Rapid optimization of continuous trajectory for multi-target exploration propelled by electric sails

As an innovative spacecraft propellantless propulsion technology, the electric sail can generate electric fields that interact with the solar wind, generating continuous propulsive thrust. However, unlike conventional electric thrusters, the thrust vector of the electric sail is constrained, and the attitude cannot be adjusted quickly. Consequently, the position and velocity of each flight trajectory at the connecting node and the direction of propulsion acceleration must be continuous. In this study, the continuous trajectory optimization of the electric sail–based probe in multi-target exploration is investigated. An integrative Bezier shaping approach (IBSA) is proposed to realize the rapid optimization of a multi-target exploration trajectory with continuous acceleration. The relationship between boundary constraints, intermediate constraints, and Bezier basis function coefficients is derived, transforming the original continuous optimal control problem of multiple stages into a problem of nonlinear programming that naturally satisfies the boundary and intermediate constraints. Numerical simulation results demonstrate that the IBSA can obtain a better interplanetary trajectory with a shorter calculation time than that obtained with the traditional Bezier shaping approach using piecewise optimization. Furthermore, the simulation results are successfully applied to the initial value estimation of the Gauss pseudospectral method (GPM). Compared with the GPM, the proposed shaping approach differs from the objective function by approximately 2%–6%, but requires approximately 1.5% of the computational time. During the preliminary mission design stage, the IBSA can be used for rapid feasibility assessments of different electric sail–based probe mission profiles.