Variable-time-domain neighboring optimal guidance applied to space trajectories

Pontani, Mauro; Cecchetti, Giampaolo; Teofilatto, Paolo

doi:10.1016/j.actaastro.2015.05.020

Cited by 23 publications

(24 citation statements)

References 14 publications

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“…This research is focused on the original combination of two techniques applied to low-thrust orbit transfers, i.e. (i) the recently-introduced variable-time-domain neighboring optimal guidance (VTD-NOG) [13][14][15] , and (ii) a proportional-derivative approach based on rotation matrices (PD-RM) for the attitude control algorithm. VTD-NOG belongs to the class of feedback implicit guidance approaches, aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…Let the dot denote the derivative with respect to  hence forward. Equations [10] are rewritten as [15] where a collects all the unknown parameters of the problem ( f t = a for the problem at hand).…”

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confidence: 99%

“…respectively the adjoint variable conjugate to the dynamics equations[15] and to the boundary conditions[13], with components   1, The first-order necessary conditions for optimality include the adjoint (or costate) equations21 , in conjunction with the related boundary conditons, * u can be expressed as a function of the costates through the Pontryagin minimum principle,…”

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confidence: 99%

“…. Further, considerable analytical developments13,15 (not reported for the sake of conciseness) lead to the following modified sweep equations: In the end, the gain matrices involved in the sweep method, i.e. S, Ŝ , R, Q, n, m, and α , can be backward integrated in two steps:(a) in the interval   ,1 sw  the equations of the classical sweep method 13 , with the respective boundary conditions are used, (b) in the interval   is set to 0.99.…”

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confidence: 99%

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Variable-time-domain neighboring optimal guidance and attitude control of low-thrust lunar orbit transfers

Pontani

Celani

2020

Acta Astronautica

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Lunar orbit dynamics and transfers at low altitudes are subject to considerable perturbations related to the gravitational harmonics associated with the irregular lunar mass distribution. This research proposes the original combination of two techniques applied to low-thrust lunar orbit transfers, i.e. (i) the variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a proportional-derivative attitude control algorithm based on rotation matrices (PD-RM). VTD-NOG belongs to the class of feedback implicit guidance approaches, aimed at maintaining the spacecraft sufficiently close to the reference trajectory. This is an optimal path that satisfies the second-order sufficient conditions for optimality. A fundamental original feature of VTD-NOG is the use of a normalized time scale, with the favorable consequence that the gain matrices remain finite for the entire time of flight. VTD-NOG identifies the trajectory corrections by assuming the thrust direction as the control input. Because the thrust direction is fixed with respect to the spacecraft, VTD-NOG generates the desired orientation pursued by the attitude control system. A proportional-derivative approach using rotation matrices (PD-RM) is employed in order to drive the actual spacecraft orientation toward the desired one. Reaction wheels are considered as the actuators that perform attitude control. Extensive Monte Carlo simulations are performed, in the presence of nonnominal flight conditions related to (i) lunar gravitational harmonics, (ii) gravitational pull of the Earth and the Sun as third bodies, (iii) unpredictable propulsive fluctuations, and (iv) errors on initial attitude. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and PD-RM control represents an accurate and effective methodology for guidance and control of low-thrust lunar orbit transfers.

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Section: Introductionmentioning

confidence: 99%

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Variable-time-domain neighboring optimal guidance and attitude control of low-thrust lunar orbit transfers

Pontani

Celani

2020

Acta Astronautica

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“…[36][37][38][39][40] and the references therein, on the topic of the NOG for orbital transfer problems have been published. More recently, a variable-timedomain NOG was proposed by Pontani et al [33,34] to avoid the numerical difficulties arising from the singularity of the gain matrices while approaching the final time and it was then applied to a continuous thrust space trajectories [35].…”

Section: Introductionmentioning

confidence: 99%