Application and Analysis of Bounded-Impulse Trajectory Models with Analytic Gradients

Abstract

In the companion paper, analytic methods were presented for computing the Jacobian entries for two-sided direct shooting trajectory models that utilize the bounded-impulse approximation. In this paper we discuss practical implementation considerations. Efficient computation of the mathematical components required to compute the partials is discussed and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cut-off events that result in non-smooth derivatives. The challenges associated with incorporating the SPICE ephemeris system into an optimization framework are discussed and an alternative is presented that results in smooth time partials.Application problems illustrate the benefits of employing analytic Jacobian calculations vs. using the method of finite differences. The importance of accurately modeling hardware and operational constraints at the preliminary design stage, and the benefits of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored.

A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

“…For these representative quartic polynomial surrogate models given in Eqs. (5) and (6), Table 1 summarizes the surrogate model coefficients of six SEP engines [54,43], which we adopt for the present study. The input power is in kilowatts and the mass flow rate is in milligram/s.…”

“…In the heliocentric phase of flight, the spacecraft motion is predominantly governed by the gravitational attraction of the Sun. In addition, the space- NEXT TT10 (High-Thrust) NSTAR Figure 1: Performance of engines listed in Table 1 over their admissible power ranges [43,54].…”

“…There are multiple strategies to specify operational logic for multi-engine spacecraft [43], (e.g., 1) the maximum number of active engines, and 2) the minimum number of active engines). We focus our attention to a particular case where each engine needs to be switched off or operate only either at its maximum or minimum power setting, i.e., P en ∈ {0, P min , P max }.…”

“…In Eq. ( 4), σ denotes the efficiency decay rate of the solar arrays measured as a fractional rate per year (usually 0.02 to 0.04 per year) and τ (t) denotes elapsed time from the launch time measured in years [43]. For numerical results in this paper, P s/c = P ppu and P ppu is assumed to be the required power to operate all spacecraft sub-systems other than the engine(s).…”

“…However, the actual performance of SEP systems depends on the input power, which has to be taken into consideration for obtaining more realistic trajectories [31,32,33,34,35,36,37,38,39,40]. More accurate knowledge of the capability of a spacecraft to change its trajectory is obtained when more realistic models of the SEP system and dynamics are used [41,42,43].…”