Sliding Mode Control of a Mobile Robot for Dynamic Obstacle Avoidance Based on a Time-Varying Harmonic Potential Field Antonella Ferrara and Matteo Rubagotti Abstract— In this paper, a harmonic potential field method for dynamic environments is proposed to generate an on-line reference trajectory for a wheeled mobile robot. A sliding mode controller is used to make the robot move along the prescribed trajectory determined by the gradient lines. The potential field is modified on-line, in order to make the robot avoid the collision with obstacles which move along non a-priori known trajectories with time-varying speed. The mechanism through which the field is modified is based on the so-called ‘collision cone’ concept. I. INTRODUCTION Various methods for path control of autonomous mobile robots have been the object of many research works during the past years. The potential field method, first used with robotic manipulators [1], is one of the most commonly applied in mobile robotics, because of its simplicity and plain mathematical analysis. The basic idea of this method is to consider an artificial potential field in the robot workspace, so that the robot turns out to be attracted by the goal point and repulsed away from the obstacles. Following the gradient lines of the considered potential field, the robot will reach the goal point avoiding the obstacles. The potential field method can also be used in the so-called path deformation, in order to modify on-line the pre-determined desired trajectory when unexpected obstacles are detected (see [2] and the references therein). Clearly, local minima in the potential field could make the robot stop in an undesired position: to circumvent this problem, in [3] a harmonic potential field is proposed for path following, together with sliding mode control [4], [5], which makes the control system robust with respect to parameter variations and external disturbances. Harmonic potential fields enable to avoid local minima because the gradient lines of a harmonic potential field begin and terminate at an obstacle position, at the goal point, or at infinity. This idea has been developed in [6], [7], [8] and [9] for different cases, all concerning static obstacles. In order to solve the problem of motion planning in a dynamic environment, that is when the obstacles move in the robot workspace, different approaches have been used. For instance, in [10] and [11] time is considered as a dimension of the model world and the moving obstacles are regarded as stationary; this approaches require an a-priori knowledge of the obstacles trajectories, which makes this approach difficult to be used in real applications. Another Antonella Ferrara and Matteo Rubagotti are with the Department of Computer Engineering and Systems Science, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy; e- mail contact authors: antonella.ferrara@unipv.it, matteo.rubagotti@unipv.it possible approach is proposed in [12], where the potential field method is extended to the case of moving obstacles, taking into account, for the construction of the potential field, the velocity of the obstacle, but not that of the robot. In other papers, like [13], the construction of the potential field exploits the measure of the relative velocity between robot and obstacle, but the potential fields are quadratic functions, and the problem of local minima needs to be solved. Obviously, one can consider methods which do not use the potential field method: an approach of this kind can be found for instance in [14]. In this paper, a new harmonic potential field method for moving obstacles avoidance is proposed. The key idea is to modify the radius of the ‘security circle’ around each obstacle on the basis of the so-called ‘collision cone’ [15], this latter being, at any time instant, the set of the possible directions of the relative velocity vector for which a future collision is going to occur. More specifically, the on-line variation of the radius of the security circle is performed so that the relative velocity vector is steered outside the collision cone. Relying on this variation, the overall harmonic poten- tial field becomes time-varying. However, basic properties analogous to those of the static method are proved in the paper. II. PROBLEM FORMULATION The mobile robot considered in this paper can be described by a couple of wheels with a common axle and independent wheel motors, as indicated in Fig. 1. This model can be used to approximate three-wheeled vehicles, as shown in [6]. Assuming rolling contact without slip between the tires and the ground, each wheel can only move along its longitudinal direction, with velocity v R (t) and v L (t), respectively: this condition points out the obvious presence of a nonholonomic constraint. The vehicle configuration is represented by q = [x, y, φ] T ∈R 3 in the world coordinate frame [x W ,y W ]. The resulting longitudinal velocity and the rotational velocity of the vehicle are v C (t) and ω(t), respectively, where v C (t)= (v R (t)+ v L (t))/2 and ω =(v R (t) − v L (t))/2D (D being the distance between the two wheels). Then, the kinematic part of the model of the vehicle can be expressed as ˙ x(t) = v C (t) cos φ(t) ˙ y(t) = v C (t) sin φ(t) ˙ φ(t) = ω(t) (1) while the dynamic part of the model is represented by τ t (t) = m ˙ v C (t)+ N t (t) (2) τ r (t) = J ˙ ω(t)+ N r (t) (3) ICRA 2007 Workshop: Planning, Perception and Navigation for Intelligent Vehicles