Collision and re-entry analysis under aleatory and epistemic uncertainty

This paper presents an approach to the design of optimal collision avoidance and re-entry maneuvers considering different types of uncertainty in initial conditions and model parameters. The uncertainty is propagated through the dynamics, with a non-intrusive approach, based on multivariate Tchebycheff series, to form a polynomial representation of the final states. The collision probability, in the cases of precise and imprecise probability measures, is computed considering the intersection between the uncertainty region of the end states of the spacecraft and a reference sphere. The re-entry probability, instead, is computed considering the intersection between the uncertainty region of the end states of the spacecraft and the atmosphere

Optimal role and position assignment in multi-robot freely reachable formations

Many multi-robot problems require the achievement of formations as part of the overall mission. This work considers a scenario in which unlabeled homogeneous robots must adopt a given formation pattern buildable anywhere in the environment. This involves finding the relative pose of the formation in regard to the initial robot positions, understood as a translation and a rotation; and the optimal assignment of the role of each robot within the formation. This paper provides an optimal solution for the combined parameters of translation, rotation and assignment that minimizes total displacement. To achieve this objective we first formally prove that the three decision variables are separable. Since computing the optimal assignment without accounting for the rotation is a computationally expensive problem, we propose an algorithm that efficiently computes the optimal roles together with the rotation. The algorithm is provably correct and finds the optimal solution in finite time. A distributed implementation is also discussed. Simulation results characterize the complexity of our solution and demonstrate its effectiveness

Distributed Dynamic Sensor Assignment of Multiple Mobile Targets

Distributed scalable algorithms are sought in many multi-robot contexts. In this work we address the dynamic optimal linear assignment problem, exemplified as a target tracking mission in which mobile robots visually track mobile targets in a one-to-one capacity. We adapt our previous work on formation achievement by means of a distributed simplex variant, which results in a conceptually simple consensus solution, asynchronous in nature and requiring only local broadcast communications. This approach seamlessly tackles dynamic changes in both costs and network topology. Improvements designed to accelerate the global convergence in the face of dynamically evolving task rewards are described and evaluated with simulations that highlight the efficiency and scalability of the proposal. Experiments with a team of three Turtlebot robots are finally shown to validate the applicability of the algorithm

An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra

The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra. Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost

Constraints on the near-Earth asteroid obliquity distribution from the Yarkovsky effect

Aims. From lightcurve and radar data we know the spin axis of only 43 near-Earth asteroids. In this paper we attempt to constrain the spin axis obliquity distribution of near-Earth asteroids by leveraging the Yarkovsky effect and its dependence on an asteroid’s obliquity. Methods. By modeling the physical parameters driving the Yarkovsky effect, we solve an inverse problem where we test different simple parametric obliquity distributions. Each distribution results in a predicted Yarkovsky effect distribution that we compare with a X2 test to a dataset of 125 Yarkovsky estimates. Results. We find different obliquity distributions that are statistically satisfactory. In particular, among the considered models, the best-fit solution is a quadratic function, which only depends on two parameters, favors extreme obliquities, consistent with the expected outcomes from the YORP effect, has a 2:1 ratio between retrograde and direct rotators, which is in agreement with theoretical predictions, and is statistically consistent with the distribution of known spin axes of near-Earth asteroids

Collision avoidance as a robust reachability problem under model uncertainty

The paper presents an approach to the design of an optimal collision avoidance maneuver under model uncertainty. The dynamical model is assumed to be only partially known and the missing components are modeled with a polynomial expansion whose coefficients are recovered from sparse observations. The resulting optimal control problem is then translated into a robust reachability problem in which a controlled object has to avoid the region of possible collisions, in a given time, with a given target. The paper will present a solution for a circular orbit in the case in which the reachable set is given by the level set of an artificial potential function

Analysis, evaluation and improvement of RT-WMP for real-time and QoS wireless communication: Applications in confined environments

En los ultimos años, la innovación tecnológica, la característica de flexibilidad y el rápido despligue de las redes inalámbricas, han favorecido la difusión de la redes móviles ad-hoc (MANETs), capaces de ofrecer servicios para tareas específicas entre nodos móviles. Los aspectos relacionados al dinamismo de la topología móvil y el acceso a un medio compartido por naturaleza hacen que sea preciso enfrentarse a clases de problemas distintos de los relacionados con la redes cableadas, atrayendo de este modo el interés de la comunidad científica. Las redes ad-hoc suelen soportar tráfico con garantía de servicio mínimo y la mayor parte de las propuestas presentes en literatura tratan de dar garantías de ancho de banda o minimizar el retardo de los mensajes. Sin embargo hay situaciones en las que estas garantías no son suficientes. Este es el caso de los sistemas que requieren garantías mas fuertes en la entrega de los mensajes, como es el caso de los sistemas de tiempo real donde la pérdida o el retraso de un sólo mensaje puede provocar problemas graves. Otras aplicaciones como la videoconferencia, cada vez más extendidas, implican un tráfico de datos con requisitos diferentes, como la calidad de servicio (QoS). Los requisitos de tiempo real y de QoS añaden nuevos retos al ya exigente servicio de comunicación inalámbrica entre estaciones móviles de una MANET. Además, hay aplicaciones en las que hay que tener en cuenta algo más que el simple encaminamiento de los mensajes. Este es el caso de aplicaciones en entornos subterráneos, donde el conocimiento de la evolución de propagación de la señal entre los diferentes nodos puede ser útil para mejorar la calidad de servicio y mantener la conectividad en cada momento. A pesar de ésto, dentro del amplio abanicos de propuestas presente en la literatura, existen un conjunto de limitaciones que van de el mero uso de protocolos simulados a propuestas que no tienen en cuenta entornos no convencionales o que resultan aisladas desde el punto de vista de la integración en sistemas complejos. En esta tesis doctoral, se propone un estudio completo sobre un plataforma inalámbrica de tiempo real, utilizando el protocolo RT-WMP capaz de gestionar trafíco multimedia al mismo tiempo y adaptado al entorno de trabajo. Se propone una extensión para el soporte a los datos con calidad de servicio sin limitar las caractaristícas temporales del protocolo básico. Y con el fin de tener en cuenta el efecto de la propagación de la señal, se caracteriza el entorno por medio de un conjunto de restricciones de conectividad. La solución ha sido desarrollada y su validez ha sido demostrada extensamente en aplicaciones reales en entornos subterráneos, en redes malladas y aplicaciones robóticas

Trajectory Planning Under Time-Constrained Communication

In the present paper we address the problem of trajectory planning for scenarios in which some robot has to exchange information with other moving robots for at least a certain time, determined by the amount of information. We are particularly focused on scenarios where a team of robots must be deployed, reaching some locations to make observations of the environment. The information gathered by all the robots must be shared with an operation center (OP), thus some robots are devoted to retransmit to the OP the data of their teammates. We develop a trajectory planning method called Time-Constrained RRT (TC-RRT). It computes trajectories to reach the assigned primary goals, but subjected to the constraint determined by the need of communicating with another robot acting as moving relay, just during the time it takes to fulfill the data exchange. Against other methods in the literature, using this method it is not needed a task allocator to assign beforehand specific meeting points or areas for communication exchange, because the planner finds the best area to do it, simultaneously minimizing the time to reach the goal. Evaluation and limitations of the technique are presented for different system parameters

SMART-UQ : uncertainty quantification toolbox for generalised intrusive and non intrusive polynomial algebra

The paper is presenting a newly developed modular toolbox named Strathclyde Mechanical and Aerospace Research Toolbox for Uncertainty Quantification (SMART-UQ) that implements a collection of intrusive and non intrusive techniques for polynomial approximation and propagation of uncertainties. Non intrusive methods build the polynomial approximation of the uncertain states through sampling of the uncertain parameters space and interpolation. Intrusive methods redefine operators in the states model and perform the states evaluation according to the newly defined operators. The main advantage of non intrusive methods is their range of applicability since the model is treated as a black box hence no regularity is required. On the other hand, they suffer from the curse of dimensionality when the number of required sample points increases. Intrusive techniques are able to overcome this limitation since they have lower computational cost than their corresponding non intrusive counterpart. Nevertheless, intrusive methods are harder to implement and cannot treat the model as a black box. Moreover intrusive methods are able to propagate nonlinear regions of uncertainties while non intrusive methods rely on hypercubes sampling. The most widely known intrusive method for uncertainty propagation in orbital dynamics is Taylor Differential Algebra. The same idea has been generalized to Tchebycheff and Newton polynomial basis because of their fast uniform convergence with relaxed continuity and smoothness requirements. However the SMART-UQ toolbox has been designed in a flexible way to allow further extension of the intrusive and non-intrusive methods to other basis. The Generalized Intrusive Polynomial Expansion (GIPE) approach, implemented in the toolbox and presented here in the paper, expands the uncertain quantities in a polynomial series in the chosen basis and propagates them through the dynamics using a multivariate polynomial algebra. Hence the operations that usually are performed in the space of real numbers are now performed in the algebra of polynomials therefore a polynomial representation of the uncertain states is available at each integration step. To improve the computational complexity of the method, arithmetic operations are performed in the monomial basis. Therefore a transformation between the chosen basis and the monomial basis is performed after the expansion of the elementary functions. Non intrusive methods have been implemented for a set of sampling techniques (Halton, Sobol, Latin Hypercube) for interpolation in the complete polynomial basis as well as on sparse grid for a reduced set of basis. In the paper the different intrusive and non intrusive techniques integrated in SMART-UQ will be presented together with the architectural design of the toolbox. Test cases on propagation of uncertainties in space dynamics with the corresponding intrusive and non intrusive approaches will be discussed in terms of computational cost and accuracy