Optimal Control of Free-Floating Spin-Stabilized Space Robotic Systems

Future robotic manipulators mounted on small satellites are expected to perform important tasks in space, like servicing other satellites or automating extravehicular activities on a space station. In a free-floating space manipulator, the motion of the manipulator affects the carrier satellite’s position and attitude. Spin-stabilization improves the system performance, but further complicates the dynamics. The combination of satellite and multi-link manipulator is modeled as a rigid multi-body system. A Maximum Principle based approach is used to calculate optimal reference trajectories with high precision. To convert the optimal control problem into a nonlinear multi-point boundary value problem, complicated adjoint differential equations have to be formulated and the full apparatus of optimal control theory has to be applied. For that, an accurate and efficient access to first- and higher-order derivatives is crucial. The special modeling approach described in this paper allows it to generate all the derivative information in a structured and efficient way. Nonlinear state and control constraints are treated without simplification by transforming them into linear equations; they do not have to be calculated analytically. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS.