Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh
Sinusoidal control and limit cycle analysis of the dissipative Chaplygin sleigh
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DOI：
10.1007/s11071-018-4230-1
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发表时间：
2018-07-01
影响因子：
5.6
通讯作者：
Tallapragada, Phanindra
中科院分区：
文献类型：
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作者：
Fedonyuk, Vitaliy;Tallapragada, Phanindra
本文研究了一个欠驱动混合动力学非完整系统，一个Chaubergin雪橇，在粘性耗散和正弦强迫作用下的行为。粘性耗散在允许的运动方向上，并保持非完整约束。包含这样的耗散效应在约化速度空间中产生极限环振荡。我们发现这种极限环的解析近似，并使用这些来确定正弦输入来控制雪橇的速度。我们进一步表明，正弦输入的微小变化可以将雪橇转向任何所需的方向。当考虑粘性耗散的影响时，在其他非完整系统的动力学中也可以看到类似极限环这样的不变结构。因此，我们在这里报告的研究结果适用于广泛的一类陆地和水生运动系统的非完整约束。
In this paper, we investigate the behavior of an underactuated mixed-dynamic nonholonomic system, a Chaplygin sleigh, subjected to viscous dissipation and sinusoidal forcing. The viscous dissipation is in the allowable directions of motion and preserves the nonholonomic constraint. The inclusion of such dissipative effects produces limit cycle oscillations in a reduced velocity space. We find analytical approximations to such limit cycles and use these to determine sinusoidal inputs to control the speed of the sleigh. We further show small changes to the sinusoidal input can steer the sleigh to any desired direction. Invariant structures like limit cycles can be expected to be seen in the dynamics of other nonholonomic systems when the effects of viscous dissipation are included. The findings we report here are therefore applicable to a broad class of both terrestrial and aquatic locomotion systems with nonholonomic constraints.