Abstract This paper investigates the numerical computation of minimum-fuel low-thrust trajectories subject to bound constraints on the duration of thrust and coast arcs. First, an optimal control problem is formulated. The constraints on thrust and coast periods are written as a single discontinuous bound constraint on the control norm depending on time and on a set of free parameters considered as additional state variables. Then, the constraint is regularized and the problem is converted into an equivalent one where the norm of the control is simply upper-bounded by one. Finally, the latter problem is solved efficiently through an indirect single shooting algorithm. The great advantage of this approach is that it does not require knowing beforehand the control switching profile. Moreover, it has the ability to generate multiple suboptimal solutions in addition to the optimal one, thus offering more options for mission design. Numerical results are provided to illustrate the interest and effectiveness of the method. An electric small satellite rendezvous problem in circular orbit is considered. The fuel-optimal control of the constrained problem as well as several suboptimal controls are computed and analyzed, each of which showing a different number of thrust and coast arcs.

Highlights • A set of parameters, considered as additional state variables, is introduced. • Thrust and coast times constraints are written as a constraint on the control norm. • A regularization method is used to make the constraint continuously differentiable. • The approach converges to the optimal solution of the constrained problem. • No prior information on the structure of the control law is required.