Mathematical Modelling of Turning Delays in Swarm Robotics

We investigate the effect of turning delays on the behaviour of groups of differential wheeled robots and show that the group-level behaviour can be described by a transport equation with a suitably incorporated delay. The results of our mathematical analysis are supported by numerical simulations and experiments with e-puck robots. The experimental quantity we compare to our revised model is the mean time for robots to find the target area in an unknown environment. The transport equation with delay better predicts the mean time to find the target than the standard transport equation without delay.Comment: Submitted to the IMA Journal of Applied Mathematic

Effect of Communication Delays on the Successful Coordination of a Group of Biomimetic AUVs

In this paper, the influence of delays on the ability of a formation control algorithm to coordinate a group of twelve Biomimetic Autonomous Underwater Vehicles (BAUVs) is investigated. In this study the formation control algorithm is a decentralized methodology based on the behavioural mechanisms of fish within school structures. Incorporated within this algorithm is a representation of the well-known and frequently used communication protocol, Time-Division-Multiple-Access (TDMA). TDMA operates by assigning each vehicle a specific timeslot during which it can broadcast to the remaining members of the group. The size of this timeslot varies depending on a number of operational parameters such as the size of the message being transmitted, the hardware used and the distance between neighbouring vehicles. Therefore, in this work, numerous timeslot sizes are tested that range from theoretical possible values through to values used in practice. The formation control algorithm and the TDMA protocol have been implemented within a validated mathematical of the RoboSalmon BAUV designed and manufactured at the University of Glasgow. The results demonstrate a significant deterioration in the ability of the formation control algorithms as the timeslot size is increased. This deterioration is due to the fact that as the timeslot size is increased, the interim period between successive communication updates increases and as a result, the error between where the formation control algorithm estimates each vehicle to be and where they actually are, increases. As a result, since the algorithm no longer has an accurate representation of the positioning of neighbouring vehicles, it is no longer capable of selecting the correct behavioural equation and subsequently, is unable to coordinate the vehicles to form a stable group structure

Informative and misinformative interactions in a school of fish

It is generally accepted that, when moving in groups, animals process information to coordinate their motion. Recent studies have begun to apply rigorous methods based on Information Theory to quantify such distributed computation. Following this perspective, we use transfer entropy to quantify dynamic information flows locally in space and time across a school of fish during directional changes around a circular tank, i.e. U-turns. This analysis reveals peaks in information flows during collective U-turns and identifies two different flows: an informative flow (positive transfer entropy) based on fish that have already turned about fish that are turning, and a misinformative flow (negative transfer entropy) based on fish that have not turned yet about fish that are turning. We also reveal that the information flows are related to relative position and alignment between fish, and identify spatial patterns of information and misinformation cascades. This study offers several methodological contributions and we expect further application of these methodologies to reveal intricacies of self-organisation in other animal groups and active matter in general

Interacting particles with L\'{e}vy strategies: limits of transport equations for swarm robotic systems

L\'{e}vy robotic systems combine superdiffusive random movement with emergent collective behaviour from local communication and alignment in order to find rare targets or track objects. In this article we derive macroscopic fractional PDE descriptions from the movement strategies of the individual robots. Starting from a kinetic equation which describes the movement of robots based on alignment, collisions and occasional long distance runs according to a L\'{e}vy distribution, we obtain a system of evolution equations for the fractional diffusion for long times. We show that the system allows efficient parameter studies for a search problem, addressing basic questions like the optimal number of robots needed to cover an area in a certain time. For shorter times, in the hyperbolic limit of the kinetic equation, the PDE model is dominated by alignment, irrespective of the long range movement. This is in agreement with previous results in swarming of self-propelled particles. The article indicates the novel and quantitative modeling opportunities which swarm robotic systems provide for the study of both emergent collective behaviour and anomalous diffusion, on the respective time scales.Comment: 23 pages, 3 figures, to appear in SIAM Journal on Applied Mathematic

Formation morphing and collision avoidance in swarms of robots

Formation maintenance and collision avoidance are two of the key factors in swarm robotics. The demand for autonomous fleets of robots is ever increasing from manufacturing to product deliveries to surveillance to mapping and so on. Moreover, for resource constrained autonomous robots, such as UAVs and UGVs, energy-efficiency is very vital due to their limited batteries. Therefore formation maintenance and collision avoidance developed for such robots need to be energy-efficient. Integration between these two approaches needs to be performed systematically. The experimental analysis of the proposed approaches presented in this thesis target two main branches: 1) action based and 2) perception based energy consumption in a swarm of robots. In the first branch, there are two different paths: i) optimal formation morphing: the main goal is to the optimize the reformation process from the highest level of agitation of the swarm, i.e., maximum disturbance in the formation shape and ii) congestion minimization: the main goal here is to find an optimal solution for distribution of the swarm into sub-swarms to minimize the delays due to over population of the agents while bypassing the obstacles. In the second branch, i.e., perception based energy consumption, the main goal is to increase the mission life on a single charge by injecting the adaptive consciousness into the agents so they can turn off their ranging sensors and navigate while listening to their leader. For formation collision co-awareness, we systematically integrated the methodologies by designing a multi-priority control and utilized the non-rigid mapping scheme of thin-plate splines technique to minimize the deformation caused by obstacle avoidance. For congestion-aware morphing and avoidance maneuvers, we discuss how the delays caused by over population can be minimized with local sense and avoid approach. The leader, upon detection of obstacles, pre-estimates the optimal configuration, i.e., number of agents in the sub-swarms, and divides the swarm as such. We show the efficiency of the proposed approach experimentally

Signal propagation and linear response in the delay Vicsek model

Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that: (i) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (ii) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (iii) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; (iv) the linear response breaks down when orientation conservation is broken.Comment: 13 pages, 9 figue

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation

Design and implementation of a bristle bot swarm system

Swarm robotics focuses on the study and development of robot systems containing a large number of agents that interact with each other in a collective behaviour in order to achieve tasks or overcome obstacles. Bristlebots are vibration-driven mobile robots. They are characterized by small size, high speed, simple design and low costs for production and application – qualities which are advantageous for agents of swarm robotic systems. However, most studies have been developed over systems with no control or systems with two or more actuators. The aim of this master thesis is the development of a bristle based robot agent for a swarm robotics microsystem with units for locomotion, sensing, data processing, control, communication and energy storage. New approaches in modelling and development of swarm agents are given, and a robot prototype is presented. The robot is driven by a single DC motor and uses a bristle system to create locomotion. It should be noted, that within the system design, considerations for the size, weight and minimalist architecture are taken. Experiments are presented and the system’s capabilities for displacement, velocity and trajectory generation are analysed. While the parallel velocity maintains a positive magnitude in both motor rotation directions, the rotation speed and transversal velocity of the robot have opposite directions, creating curved trajectories with opposite orientations. In Frequencies up to 210 Hz, the rotation direction of the robot is maintained while the magnitude slightly varies. However, for higher frequencies, the rotation direction of the robot is reversed, maintaining a similar magnitude. The transversal speeds at this frequency range, maintain their direction but are clearly reduced compared to lower frequencies.Tesi