotor are passive, it is required for the locomotor to avoid singular attitudes in which it cannot move in some direction while maintaining its desired motion. In this control method, the desired angular velocities of the joints for causing the centroid of the base to follow a target point on the desired path and for causing the base to be directed in the orientation of the tangent of the path can be equalized to those for causing the links to be directed in their desired orientations periodically changed by control of the angles of its four steering systems. In other words, the locomotor has a particular structure which facilitates to achieve the desired motion of the base and the desired rotations of the links simultaneously. The asymptotic stability of this control method is guaranteed by the Lyapunov's second method. Especially, the cost of the control input calculation is much lower compared with that in a control method based on chained form which requires convergent calculations for the estimation of the locomotor position in a curvilinear coordinate system and high order Lie derivatives. The validity of this control method is verified in experiments where the locomotor follows a 9th-order Bezier curve path.

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© 2019 The Society of Instrument and Control Engineers
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