The objective of the present work is to find an optimal path for a mobile of four wheels. The kinematic model related to the studied engine is a nonlinear system, where several nonlinear objective functions must be optimized in a conflicting situation. Under these circumstances, we propose to apply the algorithm studied in [13] for the planification of this optimal trajectory. For more efficiency, we took advantage of artificial neural networks parallelism by using neurons commonly used seen in [14], [13] and some other new created ones. Also a Matlab M. Khouil, I. Sanou, M. Mestari and A. Aitelmahjoub simulation has been programmed in the last section toward observing the convergence of the results obtained.

In this paper, we discuss the problem of safe navigation by solving a non-linear model for a four-wheel robot while avoiding the upcoming obstacles that may cross its path using the Decomposition Coordination Method (DC). The method consists of first, choosing a non-linear system with the associated objective functions to optimize. Then we carry on the resolution of the model using the Decomposition Coordination Method, which allows the non-linearity of the model to be handled locally and ensures coordination through the use of the Lagrange multipliers. An obstacle-avoidance algorithm is presented thus offering a collision-free solution. A numerical application is given to concert the efficiency of the method employed herein along with the simulation results.

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