1 Dynamical and computational structures under the sea: modelling of fish motion Timothy James Roberts University of Manchester School of Computer Science Supervisor: Dr. Eva M. Navarro-Lopez´ Abstract—A simulation comprised of a multi-agent system A. Fish Swarming based upon Couzin’s Model of swarming/flocking is created to demonstrate the movement and behaviour of fish. The model Shoals of fish exhibit a behaviour known as swarming in used is a modified version of Couzin’s Model in that two species which multiple fish seemingly move together as one unit. of fish can interact with one another. The two species have their Visually, swarms of fish can create very complex and unique own parameters to determine how they react to their own species shapes, which was an interest throughout this project. Fish in and the other species. The parameters can be altered in order to swarms have many advantages compared to solitary fish such observe unique behaviours of the fish. These behaviours can then be compared to real fish behaviour to measure the effectiveness as predator avoidance and a higher foraging success. This is of the simulation. A future implementation would allow more due to the fact that if a fish detects something of interest, parameters of the fish to be available. it will essentially transfer this information to the rest of the Index Terms—Dynamical Systems, Swarming, Couzin’s Model, swarm through it’s movement. A lone fish will react quicker Multi-agent Systems, Vectors. to a predator than a swarm of fish ; however, the swarm will confuse the predator and allow the fish to conserve energy for other tasks [1]. CONTENTS I Introduction 1 I-A Fish Swarming . .1 I-B Report Overview . .2 I-C Objectives . .2 I-D Summary of Results . .2 II Background Information 2 II-A Multi-agent Systems . .2 II-B Swarming Models and Algorithms . .3 II-C Couzin’s Model . .3 Fig. 1. An example of fish swarming [2]. The fish will organise themselves III Implementation 4 into a cohesive group. III-A Fish Variables . .4 III-B Functions, Trigonometry and Vectors . .4 Fish will form a swarm by observing the other fish around III-C Two Species . .6 themselves and moving similarly to them. An interference at one end of the swarm will usually be passed through the whole IV Results and Evaluation 6 swarm. The fish will try to avoid colliding with other fish, IV-A Single Species Behaviour . .6 by keeping a certain distance away from the others and they IV-B Dual Species Behaviour . .6 will move towards other nearby fish so as to increase their numbers. The fish also align themselves with nearby fish, so V Conclusions 7 that a group of fish in the swarm will have a similar orientation. Fig. 1 shows how the fish align themselves. If you split up the References 8 image, the fish in each section will be pointing roughly in the same direction. The structure of a swarm can be described to some extent, I. INTRODUCTION although it can be difficult due to the vast amount of fish. The This project is about simulating a dynamic model of fish most obvious is the swarm size. A swarm with many fish can swarming. The movement and behaviour of fish must be produce more varied behaviour than a smaller swarm. Some understood in order to replicate these characteristics in a swarms can contain upwards of 10 million fish [3]. computer simulation. Polarity describes the orientation of the fish as previously 2 mentioned. The polarity of the entire swarm can be calculated II. BACKGROUND INFORMATION by first finding the average orientation of the fish. Then for A. Multi-agent Systems each fish, find the angle between it’s orientation and the swarm orientation. The average of all of these angles will be the Due to the way fish interact with one another, the simu- swarm polarity [4]. lation was implemented as a multi-agent system. This is a A measure of how compact the swarm is, is the nearest computerised realisation of intelligent agents interacting in neighbour distance. This involves finding the distances be- an environment. In this case, the fish are the agents and the tween each fish and it’s closest neighbour and then averaging environment is the ocean or an aquarium. the results. Some fish, such as sardines, will group together to An intelligent agent is an autonomous entity, in the sense form a sphere like object known as a bait ball as a last ditch that it can perform actions on it’s own without the need for user attempt to fend off predators. input. The agents will observe the environment through sensors More detailed knowledge of fish movement isn’t necessary ,which determine what specific information it will need, and for this project. The report structure will be explained next. then perform an action based on that information. Stuart J. Russell and Peter Novig defined five types of intelligent agents B. Report Overview [5]: The basic structure of this report is as follows. This section • Simple reflex agents of the paper will provide a brief description of what was set out • Model-based reflex agents to be achieved and what the results show. The second section • Goal-based agents will focus on background information used to implement • Utility-based agents the simulation, with the third section explaining how the • Learning agents simulation was implemented. The fourth section will discuss Simplex reflex agents are the what was previously described. an in-depth evaluation of the results and the final section will They only perform an action based on how the environment give some conclusions on what was achieved. state is at that point in time and ignore anything that was observed before. C. Objectives The goals of this project were: • To investigate different methods of modelling swarming. – Study the swarming behaviour of fish and see what mathematical models are available. – Choose a model that best suits fish swarming. • To implement a swarming model. – Decide what language to use. – Design how to map the model to code. • To modify the model to allow two species. – Decide how the model must be changed. • To observe how the simulation changes with respect to the parameters. Fig. 2. A diagram of how a simple reflex agent works [6]. – Find settings to provide distinct behaviour. These steps ensure the end result has no major flaws. Model-based reflex agents are similar to reflex agents, ex- cept that they store a structure describing how the environment D. Summary of Results has evolved over time. This allows the agent to observe the The behaviour that was set out to be emulated, was that environment that it can’t see. It then acts the same as a simple of the behaviour shown in one of Iain Couzin’s papers [5]. reflex agent. The paper shows how different behaviours emerge as the Goal-based agents and utility-based agents expand upon parameters change. The three main behaviours shown, for one model-based reflex agents. Goal-based agents will use ’goals’ species, were a swarm, a torus and a polarised group. These to decide what action to take. The action that will be performed behaviours were discovered in the simulation. ill be the one that best suits one of the goals it wants to The second set of results were for two species. Due to the achieve. A utility-based agent uses a utility function in order fact that there are lots of parameters to modify for two species, the measure the desirability of the state of the environment. finding interesting behaviour was a challenge. The results show The action performed will be the one that produces the best a groups of fish avoiding a polarised swarm of fish and it utility of the environment state. shows how some fish would be extremely cautious even when Finally, learning agents have a ’performance element’, the fish they are avoiding have no interest in them. Another which determines which actions to take, and the ’learning ele- set of results show how the prey formed a structure similar to ment’, which improves the performance element, thus ensuring a bait ball previously mentioned. The prey would stay within that the learning agent will operate more effectively over time. a small area and move out of the way of the predators that Intelligent agents have three characteristics, as specified in were surrounding them. Michael Wooldridge’s textbook [7]: 3 • Autonomy - Agents are autonomous to some extent. Model was used as it is very simple to understand and each of • Local views - Agents won’t have a global view of the the steps associated with it can be broken down into multiple system. sub-steps. It was designed by Iain Couzin as a variant to the • Decentralisation - No agent is in control of the others. Boids model. Couzin’s Model represents an agent as having It’s unreasonable to suggest that an agent would have a full three zones around it, similarly to the three rules described in view of it’s environment. In the context of fish, how would the previous sub-section. They are: one fish know the positions and orientations of every other • Zone of repulsion (ZOR). fish in it’s swarm? It could only know information about the • Zone of orientation (ZOO). fish close to it and the ones it can see. • Zone of attraction (ZOA). The multi-agent system used in the simulation will be a The zones work in the same way as the previous rules only simple reflex agent as it best represents the behaviour of the that sizes of the zones are, from smallest to largest, ZOR, fish.