Optimal control of a rigid body based on Hamel’s variational integrators

Based on the discrete mechanics and optimal control framework, Hamel’s variational integrators are employed to solve the fuel-optimal and time-optimal control problems for a single rigid body. The optimal control problem is discretized via the discrete d’Alembert-Lagrange principle, and the corresponding discrete necessary conditions for optimality are derived. The sensitivity matrix is constructed and solved using the Newton-Armijo iteration method. This approach effectively linearizes the nonlinear problem, enhancing computational efficiency and ease of implementation. Finally, two numerical examples involving the optimal control of spacecraft orbital transfers are presented to verify the effectiveness and applicability of the proposed method.