Efficient Numerical Trends for Nonlinear Model Predictive Control of a Rigid Body Spacecraft on SE(3)

In this paper, nonlinear model predictive control of mechanical systems evolving on Lie group SE(3) is studied. Discrete-time equations of motion referred to as LGVI are used in order to extract the necessary conditions of optimality. Then, TPBVP equations are solved using sensitivity derivatives to find Lagrange multipliers. A fast solver for NMPC is used to solve the problem. Extracting necessary conditions of optimality based on LGVI leads to group structure preservation and good convergence behavior of the system under study. Subsequently, some modifications based on removing non-essential nonlinear terms are applied to sensitivity derivatives and TPBVP equations, aiming to reduce the computation time of solving the NMPC problem. The presented method is applied on a spacecraft evolving on SE(3) with constraints as an example and the simulation results show the efficiency of the proposed method. Also, it is shown that introducing the aforementioned modifications reduces the computation time by a considerable amount.