In this letter, we propose a gradient-based nonlinear control approach for stabilizing a nonholonomic Wheeled Mobile Robot (WMR) to a target position in environments with and without obstacles. This approach enables any gradient-based feedback control law (with bounded or unbounded gradients) developed for a holonomic point-mass robot model to be adapted to control a nonholonomic robot. The proposed controller is defined in terms of smooth continuous functions, which produce smooth robot trajectories and can be tuned to stabilize the robot to the goal position at a desired convergence rate. We first prove that the controller will stabilize a nonholonomic robot to a target point in an obstacle-free environment. To stabilize the robot's position in environments with obstacles, we modify our controller to utilize the gradient of an artificial potential function and use Lyapunov stability theory to prove that the robot is guaranteed to converge to the target position under this controller. We demonstrate the effectiveness of our controller for various initial robot positions and environments, and two types of potential fields that are widely used in gradient-based methods for obstacle avoidance, through MATLAB simulations and experiments with a commercial nonholonomic WMR.

中文翻译：

---

基于梯度的完整机器人导航控制对非完整机器人的适应性

在这封信中，我们提出了一种基于梯度的非线性控制方法，用于在有障碍物和无障碍物的环境中将非完整轮式移动机器人 (WMR) 稳定到目标位置。这种方法使为完整点质量机器人模型开发的任何基于梯度的反馈控制律（具有有界或无界梯度）都适用于控制非完整机器人。所提出的控制器是根据平滑连续函数定义的，它产生平滑的机器人轨迹，并且可以进行调整以将机器人以所需的收敛速度稳定到目标位置。我们首先证明控制器将在无障碍环境中将非完整机器人稳定到目标点。为了在有障碍物的环境中稳定机器人的位置，我们修改我们的控制器以利用人工势函数的梯度，并使用李雅普诺夫稳定性理论证明机器人在该控制器下保证收敛到目标位置。我们通过 MATLAB 模拟和商业非完整 WMR 实验，证明了我们的控制器对各种初始机器人位置和环境的有效性，以及广泛用于基于梯度的避障方法的两种势场。