In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.

在本文中，我们提出了一种基于反馈的控制方法来执行差动驱动机器人的时间最优运动轨迹。这些轨迹由直线和原地旋转组成。我们表明，在局部参考系中，单个地标位置随时间的演变使得可以根据地标位置的反馈跟踪规定的时间最优机器人的轨迹。我们还表明，闭环系统是一个指数稳定的系统，具有非零扰动，并且可以实现全局一致的跟踪误差最终有界。这项工作的两个主要结果是：1）我们的方法利用视觉伺服控制类型的方法和最佳控制工具，根据反馈信息在状态空间中执行时间最佳轨迹。基于地标的导航的充要条件。展示了在物理机器人（配备全向激光传感器的非完整差分驱动系统）中的实验，验证了所提出的理论建模。