Robust control approach for robot manipulators in the presence of uncertain dynamics due to the unknown load. The robust control was formulated in an equivalent optimal control framework by incorporating the uncertainty bounds into the cost functional such that both robust stability and optimality can be achieved. The optimal method of θ-D is used to obtain the optimal feedback control law. The optimal method θ-D is based on the ap-proximate solution of the Hamilton–Jacobi–Bellman equation (HJB) through the perturbation process. The solu-tion of the HJB equation can be transformed into a series of algebraic Lyapunov equations. Added a part of dis-turbances to the system cost function to ensure optimality and achieve global stability. Adjustable parameters in the system disturbance components allow for flexible adjustment of system performance. The resulting problem of nonlinear optimal control was solved by the θ-D method, which provides an approximate analytical feedback solution. The simulation results showed that this new robust control is able to drive the manipulator to the de-sired position precisely under large load variations. This robust control method with an optimal control solution can be applied to a wide range of nonlinear dynamic systems with uncertainties.

Authors: M. P. Belov, D. K. Tran, Hu. Ph. Tran

Direction: Electrical Engineering

Keywords: Hamilton–Jacobi–Bellman, optimal method θ-D, robust control, Riccati equation

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