Relative Space-Time Kinematics of an Anchorless Network

The work described in this thesis was in part financially supported by STW-sponsored OLFAR project (Contract Number: 10556) within the Dutch ASSYS perspectief programCircuits and System

Relative Kinematics Estimation Using Accelerometer Measurements

For a network of mobile nodes, the problem of estimation of relative kinematics, given pairwise distances between the nodes, has received limited attention in literature. In this context, relative kinematics includes relative position, relative velocity and other higher order kinematic parameters defined with respect to a common frame of reference within the network. For numerous application domains in engineering, the nodes are highly dynamic, making the estimation task much harder. To solve the estimation problem uniquely, conventional methods either require the positions of some nodes of the mobile network to be known [2] or impose rigid body constraints on the mobile network [3]. These conditions limit the scope of proposed methods. Given a network of mobile nodes and time-varying pairwise distance measurements, we introduce a time-varying Grammian-based data model under the assumption that the mobile nodes have polynomial trajectories. Using the results in [4] and [5], estimators are proposed to estimate the relative kinematic parameters. Furthermore, we consider a scenario where the nodes have on-board accelerometers and the mobile nodes are holonomic. Under such assumtpions, the proposed data model is extended to include these accelerometer measurements, leading to improvements in relative kinematics estimation. We conduct simulations to showcase the performance of the proposed estimators, which show improvement against state-of-the-art methods.Circuits and System

Relative Affine Localization for Robust Distributed Formation Control

Multiagent systems have been widely researched and deployed in the industry for their potential to collectively achieve goals by distributing tasks to individual agents [1]–[4]. Formation control, one of the many applications of multiagent systems, aims at steering agents into a stable geometric pattern in space [3], [4]. There has been a variety of crafted distributed controllers in literature based on different dynamics that agents follow, and different variables that agents sense and control [5]. Affine formation control is brought to the spotlight where N agents in RD converge to the target formation up to an affine transformation [6]. A more general scenario of affine formation control is the dynamic formation maneuvering problem where the target configuration is time-varying and the agents need to not only converge to the desired formation but also track the maneuvering pattern. This problem is addressed in [7] where a series of controller designs are introduced depending on the dynamics of the agents...Circuits and System

Distributed Detect-and-Avoid with Non-Stationary Obstacles

Detect-and-avoid is a crucial challenge in the autonomous navigation of single or multiple agent systems. For safe and reliable autonomous navigation in unknown and dynamic environments, obstacles should be sensed using onboard sensors and the trajectory should be adjusted accordingly. Additional challenge is introduced in the case of multi-agent systems, where the adjusted trajectory could introduce collisions between agents, for example in satellite swarms in Low Earth Orbits (LEO). The increasing amount of occupancy of the low orbit and the presence of space debris gives high risk of damaging satellites due to collisions. With communication between nearby satellites, cooperative methods enable the avoidance of collisions with dynamic obstacles while simultaneously finding an optimal trajectory of the cooperative agents. Drone swarms equipped in industrial settings encounter the challenge of navigating through a dynamic environments in a similar way. The dynamic obstacles are now other autonomous systems as well as humans, performing tasks simultaneously.Circuits and System

Performance Bounds for Cooperative Localisation in Starlink

Large satellite constellations in Low Earth Orbit (LEO) have the potential to revolutionise worldwide internet access. The concomitant potential of these large constellations to impact space sustainability, however, has prompted concern from space actors as well as provoking concern in the ground-based astronomy community. Increasing the positional accuracy of the orbital state of satellites in mega-constellations improves space situational awareness, reducing the need for collision avoidance manoeuvres and allowing astronomers to prepare better observational mitigation strategies. Current state-of-the-art solutions rely on Earth-based ground segments or onboard Global Navigation Satellite Systems hardware to precisely localise satellites. These methods can be augmented by cooperative navigation within the satellite network using existing intersatellite links. In this paper, we present a model of Phase 1 of Starlink, one of the more well-studied large constellations in LEO and investigate the potential of cooperative localisation using time-of-arrival measurements from the optical intersatellite links in the constellation. We establish the achievable performance of cooperative localisation between 1584 Starlink satellites and 87 ground stations by calculating the theoretical lower bounds on the accuracy of the position estimation e.g., Cramer-Rao Bound over the course of one orbit at 573 simulated time steps. Our results show that the standard deviation for localising the Starlink satellites has a value of 10.15 m and varies between a maximum of 36.5 m and a minimum of approximately 2m. This result is determined primarily by the geometry of the constellation and the characteristics of the intersatellite links. We discuss our results and lay out options for more sophisticated modelling and investigations for improved position accuracy of large satellite constellations.Circuits and System

Relative Kinematics Estimation Using Accelerometer Measurements

Given a network of N static nodes in D-dimensional space and the pairwise distances between them, the challenge of estimating the coordinates of the nodes is a well-studied problem. However, for numerous application domains, the nodes are mobile and the estimation of relative kinematics (e.g., position, velocity and acceleration) is a challenge, which has received limited attention in literature. In this paper, we introduce a time-varying Grammian-based data model for estimating the relative kinematics of mobile nodes with polynomial trajectories, given the time-varying pairwise distance measurements between the nodes. Furthermore, we consider a scenario where the nodes have on-board accelerometers, and extend the proposed data model to include these accelerometer measurements. We propose closed-form solutions to estimate the relative kinematics, based on the proposed data models. We conduct simulations to showcase the performance of the proposed estimators, which show improvement against state-of-the-art methods.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Signal Processing System

End-of-life of satellite swarms

Satellite swarms offer a high-capability mission architecture with a variety of potential applications in space exploration and discovery. Swarm-based architectures —which comprise multiple agents operating collectively as a distributed system— have been proposed for Earth observation, astronomy, planetary exploration, and heliophysics. Some of the key technology demonstration missions have already successfully flown in the past decades. The increasing interest in satellite swarms suggests that this innovative architecture will be adopted in a variety of future missions in the coming years, raising the question of how to dispose of satellite swarms at the end of their operational lifetimes. Mega-constellations or swarms comprising of numerous small satellites are difficult to track by Earth-based networks. They also increase the risk of collisions, particularly during end-of-life when these small satellites cannot be maneuvered to avoid collisions with functional satellite systems. Previously, distributed small satellite missions such as KickSat-2 and SpaceBEES 1-4 were designed to passively deorbit and burn up during atmospheric re-entry at the end of their lifetimes. However, disposing of satellite swarms outside low LEO (Low-Earth Orbit) has no trivial solution which both meets space situational awareness requirements and aligns with the philosophy of space sustainability. The distributed functionality which makes swarm missions so flexible and adaptable also means that many individual swarm agents have to be disposed of at end-of-life, rendering traditional approaches such as migration to the GEO (Geosynchronous Earth Orbit) graveyard orbit problematic. The challenges of disposing satellite swarms are as varied as the environments they could operate in — swarms used for planetary exploration will have to respect planetary protection policies while swarms engaged in Earth observation missions will have to be safely deorbited amidst an increasingly crowded LEO environment. In this paper we explore how the autonomy and distributed nature of swarms both complicates end-of-life disposal and simultaneously enables novel solutions to post-mission disposal. We then survey existing end-of-life scenarios for satellite swarms and propose a novel research approach to swarm disposal that could comply with both legal requirements and the philosophy of space sustainability.Signal Processing System

Distributed Gaussian Process Hyperparameter Optimization for Multi-Agent Systems

Gaussian Process (GP) is a flexible non-parametric method which has a wide variety of applications e.g., field estimation using multi-agent systems. However, the training of the hyperparameters suffers from high computational complexity. Recently, distributed hyperparameter optimization with proximal gradients has been proposed to reduce complexity, however only for a network with a central station. In this work, exploiting edge-based constraints, we propose two fully-distributed algorithms pxADMMfd and pxADMMfd,fast for a network of multi-agent systems, which do not rely on a central station. In addition, asynchronous versions of the algorithms are also proposed to reduce the synchronization overhead in heterogeneous networks. Simulations are conducted for a field estimation problem, using both artificial, and real-world datasets, which show that the proposed fully-distributed algorithms successfully converge, at the cost of an increased number of iterations.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Signal Processing System

Distributed Gaussian Process for Multi-agent Systems

Distributed multi-agent systems (MAS) offer higher robustness and scalability compared to single-agent systems employing centralized solutions. The challenge of learning unknown environmental phenomenons can be regarded as learning a hidden function, which can be modeled through non-parametric methods e.g., Gaussian Processes (GP). Our main challenge is to develop a distributed non-parametric model e.g., GP for environment monitoring. In this work, we specifically focus on developing fully-distributed algorithm for GP hyperparameter optimization. An example of hyperparameter set is θ = {sf , l1, l2} for a squared exponential kernel, where signal variance sf indicates the range of function, and the characteristic lengths l1, l2 indicate the smoothness. We also develop an asynchronous version to deal with heterogeneous processing time of agents. Assuming that local datasets at agents are independent with each other, we approximate hyperparameter optimization by maximizing the sum of local Likelihoods. By further defining a unique θ across the network, the problem can be regarded as a distributed consensus problem. Alternating direction method of multipliers (ADMM) with proximal θ update have been applied by Xie et al. [1], which still requires a center computing unit for auxiliary variable update. We propose a fully-distributed algorithm with centralized update replaced by local consensus. In each iteration, an agent collects auxiliary variables from neighbor agents, and use their average in new iteration. Asynchronous behavior is introduced by allowing fast agents to start new iterations without collecting update from slowest agents. Our proposed algorithm allows agents in the network to perform faster iterations and thus saving time. We perform simulations with artificially generated 2D GP field under pre-defined hyperparameter setting. Noisy measurements are randomly allocated to agents for distributed hyperparameter optimization. Simulation results show that the optimal hyperparameters at agents converge to the expected values...Circuits and System

Technical Note on Simulated Megaconstellation Ephemerides Dataset

This technical note accompanies a dataset providing the time-varying positions of 1584 satellites in a simulated megaconstellation modelled on Phase 1 of SpaceX’s Starlink. This note explains the context, creation, format, and potential uses of the dataset. The code used to create these data is publicly available.Circuits and System