The problem of collision avoidance among mobile robots moving along crossing and joining paths is formulated as a motion planning problem in terms of the velocity vector modification. In this paper, a local approach based on a nonlinear programming is applied to solve this problem. Here, the velocity vector constraint for robots are set up using the relative position and velocity information of neighboring robots. The desired velocity vector, which enables robots to navigate without collision, is given as the optimal solution of objective function under this velocity vector constraint. This method is implemented using both experimental robots system and computer simulated one. From the results, it is shown that the experimental robots achieves acceptable performance both in case of crossing and joinig. The feasibility and effectiveness of our method are also discussed through the simulation results.