Stochastic Differential Dynamic Programming with Unscented Transform for Low-Thrust Trajectory Design

Tsourdos

Progress in Aerospace Sciences

et al. 2019

110

For most atmospheric or exo-atmospheric spacecraft flight scenarios, a welldesigned trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective

“…Based on this principle, DP calculates the optimal solution for every possible decision variable. Hence, it is highly likely to result in the curse of dimensionality [48].…”

Section: Dynamic Programming-based Methodsmentioning

confidence: 99%

Section: Optimization Algorithmsmentioning

confidence: 99%

A review of optimization techniques in spacecraft flight trajectory design

Tsourdos

Progress in Aerospace Sciences

et al. 2019

110

“…A method based on Taylor polynomials algebra was recently developed to deal with uncertain boundary conditions around a reference trajectory [8] and produce a robust guidance law. In addition, stochastic differential dynamic programming has been applied to space trajectory optimisation with uncertainty with an expected value formulation using the unscented transform [9].…”

Section: Introductionmentioning

confidence: 99%

Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty

et al. 2020

This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets.The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.

AIAA Scitech 2020 Forum

“…The case of a temporary engine failure were investigated by stochastic programming [5,6]. Differential dynamic programming was applied to trajectory optimisation with an expected value formulation for Gaussian-modelled uncertainties [7]. Approaches based on evidence theory to model uncertainty was developed for the robust optimisation of transfers under system and dynamical uncertainties [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Robust Space Trajectory Design using Belief Stochastic Optimal Control

Greco¹,

Campagnola

Vasile³

2020

Self Cite

This paper presents a belief-based formulation and a novel approach for the robust solution of optimal control problems under uncertainty. The introduced formulation, based on the Belief Markov Decision Process model, reformulates the control problem directly in terms of uncertainty distributions, called beliefs, rather than on realisations of the system state. Successively, an approach inspired by navigation analysis is developed to transcribe and solve such problem in the presence of observation windows, employing a polynomial expansion for the dynamical propagation. Finally, the developed method is applied to the robust optimisation of a flyby trajectory of Europa Clipper mission in a scenario characterised by knowledge, execution and observation errors.