arXiv subjects

Pedro Lourenço

Publications and source records attributed to Pedro Lourenço.

7 recordsLinked to original sources

arXiv2026

An Equivariant Filter for Spacecraft Nonlinear Relative Navigation with Range and Bearing Measurements

Relative navigation is a fundamental task in space proximity operations and autonomous rendezvous. The nonlinear relative orbital dynamics are equivariant and admit a semidirect product Lie group symmetry. This property is used to design an Equivariant Filter (EqF). The filter estimates the relative position and velocity between a chaser spacecraft and a target by lifting the filter dynamics to the group, while respecting the underlying geometry of the problem. Simulations demonstrate the filter's performance and effectiveness.

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arXiv2026

Structure Theorems for locally compact modules over localizations of the integers

Given a multiplicatively closed subset $S$ of the integers, there exist Structure Theorems for $LC$ modules over the localization $\mathbb{Z}S^{-1}$ that are "similar" to those of $LCA$ groups. The most notable one is the 1st Theorem: Given such a module $M$, there exists a unique set of prime numbers $Σ$ (purely dependent on $S$) for which $M \cong \mathbb{R}^n \times \sideset{}{'}\prod_{q \in Σ} \mathbb{Q}_p^{n_p} \times N$, where $(n, (n_p)_{p \in Σ})$ is a sequence of nonnegative integers and $N$ contains a compact open submodule $K$ such that $K/K_0$ is a topological module over $\prod_{ q \in \mathbb{P}\setminusΣ} \mathbb{Z}_q$. Just like for $LCA$ groups, it is also possible to characterize the locally compact, compactly generated modules over $\mathbb{Z}S^{-1}$, as well as their Pontryagin Duals (which then allows to conclude that any locally compact $\mathbb{Z}S^{-1}$-module is an inverse limit of modules within a specific family). These characterizations are given in the 2nd and 3rd Structure Theorems respectively. Furthermore, as an elementary consequence of the 1st Structure Theorem, one can obtain a full classification of locally compact vector spaces over $\mathbb{Q}$.

math.GR↗

arXiv2026

Equivariant Filter for Relative Attitude and Target's Angular Velocity Estimation

Accurate estimation of the relative attitude and angular velocity between two rigid bodies is fundamental in aerospace applications such as spacecraft rendezvous and docking. In these scenarios, a chaser vehicle must determine the orientation and angular velocity of a target object using onboard sensors. This work addresses the challenge of designing an Equivariant Filter (EqF) that can reliably estimate both the relative attitude and the target angular velocity using noisy observations of two known, non-collinear vectors fixed in the target frame. To derive the EqF, a symmetry for the system is proposed and an equivariant lift onto the symmetry group is calculated. Observability and convergence properties are analyzed. Simulations demonstrate the filter's performance, with Monte Carlo runs yielding statistically significant results. The impact of low-rate measurements is also examined and a strategy to mitigate this effect is proposed. Experimental results, using fiducial markers and both conventional and event cameras for measurement acquisition, further validate the approach, confirming its effectiveness in a realistic setting.

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arXiv2025

Equivariant Filter Cascade for Relative Attitude, Target's Angular Velocity, and Gyroscope Bias Estimation

Rendezvous and docking between a chaser spacecraft and an uncooperative target, such as an inoperative satellite, require synchronization between the chaser spacecraft and the target. In these scenarios, the chaser must estimate the relative attitude and angular velocity of the target using onboard sensors, in the presence of gyroscope bias. In this work, we propose a cascade of Equivariant Filters (EqF) to address this problem. The first stage of the cascade estimates the chaser's attitude and the bias, using measurements from a star tracker, while the second stage of the cascade estimates the relative attitude and the target's angular velocity, using observations of two known, non-collinear vectors fixed in the target frame. The stability of the EqF cascade is theoretically analyzed and simulation results demonstrate the filter cascade's performance.

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arXiv2025

The impact of modeling approaches on controlling safety-critical, highly perturbed systems: the case for data-driven models

This paper evaluates the impact of three system models on the reference trajectory tracking error of the LQR optimal controller, in the challenging problem of guidance and control of the state of a system under strong perturbations and reconfiguration. We compared a smooth Linear Time Variant system learned from data (DD-LTV) with state of the art Linear Time Variant (LTV) system identification methods, showing its superiority in the task of state propagation. Moreover, we have found that DD-LTV allows for better performance in terms of trajectory tracking error than the standard solutions of a Linear Time Invariant (LTI) system model, and comparable performance to a linearized Linear Time Variant (L-LTV) system model. We tested the three approaches on the perturbed and time varying spring-mass-damper systems.

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arXiv2024

Convex MPC and Thrust Allocation with Deadband for Spacecraft Rendezvous

This paper delves into a rendezvous scenario involving a chaser and a target spacecraft, focusing on the application of Model Predictive Control (MPC) to design a controller capable of guiding the chaser toward the target. The operational principle of spacecraft thrusters, requiring a minimum activation time that leads to the existence of a control deadband, introduces mixed-integer constraints into the optimization, posing a considerable computational challenge due to the exponential complexity on the number of integer constraints. We address this complexity by presenting two solver algorithms that efficiently approximate the optimal solution in significantly less time than standard solvers, making them well-suited for real-time applications.

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arXiv2022

COSMIC: fast closed-form identification from large-scale data for LTV systems

We introduce a closed-form method for identification of discrete-time linear time-variant systems from data, formulating the learning problem as a regularized least squares problem where the regularizer favors smooth solutions within a trajectory. We develop a closed-form algorithm with guarantees of optimality and with a complexity that increases linearly with the number of instants considered per trajectory. The COSMIC algorithm achieves the desired result even in the presence of large volumes of data. Our method solved the problem using two orders of magnitude less computational power than a general purpose convex solver and was about 3 times faster than a Stochastic Block Coordinate Descent especially designed method. Computational times of our method remained in the order of magnitude of the second even for 10k and 100k time instants, where the general purpose solver crashed. To prove its applicability to real world systems, we test with spring-mass-damper system and use the estimated model to find the optimal control path. Our algorithm was applied to both a Low Fidelity and Functional Engineering Simulators for the Comet Interceptor mission, that requires precise pointing of the on-board cameras in a fast dynamics environment. Thus, this paper provides a fast alternative to classical system identification techniques for linear time-variant systems, while proving to be a solid base for applications in the Space industry and a step forward to the incorporation of algorithms that leverage data in such a safety-critical environment.

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