This paper proposes a novel approach for optimizing feasible trajectories for nonholonomic systems. The method is iterative and based on the perturbation of the input functions of the system along the trajectory. The input functions are perturbed in such a way that a criterion relative to the path is minimized. We briefly present two applications of the method: one in trajectory optimization for complex nonholonomic systems and one in reactive obstacle avoidance for multi-body wheeled mobile robots. In both cases, the criterion to optimize is related to the distance to obstacles. The method thus modifies the current trajectory in order to make it maximize the distance to obstacles, while keeping the kinematic constraints satisfied at any time
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