Higher order method for non linear equations resolution: application to mobile robot control

In this paper a novel higher order method for the resolution of non linear equations is proposed. The method is based on the embedded-relaxed approach in which the dimension of the resolution space is augmented and the new dimension is used to compute a direction toward the solution such that the method converges with higher order with respect to classical methods such as Newton´s. The proposed method converges with order n + 1 for augmented resolution space of dimension n <; 6. The proof with n = 2 and 3 is reported in the paper. We conjecture that this is true for any n but the proof is still under development. Finally, the proposed method is applied to the case-study of mobile robot navigation among obstacles. The robot motion planning may be solved with the proposed method in different ways. In particular, two different possible applications of the method are proposed for the navigation along with obstacles and a local minima escape strategy is also proposed.