Optimal Reconfiguration Trajectory of Multi-satellite Electromagnetic Formation System

The multi-satellite electromagnetic formation flight system is nonlinear and strongly coupled, which makes modeling and optimization challenging. To simplify electromagnetic force evaluation and dynamics modeling, we introduce a reference frame consistent with each satellite body frame, in which the electromagnetic dipoles and electromagnetic forces are represented as two-dimensional vectors. Then, the maneuver time is divided into time intervals, and different satellite sets are activated in each interval, converting the multi-satellite formation reconfiguration problem into an optimal trajectory problem of each two-satellite subsystem. To this end, a token-based dynamic programming method with a switching penalty of active satellite sets is proposed to determine the sequence of satellite sets participating in each time interval, thereby enabling all satellites to reach their desired states. For the two-satellite subsystem with the objectives of minimizing maneuver time and energy consumption, the Gauss pseudo-spectral method is employed to generate the optimal reconfiguration trajectory. Numerical simulations verify the effectiveness of the proposed optimization method.