arXiv subjects

Roberto Armellin

Publications and source records attributed to Roberto Armellin.

50 records · Page 3Linked to original sources

arXiv2023

A Multifidelity Approach to Robust Orbit Determination

This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem and detect possible outliers in the processed measurements. The uncertainty on the initial estimate is propagated forward in time and progressively reduced by exploiting sensor data available in said propagation window. Differential algebra techniques and a novel automatic domain splitting algorithm for second-order Taylor expansions are used to efficiently propagate uncertainties over time. A multifidelity approach is employed to minimize the computational effort while retaining the accuracy of the propagated estimate. At each observation epoch, a polynomial map is obtained by projecting the propagated states onto the observable space. Domains that do no overlap with the actual measurement are pruned thus reducing the uncertainty to be further propagated. Measurement outliers are also detected in this step. The refined estimate and retained observations are then used to improve the robustness of batch orbit determination tools. The effectiveness of the algorithm is demonstrated for a geostationary transfer orbit object using synthetic and real observation data from the TAROT network.

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arXiv2023

A low-order automatic domain splitting approach for nonlinear uncertainty mapping

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first introduced to rigorously estimate the Jacobian variation of a nonlinear transformation. This index is then embedded into a low-order automatic domain splitting algorithm that accurately describes the mapping of an initial uncertainty set through a generic nonlinear transformation by splitting the domain whenever some imposed linearity constraints are non met. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging algorithm that limits the growth of the domains in time by recombining them when nonlinearities decrease. The low-order automatic domain splitting algorithm is then combined with Gaussian mixtures models to accurately describe the propagation of a probability density function. A detailed analysis of the proposed method is presented, and the impact of the different available degrees of freedom on the accuracy and performance of the method is studied.

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arXiv2023

Perturbed Initial Orbit Determination

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.

astro-ph.EP↗

arXiv2023

Convex Optimization-Based Model Predictive Control for the Guidance of Active Debris Removal Transfers

Active debris removal (ADR) missions have garnered significant interest as means of mitigating collision risks in space. This work proposes a convex optimization-based model predictive control (MPC) approach to provide guidance for such missions. While convex optimization can obtain optimal solutions in polynomial time, it relies on the successive convexification of nonconvex dynamics, leading to inaccuracies. Here, the need for successive convexification is eliminated by using near-linear Generalized Equinoctial Orbital Elements (GEqOE) and by updating the reference trajectory through a new split-Edelbaum approach. The solution accuracy is then measured relative to a high-fidelity dynamics model, showing that the MPC-convex method can generate accurate solutions without iterations.

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arXiv2022

Detection and estimation of spacecraft maneuvers for catalog maintenance

Building and maintaining a catalog of resident space objects involves several tasks, ranging from observations to data analysis. Once acquired, the knowledge of a space object needs to be updated following a dedicated observing schedule. Dynamics mismodeling and unknown maneuvers can alter the catalog's accuracy, resulting in uncorrelated observations originating from the same object. Starting from two independent orbits, this work presents a novel approach to detect and estimate maneuvers of resident space objects, which allows for correlation recovery. The estimation is performed with successive convex optimization without a-priori assumption on the thrust arcs structure and thrust direction.

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arXiv2022

Design and Guidance of a Multi-Active Debris Removal Mission

Space debris have been becoming exceedingly dangerous over the years as the number of objects in orbit continues to rise. Active debris removal (ADR) missions have garnered significant attention as an effective way to mitigate this collision risk. This research focuses on developing a multi-ADR mission that utilizes controlled reentry and deorbiting. The mission comprises two spacecraft: a Servicer that brings debris down to a low altitude and a Shepherd that rendezvous with the debris to later perform a controlled reentry. A preliminary mission design tool (PMDT) is developed to obtain time or fuel optimal trajectories for the proposed mission while taking the effect of $J_2$, drag, eclipses, and duty ratio into account. The PMDT can perform such trajectory optimizations within computational times that are under a minute. Three guidance schemes are also studied, taking the PMDT solution as a reference, to validate the design methodology and provide guidance solutions for this complex mission profile.

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arXiv2022

Team theAntipodes: Solution Methodology for GTOC11

This paper presents the solution approach developed by the team "theAntipodes" for the 11th Global Trajectory Optimization Competition (GTOC11). The approach consists of four main blocks: 1) mothership chain generation, 2) rendezvous table generation, 3) the dispatcher, and 4) the refinement. Blocks 1 and 3 are purely combinatorial optimization problems that select the asteroids to visit and allocate them to the Dyson ring stations. The rendezvous table generation involves interpolating time-optimal transfers to find all transfer opportunities between selected asteroids and the ring stations. The dispatcher uses the data stored in the table and allocates the asteroids to the Dyson ring stations optimally. The refinement ensures each rendezvous trajectory meets the problem accuracy constraints and introduces deep-space maneuvers to the mothership transfers. We provide the details of our solution that, with a score of 5,992, was worth 3rd place.

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arXiv2022

Exploiting Scaling Constants to Facilitate the Convergence of Indirect Trajectory Optimization Methods

This note develops easily applicable techniques that improve the convergence and reduce the computational time of indirect low thrust trajectory optimization when solving fuel- and time-optimal problems. For solving fuel optimal (FO) problems, a positive scaling factor -- $Γ_{TR}$ -- is introduced based on the energy optimal (EO) solution to establish a convenient profile for the switching function of the FO problem. This negates the need for random guesses to initialize the indirect optimization process. Similarly, another scaling factor-$β$-, is introduced when solving the time-optimal (TO) problem to connect the EO problem to the TO. The developed methodology for the TO problem was crucial for the GTOC11 competition. Case studies are conducted to validate the solution process in both TO and FO problems. For geocentric cases, the effect of eclipses and $J_2$ perturbations were also considered. The examples show that EO can provide a good guess for TO and FO problems and that introducing the constants can reduce the initial residuals and improve convergence. It is also shown that the equation for the Lagrangian multiplier of mass and the associated boundary condition can be ignored for both FO and TO cases without affecting optimality. This simplification reduces the problem dimensions and improves efficiency.

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arXiv2022

A Koopman-Operator Control Optimization for Relative Motion in Space

A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal inverse control methodology. The operator theory can reformulate a nonlinear dynamical system of finite dimension into a linear system with an infinite number of dimensions. As a results, the state of any nonlinear dynamics is represented as a linear combination of high-order orthogonal polynomials, which creates the state transition polynomial map of the solution. Since the optimal control technique can be reduced to a two-points boundary value problem, the Koopman map is used to connect the state and control variables in time, such that optimal values are obtained through map inversion and polynomial evaluation. The new technique is applied to rendezvous applications in space, where the relative motion between two satellites is modelled with a high-order polynomial series expansion of the Lagrangian of the system, such that the Clohessy-Wiltshire equations represent the reduction of the high-order model to a linear truncation.

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arXiv2022

Multifidelity Orbit Uncertainty Propagation using Taylor Polynomials

A new multifidelity method is developed for nonlinear orbit uncertainty propagation. This approach guarantees improved computational efficiency and limited accuracy losses compared to fully high-fidelity counterparts. The initial uncertainty is modeled as a weighted sum of Gaussian distributions whose number is adapted online to satisfy the required accuracy. As needed, univariate splitting libraries are used to split the mixture components along the direction of maximum nonlinearity. Differential Algebraic techniques are used to propagate these Gaussian kernels and compute a measure of nonlinearity required for the split decision and direction identification. Taylor expansions of the flow of the dynamics are computed using a low-fidelity dynamical model to maximize computational efficiency and corrected with selected high-fidelity samples to minimize accuracy losses. The effectiveness of the proposed method is demonstrated for different dynamical regimes combining SGP4 theory and numerical propagation as low- and high-fidelity models respectively.

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arXiv2021

Collision Avoidance Maneuver Optimization with a Multiple-Impulse Convex Formulation

A method to compute optimal collision avoidance maneuvers for short-term encounters is presented. The maneuvers are modeled as multiple-impulses to handle impulsive cases and to approximate finite burn arcs associated either with short alert times or the use of low-thrust propulsion. The maneuver design is formulated as a sequence of convex optimization problems solved in polynomial time by state-of-the-art primal-dual interior-point algorithms. The proposed approach calculates optimal solutions without assumptions about the thrust arc structure and thrust direction. The execution time is fraction of a second for an optimization problem with hundreds of variables and constraints, making it suitable for autonomous calculations.

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arXiv2019

On the predictability of Galileo disposal orbits

The end-of-life disposal of Galileo satellites is needed to avoid collisions with operational spacecraft and to prevent the generation of space debris. Either disposal in stable graveyard orbits or disposal into the atmosphere exploiting eccentricity growth caused by lunisolar resonances are possible. However, there is a concern about the predictability of MEO orbits because of possible chaotic behaviour caused by the overlap of resonances. In this work, we investigate if Galileo disposal orbits are predictable and if safe disposal is possible under initial uncertainties. For this, we employ finite-time Lyapunov exponents (FTLE) and sensitivity analysis and compare these two methods regarding their practicality for analysing the predictability of disposal orbits. The results show that FTLE are not suitable for determining if an orbit behaves chaotically or not on the time scale of interest. Sensitivity analysis, on the other hand, can be used to quantify the effect of uncertainties on the orbital evolution and to determine if safe disposal is possible. In addition, we show that reliable re-entry disposal is feasible with a limited ΔV budget. However, safe disposal into a graveyard orbit is not always feasible considering uncertainties in the disposal manoeuvre and dynamical model when the available ΔV for disposal is low.

astro-ph.EP↗

arXiv2018

Element sets for high-order Poincaré mapping of perturbed Keplerian motion

The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in celestial mechanics and astrodynamics, e.g. to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits over many revolutions. For this, the method uses the high-order Taylor expansion of a Poincaré or stroboscopic map, which is accurate close to the expansion point. In this paper, we investigate the performance of the HOTM method using different element sets for building the high-order map. The element sets investigated are the classical orbital elements, modified equinoctial elements, Hill variables, cylindrical coordinates and Deprit's ideal elements. The performances of the different coordinate sets are tested by comparing the accuracy and efficiency of mapping low-Earth and highly-elliptical orbits perturbed by $J_2$ with numerical propagation. The accuracy of HOTM depends strongly on the choice of elements and type of orbit. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and centre manifolds of Poincaré maps.

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arXiv2018

A differential algebra based importance sampling method for impact probability computation on Earth resonant returns of Near Earth Objects

A differential algebra based importance sampling method for uncertainty propagation and impact probability computation on the first resonant returns of Near Earth Objects is presented in this paper. Starting from the results of an orbit determination process, we use a differential algebra based automatic domain pruning to estimate resonances and automatically propagate in time the regions of the initial uncertainty set that include the resonant return of interest. The result is a list of polynomial state vectors, each mapping specific regions of the uncertainty set from the observation epoch to the resonant return. Then, we employ a Monte Carlo importance sampling technique on the generated subsets for impact probability computation. We assess the performance of the proposed approach on the case of asteroid (99942) Apophis. A sensitivity analysis on the main parameters of the technique is carried out, providing guidelines for their selection. We finally compare the results of the proposed method to standard and advanced orbital sampling techniques.

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