Modelling and recreating complex, natural flocking and predatory behaviour using a limited rule set. BSc (Hons.) in Computer Science

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1 Modelling and recreating complex, natural flocking and predatory behaviour using a limited rule set. BSc (Hons.) in Computer Science Samuele Pavone 2004

2 Modelling and recreating complex, natural flocking and predatory behaviour using a limited rule set. Submitted by Samuele Pavone Copyright Attention is drawn to the fact that copyright of this thesis rests with its author. The Intellectual Property Rights of the products produced as part of the project belong to the University of Bath (see This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written consent of the author. Declaration This dissertation is submitted to the University of Bath in accordance with the requirements of the degree of Batchelor of Science in the Department of Computer Science. No portion of the work in this dissertation has been submitted in support of an application for any other degree or qualification of this or any other university or institution of learning. Except where specifically acknowledged, it is the work of the author. This thesis may be made available for consultation within the University Library and may be photocopied or lent to other libraries for the purposes of consultation.

3 Abstract In nature, we have all witnessed large groups of birds flying in the sky, or a herd of sheep in a field; both are examples of flocking, a behaviour used in the animal kingdom for mutual protection from predators. In 1987 Craig Reynolds showed how flocking was an emergent behaviour derived from a small number of simple rules that governed behaviour. Reynolds work stipulates high level rules that can be implemented in a number of different ways. Starting from the original high level rules, an analysis and evaluation of contrasting implementation methods is produced. An implementation of the rules is designed and subsequently modified during coding. Work by Pocknell, Shultz and Vaughan adds solitary predators and shepherds to Reynolds model using a variety of different methods for governing predator behaviour. The different approaches are examined and a set of simple rules for predators is derived. Further suggestions are included about expanding the rule set so that co-ordinated predation between a group of predators appears more realistic. It is shown that while there is potential for predation to be simulated as emergent behaviour, it is not deemed viable or realistic without the addition of a more complex rule set involving the use of multiple predatory states.

4 Acknowledgements With heartfelt thanks to my family for the support shown and Dr Dan Richardson, for supervising my progress.

5 Contents 1 Introduction A gentle start Compelling factors Additional work Literature Survey Introduction Definitions Background information Representing and storing boids Basic flocking theory Forerunners to Reynolds Reynolds basics for flocks Obstacle avoidance techniques Steer away from surface Steer away from centre Curb Feeling Avoiding inter-flock collision Other means of collision avoidance Predation and Predator-Prey implementation techniques Using Finite State Machines Seek and Pursuit behaviours In summation Requirements analysis and specification Requirements elicitation What is a flock? Aggregation Further derived requirements Graphics and Graphical user interfaces Technology and Programming Test plan Project Design Explaining the development environment Programming language Design Methodology Implementing the boid simulation On the storage of boids Representing Direction: Vectors and Scalars The Five Class Boid Model Introduction and Background Object identification Intra-object communication Creating obstacles The Main Screen The two class boid model Differences and Alterations...30

6 4.5 Rule Implementation techniques Linear Boid Movement Non-linear Boid Movement: Static Obstacles Non-linear Boid Movement: Flock cohesion and avoidance Modelling Predation Predation techniques Simple Co-operation Proposing advanced behaviour System Testing...36 Testing the flocking behaviour Conclusions and Future Work Conclusions Reached A Critical Review Further Work Summation Bibliography...40

7 1 Introduction The classical definition of a flock is a group of objects that exhibit the general class of polarized, non-colliding, aggregate motion [reynolds87]. 1.1 A gentle start In nature, we have all witnessed large groups of birds in the sky, or shoals of fish swimming in the ocean. These are both examples of flocking, whereby a group of individual entities travel as one larger collective. Other examples of flocking include the movement of sheep while being rounded up and herd or herd like behaviour exhibited by Zebra, Wildebeest and the like. By extension, an accurate flocking simulation can be used as a tool for modelling natural behaviour within animals that herd or group. Examples of this can be seen in such films as Batman Returns (1992) and Disney s The Lion King. One can envision (controlled or directed) flock behaviour being useful in a military context, whereby offensive robot swarms can be used to create a large overwhelming attack, and also reduce dependency on one commander figure, providing flexibility and autonomy. Alternatively, on a more advanced level, it may be possible for a something similar to ant behaviour where a large group of small entities co-operate and perform a collective activity, which they would be unable to do individually (like carry something many times larger than themselves). 1.2 Compelling factors The main work of this project is to produce an accurate flock simulation from the rules that Reynolds initially proposed in his seminal paper on the subject. ([reynolds87]) In the paper he states that the rules that lead to flocking are: 1. Collision Avoidance: avoid collisions with nearby flockmates 2. Velocity Matching: attempt to match velocity with nearby flockmates 3. Flock Centring: attempt to stay close to nearby flockmates Some discussion is included within the paper as to what each of these rules entails however, no real elaboration is present as to how to implement the rules and what the optimum method would be. However, in his paper of the year after [reynold88] he does provide some collision avoidance methods. Obviously it is at the programmers discretion as to whether he uses them or not. Even so, Reynolds still leaves questions unanswered such as how close should the boid stay to flockmates? and what happens if a boid cannot avoid a flockmate? This gives the programmer a large amount of scope and a great deal of variables to manipulate. The effect of this is that if you view virtually any implementation of Reynolds flocking rules, each programmer will have had his own ideas as to how to best implement the rules using differing data structures and parameters. By following the same process and viewing how others have implemented their code, this 1

8 project shows a process of development and refinement that is used to arrive to a boid simulation, and the assumptions that have to be made. The attraction of this project lies in the underlying control that one has over the flock. By changing a small number of variables, one can radically alter the cohesion, bearing and other such properties of the flock, giving it different characteristics one can create a fast moving, aggressive flock or similarly, a placid, docile flock just as easily. Therefore, one can create both realistic flocks, yet also be in control of flocks that can be outlandish and improbable, but nonetheless have interesting properties. 1.3 Additional work Of further appeal is the possibilities for scope within the project; one can begin with a simple flock flying through empty space governed by a simple set of rules and then add further elements to the simulation. These can include obstacles for the flock to negotiate, the addition of a flock leader that can somehow govern flock movement, predator(s) who may threaten the flock (who may then themselves be working in a group) or the addition of a destination or goal for the flock to head to. One can also quite easily see where areas such as Artificial Life and AI can overlap within the subject. Of particular interest to me is the addition of predators to the boid model. Initial research shows that others (such as [pocknell99]) have successfully added solitary predators that use a simple rules set to hunt the boids, Naturally, some modification of the initial flocking rules is required to account for the extra obstacle that is the predator, however it is still within the spirit of the initial concept: that of complex emergent behaviour from a simple rules set. What interests me is whether it could be possible to have predation as emergent behaviour derived from a simple rules set. Existing work of a similar nature is in existence and can be used to gather ideas and as a basis. As an example, [ling03] experiments with shepherding behaviour whereby the objective is not to eat the boid but to move it towards a point or target. This however can be adapted and used to simulate the co-operation that predators use to manipulate the flock to single out a target. Within this paper is the discussion and ideas that could form the basis of emergent predatory behaviour. 2

9 2 Literature Survey 2.1 Introduction Definitions Flock A group of objects that exhibit (this) general class of polarized, non colliding, aggregate motion [Reynolds, 87] where polarized motion, in zoological terms refers to the (physical) alignment of an animal group. Boid A generic term first seen in [Reynolds, 87] for simulated bird-like birdoid objects that exhibits flocking behaviour and encompasses not only birds but also schools of fish and herds of animals Background information On initial inspection, a superficial view of the research area regarding flocks, herds and swarms seems to present the impression that all of what can be achieved within the field has been achieved at some level or another with further advances refining or providing alternative methods of improving the basics. The seminal work in this field is widely regarded as being Craig Reynolds 1987 paper Flocks, Herds, and Schools: A Distributed Behavioral Model [Reynolds, 87]. Within this paper, Reynolds lays down the basic concepts and ideas upon which much of the subsequent research is based. It is here that we first find use of the word boid that has become synonymous with flocking simulations since. Reynolds was to add to his initial paper a year later by publishing Not Bumping into Things, a collection notes on obstacle avoidance written for the course on Physically Based Modelling at SIGGRAPH88 [Reynolds, 88]. This paper refined and added detail to ideas and concepts that he had defined in his previous publication, allowing a greater realism to be portrayed in flocking simulations. Much of the work that now exists is based on Reynolds initial papers. One can see that the field has branched into various directions, one of the largest movements having driven towards different applications of Reynolds underlying concept. After collision avoidance had been tackled one could also see the possibility for other additions to the basic Reynolds model; these included predators and the existence of multiple flocks in the same environment. Indeed, Reynolds himself proposed possible uses of the models for simulating traffic flow or for modelling large crowds of people. In addition to the group of people that have added to Reynolds model, there is a group who have taken the basic model and then added their own, usually complex, structures on top to increase realism, provide greater simulation 3

10 accuracy or to shift the emphasis of the behaviour from the flocking to another area. Examples of such work include the use of smell explored in [Zhang, 97] or the framework proposed in [Sims, 94] for evolving different creatures with different attributes such as walking, flying or swimming speeds through further generations. Moving into the field of robotics, flocking ideas were modified and used to create ant army style collaborations whereby a group of robots working together produced greater results than that achievable by a single entity [Unsal, 93]. On a similar note, work by Balch and Arkin attempted to provide some order and formation to flocking, notably in [Balch, 98] with a possible eye towards military usage, or participation in the RoboCup Soccer tournament. From a slightly different perspective, [Reynolds, 87] notes that computationally 2 the flocking implementation proposed has a complexity of O ( N ) as each flock member must reason about every other flock member, even if only to decide to ignore it. He mentions two possible ways of reducing this, dynamic spatial partitioning and incremental collision detection Representing and storing boids In dynamic spatial partitioning the boids are sorted into a lattice of "bins" based on their position in space. It is analogous to the use of a hash table where each cell is an array to a doubly linked list of boids and XY or XYZ co-ordinates. This allows bin membership information to be changed in constant time as opposed to proportional to bin population. A boid trying to navigate inside the flock could get quick access to the flockmates that are physically nearby by examining the "bins" near its current position as opposed to examining each boid individually. An implementation of such a method is described in [Popovic, 94] originally (but referenced from [Reynolds, 00] where a locality query identifies which objects are within a certain radius and therefore require collision testing which is then handled by a separate method. [Pocknell, 99] extends this structure so that the density of the boids within each bin determines where the centre of the flock is and so affects steering behaviour in that way too. The advantage of the dynamic spatial partitioning is that because boids tend to keep a minimum distance from each other, the number of boids within a particular radius is bounded. Therefore, as [Reynolds, 00] notes, complexity is reduced to O( k. n) where k is the maximum density of boids within the radius tested. Essentially, as k is a constant, we can consider the true complexity to be asymptotically equivalent to O (n) making this method very efficient indeed. Incremental collision detection or x nearness testing which is based on a snapshot of current boid positions and is only updated as and when the boids 4

11 actually change position. This allows it to be updated faster and work more efficiently as long as the incremental changes are small. Further investigating the issue, it seems that dynamic spatial partitioning is the more widely used of the two techniques but, due to the large increases in computing power recently the need for efficiency appears to be less of an issue than in 1987 unless dealing with very large simulation, whereby efficiency becomes a significant factor. [Reynolds, 00] notes that in one test using a flying flock of 1000 simulated birds (versus about 300 in the Pigeons in the Park demo) performing locality queries with the bin-lattice spatial subdivision was about 16 times faster than the naive O( n 2 ) implementation. 2.2 Basic flocking theory From the above, one can see that the scope within the field is much larger than originally thought, in some cases encroaching other fields. For example, one can easily see how adding predators to the model can lead to discussing how predators hunt in nature, and then rule formulation that simulates that behaviour Forerunners to Reynolds In his 1987 paper, Reynolds attempts to provide a solution to the problem of animating realistic flocks of birds. From the above, the impression is given that the ideas and theories of flocking started with Reynolds and indeed, his work and the ideas presented within are used as a basis by a significant number of papers within the field. However, an alternative theory for producing flocking was available before [Reynolds, 87]. At SIGGRAPH 85, a short piece of work entitled Eurythmy was shown, with a flock of birds ascending a minaret, passing between columns. The technique used to make the animation was not specifically intended for flock modelling and remained unpublished but is noted in [Reynolds, 87] as being called "the force field animation system." Force fields are defined by a 3 x 3 matrix operator that transform from a point in space (where an object is located) to an acceleration vector: the birds trace paths along the "phase portrait" of the force field. There are "rejection forces" around each bird and around static objects. The force field associated with each object has a bounding box, so object interactions can be culled according to bounding box tests. An incremental, linear time algorithm finds bounding box intersections. The "animator" defines the space field(s) and sets the initial positions, orientations, and velocities of objects. The rest of the simulation is automatic. This precursor to Reynolds ideas, while remaining unpublished, is an alternative way of looking at the problem. However, as it was not primarily for use of flocking simulation, and similarly quite complex compared to later proposals, it has been largely forgotten and unused. An alternative method of flocking is proposed in [Brogan, 97] whereby the flocking behaviour is regulated based on the average distance from neighbours in 5

12 the flock. Indeed, [Blumberg, 95] and [Tu, 94] both describe alternative ways of controlling flock behaviour using a hierarchical control system that defines complex behaviour in terms of simpler ones. [Blumberg, 95] takes the view that each boid would in fact be an autonomous agent controlled by a five-layer model taking sensory information from its environment that it could then respond to using part of a set of motor functions that is has access to. Each motor function would be limited in what it could do but could be combined with other motor functions to produce more complex functions. [Helser, 98] mentions these alternatives but notes that while he believes that the model would provide a more stable motion for the flock it was difficult to integrate with Reynolds model for collision avoidance Reynolds basics for flocks Reynolds Flock Definition (Definitions 2.1.1) sets out criteria for what defines a flock in his view. Taking a purely conditional view, a flock is deemed to be such if its members are able to travel in the same direction (polarization) at roughly the same speed, staying within reasonable proximity of other members (aggregate motion) whilst simultaneously avoiding contact. However, aesthetically a realistic flock exhibits other, emergent behaviour such as the impression of centralised, intentional control and an overall fluid motion despite the fact the flock is made up of discrete bodies, only aware of their immediate neighbours. He notes that treating each object individually and then scripting each path for a large number of objects that would follow the above criteria is tedious. Given the complex paths that birds follow, it is doubtful this specification could be made without error It is unlikely that the constraints of flock motion could be maintained. [Reynolds, 87] Therefore, his propositions are that to produce realistic flocking, each member of the flock must obey the following three steering behaviours (in order of decreasing importance) which allows each boid to manoeuvre based on the positions and velocities of nearby flock mates: Collision Avoidance: avoid collisions with nearby flock mates (Separation) Velocity Matching: attempt to match velocity with nearby flock mates (Alignment) Flock Centring: attempt to stay close to nearby flock mates (Cohesion) 6

13 Obviously, one can see that the conflicting rules of separation and cohesion work together to both keep the flock together while simultaneously keeping its individual members from crashing into each other. The result is rather like a dampener effect with each boid, rather than keeping a fixed distance from each other member, closing up then moving away to other members depending on the direction taken. Velocity is measured as a vector rather than a scalar, allowing the heading of each bird to be changed as well as the speed at which it travels in that heading. Obviously, this can apply equally in both two and three dimensional space allowing vertical (height) movement of flocks in the air. Figure 2.1: A boids' area of influence By focusing solely on the local flock mates of a boid and basing its reaction to their movements, the basic simulation of a flock can be achieved. However, to make this work, a boid requires an area of influence round it that will limit what boids influence it. Modelling the area of influence on a birds vision provides us with workable results. The possibility of changing this area depending on the creature being simulated is then available. For now however, it suffices to have Reynolds initial model which is illustrated in figure 2.1. The angle is measured either side of the boids facing (denoted by the arrow) and a uniform distance of influence is kept as we go round the boid to the point of cut off. Naturally, were we to model in three dimensions, then the area of influence would extend both above and below the boid as well. A simple check could then work out whether another boid can be seen by the first boid. If we were to take a more complex approach to this, rather than a uniform field of vision, one can change the shape to emphasise the greater forward vision that the boid would have. This would elongate the circle of vision into an ellipse and would improve the realism of our results as now a boid would be able to see further ahead than at the sides. Obviously however, it is more complex to model this form of vision compared to the simpler method. In addition to the above, to help collision and obstacle avoidance, Reynolds proposes weighting the various responses that the boid receives depending on distance and the type of collision that will occur (whether boid boid or boid obstacle) allowing each input to be prioritised and thus to place greater or lesser emphasis on each of the flocking rules. 7

14 2.3 Obstacle avoidance techniques When taking into account the movement of a boid around an obstacle, it is of value to note that the path taken by a boid approaching an obstacle from (x,y) may differ depending on whether he is alone or within a flock. Figures 2.2 and 2.3 illustrate the difference that flocking can make. Figure 2.2: Blue boid and red boid are from separate flocks Figure 2.3: Blue boid and red boid are part of same flock In the second example, as the blue boid is in front of the red boid, it is affected by the sphere of influence of the obstacle first and so turns to avoid it. The response of the red boid is to start turning to match the alignment of the blue boid and then move towards the blue boid (as the distance between them has increased). This causes the obstacle to now be to the right of boid instead of to the left, causing the boid to turn left to avoid the obstacle. However, despite this, the flock may still split if some elements of it are too close to align themselves with the rest of the group. This often happens in large flocks that are quite widely spread out, where the boids do not turn with the rest of the flock as the obstacle is too near. Often, it is only the lead boids that are affected by the obstacle, [Crombie, 97] calls this feature The alignment effect and notes that by reacting to their environment the leading boids change the environment of following boids. In [Reynolds, 88], a number of different ways of implementing a collision avoidance system are proposed, some based on geometric models and some on image processing in addition to outlining a number of techniques that use artificial intelligence. Of these three categories, for the purposes of the project, the artificial intelligence implementations can be discarded, as they rely on such concepts as memory, learning and planning and are thus too complex for the scope of this project. It may be possible that a simple AI scheme is used for the predatory behaviour model, but it is more likely either to be a behavioural simulation (an artificial system with lifelike properties) or a simple set of rules governing behaviour rather than proper artificial intelligence. Both the other two categories (geometric based collision avoidance models and image processing based models) are heuristic in nature and involve no real 8

15 rational thinking. The image processing models get their information from viewing the environment as an image. If they were to be implemented, one would have to take into account (and calculate) a boids eye view at every step of the way, for every boid. This technique is incompatible if used with the basic implementation technique described above as it relies on a three dimensional view being projected and calculated. As the simulation will be limited to two dimensions it is understandable to disregard this category of methods as well. It is clear then, that we should use a geometric based model to go with our geometric based simulation. The scope is there to adapt an AI style behavioural simulation at a later date, time permitting. [Reynolds, 88] proposes four alternative methods for collision avoidance of which three are detailed below. The final method described by Reynolds, silhouette avoidance, is another based on taking a boids eye view of things. It is similar in nature to the curb feeling method described below, but requires us to work in three dimensions, and so is more akin to an image processing method similar to the ones described above. Due to the relative complexity of this model it is judged that this method could be introduced within the simulation at a later date should there be time remaining, but that one of the other methods described below would be better suited, at least to begin with. The methods described below are described at a high level; within the design of the project, it is discussed the best way to represent the repelling and attracting forces described in the simulation. In addition to Reynolds methods, a slightly more specific method for avoiding collisions between two moving objects, as used in [Pocknell, 99], is also discussed below as an alternative implementation. Most of the methods described below are primarily used for avoidance of static object but can, with some alteration be used with obstacles in motion. 9

16 2.3.1 Steer away from surface Intuitive path around obstacle Wall (Obstacle) Repelling force Actual Path taken. Repelling force exactly opposite to boid velocity Boid Figure 2.4: Effect of approaching an obstacle square on Also known as the force field effect, this presumes that the surface of the obstacle has a strong repellent force and that the obstacle is stationary and immobile. The object approaching the obstacle is repelled away from the obstacle by a force whose strength is inversely related to the distance to the object. The advantage of this method is that often the repelling force can be modelled using one equation and so calculated easily, and quickly. Unfortunately, this method does not always produce movement that can be deemed steering round an object. If the obstacle is being approached square on, for example a wall, the repelling motion is directed directly away from the direction of motion of the object, eventually exactly opposing the velocity of the object, bringing it to a stop. Figure 2.5: Graph of lateral movement compared to horizontal offset 10

17 The reason this happens is because this technique relies on setting the amount of lateral movement depending on the horizontal offset to the obstacle. If we are to graph the function then the result in Figure 2.5 is achieved. One can immediately see the dead zone at the centre of the graph that is the equivalent to the object being approached square on. Additionally, another problem with the force field method is that it is not directionally discriminatory; this means that an obstacle affects object movement even though the obstacle may not be in the path of the object. The result of this is that the boid steers away from the object even if it is flying parallel to it. In order to rectify this, we need to impose a number of different weightings that cause an exaggeration of the curve seen in Figure 2.5. These weightings must be based on the angle of intersection (if any) that the obstacle and boid create. Obviously, no intersection will result in no repelling force. Without these adjustments, the effect of the repulsion is far too strong when flying alongside an obstacle, and far too weak when flying towards one. The result of these changes are that objects are far more sensitive to obstacles directly in front of them, causing them to turn earlier to avoid them, resulting in a more aesthetically pleasing and realistic avoidance. 11

18 2.3.2 Steer away from centre Example path taken around obstacle Intuitive path around obstacle Wall (Obstacle) Repelling force around centre of wall Boid Figure 2.6: Boid negotiating obstacle using Steer from Centre technique This technique considers the obstacle to be a point rather than a plane or geometric shape. The dead spot encountered in the previous method is removed by reducing the obstacle to a point; if we are to the left of centre then we steer to the left, if we are above then we steer upwards. One can visualise this as a spherical force field based around a point and model it as such. This causes a boid wishing to traverse the obstacle to exhibit uniform lateral acceleration which in general proves to be better than the technique described above. As a refinement one can, as above, make the repulsion force inversely proportional to the distance from the centre producing a more realistic obstacle negotiation effect. In addition, it is easier to calculate intersection of the force field with a boid than in the previous technique, as only the centre of the obstacle needs to be stored. In order to allow some directional discrimination, one can bind the radius of influence that the obstacle has and any object outside that radius can remain unaffected. In a further refinement, the sphere of influence can be stretched into ellipses easily by editing a small part of the equation, thus allowing a more accurate covering of shapes such as walls and thus, a more realistic negotiation. This method is similar to the method used in [Pocknell, 99] for collision avoidance between moving objects. 12

19 2.3.3 Curb Feeling Feeler deflected down to edge of obstacle Feeler New Feeler gives direction to take to avoid collision Boid Figure 2.7: Curb Feeler technique This technique takes a different approach to the above. Rather than being obstacle orientated, it is boid orientated but at the same time, it is possible to combine either of the above techniques with this method. The basics of the method require that each boid is equipped with a feeler, a probe that extends along the axis of each boid in the direction of travel. When the probe intersects an obstacle (or area of repulsion such as one above) it is pushed to the edge of the obstacle. This movement provides the boid with a directional vector, a direction to take to avoid the object for now. Obviously, if the feeler intersects the object again, then the process is repeated, and so the boid has to change heading yet again until the feeler no longer intersects with the object. The length of the probe is governed by how quickly the boid is moving. A fast moving boid will have a longer probe than a slow moving boid and so each probe length will be dynamically altered as the bird speeds up or slows down. In addition, one can multiply the length of the probe by a factor that Reynolds calls predictiveness. The predictiveness factor determines how much time prior to a potential collision is allocated to steering away from the obstacle [Reynolds, 88] and using this we can individualise certain boids so that some will fly nearer the obstacle before turning away whereas others will be more cautious. In addition, one can check by how much the probe has been displaced and then change the velocity of the boid by the same amount, thus giving us the next probe length. The combination of the above provides a greater realism to the flock as there is a greater variety of movement within the individual members. As with the methods above, the curb feeler is best suited to when the obstacle to be traversed is static however, unlike the steer away from surface method, it is possible to be able to implement this model to avoid collision between two moving obstacles as well. In addition, it allows a more accurate representation of obstacles that may be irregularly shaped, thereby allowing more a complex environment to be created. 13

20 2.3.4 Avoiding inter-flock collision Direction of facing Greater priority given to intersections occurring in spheres nearer boid Figure 2.8: Phil Pocknells' "Sphere of influence" model [Pocknell, 99] [Reynolds, 87] makes no mention of multiple flocks. If more than one flock appears in space then they are all part of the same flock that have not been attracted to each other and joined together yet. In [Crombie, 97], there are multiple, separate flocks that do not wish to flock together (one can visualise this as different species perhaps) and so repel each other. They are implemented using the steer away from centre technique described above, treating the rival boid as an object to avoid and thus be repelled from, at the same time as the other boid is doing the same. The avoidance behaviour used whilst satisfactory does not, to me, seem to be very realistic, causing whole flocks to swerve to avoid one or two boids, whereas in reality, such a large swerve would be more akin to a scenario such as a cat jumping into the midst of a large group of birds. It is possible that it could be put to use, and better suited for a predator-prey scenario rather than flock avoidance. An alternative method to use is from [Pocknell, 99] who takes inspiration from [Brooks, 89] where the robot Allen uses sonar distance sensors to avoid both static obstacles and dynamic obstacles such as boids. Pocknell proposes using the vector sum of the repulsive forces to tell each boid what action they should take. In this way, as soon as potential collision is detected, each boid starts to turn away. This has the advantage of taking into account the relative speeds of the two boids, causing fast boids to turn less than slower moving boids. It is then a case of moving the simulation forward one step and, if collision is still imminent, recalculating the vectors again. Pocknell notes that an emergent behaviour of using vector calculation is when a lone tadpoid (boid) heads at a perpendicular 14

21 angle towards a large group. The individual tadpoid just swoops right along with the group. In this respect at least, this emergent behaviour is welcome. The detection method described by Pocknell is very similar in concept to the curb feeler method. In his version, each boid has a feeler of identical length, and a cone of perception pointing the way the boid is facing. The cone is split into three sections to represent how close to the boid the potential collision is. Each area is allocated a certain priority which determines how quickly the boid speeds up or slows down to avoid collision as well as how much to turn. However, Pocknells method does not work very well when it comes to static object detection, as a static object does not have a velocity vector and so erroneous results would be produced were the above method to be used. To circumvent this Pocknell uses a simple rules table to allow his boids to navigate the confined environment in which they inhabit. He labels each wall in his environment and works out the angle of potential collision and then uses a combination of these two factors to explicitly instruct the boid to either turn left or right. While this method is less satisfying than the more autonomous methods described above, it does serve a purpose, especially if the boids are confined to within an environment like the confines of a screen where they may have a corner that they could get stuck in Other means of collision avoidance As part of a 3 layer system similar to the one in [Blumberg, 95], [Reynolds, 99] proposes an alternative system of path determination based on a number of simple common steering behaviours that can be combined into more complex ones. However, Reynolds notes that this system is primarily for use for fast motion ; when the typical velocity of a character (object) is large relative to its maximum turning acceleration as without limiting changes of orientation it allows manoeuvres that appear unrealistic if the object is at a lower speed. Reynolds proposes a large set of behaviours with such titles as seek, pursuit and evasion and an additional locomotion level for implementing the movement associated with the behaviours; these can be viewed as an extension and generalisation of his flocking work but one that can also be used to model other behaviour, such as predation. The locomotion model used is a point mass approximation and therefore does not take into account inertia but is however computationally cheap. Each object within the model has a mass, position vector, velocity vector, and two other scalar values; one for maximum speed and one called max thrust. Additionally, each object also has a vector storing its orientation (and heading). At each simulation step, steering forces (as determined by the active behaviour and limited by the max thrust) are applied to the mass of the object. This results in an acceleration that can then be used to modify the velocity of the object and thus produce the resultant velocity that is used to calculate the objects new position. 15

22 Of the steering behaviours proposed, the ones that are directly interesting to us are undoubtedly the separation, cohesion, alignment and flocking behaviours. However other proposed behaviours by Reynolds are certainly worth investigating further and possibly implementing within the simulation. Behaviours such as pursuit and offset pursuit would enable predators to track their prey from a safe distance. However, some work would still be necessary to enable the predators to work co-operatively, perhaps by slightly modifying other behaviours to suit our purposes. The behaviours outlined above and other discussions can be found in the following section: Predation and predator-prey implementation techniques. 16

23 2.4 Predation and Predator-Prey implementation techniques As mentioned before, there is a large amount of scope within the field of flocking for variation as to what to focus on. Having seen what has been done, the ideal solution would be to implement a predator-prey system whereby a flock, or possibly a number of flocks are hunted by one or more predators. It is important to note that the word predator does not necessarily solely imply that the prey are to be chased and eaten, but should imply that the predator is perceived as a threat by the prey who will take steps to avoid the predator as much as possible. This therefore includes shepherding scenarios involving sheep and sheepdogs. One can view the predation process as a game of tag between predator and prey. [Reynolds, 94] describes theories and strategies behind playing tag based on a one-on-one competition between autonomous agents but notes that it is primarily used to study the use competitive fitness and mentions that this work is not about optimal control theory. Regardless, it is worthwhile as different evasion strategies are mentioned and various stimulus diagrams are produced showing optimal turning angles; these could be used at a later date if a more advanced AIlike model is used to govern behaviour. If we return to [Pocknell, 99], his simulation involves the use of a solitary predatory whose predation strategy is similar to his collision approach; By using [Brooks, 89] as his basis, he defines that each predator has a sphere of influence based on how fast it is moving. A slow moving predator does not pose much of a threat and so has a smaller sphere of influence compared to a fast moving predator, in the same way a slow moving boid has a shorter feeler in the curb feeling method. A boid entering the sphere of influence of the predator (or vice versa) is diverted and repelled from its path by the predator, much like the scattering of a herd. Pocknell implements the predator method so that rather than completely avoiding the predator, if a lone boid is trying to join the rest of the flock it will try and avoid the predator by arcing it s path so it moves further away from the predator but still towards it s target. This seems to be more realistic as one often sees in nature herd stragglers instinctively trying to rejoin by use of a longer route, if only for the protection a herd offers instead of being left to face a hungry predator. In [Pocknell, 99] the predator is controlled by the user whereas in the game of tag implemented in [Helser, 94] the it boid uses a hunt-the-nearest approach in choosing and then pursuing a target. Implementing the Pocknell technique requires additions to be made to the basic simulation. Each boid would have an ideal target spot that they would like to go to, usually somewhere in the middle of the herd. However, if an obstacle or predator were to obstruct the way to that spot, the boid, instead of being repelled, would have to keep the same target and try and jink round the object or predator. Obviously, were the target to move, or predator to move then the boid would have to re-evaluate its options. For an application such as this, then one could possibly apply the strategies discussed in Reynolds tag game. 17

24 Ideally one would like to be able to model a real-life hunting strategy for either a single animal or hunting pack based on real natural behaviour. One can take hunting strategies such as those employed by a pride of lions and break them down into simpler sub rules following the guidelines published in [Blumberg, 95] for use to implement a lion-like predation system. Similarly, using similar work again one can develop counter strategies. Unfortunately, it is far too easy for one to get carried away with programming strategy and counter-strategy; in order to keep the project feasible the rules governing predation must be kept as simple as possible Using Finite State Machines A possible implementation strategy can be derived from ideas set out in [Reynolds, 00]. In this paper, rather than the prey following simple behaviour rules slavishly, they are modelled as finite state machines with differing behaviour depending on which state they are in. Reynolds uses the example of a pigeon in the park and defines it in its simplest form as having two states: walk and fly. Its default state is walk, but if it is startled then it will change its state to fly which changes the restrictions placed on the pigeon. For example, if the pigeon is in the fly state, it no longer has to remain on the ground when moving but can instead take to the air. Additionally, it can have a higher top speed than in the walking state as it can fly faster than it can walk. Reynolds also adds the concept of an abstract factor that influences future behaviour. In his simulation, he adds an annoyance level that influences how far the pigeon will fly away if it is startled. The annoyance factor is increased every time the pigeon is disturbed and decreases slowly over time. As well as the pigeon changing state, Reynolds also introduces the concept of contagiousness whereby the effect of an abnormal (non default) action (in this case, flying away) can influence the states of birds which are nearby, causing them to take too. As a result, if a single bird in a dense crowd is scared and starts flying away, other birds may react to the fact that he is flying away and do the same. As more birds fly away, so the chance of other birds doing the same is increased. This could be used in a flock so that if one boid is startled by a predator and starts to take evasive action, this will cause the rest of the flock to follow suit Seek and Pursuit behaviours The following behaviours are defined in [Reynolds, 99] and are reproduced here as I believe they are of use in helping to mimic predatory behaviour. Seek Seek is the pursuit of a static target. Essentially, the behaviour acts to steer the object towards a specified target point by adjusting the velocity of the object so that it is aligned towards the target. This behaviour however, does not cause the object to slow down or stop once it reaches its target and so once the object has overshot the target the behaviour will cause the object to loop round and approach the target again. 18

25 Pursuit Pursuit is similar to seek except that the target is moving. Essentially, it involves prediction of where the target will end up and then seek towards that point. A linear velocity-based predictor can be used to work out a target point. This assumes that the quarry will not turn during the prediction interval. While this is unrealistic, it is of use as the resulting prediction will only be in use for a short amount of time. Using this method we can predict the location of an object after T moves by simple vector arithmetic and use this as our target. However, Reynolds proposes that T should be proportional to distance from our quarry; the closer we are to our prey the smaller T should be and the less in advance we should predict. Additionally, we can increase the sophistication of this model by taking into account relative headings of pursuer and prey. Offset pursuit behaviour is similar to normal pursuit behaviour but is more analogous to a strafing run. In our boid simulation it could be used to stalk prey and allow the predator to get into a better position by just staying far enough away so as not to panic the prey In summation Overall, I believe that an optimal solution to mimicking predatory behaviour within the simulation would be to combine the ideas proposed in [Reynolds, 99] and [Reynolds, 00]. While discussed further in the design, that basis for a predator would have a hunt state and a pounce state that it enters once it has chosen a target. Additional rules would have to be added to each state to ensure that multiple predators would choose the same target and then attempt to corner it cooperatively. Initially, while a simple boid simulation (as set out in [Reynolds, 87]) would suffice the scope could easily be extended to add the finite state machine idea at a later date. 19

26 3 Requirements analysis and specification The initial aim of this project is to create a flocking simulation based on Chris Reynolds work on flocks and boids as outlined in [Reynolds, 87]. Deriving requirements from this paper, we can then define what a flock is and the properties of a flock. The simulation should then exhibit the properties defined in order to be seen as successful. 3.1 Requirements elicitation The basic implementation is a relatively simple and open project, with few requirements of note. Most derived requirements are definitions of behaviour (such as what constitutes flocking? ) and the accompanying test for checking that the requirement is fulfilled. Additional requirements would therefore mostly be self imposed, depending on the additional feature that was to be implemented. 3.2 What is a flock? As discussed in the previous section, [Reynolds, 87] defines a flock as A group of objects that exhibit (this) general class of polarized, non colliding, aggregate motion. From that sentence it is possible to derive the initial 3 requirements that our flock must stick to. Essentially, each of the 3 requirements is linked to one of the rules of flocking proposed by Reynolds. We can view the requirements as a test to see whether we have correctly implemented Reynolds rules; should the behaviour not be present, then that particular rule is not being adhered to Polarization Polarization, or in this case polarized motion, refers to the collective group movement of the flock that gives the impression of it being under centralised control. If one is to link the behaviour to a rule, then it is best described as the direct result of velocity matching, where the heading and speed of nearby boids is kept at more or less similar levels. We can test this condition simply if we implement the simulation graphically; If the condition is being fulfilled, the boids will be seen to be lining up and heading in a similar direction at a similar speed, thereby more or less keeping a constant distance between each boid member; naturally, this behaviour may change should an obstacle be introduced Non-collision Strictly speaking, the ideal boid simulation would ensure that no collisions between entities are possible. However, if one wishes to create a realistic simulation, then one must accept the view that in real life collisions do occur. Generally, collisions occur because of a misjudgement of distance or speed. In our simulation, it is entirely feasible that a boid may veer into the path of another boid and thus give the first boid enough time to react and change course quickly enough. If we were to strictly implement this rule then the avoidance behaviour 20