The design of the mobile robot path is important when obstacles are present in the environment. In the present study, the theory of optimal control for path design and obstacle avoidance via simultaneous minimization of the time and kinetic energy is proposed. Nonlinear equations of robot motion without simplification are considered in optimum control problems, and in order to prevent collisions, the potential functions are utilized. In the next phase, the cost function is proposed that includes velocity inputs, time, and the potential function for obstacle avoidance, in which the nonlinear equation of the motion of the mobile robot is deemed as a constraint. The final equations are numerically solved, and the capability and effectiveness of the presented method will be presented via different simulations on the mobile robot.
Tractor-trailer wheeled platforms are recognized as articulated robotic platforms contain a frontrunner active mobile platform (the tractor) pulling one or more passive ones (the trailers). These categories of mobile platforms are broadly implemented in cooperative activities thanks to their novel features like as: maximum load carrying capacity and minimum energy consumption. The presented article deals with path tracking optimization of the tractor-trailer moving platform employing indirect method of the optimal control. Firstly, the nonlinear motion relations of the modular platform are obtained pertaining to kinematic constraints and inertia characteristics of wheels. Then, the obtained dynamic equations are supposed as constraints of the problem and an appropriate objective criterion is determined for the optimal trajectory tracking. Then, the problem is solved and various simulations are presented. The obtained results reveal proficiency and applicability of the proposed procedure for the optimal tracking of the tractor-trailer wheeled mobile platforms.
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