  The travelling salesman problem (TSP) of space trajectory design is
complicated by its complex structure design space. The graph based tree search
and stochastic seeding combinatorial approaches are commonly employed to tackle
the time-dependent TSP due to their combinatorial nature. In this paper, a new
continuous optimization strategy for the mixed integer combinatorial problem is
proposed. The space trajectory combinatorial problem is tackled using
continuous gradient based method. A continuous mapping technique is developed
to map the integer type ID of targets on the sequence to a set of continuous
design variables. Expected flyby targets are introduced as references and used
as priori to select the candidate target to fly by. Bayesian based analysis is
employed to model accumulated posterior of the sequence and a new objective
function with quadratic form constraints is constructed. The new introduced
auxiliary design variables of expected targets together with the original
design variables are set to be optimized. A gradient based optimizer is used to
search optimal sequence parameter. Performances of the proposed algorithm are
demonstrated through a multiple debris rendezvous problem and a static TSP
benchmark.
