Space mission trajectory design using low-thrust capabilities is becoming increasingly popular. However, trajectory optimization is a very challenging and time-consuming task. In this paper, we build upon existing shapebased techniques to present an alternative Fourier series approximation for rapid low-thrust-rendezvous/orbitraising trajectory construction with thrust-acceleration constraint-handling capability. The new flexible representation, along with the constraint-handling capability, makes this method a suitable candidate for feasibility assessment of a whole range of trajectories within the given system propulsive budget. In addition, the solutions present opportunities for direct optimization techniques. A key point in the proposed method is its ability to solve problems with a greater number of free parameters than in shape-based methods. Several case studies are presented: simple Earth-Mars rendezvous, rendezvous/orbit raising for low Earth orbit to geostationary orbit, and two phasing problems. Results clearly depict the advantage of the proposed method in handling thrust constraints and its applicability to a wide range of problems.
Nomenclature
AU= astronomical unit, 149,598,000 km -cubic polynomial approximation for r(t) = cubic polynomial approximation for d(t) = tangent hyperbolic approximation for r(t) A'rev = number of revolutions n, = number of Fourier terms for r(t) Hg = numberof Fourier terms for ^(r) r = radius, DU ry = final radius value, DU f-f = final radial velocity, DU/TU r, = initial radius value, DU r, = initial radial velocity, DU/TU T = total time of flight, TU r" = thrust acceleration, DU/TUâ = thmst pointing angle, rad Y = flight-path angle, rad 9 = polar angle, rad 9f = final polar angle, rad Of = final angular velocity, rad/TU 9¡ = initial polar angle, rad 0; = initial angular velocity, rad/TU oo = polar angle between the position vectors, 0 < 6*0 < 2;r, rad ß = gravitational parameter a> = measure of the width of the function, TU/rad