Linearized Impulsive Fixed-Time Fuel-Optimal Space rendezvous: A New Numerical Approach

Arzelier, Denis; Bréhard, Florent; Deak, Norbert; Joldeş, Mioara; Louembet, Christophe; Rondepierre, Aude; Serra, Romain

doi:10.1016/j.ifacol.2016.09.064

Cited by 9 publications

(23 citation statements)

References 6 publications

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“…As seen from the numerical simulations, the IRLS algorithm generates optimal control sequences which takes the active spacecraft from its initial to its final states. It is observed that the minimum ℓ 1 norm for fuel consumption is around 2% greater than the algorithm proposed in [32]. Hence the IRLS algorithm is able to generate control sequences whose ℓ 1 norm is close to the optimal ones.…”

Section: A Out-of-plane Maneuvers For a Geostationary Transfer Orbit ...mentioning

confidence: 90%

“…An Automated Vehicle Transfer (ATV) mission is considered where the in-plane motion is as in [32]. For the in-plane rendezvous, two different examples are studied, one is a single gimbaled thruster (thrust vectoring) in which the fuel consumption is determined by the ℓ 2 /ℓ 1 norm of the control sequence.…”

Section: B Coplanar Maneuvers For Automated Vehicle Transfer (Atv) Mi...mentioning

confidence: 99%

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Minimum-fuel Spacecraft Rendezvous based on Sparsity Promoting Optimization

Zinage¹,

Bakolas²

2021

Preprint

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In this paper, we consider the classical spacecraft rendezvous problem in which the so-called active spacecraft has to approach the target spacecraft which is moving in an elliptical orbit around a planet by using the minimum possible amount of fuel. Instead of using standard convex optimization tools which can be computationally expensive, we use modified versions of the Iteratively Reweighted Least Squares (IRLS) algorithm from compressive sensing to compute sparse optimal control sequences which minimize the fuel consumption for both thrust vectoring and orthogonal vectoring (active) spacecraft. Numerical simulations are performed to verify the efficacy of our approach.

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Section: A Out-of-plane Maneuvers For a Geostationary Transfer Orbit ...mentioning

confidence: 90%

Section: B Coplanar Maneuvers For Automated Vehicle Transfer (Atv) Mi...mentioning

confidence: 99%

Minimum-fuel Spacecraft Rendezvous based on Sparsity Promoting Optimization

Zinage¹,

Bakolas²

2021

Preprint

View full text Add to dashboard Cite

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“…The first attempts to solve the latter class of problems (see, for instance, [8][9][10][11]), which were based on variational techniques along with sophisticated numerical techniques, did not enjoy strong guarantees of convergence. Some more recent solution techniques [12,13] seem to yield more promising results. The latter techniques leverage one of the most significant theoretical results on the minimum 1 -norm controllability problem, which was proposed by Neustadt [14], according to which the latter problem can be recast as a semi-infinite convex optimization problem by means of functional analysis tools and relaxation techniques.…”

Section: Introductionmentioning

confidence: 99%

“…The latter techniques leverage one of the most significant theoretical results on the minimum 1 -norm controllability problem, which was proposed by Neustadt [14], according to which the latter problem can be recast as a semi-infinite convex optimization problem by means of functional analysis tools and relaxation techniques. The approaches proposed in [12,13], however, rely on sophisticated tools that may not be appealing to the non-expert. More importantly, given the complexity of the latter approaches, their application in problems requiring real-time computations, such as in spacecraft proximity operations by autonomous spacecraft, is difficult in practice.…”

Section: Introductionmentioning

confidence: 99%

On the Computation of Sparse Solutions to the Controllability Problem for Discrete-Time Linear Systems

Bakolas

2019

J Optim Theory Appl

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In this work, we address the fundamental problem of steering the state of a discretetime linear system to the origin after a given (finite) number of stages by means of the sparsest possible control sequence, that is, the sequence of inputs comprised of the maximum possible number of null elements. In our approach, the latter controllability problem is associated with the problem of finding either the minimum 1-norm solution or the minimum p-norm, with p taking values greater than zero and less than one, solution of an under-determined system of linear equations, which are both known to exhibit good sparsity properties under certain technical assumptions. Motivated by practical considerations, we compute approximate solutions to the latter optimization problems by utilizing the class of iteratively weighted least squares algorithms from the literature of compressive (or compressed) sensing. This particular choice of algorithms is motivated by (1) their straightforward implementation, which makes them appealing to the non-expert and (2) the fact that some of the most costly operations involved in their implementation can be carried out recursively by leveraging wellknown properties of the controllability Grammian of a discrete-time linear system. Finally, we apply the proposed approach to a spacecraft proximity operation problem and in particular, a linearized impulsive fixed-time minimum-fuel rendezvous problem in which the 1-norm serves as a proxy to the fuel consumption at a given time interval. KeywordsSparse control • Iterative least squares algorithm • Discrete-time linear systems • Compressive sensing • Linearized impulsive minimum fuel control Mathematics Subject Classification 49N05 • 49N90 Communicated by Martin Corless.

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“…A common aspect among most of these methods is that they rely solely on impulsive-based solutions. Application of semi-infinite convex optimization using a relaxation scheme and duality theory in normed linear spaces is demonstrated in [52] for fixed-time minimum-fuel rendezvous between close elliptic orbits without fixing a priori the number of impulses.…”

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confidence: 99%

How Many Impulses Redux

Taheri

Junkins

2019

J Astronaut Sci

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A central problem in orbit transfer optimization is to determine the number, time, direction and magnitude of velocity impulses that minimize the total impulse. This problem was posed in 1967 by T. N. Edelbaum, and while notable advances have been made, a rigorous means to answer Edelbaum's question for multiple-revolution maneuvers has remained elusive for over five decades. We revisit Edelbaum's question by taking a bottom-up approach to generate a minimum-fuel switching surface. Sweeping through time profiles of the minimum-fuel switching function for increasing admissible thrust magnitude, and in the high-thrust limit, we find that the continuous thrust switching surface reveals the N -impulse solution. It is also shown that a fundamental minimum-thrust solution plays a pivotal role in our process to determine the optimal minimum-fuel maneuver for all thrust levels. Remarkably, we find the answer to Edelbaum's question is not generally unique, but is frequently a set of equal-∆v extremals. We further find, when Edelbaum's question is refined to seek the number of finite-duration thrust arcs for a specific rocket engine, that a unique extremal is usually found. Numerical results demonstrate the ideas and their utility for several interplanetary and Earth-bound optimal transfers that consist of up to eleven impulses or, for finite thrust, short thrust arcs. Another significant contribution of the paper can be viewed as a unification in astrodynamics where the connection between impulsive and continuous-thrust trajectories are demonstrated through the notion of optimal switching surfaces. NOMENCLATURE f = vector function of unforced dynamics B = control influence matrix c = exhaust velocity, m/s g 0 = Earth gravitational acceleration, m/s 2 h = specific angular momentum vector, km 2 /s H = Hamiltonian I sp = specific impulse, s J = cost functional

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Linearized Impulsive Fixed-Time Fuel-Optimal Space rendezvous: A New Numerical Approach

Cited by 9 publications

References 6 publications

Minimum-fuel Spacecraft Rendezvous based on Sparsity Promoting Optimization

Minimum-fuel Spacecraft Rendezvous based on Sparsity Promoting Optimization

On the Computation of Sparse Solutions to the Controllability Problem for Discrete-Time Linear Systems

How Many Impulses Redux

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