Neural Predictive Control for Mobile Robot Navigation in a Partially Structured Static Environment

8125 8126 8127 8128 NSF f(x) = L 9i(X) + 19i(X)1 i=1 is zero inside the convex region and increases linearly out of it, as the distance to the frontier is augmented. N S F is the number of segments of the obstacle frontier. The following potential function is used: 1 Pevx(x) = [8 + f(x)]-1 = --N-S-F------ 8 + L (9i(X) + 19i(X)I) i=1 where 8 is a small constant that limits the value of Pcvx(x) inside the convex region. Pevx(x) reaches its maximum value 8- 1 inside the region occupied by the obstacle, and decreases with the distance between the robot and the obstacle. A graphic example of this function is shown in figure 5, where two rectangular shape static obstacles are present in the proximity of the robot. Fig. 5. Convex regions potential function. Potential function for a concave polygon. A concave region will be described by a set of inequalities vex) ::::: 0, v E Lm, x E IR n The potential function used in this case is 1 Peel' ( x) = 8 + () gee" X where 8 is a small constant and 9ccv(X) is the minimum of the distances between the robot position and every straight line that defines the obstacle frontier. This function has the same characteristics as Peex(x). An example of cost function J, for a one step prediction horizon (which is the only one that can be graphically represented), is shown in figure 6. In this figure the value of J for different left and right wheel velocities is represented. The existence of a rectangular obstacle can be noticed. Furthermore, the influence of the non linear prediction model can be observed. Fig. 6. Objetive function J. 3. THE NEURAL NETWORK APPROACH As was mentioned before, the minimization of the cost function J has to be carried out by a numerical optimization method which requires too much computation to be used in real time. A Neural Network solution is proposed, which guarantees real time for the robot control. Neural Network approaches for robot guidance has been proposed by other researchers (Pomerlau, 1990), (Meng and Kak, 1993). The modules of the control scheme used in this work (see figure 7) are: Fig. 7. Predictive neural network scheme for mobile robot navigation. • Artificial neural network controller. The ANN architecture chosen here is a Multilayer Perceptron, with one hidden layer (see figure 8). The input layer consists of twelve neurons (see figure 8). The first two inputs correspond to the previous linear and angular velocities of the robot. The next three inputs are associated to the parametrization of the desired trajectory over the prediction horizon. In order to reduce the number of inputs, the parameters given to the network are the distance d from the robot guide point to the path, the angle 8 between the robot heading and the path orientation and an average of the inverse of the curva- 8129 8130