Finite-time state-dependent Riccati equation regulation of anthropomorphic dual-arm space manipulator system in free-flying conditions

This paper introduces a novel approach for regulating the pose of a free-flying dual -arm anthropomorphic space manipulator system (SMS) using a finite -time state-dependent Riccati equation (SDRE) controller. The proposed system finds applications in on-orbit satellite inspection, servicing, space structure assembly, and debris manipulation. The dual -arm SMS presented in this work consists of two 7 degrees of freedom (DoF) robotic arms mounted on a free-flying spacecraft, resulting in a complex 20-DoF system. Due to the high number of DoFs, advanced controller design and efficient computations are necessary. The finite -time SDRE controller relies on the state-dependent coefficient (SDC) parameterization matrices, which are nonlinear apparent linearizations of the dynamics. Conventionally, the computation of SDC matrices is offline and relies on the a priori derivation of the analytical equations governing the dynamics of the system. However, this strategy becomes computationally impractical for high DoF plants. To overcome this issue and deliver a more viable solution, a numerical method to construct and update the SDC matrices at each time step is presented. This approach relies on a screw-theory-based recursive Newton-Euler algorithm designed to reconstruct the manipulator inertia and Coriolis matrices. These quantities are the building blocks of the SDC parameters used in the synthesis of the SDRE controller. Simulation results demonstrate the performances of the finite -time SDRE controller augmented with the online update of the state-dependent coefficients.