约束耦合影响下的差动机器人主动调速路径跟踪

Active speed-regulating path tracking for differential robots under the influence of constraint coupling

  • 摘要: 差动机器人相比其他类型的机器人展现出更高的灵活性和可扩展性,针对在差动机器人的路径跟踪控制中,约束耦合导致路径跟踪控制精确性不足问题,以非线性模型预测控制(Nonlinear model predictive control, NMPC)为基础,通过分析差动机器人纵向行驶速度与横摆角速度约束之间的耦合关系,以左右侧履带线速度为输入构建了预测模型,利用NMPC中纵向行驶速度与参考路径坐标点之间的耦合关系,提出了一种约束耦合影响下基于NMPC的差动机器人主动调速路径跟踪控制方法. 为了验证提出控制方法的有效性,进行了Simulink仿真和真实差动机器人实验验证. 结果表明,该运动控制系统提升了差动机器人在路径跟踪控制上的精度,其中位移误差的绝对值不超过0.0723 m,航向误差的绝对值不超过0.0964 rad,相比恒速路径跟踪控制系统,能够将位移误差最大幅值减小达99.22%,航向误差最大幅值减小达93.32%. 同时相比现有的主动调速路径跟踪控制系统,能够将位移误差最大幅值和航向误差最大幅值分别减小87.55%和29.69%. 此外该控制系统在仿真与实验中的解算时间18.00 ms,满足实时性要求.

     

    Abstract: Differential robots, which include both tracked and wheeled robots, have simplified structures and the capability for in situ steering when compared with other robot types, such as car-like robots. Because these features endow enhanced flexibility and scalability, differential robots have been widely used in intelligent manufacturing, logistics, military, agriculture, and other fields. Path tracking control is a pivotal technology within the autonomous navigation system of differential robots, and it maintains the differential robot’s traveling behavior along a given reference path by minimizing the distance between the robot and path. However, existing path tracking control methods are vulnerable to deviations stemming from the coupling between yaw rate constraints and travel speeds. Specifically, the pendulum angular velocity limits of differential robots become increasingly pronounced at higher speeds owing to this coupling, thereby impeding steering capabilities. This coupling leads to a deterioration of the accuracy of the path tracking control when the reference path curvature is large. To address this issue, we introduce a novel path tracking control method based on nonlinear model predictive control (NMPC). Initially, the coupling between the longitudinal travel speed and yaw rate constraints, which primarily arises from constraint conversion, is analyzed. The constraint range of the system can be fully leveraged by directly employing the left and right track line speeds as inputs, thereby averting under-constraint issues. Subsequently, a kinematic model is formulated using the track line speeds as inputs, and a nonlinear prediction model is constructed accordingly. An optimization objective function is then devised by leveraging the coupling between the longitudinal travel speed and reference path points. Thus, an NMPC-based active speed-regulating path tracking algorithm tailored for differential robots operating under constraint coupling is developed. Finally, an active speed-regulating path tracking control system is developed for differential robots to validate the efficacy of the proposed control method. The results of Simulink simulations and real-world differential robot experiments demonstrate that the proposed control system enhances the path tracking control accuracy of differential robots. Across all simulations and experiments, the absolute value of the maximum displacement error does not surpass 0.0723 m, whereas that of the heading error remains below 0.0964 rad. Compared with constant-speed path tracking control systems based on NMPC and linear model predictive control, the proposed system reduces the maximum displacement error by up to 99.22% and the maximum heading error by up to 93.32%. Furthermore, in contrast to an existing active speed-regulating path tracking control system that combines a speed adjustment controller with an NMPC path-tracking controller, the proposed system decreases the maximum displacement error magnitude by 87.55% and maximum heading error magnitude by 29.69%. Notably, the computation time of the control system does not exceed 18.00 ms throughout the simulations and experiments, with the control period set to a constant 50 ms. As the computation time of the proposed control system is significantly less than the control period, the system can satisfy the demand for path tracking control in real time.

     

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