A Guiding Vector-Field Algorithm for Path-Following Control of Nonholonomic Mobile Robots

Abstract

Abstract-In this paper we propose an algorithm for pathfollowing control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level set of a predefined smooth function. Using this function and the robot's kinematic model, we design a GVF, whose integral curves converge to the trajectory. A nonlinear motion controller is then proposed which steers the robot along such an integral curve, bringing it to the desired path. We establish global convergence conditions for our algorithm and demonstrate its applicability and performance by experiments with real wheeled robots.

Guiding vector field algorithm for a moving path following problem

“…In comparison with the original solution of the path following problem for the driftless nonholonomic model (Kapitanyuk et al, 2016), the additional components such as the constant disturbance vectorw and the kinematic of the moving frame O T have been added. Fortunately, using the changing of coordinates (8) and (18) and under Assumption 1, one can transform a moving path following problem to the standard form considered in the paper (Kapitanyuk et al, 2016). Moreover, the theorems about the existence of solutions are valid for the problem considered in this paper.…”

“…The method of path following, presented in this paper, is an extension of the guidance algorithm for nonholonomic robots given in (Kapitanyuk et al, 2016;Garcia de Marina et al, 2016b) to the case where a general C 2 -smooth curvilinear path is attached to an external reference frame that moves uniformly with respect to a global inertial coordinate frame. The robot's motion is influenced by a constant disturbance.…”

Path following control in 3D using a vector field

“…This is partly due to the fact that usually there are singular points 1 in the vector field. Recently, the work [8] analyzes in details the properties of a 2D vector field for any desired path that is sufficiently smooth. The analysis of the singular points is also presented, and almost global convergence to the path is proven.…”

“…The previous study [8], as well as many other existing works [4,11,14], only consider planar desired paths, while the 3D counterpart is less studied. In [6], given that the desired path is described by the intersection of several (hyper-)surfaces, a general vector field is proposed for robot navigation in the n-dimensional Euclidean space.…”

“…Compared with [8] and some other studies, we have provided additional analysis and features in this paper as follows: 1) Our analysis of the 3D vector field can be directly applied to higher-dimensional vector fields by minor modifications, while that of [8] might not. 2) We have presented rigorous analysis for unbounded desired paths.…”