Predictive control and stabilization of nonholonomic formations with integrated spline-path planning

Abstract

A path planning in the space of multinominals integrated into a model predictive control mechanism for driving formations of autonomous mobile robots is presented in this paper. The proposed approach is designed to stabilize the formations in desired shapes, and to navigate the group into a final position in a partly known environment with dynamic obstacles. In addition, the system provides inter-vehicle coordination and collision avoidance in the event of failure of a team member. The method is aimed at reaching the final position of the formation in the desired shape, but it enables to change temporarily this shape if it is enforced by the environment (in narrow corridors, on response to an impending collision with obstacles and faulty team members, etc.). This autonomous emergent behaviour increases the robustness of the system and its usability. It enables a proper compromise to be found between the formation driving requirement and the effort to fulfil the mission objective, i.e., to move the group from the current state into the required position. In this paper, the convergence of the method and the requirements for stability are shown on the basis of the results of the Lyapunov theorems of stability. These theoretical achievements imply constraints on the applicability of the system, which are verified in numerical simulations and in various tests with real autonomous robots. The performances of the entire system and of independent sub-systems in various formation driving scenarios are also shown in these tests.