A Neural Network Model that Calculates Dynamic Distance Transform ...

Proceedings of the 2003 IEEE International Conference on Robotics & Automation Taipei, Taiwan, September 14-19, 2003

A Neural Network Model that Calculates Dynamic Distance Transform for Path Planning and Exploration in a Changing Environment Dmitry V. Lebedev, Jochen J. Steil, Helge Ritter AG Neuroinformatik, Faculty of Technology, University of Bielefeld, P.O.-Box 10 01 31, 33501 Bielefeld, Germany Abstract – In this paper, we present a neural network model that realizes a dynamic version of the distance transform algorithm (used for path planning in a stationary domain). The novel version is capable of performing path generation for highly dynamic environments. The neural network has discrete-time dynamics, is locally connected, and, hence, computationally efficient. No preliminary information about the world status is required for the planning process. Path generation is performed via the neural-activity landscape, which forms a dynamicallyupdating potential field over a distributed representation of the configuration space of a robot. The network dynamics guarantees local adaptations and includes a set of strict rules for determining the next step in the path for a robot. According to these rules, 
metric. Simulation replanned paths tend to be optimal in a sults in a series of experiments for various dynamical situations prove the effectiveness of the proposed model. I. INTRODUCTION One of the most important attributes of a robotic system is its ability to plan the paths and to navigate autonomously. At the same time, an ”intelligent” navigation is characterized by the capability of adapting a route dynamically in the case of sudden appearance of other objects, or obstacles. There exists a lot of research on path planning (see, e.g., [1]-[5]). A number of neural network approaches has also been proposed to solve this problem ([6]-[17]). The capability of a multilayer perceptron to learn successfully the navigation task in a maze-like environment has been demonstrated in [6]. In [7], a self-organizing Kohonen net with nodes of two types has been used. In [8], a description of a network with oscillating behavior, that solves the problem of path planning for an object with two degrees of freedom (DOFs), formulated as a dynamic programming task, is given. The algorithm, proposed in [9], uses a set of intermediate points, connected by elastic strings. Gradient forces of the potential field, generated by a multilayer neural network, minimize the length of the strings, forcing them at the same time to round the obstacles. In [10], a multilayer feed-forward network for performing real-time path planning was applied. The neural network for path finding described in [11] has three layers of neurons with recurrent connections in the local neighborhoods. The dynamics of the network emulates the diffusion process. Most of the known neural network approaches require, however, full knowledge of environment and can be applied only

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for a stationary domain. Besides that, optimality of the path is often left out of consideration. For a non-stationary domain, a topologically-organized Hopfield-like neural network for dynamic trajectory generation has been proposed in [15] and improved recently in [16], but some additional efforts are required for tuning the network parameters. In this paper we present a novel neural network dynamics for finding a path in a dynamic world. The model is based in interweaving manner on three paradigms, (a) the notation of configuration space as a framework for a flexible object representation [18]; (b) potential field building, which is a generic and elegant method for formation/reconstruction of a path; and, (c) a wave expansion mechanism, that guarantees an efficient construction of the potential field. In comparison with our previous results in [19], the network dynamics has been reconsidered, simplified, and yields now shorter and smoother paths. The model has been simulated and tested in the context of autonomous path planning and exploration for various types of dynamical changes in the environment, and has demonstrated efficient and effective path generation capabilities. The paper is organized as follows. In section 2, we describe the general idea of the proposed algorithm and give a formalization of the problem. Section 3 contains the description of the neural network model. We illustrate simulation results in section 4 and conclude with a discussion in section 5. II. THE PROPOSED ALGORITHM A. The General Idea The original version of the distance transform algorithm was presented first in [20] and then exploited extensively for path planning and navigation tasks in a stationary domain (see in [21]-[23]). In the essence of this algorithm lies the idea of distance propagation in the workspace around the goal position, such that the value of a cell after application of the algorithm corresponds to the cost of the path to the goal (for more details see [20], [21]). The path itself is found by following the steepest descent with respect to the calculated distance values. One could notice, that the idea of distance transform is very similar to the generation of discretized numerical potential fields (see, e.g., [17] and [24]). So, in [17] the model of a wave expansion neural network has been proposed, that computes a distance transform (named ”grid potentials”) over a discretized

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B. Formalization of the Problem Without loss of generality, we can define the configuration space    to be a regularly discretized hypercube, where is the number of DOFs of a robot. For a robot in  the starting and the final configurations, denoted accordingly  and  , are defined. Suppose at the time   , there is a number  of obstacles (i.e. of forbidden configurations) in  . At that moment of time, positions of all obstacles in  form the obstacle region                    !  , where the obstacle coordi  nates in  are denoted by vectors            ! , "$#&%'#($ . Let )*   ! + ,-    !     ,    ! ! define the configuration of a robot in  at the time   . The task is to find a safe (i.e. a collision-free) path ) , that satisfies the conditions: )*  . ! / ,

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 representation of the configuration space of a robot. The methods [17], [21] and [24] can be characterized as ”one-time-gothrough”. This means that the procedure of potential field generation is performed only one time and is finished usually as soon as each position in the whole workspace (or configuration space) a numerical value has been assigned. Thus, these methods can not be applied effectively for a dynamic domain. In [23], e.g., a replanning of the whole path is initiated each time, when the robot encounters an obstacle. However, in an environment populated densely by obstacles or other agents, the replanning of the whole path can become a restricting factor for real-time navigation capabilities of a robot. For planning a path in a time-varying world, we propose a novel neural network model that calculates dynamic distance transform, or dynamic grid potentials. To form the desired grid potentials, a wave-expansion mechanism is used. During the process of potential generation, the activity is spread around the source of excitation, and the minimum value of the generated potential field stays always at the excitory point, which in turn attracts the robot. The most important challenge, distinguishing our model from the approach described in [17], is the proposed neural network dynamics, which makes an effective combination of (1) repetitive wave expansions, and (2) rules to cope with dynamically-generated waves of neural activity. These rules are based on a set of threshold-like functions and are included into the network dynamics to ensure the proper formation of a dynamic distance transform and to guarantee that a robot will move only along a safe route. To provide the repetitive wave expansions, a regular excitation source is fed at the target neuron. This results in origination at each time step of a new wave of neural activity in the network field. Neural activity, therefore, changes locally, while propagating through the network field, and adapts to the dynamical status of environment. Since in the case of a stationary environment, wave fronts yield paths, which are optimal in a  metric (see [17]), dynamical paths, which are generated by the proposed model, also tend to keep such optimality. Consequently, longer paths to the target are cut off automatically by the algorithm.

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