Coordination control of multiple ellipsoidal agents with collision avoidance and limited sensing ranges

This paper contributes a design of cooperative controllers that force N mobile agents with an ellipsoidal shape and a limited sensing range to track desired trajectories and to avoid collision between them. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise collision avoidance functions to design coordination controllers. The proposed control design guarantees (1) smooth coordination controllers despite the agents’ limited sensing ranges, (2) no collision between any agents, (3) asymptotical stability of desired equilibrium set, and (4) instability of all other undesired critical sets of the closed loop system

Flocking for multiple ellipsoidal agents with limited communication ranges

This paper contributes a design of distributed controllers for flocking of mobile agents with an ellipsoidal shape and a limited communication range. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise potential functions to design flocking control algorithms. The proposed flocking design results in (1) smooth controllers despite of the agents’ limited communication ranges, (2) no collisions between any agents, (3) asymptotic convergence of each agent’s generalized velocity to a desired velocity, and (4) boundedness of the flock size, defined as the sum of all distances between the agents, by a constant

Robust Decentralized Abstractions for Multiple Mobile Manipulators

This paper addresses the problem of decentralized abstractions for multiple mobile manipulators with 2nd order dynamics. In particular, we propose decentralized controllers for the navigation of each agent among predefined regions of interest in the workspace, while guaranteeing at the same time inter-agent collision avoidance and connectivity maintenance for a subset of initially connected agents. In that way, the motion of the coupled multi-agent system is abstracted into multiple finite transition systems for each agent, which are then suitable for the application of temporal logic-based high level plans. The proposed methodology is decentralized, since each agent uses local information based on limited sensing capabilities. Finally, simulation studies verify the validity of the approach.Comment: Accepted for publication in the IEEE Conference on Decision and Control, Melbourne, Australia, 201

Bounded Coordination Control of Second-order Dynamic Agents

This paper presents a constructive design of distributed and bounded coordination controllers that force mobile agents with second-order dynamics to track desired trajectories and to avoid collision between them. The control design is based on the new bounded control design technique for second-order systems, and new pairwise collision avoidance functions. The pair wise collision functions are functions of both the relative position and velocity of the agents instead of only the relative position as in the literature. Desired features of the proposed control design include:1) Boundedness of the control inputs by a predefined bound despite collision avoidance between the agentsconsidered,2) No collision between any agents,3) Asymptotical stability of desired equilibrium set, and4) Instability of all other undesired critical sets of the closed loop system. The proposed control design is then applied to design a coordination control system for a group of vertical take-off and landing (VTOL) aircraft

Coordination Control of Quadrotor VTOL Aircraft in Three-Dimensional Space

This paper presents a constructive design of distributed coordination controllers for a group of N quadrotor vertical take-off and landing (VTOL) aircraft in three-dimensional space. A combination of Euler angles and unit-quaternion for the attitude representation of the aircraft is used to result in an effective control design, and to reduce singularities in the aircraft’s dynamics. The coordination control design is based on a new bounded control design technique for second-order systems and new pairwise collision avoidance functions. The pairwise collision functions are functions of both relative positions and relative velocities between the aircraft instead of only their relative positions as in the literature. To overcome the inherent underactuation of the aircraft, the roll and pitch angles of the aircraft are considered as immediate controls. Simulations illustrate the results

UAV Optimal Cooperative Obstacle Avoidance and Target Tracking in Dynamic Stochastic Environments

Cette thèse propose une stratégie de contrôle avancée pour guider une flotte d'aéronefs sans pilote (UAV) dans un environnement à la fois stochastique et dynamique. Pour ce faire, un simulateur de vol 3D a été développé avec MATLAB® pour tester les algorithmes de la stratégie de guidage en fonctions de différents scénarios. L'objectif des missions simulées est de s'assurer que chaque UAV intercepte une cible ellipsoïdale mobile tout en évitant une panoplie d'obstacles ellipsoïdaux mobiles détectés en route. Les UAVs situés à l'intérieur des limites de communication peuvent coopérer afin d'améliorer leurs performances au cours de la mission. Le simulateur a été conçu de façon à ce que les UAV soient dotés de capteurs et d'appareils de communication de portée limitée. De plus, chaque UAV possède un pilote automatique qui stabilise l'aéronef en vol et un planificateur de trajectoires qui génère les commandes à envoyer au pilote automatique. Au coeur du planificateur de trajectoires se trouve un contrôleur prédictif à horizon fuyant qui détermine les commandes à envoyer à l'UAV. Ces commandes optimisent un critère de performance assujetti à des contraintes. Le critère de performance est conçu de sorte que les UAV atteignent les objectifs de la mission, alors que les contraintes assurent que les commandes générées adhèrent aux limites de manoeuvrabilité de l'aéronef. La planification de trajectoires pour UAV opérant dans un environnement dynamique et stochastique dépend fortement des déplacements anticipés des objets (obstacle, cible). Un filtre de Kalman étendu est donc utilisé pour prédire les trajectoires les plus probables des objets à partir de leurs états estimés. Des stratégies de poursuite et d'évitement ont aussi été développées en fonction des trajectoires prédites des objets détectés. Pour des raisons de sécurité, la conception de stratégies d'évitement de collision à la fois efficaces et robustes est primordiale au guidage d'UAV. Une nouvelle stratégie d'évitement d'obstacles par approche probabiliste a donc été développée. La méthode cherche à minimiser la probabilité de collision entre l'UAV et tous ses obstacles détectés sur l'horizon de prédiction, tout en s'assurant que, à chaque pas de prédiction, la probabilité de collision entre l'UAV et chacun de ses obstacles détectés ne surpasse pas un seuil prescrit. Des simulations sont présentées au cours de cette thèse pour démontrer l'efficacité des algorithmes proposés

Formation Control of Localised and Decentralised Robotic Swarms

Robot swarms consist of multiple autonomous robots, which detect and interact with their local environments. The fundamental intelligence is observed when a chaotic swarm reaches a stable and orderly objective formation. The process is important because the objective formation is designed such that the swarm achieves more than the sum of its individuals. A formation is a set of positions or tasks, and intelligent swarms are capable of self-organising and task allocating. Given an objective formation, individuals of a swarm reach different objective positions and perform different tasks. This implies task allocation in different possible choices. For each individual, the path to its objective position is regarded as the efort to take, and the inclination to different objective tasks means different eforts. The challenge is that it needs to choose wisely in the interaction with its neighbourhood. Changes of choices are compromises and each progress to the objective position imposes in uence on its neighbourhood. The collective intelligence comes from series of individual decisions in the process. In this thesis, we consider four problems that arise with the challenge. We use techniques from graph theory and agent-based design to address them. Formation control algorithms should not impose heavy burden in the communication network. Thus, to start with, limited sensing and communication are assumed, and the robots have minimal access to each other's identity through locally established channels. The control strategy is proposed based on local optimisation and multi-object mapping for a team of robots. Robots are able to make mapping decisions based on local information. To achieve the local optimal mapping decisions for each robot, two novel multi-object mapping protocols are designed. The first protocol performs confict locating and resolving, and the second adopts a most-neighbour mapping strategy. The formation problem is further addressed for a scalable team of robots subject to limited sensing with no communication. The robots themselves are fully independent with no designated roles. Scalable objective formation design is proposed such that the robot formation is scalable. Under the assumption that the data transmission among the robots is not available, a novel controller and a protocol are designed that do not rely on communication. As the controller only drives the robots to a partially desired formation, a distributed coordination protocol is proposed to resolve the imperfections. The case is investigated where the objective formations are arbitrary and have fixed sizes. Multi-objective mapping is proposed for the individual robots to identify their positions in the objective formation. The fixed formation size induces mapping loops, and to avoid local optimum traps, an evaluation method imposes a weak restriction on the predened formation, rendering it almost arbitrary. To enhance the robustness, the minimal local topology is proposed, and to reduce the computation burden and avoid the infnite trajectory loop, the coordination protocol is modifed by introducing probability. The practical problem of collision avoidance is also studied. The leaderfollower scheme is implemented on a multi-robot platform. On the premise of coordinated control laws, globally desired formation is achieved. The same problem in the path-planning perspective is considered on a global scale. Disc obstacles are filtered and clusters are identified based on their intersections. The path planning algorithm is designed based on obstacle clusters.Thesis (Ph.D.) -- University of Adelaide, School of Electrical & Electronic Engineering, 201

Analysis of the traffic conflict situation for speed probability distributions

The increasingly widespread application of drones and the emergence of urban air mobility leads to a challenging question in airspace modernisation: how to create a safe and scalable air traffic management system that can handle the expected density of operations. Increasing the number of vehicles in a given airspace volume and enabling routine operations are essential for these services to be economically viable. However, a higher density of operations increases risks, poses a great challenge for coordination and necessitates the development of a novel solution for traffic management. This paper contributes to the research towards such a strategy and the field of airspace management by calculating and analysing the conflict probability in an en-route, free-flight scenario for autonomous vehicles. Analytical methods are used to determine the directional dependence of conflict probabilities for exponential and normal prescribed speed probability distributions. The notions of geometric and speed conflict are introduced and distinguished throughout the calculations of the paper. The effect of truncating the set of available flight speeds is also investigated. The sensitivity of the calculated results to speed and heading perturbations is studied within the analytical framework and verified by numerical simulations. Results enable a fresh approach to conflict detection and resolution through distribution shaping and are intended to be used in an integrated, stochastic coordination framework

Satellite formation flying control of the relative trajectory shape and size using lorentz forces

Propellantless control approaches for small satellite formation flying represent a special interest and an important advantage for space industry nowadays. A formation flying control algorithm using the Lorentz force for Low­Earth Orbits to achieve a trajectory with required shape and size is proposed in this dissertation. The Lorentz force is produced as the result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achieving the required trajectories represents a challenge since the control is the variation of the satellite’s charge value. This control mechanism simplicity cannot provide full controllability. A Lyapunov­based control is developed for elimination of the initial relative drift after launch and it is aimed for reaching a required relative trajectory with predefined shape and size. The control algorithm is constructed to correct different parameters of the relative trajectory at different relative positions. The required amplitudes for close relative trajectories for in­plane and out­of­plane motion as well as the relative drift and shift of elliptical relative orbits are controllable using Lorentz force. Due to the absence of full controllability, the algorithm is incapable to correct the in­plane and out­of­plane motion phases, once these parameters are defined by the deployment conditions and therefore arbitrary. The proposed control allows the convergence to the trajectory with required shape and size. Centralized and decentralized control approaches are implemented and their performance is studied. The centralized approach considers two satellites formation formed by an electrically neutral leader satellite moving on a circular LEO and a follower which actively controls its orbital motion by changing its charge in order to remain in close vicinity of the leader. Formation flying consisting of more than two satellites with charge­changing capability can also be controlled by the proposed algorithm using a decentralized approach. This work also considers the control of satellite swarm trajectories in a sphere­shaped formation. Numerical simulation of the relative motion is used to study performance of the control algorithm. It implements the model of the geomagnetic field as a tilted dipole. The repulsive collision avoidance control is proposed for the case when the system elements are inside a dangerous proximity area. The convergence time and final trajectory accuracy are evaluated for different simulation parameters and conditions.Métodos de controlo para formações de voo de satélites de pequenas dimensões que não recorram ao uso de combustível representam, atualmente, um interesse especial e uma importante vantagem para a indústria espacial. Nesta dissertação é proposto um algoritmo de controlo que, recorrendo à força de Lorentz em orbitas terrestres baixas (LEO), é capaz de alcançar trajetórias com o respetivo o formato e o tamanho desejados. A força de Lorentz resulta de uma interação entre o campo magnético terrestre e o satélite eletricamente carregado. Alcançar as trajetórias solicitadas revela­se como sendo um desafio visto que o único método de controlo é a variação da carga interna do satélite. Este mecanismo de controlo revela­se como sendo incapaz de conferir controlabilidade total ao dispositivo. Um controlo baseado no método de Lyapunov é desenvolvido com o objetivo de eliminar a deriva inicial do satélite após o lançamento orbital e é destinado a atingir o tamanho e formato predefinidos da trajetória relativa objetivo. O algoritmo de controlo é construído de forma a corrigir os diferentes parâmetros da trajetória relativa em diferentes posições relativas. Usando a força de Lorentz é possível atingir tanto as amplitudes objetivo, considerando ambos os movimentos dentro e for do plano da trajetória, mas também a deriva e o deslocamento relativos da trajetória. Devido à falta de controlabilidade total, o algoritmo desenvolvido é incapaz de corrigir completamente os movimentos dentro e fora do plano da trajetória, visto que estes parâmetros são definidos na sua totalidade pelas condições de lançamento e, como tal, arbitrários. O algoritmo de controlo proposto possibilita a convergência dos valores para o formato e tamanho da trajetória desejada. Ambas as estratégias de controlo centralizadas e descentralizadas são aplicadas e a respetiva performance estudadas. No caso da estratégia centralizada, é considerado um voo em formação composto por dois satélites, onde o Líder se revela como sendo eletricamente neutro enquanto, e prescrevendo uma trajetória terrestre baixa circular, enquanto que o segundo, eletricamente ativo, é capaz de alterar o seu posicionamento relativo requerido, permutando a sua carga interna. Uma formação de voo considerando um número superior a dois satélites, com capacidades de carregamento elétrico, é também controlável considerando o algoritmo proposto. Este trabalho tem também em consideração o controlo da trajetória de um swarm de satélites num formato esférico. Simulações numéricas são usadas como método de análise da performance do algoritmo desenvolvido. Durante o processo de análise é implementado o modelo do dipolo inclinado como forma de simular o campo magnético terrestre. É também aplicado um algoritmo responsável por evitar situações de colisão eminente para casos em que a convergência de movimento dos satélites entra em zonas de proximidade critica. O tempo de convergência e a precisão da trajetória final são avaliadas para diferentes parâmetros e condições de simulação

Advances in Constrained Spacecraft Relative Motion Planning

This dissertation considers Spacecraft Relative Motion Planning (SRMP), where maneuvers are planned for one or more spacecraft to execute in close proximity to obstacles or to each other. The need for this type of maneuver planning has grown in recent years as the space environment becomes more cluttered, and the focus on space situational awareness increases. In SRMP, maneuvers must accommodate non-linear and non-convex constraints, be robust to disturbances, and be implementable on-board spacecraft with limited computational capabilities. Consequently, many standard optimization or path planning techniques cannot be directly applied to SRMP. In this dissertation, three novel SRMP techniques are developed and simulations are presented to illustrate the implementation of each method. Firstly, an invariance-based SRMP technique is proposed. Maneuvers are planned to transition a spacecraft between specified natural motion trajectories, which require no control to follow, while avoiding obstacles and accommodating minimum and maximum actuation limits. The method is based on a graph search applied to a ``virtual net'' with nodes corresponding to natural motion trajectories. Adjacency rules in the virtual net are based on safe positively invariant tubes built around each natural motion trajectory. These rules guarantee safe transitions between adjacent natural motion trajectories, even when set-bounded disturbances are present. Procedures to construct the safe positively invariant tubes and the virtual net are developed. Methods to reduce calculations are proposed and shown to significantly reduce computation time, with tradeoffs related to maneuver planning flexibility. Secondly, a SRMP technique is developed for the specific problem of satellite inspection. In this setting, an inspector spacecraft maneuvers to gather information about a target spacecraft. An information collection model is developed and used to construct a rapidly computable analytical control law based on the local gradient of the information rate. This control law drives the inspector spacecraft on a path along which the rate of information collection is strictly increasing. To ensure constraint satisfaction, the local gradient control law is combined with a state feedback control law, and rules are developed to govern switches between the two controllers. The method is shown to be effective in generating trajectories to gather information about a specified target point while accommodating disturbances. Finally, a control strategy is proposed to generate a formation containing an arbitrary number of vehicles. This strategy is based on an add-on predictive control mechanism known as a parameter governor. Parameter governors work by modifying parameters, such as gains or offsets, in a nominal closed-loop system to enforce constraints and improve performance. The parameter governor is first developed in a general setting, using generic non-linear system dynamics and an arbitrary formation design. Required calculations are minimized, and non-convex constraints are accommodated through use of a parameter update strategy based on graph colorability theory, and by limiting parameter values to a discrete set. A convergence analysis is presented, proving that under reasonable assumptions, the parameter governor is guaranteed to generate the desired formation. Two specific parameter governors, referred to as the Scale Shift Governor and Time Shift Governor, are proposed and applied to generate formations of spacecraft. These parameter governors enforce constraints by modifying either scale- or time-shifts applied to the target trajectory provided to each spacecraft in formation. Simulation case studies show the effectiveness of each method and demonstrate robustness to disturbances.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145795/1/gfrey_1.pd