Flatness-based trajectory planning for electromagnetic spacecraft proximity et operations in elliptical orbits

The inter-craft electromagnetic force, generated by magnetic coils equipped on all neighboring spacecraft, enables a novel propulsion mode without propellant consumption. The paper investigates a trajectory planning algorithm based on differential flatness for spacecraft proximity operations in elliptical orbits using the inter craft electromagnetic forces. Firstly, the time-energy optimal trajectory planning problem is formulated into the desired electromagnetic control acceleration optimization and magnetic dipoles assignment. Secondly, utilizing the system's differential flatness property, the original trajectory planning problem could be mapped into the flat output space, eliminating the differential equations and reducing the dimensionality of the planning space. Then the resulted flat output planning problem is further parameterized with a mapped Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques in order to decrease the side effect of the differentiation matrix's ill-conditioning. Finally, numerical simulations for a three spacecraft electromagnetic formation reconfiguration mission show that the proposed algorithm is feasible and efficient, compared with the Radau pseudospectral method.