1 Neural Fields for Real-Time Navigation of an Omnidirectional Robot Mohamed Oubbati G¨ unther Palm Institute of Neural Information Processing, University of Ulm, 89069 Ulm, Germany Abstract—In this paper, we implement a biologically inspired approach for the generation of real-time navigation of a real omnidirectional robot. The approach is based on a so-called neural fields, which are equivalent to continuous recurrent neural networks. Due to its dynamical properties, a neural field produces only one localized peak that indicates the optimum movement direction of the robot. Experimental results support the validity of the approach. Index Terms— Mobile Robots, Neural Fields, Behavior-based Control, Navigation. I. I NTRODUCTION The basic task the robot has to perform is to reach a goal under constraints, e.g moving towards a goal while avoiding obstacles. Approaches that have been developed for this problem can be divided into global and local methods. Global methods require the environment to be completely known and the terrain should be static, and they return a continuous free path. By contrast, local methods need only local information. It means that the path planning is done while the robot is moving, in response to environmental changes. Due to their low-computational costs, local methods are much more suitable for real application where the environmental state changes continually. The most popular local method is the potential field approach proposed by Khatib [1]. The idea is to consider that the robot moves under influences of an artificial potential field. The target applies an attractive force to the robot, while obstacles exert repulsive forces onto the robot. The sum of all forces determines the subsequent direction of the movement. While the potential field principle is particularly attractive because of its elegance and simplicity, substantial drawbacks have been identified, i.e. local minima (cyclic behavior), no passage between closely spaced obsta- cles, oscillations in narrow passages, etc [2]. Recently, the theory of dynamical systems has proven to be an elegant and easy to generate robot behavior [3][4][5]. The so-called Dynamic Approach invented by Sch¨ oner in 1995 [6] provides a framework to design differential equations for so-called behavior variables, which generates the robot’s behavior. Usually, these variables directly parameterize the elementary behavior to be generated. However, there are cases for which the behavioral variable needs a more general form. For example, a behavioral variable can have multiple values or even no value at all. In those cases, it is necessary to express it by a continuous function. The neural field’s model can represent such a behavioral variable. Originally, these fields were proposed by Amari [7] as models of the (a) (b) Fig. 1. Omnidirectional robot. (a) hardware photo. (b) CAD model neurophysiology of cortical processes. They are equivalent to continuous recurrent neural networks, in which units are laterally coupled through an interaction kernel and receive external inputs. The concept of neural fields has proven to be a simple and an elegant approach to generate a behavior- based control for mobile robots [8][9]. In [10] we used neural fields to navigate the mobile robot to its goal in an unknown environment without any collisions with static or moving obstacles. Furthermore, their competitive dynamics were used to optimize the target path through intermediate home-bases. More recently, we investigated how neural fields can produce an elegant solution for the problem of moving multiple robots in formation [11]. The objective was to acquire a target, avoid obstacles, and keep a geometric configuration at the same time. In this paper, the neural field approach is implemented on a real omnidirectional robot (Figure 1). The objective is to acquire a target without any collisions with static or moving obstacles. We begin by describing the basic concept of neural fields. Then we will present our navigation model, supported with some experimental results. II. NEURAL FIELD THEORY The field equation of a one-dimensional neural field is given by τ ˙ u(ϕ, t)= -u(ϕ, t)+ S(ϕ, t)+ h +  +∞ -∞ w(ϕ, ´ ϕ)f (u(´ ϕ, t)d ´ ϕ (1)