Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

Abstract

In this paper an optimisation algorithm based on Differential dynamic programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution. © Springer Science+Business Media B.V. 2009

A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

“…Among them we can find the classic Lagrangian multiplier method [36,37,50], the penalty method [40,[51][52][53][54], and the augmented Lagrangian method [55][56][57]. Moreover, another approach is to use active set quadratic programming methods at each stage to perform minimization while satisfying stage constraints to the first order [36,[58][59][60].…”

GPU based generation of state transition models using simulations for unmanned surface vehicle trajectory planning

“…In model predictive control, the trajectory planning problem is posed again as an optimization problem, but optimized over finite horizon. This way the solution obtained is suboptimal but takes lesser computation time than optimizing over infinite horizon [55,56,57].…”

A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 2: Application

“…GTOC4 is therefore a good test case for the multi-phase formulation of HDDP. The spacecraft has a constant specific impulse I sp of 3000 s and its maximum thrust is 0.2 N. 4 The initial mass of the spacecraft is 1500 kg and its dry mass is 500 kg. The spacecraft must launch from Earth with a departure excess velocity no greater than 4.0 km/s in magnitude, but with an unconstrained direction.…”

“…HDDP includes several standard nonlinear programming techniques (augmented Lagrangian, trust region, active set) to facilitate the inclusion of constraints in the formulation and increase robustness. In addition, HDDP is based on a state transition matrix formulation which allows for a decoupling of the dynamics from the optimization, as opposed to other modern DDP variants [3,4].…”