S.H. Sadati, K. Alipour, and M. Behroozi
Mobile robots, optimal planning, path planning, dynamics modelling, Ritz method
Mobile robots attracted much of their interest due to their locomotion. In order to make the most out of this mobility feature, it is vital to do a motion planning in the most proper way to make certain that the purpose in a given application is met. Any feasible algorithm or methodology for path/motion planning capable of meeting such application-specific needs is quite welcome. In the present study, the main concern regarding application requirements was to devise and introduce a motion planning method to guarantee system robustness against uncertainties due to any disturbances and inaccuracies in the system dynamics. We have divided the robot motion planning in two different problems: path planning and velocity planning. In the former, use was made of a “modular path planner, each module consisting of pure displacement and pure rotation. In the latter, the problem of velocity planning was transformed into an integrated planning and control one. It is quite imperative that energy be conserved as much as possible within each module of the path. As an open-loop optimal control may suffer from the lack of robustness, and plus the fact that the two-point-boundary-value problem that it leads to may not quite be as simple to solve, we have introduced the use of artificial neural networks (NNs) to close the control loop, hence guaranteeing sufficient robustness for the robot system in use. The conventional numerical methods for functional optimization have some drawbacks in optimization. Hence, as a motive, and in order to avoid such difficulties, the Ritz method as a direct approach in the calculus of variations is proposed to train the NN, thus introducing a robust closed-loop control. In this study, optimization of the sub-motions of the total motion was addressed. Yet, by some proper modification, the proposed algorithm can be generalized for near-optimality of the overall motion. Herein, a combination of optimal Ritz-based method and NN was suggested as a robust motion planning approach for differentially-driven mobile robots.
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