1,721,008 research outputs found

    Perturbed Lambert's Problem Solver based on Differential Algebra Optimization

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    Classical Lambert's problem is an astrodynamical problem implemented in industrial and scientific softwares to solve this specific two-boundary value problem under the hypothesis of a Keplerian dynamic. To design optimal trajectories or to compute initial guess for least-square orbit determination problems, it must be solved and implemented. Earlier works develop numerical and analytical techniques to solve the classical Lambert's problem in the mono-revolution and multi-revolution cases. On the one hand, this results in fast-computing and efficient methods that is employed in state-of-the-art softwares. On the other, the dynamical model is simplistic and the actual final position of the satellite differs of several kilometers once the revolutions number increases. A way to obtain a more close-to-reality solution is to consider a more complete dynamical model by taking into account orbital perturbing forces such as aerodynamic drag and perturbing gravity potential. As previously-introduced algorithms do not consider a perturbed dynamics, this paper develops an optimization algorithm based on the Taylor Differential Algebra to solve the perturbed Lambert's problem. The operations defined in the algebra allow to compute the polynomial approximation of the final state propagation as a function of the initial state to be computed. This polynomial expansion is used to reduce the final position error as in thrust-region optimization. A wide range of numerical simulation is performed in order to have a clear view of the algorithm performances. Test cases have been chosen between the main orbit families (LEO, MEO, GEO, HEO and GTO) in order to have a complete and clear overview of the developed algorithm. Moreover the influence of the polynomial order is studied and a preference expansion order is selected to maximize the performance index. Obtained results are promising and further development are proposed to increment algorithm performances

    Spacecraft Dynamics Employing a General Multi-tank and Multi-thruster Mass Depletion Formulation

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    Using thrusters for either orbital maneuvers or attitude control change the current spacecraft mass properties and results in an associated reaction force and torque. To perform orbital and attitude control using thrusters, or to obtain optimal trajectories, the impact of mass variation and depletion of the spacecraft must be thoroughly understood. Some earlier works make rocket-body specific assumptions such as axial symmetric bodies or certain tank geometries hat limit the applicability of the models. Other earlier works require further derivation to implement the provided equations of motion in simulation software. This paper develops the fully coupled translational and rotational equations of motion of a spacecraft that is ejecting mass through the use of thrusters and can be readily implemented in flight dynamics software. The derivation begins considering the entire closed system: the spacecraft and the ejected fuel. Then the exhausted fuel motion in free space is expressed using the thruster nozzle properties and the familiar thrust vector to avoid tracking the expelled fuel in the simulation. Additionally, the present formulation considers a general multi-tank and multi-thruster approach to account for both the depleting fuel mass in the tanks and the mass exiting the thruster nozzles. General spacecraft configurations are possible where thrusters can pull from a single tank or multiple tanks, and the tank being drawn from can be switched via a valve. Numerical simulations are presented to perform validation of the model developed and to show the impact of assumptions that are made for mass depletion in prior developed models

    Hardware-In-the-loop Validation of Autonomous Interplanetary Navigation Algorithms for Interplanetary Cruises with the Optical Star Stimulator

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    Thanks to the rising focus on deep-space exploration and exploitation, the demand for sustainable and efficient navigation approaches has become crucial. Standard ground-based radiometric tracking, while accurate, is expensive and resourceintensive, posing long-term sustainability challenges. Therefore, enhancing spacecraft autonomy is crucial to avoid ground station saturation. Autonomous onboard guidance, navigation, and control (GNC) offer cost reduction and expand interplanetary exploration opportunities. Among various navigation alternatives, vision-based navigation (VBN) stands out for its cost-effectiveness, ground independence, and applicability to different spacecraft classes. Ground testing campaigns are crucial to ensure accurate and robust vision-based navigation algorithms for interplanetary missions. However, obtaining real interplanetary sky-field images for validation is challenging due to limited successful missions and datasets. To overcome these limitations, high-fidelity rendering engines and hardware-in-the-loop (HIL) simulations are necessary to generate image datasets for testing. This work presents the development of a procedure for on-ground testing and validation of autonomous navigation algorithms for interplanetary cruises using Jena Optronik’s Optical Sky Stimulator (OSI) at the DLR GNC Department in Bremen. The proposed paper includes preparation activities, calibration and compensation procedures, and final hardware-in-the-loop simulations

    Variational Lambert’s Problem with Uncertain Dynamics

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    Lambert’s problem is a widely-known problem in astrodynamics that addresses the need of finding a trajectory given two position vectors and the time of flight between them. It is widely used in mission design and in on-line guidance algorithm in order to predict the needed maneuvers or the spacecraft state on the computed trajectory. Previous work has investigated the influence of uncertainty in the positions vectors and linearization of the classical Lambert’s problem for spacecraft autonomous applications. These approaches allow the uncertainty quantification, maneuver correction and orbit determination to be performed with respect to a nominal trajectory in a perfectly-known environment. Unfortunately, the increase number of missions to partially-known bodies of the Solar System, such as asteroids, comets and dwarf planets, requires to abandon the hypothesis of a deterministic dynamical environment as the forces acting on the spacecraft are accurately quantified only when the geophysical property of the body are known, thus when orbiting around it. This leads to the need of considering a stochastic dynamics to take into account uncertainties and errors introduced during mission design. This paper presents the variational Lambert’s problem with uncertain dynamics around a nominal trajectory and gather the formulas to characterize the probability density function and covariances of position, velocities and dynamical parameters. Then numerical simulations are presented by considering several dynamics effects, such as the spherical harmonics gravity, in order to validate the developed approach by comparison with Monte Carlo simulations. Results show good agreement between the two obtained solution. Finally, an operational simulation is presented to show an on-board autonomous application of the developed algorithm. In this scenario the spacecraft estimates on-board the new dynamics and corrects the guidance maneuvers by using the output of the variational Lambert’s problem and the navigation data. The corrected trajectory shows a decrease of the error with respect to the nominal trajectory that implies the effectiveness of the applied corrections
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