Adaptation of Gradient-Based Navigation Control for Holonomic Robots to Nonholonomic Robots

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.

I. Introduction

Motion control of nonholonomic Wheeled Mobile Robots (WMRs) is required in a wide variety of applications in robotics. Despite extensive work on designing motion controllers for nonholonomic WMRs, challenges still arise due to the nonholonomic constraints in the robot's kinematic model [1], [2]. Existing control approaches for stabilizing the position of a nonholonomic robot suffer from various limitations, including (1) chattering in the robot's motion that results from the use of discontinuous functions in the control law, e.g. sgn [3], arctan [4], and atan2; and (2) erratic or oscillatory transient robot motions, which are intrinsic characteristics of time-varying control laws [5] and pure geometric techniques [6]. Furthermore, many existing control approaches for obstacle avoidance (1) have been developed using a holonomic motion planner, which may introduce infeasible collision-free paths and cannot be implemented on nonholonomic robots [7]; (2) do not have mathematical guarantees on performance; and (3) can result in the robot becoming trapped in a local minimum.