  We propose a reachability approach for infinite and finite horizon
multi-objective optimization problems for low-thrust spacecraft trajectory
design. The main advantage of the proposed method is that the Pareto front can
be efficiently constructed from the zero level set of the solution to a
Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by
applying it to a low-thrust spacecraft trajectory design problem. By deriving
the analytic expression for the Hamiltonian and the optimal control policy, we
are able to efficiently compute the backward reachable set and reconstruct the
optimal trajectories. Furthermore, we show that any reconstructed trajectory
will be guaranteed to be weakly Pareto optimal. The proposed method can be used
as a benchmark for future research of applying reachability analysis to
low-thrust spacecraft trajectory design.
