A comparison of three neural networks for building local grid maps

This paper addresses the local grid map-building problem. Sensor readings are interpreted using a feedforward neural network, and a Bayesian rule is used to update the occupancy probabilities of the grid cells. A comparison of three neural network configurations is made in the map building of indoor environments, using the sonar sensors of the Nomad 200 simulator. The architecture with best results in simulations was tested in a real mobile robot. Key-words: Mobile Robots, Local Grid Maps, Neural Networks. mapping and potential field path-planning techniques. Another way of building maps was presented in [11], where occupancy grid is associated with fuzzy logic theory. Chow et al. proposed in [3] a probabilistic grid mapping where the probability distribution function is tuned by fuzzy rules. A method to build topological maps using grid-based maps is presented in [12] where the information of environment is acquired by sonars and stereovision. 2 LOCAL MAP-BUILDING PROCESS Figure 1 shows the map building architecture. The updating process of a given cell (x,y) starts with the Sensors Selector module that chooses two (or three) sensors with orientations closest to the orientation of the cell. The range readings of the selected sensors are provided to the neural network. The function of the neural network (figure 2) is to provide the conditional probability P(cxy|o) given actual sensory observation o. The cell is finally updated by using the Bayes update formula. In next sub-sections this procedure is explained in more detail. 2.1 Neural Networks In the map building architecture a feedforward neural network is used to determine de probability P(cxy|o) of a cell (x,y) being occupied given actual sensory observation o. In this paper we compare the map building method using three different feedfoward neural networks: NN1, NN2 and NN3. For a given cell (x,y), the input layer of the neural networks consists of: NN1 (Figure 2a) 1) The observation o1=(s1, s2) of the two sensors oriented in the direction of cell (x,y); 2) The distance of the center of the cell (x,y) with respect to the mobile robot coordinate system, as illustrated in the example of figure 3 for a circular mobile robot used in the experiments. NN2 (Figure 2b) 1) The observation o2=(s1, s2, s3) of the three sensors oriented in the direction of cell (x,y); 2) The distance of the center of the cell (x,y) with respect to the mobile robot coordinate system. NN3 (Figure 2c) 1) The observation o3=(s1, s2) of the two sensors oriented in the direction of cell (x,y); 2) The polar coordinates (distance and angle) of the center of the cell (x,y) with respect to the mobile robot coordinates system. Therefore, the input layer of the neural network has three nodes when we use two sensors (NN1) and has four nodes if we use three sensors (NN2) or two sensors and the polar coordinates of the center of the cell (NN3). The output layer has only one node which produces P(cxy|o). In each case the network was trained off-line with a back-propagation algorithm [5]. The training examples were generated with the mobile robot simulator. Placing the robot in a known environment, a set of examples was made recording sensor readings at various situations and for adequate ranges according to the cell’s size and the size of the grid maps. After training, the network gives values in the range [0,1] that can be interpreted as probabilities of occupancy. Fig. 1. Map-building architecture. S en so rs