Model reference adaptive state-dependent Riccati equation control of nonlinear uncertain systems: Regulation and tracking of free-floating space manipulators

Abstract

This work proposes a model reference adaptive state-dependent Riccati equation (SDRE) controller for nonlinear time-invariant systems considering uncertainty in the plant. The SDRE is vulnerable to uncertainty of nonlinear model, hence the adaptive structure is to compensate for the difference between a reference model and a real uncertain system. The application of the proposed method is dedicated to controlling a free-floating space manipulator (FFSM), a robotics system with a base in two modes: an inactive (no actuation or thrust) state, and a base reaction torque mode. A non-actuated heavy base FFSM probably performs a regulation or a tracking task precisely though that might not be a good solution. A new design is proposed for FFSM control: a heavy base is selected for base of a reference model and the uncertain system with proper weight of base will follow the reference system; and considering three motors for rotating back the base when it reorients from initial position. The new design has improved the precision of the FFSM and reduced the weight of the robot. A planar two degree-of-freedom and a 3D Stanford arm were modeled, simulated and analyzed to assess the performance of the proposed structure and adaptive SDRE controller; that successfully confirmed the claimed expectations.