Técnicas de otimização para controle e operação de máquinas inteligentes

Abstract

The use of robotic systems in various industrial and logistics situations is increasing. Methods that coordinate the activities of the robots are essential to obtain synchronized and free of collision possibilities movements. One manner to coordinate them is through optimization methods. This work focuses on an approach based on Nonlinear Programming to determine optimal velocity profiles of robots with previously specified paths. The methodology is applied to mobile robots and manipulators models. Despite the constructive differences, in general, the same optimization formulation can be shared for both cases. The arrangement is based on the maximization of the square of the time difference in which the robots reach the same point of collision. Notwithstanding a large number of papers found in the literature involving the subject, approaches related to a nonlinear modeling of the problem are scarce. The advantage of the method lies in the easiness of representing nonlinearities of the system, such as speed, acceleration and torque limitations of robots. In addition, the formulation and resolution complexity is reduced compared to other methods encompassing the processing of integer variables. The method also encompasses situations where robots may collide in the form of segments. In this sense, an approach based on the inclusion of fictitious points to represent such stretches is determined. The tests were realized in different mobile robot and manipulators systems. The results proved the efficiency of the proposed methodology, finding optimal speed profiles that determine trajectories without accidents. Comparisons with Mixed Integer Linear Programming, widely used for this purpose, proved the superiority of the proposed technique with respect to the complexity and modeling of nonlinearities, bringing the model closer to real systems.