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 引用本文: 周宇生, 文相容, 王在华. 论轮式移动结构的非完整约束及其运动控制[J]. 力学学报, 2020, 52(4): 1143-1156.
Zhou Yusheng, Wen Xiangrong, Wang Zaihua. ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1143-1156.
 Citation: Zhou Yusheng, Wen Xiangrong, Wang Zaihua. ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1143-1156.

## ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)

• 摘要: 当质点沿光滑曲线运动时,必须满足横向速度为零的条件.同样地,不同轮式移动结构在平面上做光滑曲线运动时都需要满足该非完整约束条件.本文结合轮子转速和它们运动速度的完整约束关系,理清各轮式移动结构的完整和非完整约束,然后利用 Euler-Lagrange 方程方便地推导出相应的动力学方程.另外,通过该非完整约束,将目标轨迹曲线转化为速度目标的形式,然后引入目标轨迹曲线的相对曲率设计合适的动态跟踪目标.进一步,通过采用该动态跟踪目标可以将轮式移动结构的运动规律和动力学方程有机结合起来,并将原运动任务简化为一般的 轨迹 控制问题.基于该动态跟踪目标可以为轮式移动结构设计合适的鲁棒跟踪控制器,通过跟踪目标轨迹曲线的相对曲率来实现对目标曲线的精确跟踪.最后,理论分析和仿真结果显示,采用动态目标跟踪方法能够从根本上解决初始速度误差过大和位置误差不断被累积的问题,即使前向速度误差系统不稳定的,实际运动轨迹也几乎能和目标轨迹曲线重合.

Abstract: When a particle moves along a smooth curve, the condition of zero lateral velocity should be satisfied. In the same way, different wheeled structures are all restrained by such nonholonomic constraint when they move along smooth curves on a plane. In this paper, holonomic and nonholonomic constraint equations of various kinds of wheeled structures are clarified, combined with the holonomic constraint relationship between the rotation speed of wheels and their motion speed. Then, the corresponding dynamical equations are readily derived by means of the Euler-Lagrange equation of nonholonomic mechanical systems. In addition, the target trajectory curve is converted to a form of speed target based on such nonholonomic constraint, and the relative curvature of target trajectory curve is introduced to design an appropriate dynamical tracking target. Furthermore, the motion law of the wheeled mobile structure can be organically combined with the dynamical equation by adopting such dynamical tracking target, and the original motion task can be simplified into a common trajectory tracking control problem. Consequently, an appropriate robust controller is designed to track the relative curvature of target trajectory curve on the basis of dynamical tracking target, such that the wheeled mobile structure can precisely follow the target trajectory curve. Theoretical analysis and simulation results indicate that the dynamical tracking target method can essentially solve the problem that the initial speed error is large enough and the position error is continuously accumulated. Even if the forward speed error system is not stable, the actual motion trajectory can almost be coincide with the target trajectory curve.

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