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Communication Dans Un Congrès Année : 2019

Multi-phase averaging of time-optimal low-thrust transfers

Résumé

An increasing interest in optimal low-thrust orbital transfers was triggered in the last decade by technological progress in electric propulsion and by the ambition of efficiently leveraging on orbital perturbations to enhance the maneuverability of small satellites. The assessment of a control sequence that is capable of steering a satellite from a prescribed initial to a desired final state while minimizing a figure of interest is referred to as maneuver planning. From the dynamical point of view, the necessary conditions for optimality outlined by the infamous Pontryagin maximum principle (PMP) reveal the Hamiltonian nature of the system governing the joint motion of state and control variables. Solving the control problem via so-called indirect techniques, e.g., shooting method, requires the integration of several trajectories of the aforementioned Hamiltonian. In addition , PMP conditions exhibit very high sensitivity with respect to boundary values of the satellite longitude owing to the fast-oscillating nature of orbital motion. Hence, using perturbation theory to facilitate the numerical solution of the planning problem is appealing. In particular, averaging techniques were used since the early space age to gain understanding into the long-term evolution of perturbed satellite trajectories. However, it is not generally possible to treat low-thrust as any other perturbation (whose spectral content is well defined and predictable) because the control variables may introduce additional frequencies in the system. The talk focuses on time optimal maneuvers in a perturbed orbital environment, and it addresses two questions: (1) Is it possible to average the vector field of this problem? Optimal control Hamiltonians are not in the classical form of fast-oscillating systems. However, we demonstrate that averaged trajectories well approximate the original system if the ad-joint variables of the PMP (i.e., conjugate momenta associated to the enforcement of the equations of motion) are adequately transformed before integrating the averaged trajec-tory. We discuss this transformation in detail, and we emphasize fundamental differences with respect to well-known mean-to-osculating transformations of uncontrolled motion. (2) What is the impact of orbital perturbations and their frequencies on the controlled tra-jectory? We show that control variables are highly sensitive to small exogenous forces. Hence, even the crossing of a high-order resonance may trigger a dramatic divergence between trajectories of the averaged and original system. We then discuss how averaged resonant forms may be used to avoid this divergence. The methodology is finally applied to a deorbiting maneuver leveraging on solar radiation pressure. The presence of eclipses make the original planning problem highly challenging. Averaging with respect to satellite and Sun longitudes drastically simplifies the extremal flow yielding an averaged counterpart of the PMP conditions, which is reasonably easy to solve.
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Dates et versions

hal-02387385 , version 1 (16-12-2019)

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  • HAL Id : hal-02387385 , version 1

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Lamberto Dell'Elce, Jean-Baptiste Caillau, Jean-Baptiste Pomet. Multi-phase averaging of time-optimal low-thrust transfers. KePASSA 2019 - 4th International Workshop on Key Topics in Orbit Propagation Applied to Space Situational Awareness, Apr 2019, Logrono, Spain. ⟨hal-02387385⟩
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