轮式移动机器人快速轨迹跟踪

为了克服轮式移动机器人响应能力的有限性、保证轮式移动机器人快速跟踪给定的参考轨迹,本文充分利用预演信息(即提前获取的将来参考信息),设计预演控制策略、调节轮式移动机器人的驱动电压来控制机器人,使其快速跟踪给定的参考轨迹.首先,针对运动学模型设计虚拟控制器以保证轮式移动机器人能够渐近跟踪给定的参考轨迹.其次,建立了虚拟控制器的离散时间线性状态空间模型.再次,基于轮式移动机器人的动力学模型和虚拟控制器的线性模型,将轨迹跟踪控制问题等价转化成一个具有已知输入的线性二次调节问题.最后,基于Riccati方程的解,给出了最优预演控制策略的反馈增益.事实上,本文所提出的为虚拟控制器建立线性状态空间模型的方法适用于任意离散信息,这极大地方便了信息的处理与提前使用；另一方面,由于提前使用了参考信息,本文所提的预演控制策略能够快速地跟踪给定的参考轨迹.仿真实验以类正弦曲线为参考轨迹进行跟踪,结果表明:所提控制策略能使轮式移动机器人的速度与轨迹跟踪误差快速地趋于零,验证了所提预演控制算法的有效性.

Fast trajectory tracking of wheeled mobile robots

To improve the limited response ability of wheeled mobile robots (WMRs) and ensure that WMRs track the given reference trajectories rapidly, this paper utilizes information preview (i.e. future reference information) to design a preview control strategy and driving voltage of wheeled mobile robot (WMR). First, a virtual controller was proposed for the kinematic model to ensure that the WMR tracks the given reference trajectory asymptotically. Then, a linear discrete-time state-space model of the proposed virtual controller was established, and the tracking problem was thus converted into a linear quadratic regulation problem for systems with given input on the basis of the dynamic model of the WMR and the linear model of the virtual controller. Finally, the feedback gain of the optimal preview control strategy was provided based on the solution of the Riccati equation. The proposed strategy for virtual controller modeling could be adopted for any discrete signal, which can facilitate signal processing and application. In addition, due to the utilization of the reference information in advance, the proposed strategy could realize rapid tracking with given trajectories. Simulations for sinusoid-type reference trajectories were carried out, and results show that the velocity and trajectory tracking errors of the WMR tended to zero rapidly, which verifies that the proposed preview control strategy is feasible.