An Uncertain Optimal Factorization of Cooperative Manipulators for Robust Optimal Control Schemes

This paper presents two robust optimal controllers for Cooperative Manipulators (CoMans) holding an object on the basis of a modified factorization approach. Due to advantages such as: simplicity, flexibility, systematic procedure and not canceling nonlinearities, the State-Dependent Riccati Equation (SDRE) has been chosen as a basis for robust controllers design in the literature. For developing robust optimal controllers via SDRE, the first step is to obtain uncertain State-Dependent Coefficient (SDC) representation. To design robust optimal schemes for some systems such as CoMans, some terms such as gravity, friction and the external forces have been neglected in the uncertain SDC structure and added to the control input. This study, proposes two robust optimal controllers for CoMans carrying a load: Mixing SDRE-SMC (MiSS) and transformed robust to optimal controller where the pre-mentioned terms can be included in the uncertain SDC representation called uncertain optimal SDC. Simulation results are provided to easily verify the satisfactory performance of both schemes using uncertain optimal SDC and superiority of the transformed robust to optimal control versus MiSS in trajectory tracking of CoMans.