Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

Sherrill, Ryan E.; Sinclair, Andrew J.; Sinha, Subhash C.; Lovell, T. Alan

doi:10.1007/s10569-014-9543-x

Cited by 8 publications

(3 citation statements)

References 19 publications

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“…Event triggered MPC [61] could be an applicable tool. Also, recent modelling developments (e.g., [62], [63]) could be applied to simplify handling of elliptical orbits. Many of the studies cited in this tutorial assume good quality state estimates with idealised uncertainty models and rigid-body models of the spacecraft.…”

Section: Discussionmentioning

confidence: 99%

A tutorial on model predictive control for spacecraft rendezvous

Hartley

2015

2015 European Control Conference (ECC)

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This tutorial paper provides a review of recent advances in the field of spacecraft rendezvous using model predictive control (MPC), an advanced optimal control strategy based on on-line constrained optimisation of control inputs based on predictions of future trajectories. Firstly, the rendezvous objectives, and the generic constrained MPC problem formulation are summarised. This is followed by a discussion of how to select the three key ingredients used in an MPC design: the prediction model, the constraints and the cost function. Since MPC implementation relies on finding the solution to constrained optimisation problems in real-time, computational aspects are also briefly examined. The paper concludes with conjecture on ways the use of MPC in this application could be further advanced.

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Section: Discussionmentioning

confidence: 99%

A tutorial on model predictive control for spacecraft rendezvous

Hartley

2015

2015 European Control Conference (ECC)

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“…Consequently, we intend to exploit this propitious attribute in our investigation. Applications of L-F transformations in spacecraft dynamics have been previously investigated by authors such as [8,26]. The former demonstrates how L-F theory enhances the representation of relative spacecraft dynamics in elliptical orbits, while the latter further proposes an orbit control law based on L-F theory.…”

Section: • Normal Form (Nf) Theorymentioning

confidence: 94%

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

Waswa¹,

Redkar²

2020

Advances in Spacecraft Attitude Control

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This chapter demonstrates analysis and control of the attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit. The attitude motion is modeled by nonlinear planar pitch dynamics with periodic coefficients and additionally subjected to external periodic excitation. Consequently, using system state augmentation, Lyapunov-Floquet (L-F) transformation, and normal form simplification, we convert the unwieldy attitude dynamics into relatively more amenable schemes for motion analysis and control law development. We analyze the dynamical system's periodicity, stability, resonance, and chaos via numerous nonlinear dynamic theory techniques facilitated by intuitive system state augmentation and Lyapunov-Floquet transformation. Versal deformation of the normal forms is constructed to investigate the bifurcation behavior of the dynamical system. Outcome from the analysis indicates that the motion is quasi-periodic, chaotic, librational, and undergoing a Hopf bifurcation in the small neighborhood of the critical point-engendering locally stable limit cycles. Consequently, we demonstrate the implementation of linear and nonlinear control laws (i.e., bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasiperiodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.

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“…As shown below, these can be factors of 2x in the required deflection delta-velocity and when coupled with mission planning scenarios this difference can become appreciable. A more recent analytical approach (Johnson 2010;Sherrill et al 2014, and refs therein) using elliptical Hill-Clohessy-Wiltshire equations is a promising alternative approach. However, in this paper we are seeking an approach that non-experts in astrodynamics could easily understand and utilize, in an effort to reach the broad and very diverse backgrounds of the asteroid deflection community.…”

Section: Introductionmentioning

confidence: 99%

A simplified approach to uncertainty quantification for orbits in impulsive deflection scenarios

Howley

Wasem

2014

Acta Astronautica

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For the majority of near-Earth Asteroid (NEA) impact scenarios, optimal deflection strategies use a massive impactor or a nuclear explosive, either of which produce an impulsive change to the orbit of the object. However, uncertainties regarding the object composition and the efficiency of the deflection event lead to a non-negligible uncertainty in the deflection delta-velocity. Propagating this uncertainty through the resulting orbit will create a positional uncertainty envelope at the original impact epoch. We calculate a simplified analytic evolution for impulsively deflected NEAs and perform a full propagation of uncertainties that is nonlinear in the deflection delta-velocity vector. This provides an understanding of both the optimal deflection velocities needed for a given scenario, as well as the resulting positional uncertainty and corresponding residual impact probability. Confidence of a successful deflection attempt as a function of launch opportunities is also discussed for a specific case.

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Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

Cited by 8 publications

References 19 publications

A tutorial on model predictive control for spacecraft rendezvous

A tutorial on model predictive control for spacecraft rendezvous

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

A simplified approach to uncertainty quantification for orbits in impulsive deflection scenarios

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