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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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