Optimal control for far-distance rapid cooperative rendezvous

Abstract

This study investigated the far-distance cooperative rendezvous problem for two spacecrafts. The orbital dynamics equations were represented based on the orbital elements with an improved vernal equinox and were normalized. Pontryagin's extremum principle was introduced into the dynamics equations and the co-state equations were obtained. A performance evaluation function was created by particle swarm optimization algorithm based on simulated annealing. The convergent co-state initial vector was obtained using an improved particle swarm optimization algorithm. The initial vector was set as the initial value for optimization and a rapid small-population genetic algorithm was applied, before the approximate global optimum was obtained rapidly. The fine adjustment of the search process was performed based on sequential quadratic programming and the results were sufficiently precise. The process of optimization was simulated for problems that involved far-distance coplanar cooperative rendezvous and active-passive rendezvous, which showed that cooperative rendezvous had more advantages than active-passive rendezvous in terms of fuel saving and time.

Optimization for far-distance and fuel-limited cooperative rendezvous between two coplanar spacecraft based on Lambert method

“…When the difference between the initial mass of two spacecraft is too large, a cooperative rendezvous will degenerate to an active–passive rendezvous and fuel consumption will automatically centralize to the lighter one. 4 In order to make sure that fuel consumption will be evenly burdened by two spacecraft, the standard deviation of fuel consumption of two spacecraft, noted as Δmsd is introduced. Objective function is revised as follows where Δm1 and Δm2 are fuel consumption of two spacecraft and λ is a coefficient.…”

“…Some former studies gave fuel-optimal results of cooperative rendezvous between two spacecraft under continuous thrust. [4][5][6][7] Continuous thrust is more appropriate to fardistance orbit maneuver because it has been shown that far-distance orbit maneuver under high continuous thrust is less time consuming than impulse thrust. [8][9][10] However, continuous thrust has not been adopted in practical space missions yet owing to the limitation of engine technology.…”

“…6,7,21,22 While solving optimization problems of cooperative rendezvous between two spacecraft, optimization results acquired by combined optimization algorithms show better stability and optimality. 4 Feng and co-workers [4][5][6][7] combined population-based evolutionary algorithms, for example GA, PSO, PSODE (a hybrid algorithm of PSO and different evolution), and QPSO, together with sequential quadratic programming (SQP) while investigating optimization problems of cooperative rendezvous between two spacecraft under continuous thrust. The reason why SQP, the second-step algorithm, is selected to combine with those optimization algorithms is its extraordinary capability of local search, which compensates for the shortage of first-step algorithms.…”

Optimization control for the far-distance rapid cooperative rendezvous of spacecraft with different masses

“…By adopting a separation target function and constraints method for the constraint optimization problem, the original problem is converted as follows: (17) where i points to the i-th particle, fitness(i) corresponds to the target function value sought, and voilation(i) corresponds to the problem constraint, jointly constructed by all the constraints, being sought; this value reflects the degree of closeness to the constraint boundary of particle i. Together, these two functions are the particle fitness functions.…”

“…Therefore, the control process for spacecraft cooperative rendezvous has begun to garner more research attention. Past research on spacecraft cooperative rendezvous was primarily based on a scenario in which two spacecraft had equivalent masses [8,10,11,15,17]. In actual space operation, however, there are usually differences in the masses of the two spacecraft; at times, the differences can be relatively large.…”