Optimal Control Design for a Group of Mobile Robots with Uncertainties

The paper considers the problem of optimal control design in the presence of uncertainties. Uncertainties of various nature are almost always appear in real objects. They can be caused by inaccuracy of the model, noise, uncertainty of the initial conditions and so on. It is proposed to use a new two-stage approach of synthesized optimal control, which at the first stage mathematically solves the problem of synthesis of the stabilization system and then the optimal trajectory of motion for the updated stabilized object is searched for. The implementation of such optimal control over a stabilized object makes it possible to level out model inaccuracies or other uncertainties much better than directly solving the optimal control problem, which is shown in a comparative example of solving the optimal control problem for a group of four mobile robots moving in a complex environment with phase constraints.