Computational Approach to Optimal Control in Applied Robotics

Abstract

AbstractThe optimal control problem in its classical mathematical formulation is considered. The applied challenge is that the optimal control in the form of function of time cannot be directly applied to a real object because such control is open loop, and any disturbance of the object will lead to the fact that the goal will not be reached, and the value of the criterion will not be optimal. So, engineers stabilize the movement of the real object along the optimal trajectory. However, this approach does not ensure preservation of the optimality of the obtained controls. As a result, the optimal control problem in its classical formulation is less and less solved when creating new robotic devices, while the number of robots is increasing. This work expands the formulation of the optimal control problem, introducing initially the requirement to give the system describing the control object such properties that ensure the stability of solutions. Thus, the optimal control will be calculated already for the new model of the control object, which includes a stabilization system. The approach uses modern machine learning methods of symbolic regression and evolutionary computation. An example of the optimal control problem for a mecanum-wheeled mobile robot is demonstrated.KeywordsOptimal controlStabilizationRobotic systemMachine learning controlSymbolic regressionGenetic algorithm