Differential-algebraic equation-based model predictive control for trajectory tracking of spacecraft-mounted continuum manipulators

Spacecraft-mounted continuum manipulators (SMCMs) exhibit great potential for performing dexterous operations in unstructured environments due to their inherent compliance and dexterity. However, the dynamic model of the rigid-flexible coupling SMCM is highly nonlinear and typically formulated as a set of implicit differential-algebraic equations (DAEs), posing significant challenges for precise trajectory tracking control. This paper proposes a novel model predictive control (MPC) framework specifically designed for generic DAEs to achieve precise trajectory tracking of the SMCM under uncertain disturbances and input limitations. The DAE model of the SMCM is discretized into a set of nonlinear algebraic equations. By performing implicit differentiation of these equations with respect to the system state, the state transition matrix (STM) for the DAE model is derived. The optimal control action for the SMCM can be further determined based on the derived STM. Additionally, nonlinear complementary functions are introduced to address the issue of input limitations, allowing the problem of determining the optimal control sequence to be equivalently transformed into a set of nonlinear algebraic equations for solving. Numerical simulations demonstrate that the proposed approach can achieve precise trajectory tracking of the SMCM while strictly adhering to input limitations.