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

Lantoine, Gregory; Russell, Ryan P.

doi:10.1007/s10957-012-0039-0

Cited by 88 publications

(49 citation statements)

References 62 publications

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“…Direct methods convert the optimal-control problem into a nonlinear parameter optimization [nonlinear programming (NLP)] problem with various transcription schemes (e.g., Hermite cubic, cubic polynomial, and orthogonal function approximations) applied to either states or controls, or both states and controls. In addition, an entire class of optimal-control methods exist, which exploit a quadratic localized version of Bellman's dynamic programming, referred to as differential dynamic programming [7][8][9][10][11][12]. The related static/dynamic control approach presented in [8] has been used by NASA to fly the Dawn spacecraft to the asteroids Vesta and Ceres.…”

mentioning

confidence: 99%

Enhanced Smoothing Technique for Indirect Optimization of Minimum-Fuel Low-Thrust Trajectories

Taheri

Kolmanovsky

Atkins³

2016

Journal of Guidance, Control, and Dynamics

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Indirect methods used for solving optimal-control problems, when combined with proper initialization and homotopy approaches, remain attractive for space trajectory optimization, as they are able to achieve fast convergence to a solution of the necessary conditions. In this paper, the extended logarithmic-smoothing technique is revisited and integrated with an indirect method to efficiently generate minimum-fuel time-fixed low-thrust rendezvous trajectories. This approach is considered for three cases, in which equations of motion are expressed in terms of Cartesian, spherical, and modified equinoctial coordinates. In addition, the paper addresses the calculation of the Jacobian matrix of the constraints via an implementation of the state-transition-matrix approach, which avoids the discontinuities of the control along the trajectory. The application of the method to two interplanetary missions from Earth to Mars and to asteroid Dionysus is demonstrated. It is shown that, by exploiting the state transition matrix and the homotopy method, the optimal-control problem becomes amenable to numerical treatment. The numerical results are compared in terms of the percent of converged cases, mean values for final mass, number of iterations and function evaluations, accuracy in satisfying the constraints, and computational time.

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mentioning

confidence: 99%

Enhanced Smoothing Technique for Indirect Optimization of Minimum-Fuel Low-Thrust Trajectories

Taheri

Kolmanovsky

Atkins³

2016

Journal of Guidance, Control, and Dynamics

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“…The DDP method has been successfully applied to calculate the optimal solution of some space missions. For example, in [69,70], a comprehensive theoretical development of the DDP method, along with some practical implementation and numerical evaluation was provided. In [68], a DDP-based optimization strategy was proposed and applied to calculate the rendezvous trajectory to near Earth objects.…”

Section: Dynamic Programming-based Methodsmentioning

confidence: 99%

A review of optimization techniques in spacecraft flight trajectory design

Chai

Tsourdos

Chai

et al. 2019

Progress in Aerospace Sciences

110

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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

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“…2. The low-thrust optimal control problem is solved using the hybrid differential dynamic programming (HDDP) method described in [29,30]. It is noted that the HDDP optimal control solver satisfies both the necessary and sufficient conditions of optimality.…”

Section: Orbit-raising Capabilitymentioning

confidence: 99%

Utilization of Residual Helium to Extend Satellite Lifetimes and Mitigate Space Debris

Walker

Russell

Singh

2012

Journal of Propulsion and Power

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A new electric propulsion device concept takes advantage of residual helium gas that is trapped in the chemical propellant feed system and currently unused at end of life. The helium ion thruster provides additional propellant resources to extend satellite lifetimes and transfer geostationary orbit space assets to ultrasafe disposal orbits. The predicted capability, if fully allotted to the disposal, allows for perigee heights above the geostationary altitude that are one order of magnitude greater than existing international guidelines of 250 km. Furthermore, the proposed helium ion thruster concept makes the classic propellant gauge uncertainty problem moot, as satellite operators could use all of their conventional propellant for nominal station-keeping operations. The helium ion thruster concept therefore mitigates future space debris arising from depleted assets in the geostationary orbit belt through both aggressive orbit raising and depressurization of satellites at end of life. An analysis of the helium ion thruster theoretical performance shows that the device could raise the altitude of an end-of-life 2500 kg, 5 kW spacecraft by 2200 km in two months using 2 kg of residual helium.

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

Cited by 88 publications

References 62 publications

Enhanced Smoothing Technique for Indirect Optimization of Minimum-Fuel Low-Thrust Trajectories

Enhanced Smoothing Technique for Indirect Optimization of Minimum-Fuel Low-Thrust Trajectories

A review of optimization techniques in spacecraft flight trajectory design

Utilization of Residual Helium to Extend Satellite Lifetimes and Mitigate Space Debris

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