Optimal Path Tracking by Industrial Mobile Robot using Boundary Value Problem and Nonlinear Control Method

In this study, the optimal path tracking of a mobile robot is accomplished using open-loop optimal control theory and closed-loop nonlinear control. Initially, the dynamic equations of robot are derived and utilized as constraints in the context of optimal control problems. To minimize the required torque for robot movement, cost functions are formulated, and the Pontryagin's minimum principle is employed to solve the optimal control problems. In this research, by considering the problem of finding the optimal path as a boundary value problem, optimal states are computed, and the resulting linear and angular velocities are taken as inputs for the mobile robot. Considering the errors encountered in the optimal path tracking by the robot, the utilization of nonlinear control theory for regulating the linear and angular velocities at each moment, based on the error between position and orientation, as well as their optimal states, becomes crucial. By applying this controller, the mentioned velocities are managed, resulting in improved navigation with reduced error. Ultimately, the optimal paths traversed by the robot are compared for both open-loop and closed-loop configurations.