Steering Behaviors For Autonomous Characters
Craig W. Reynolds
Sony Computer Entertainment America
919 East Hillsdale Boulevard Foster City, California 94404

craig_reynolds@playstation.sony.com http://www.red.com/cwr/ cwr@red.com

Keywords: Animation Techniques, Virtual/Interactive Environments, Games, Simulation, behavioral animation, autonomous agent, situated, embodied, reactive, vehicle, steering, path planning, path following, pursuit, evasion, obstacle avoidance, collision avoidance, flocking, group behavior, navigation, artificial life, improvisation.

Abstract This paper presents solutions for one requirement of autonomous characters in animation and games: the ability to navigate around their world in a life-like and improvisational manner. These “steering behaviors” are largely independent of the particulars of the character’s means of locomotion. Combinations of steering behaviors can be used to achieve higher level goals This paper divides motion behavior into three levels. It will focus on the (For example: get from here to there while avoiding obstacles, follow this corridor, join that group of characters...) middle level of steering behaviors, briefly describe the lower level of locomotion, and touch lightly on the higher level of goal setting and strategy. Introduction Autonomous characters are a type of autonomous agent intended for use in computer animation and interactive media such as games and virtual reality. These agents represent a This stands in character in a story or game and have some ability to improvise their actions.

contrast both to a character in an animated film, whose actions are scripted in advance, and to an “avatar” in a game or virtual reality, whose actions are directed in real time by a human player or participant. characters. An autonomous character must combine aspects of an autonomous robot with some skills of a human actor in improvisational theater. These characters are usually not real robots, and are certainly not human actors, but share some properties of each. The term “autonomous agent” is used in many contexts, so the following is an attempt to locate the terminology of this paper in relation to other fields of study. An autonomous agent can A “data mining” agent A exist in isolation, or it can be situated in a world shared by other entities. In games, autonomous characters are sometimes called non-player

is an example of the former, and a controller for a power grid is an example of the latter. situated agent can be reactive (instinctive, driven by stimulus) or it can be deliberative

(“intellectual” in the classic AI sense). An autonomous agent can deal exclusively with abstract information (“softbot”, “knowbot”, or “information agent”) or it can be embodied in a physical manifestation (a typical industrial robot or an autonomous vehicle). Combinations of situated, reactive, and embodied define several distinct classes of autonomous agents.

The category of situated, embodied agents usually suggests autonomous robots: mechanical devices that exist in the real world. simulation. Sometimes robots are studied via computational There is another class of But that practice is viewed with suspicion by purists in the robotics field because

the simulation may diverge from reality in unpredictable ways.

situated, embodied agent based on a computational model. This paper will use the term virtual (as in virtual reality) to denote these agents which, rather than being simulations of a mechanical device in the real world, are instead real agents in a virtual world. physically-based model in computer animation.) paper’s title are: situated, embodied, reactive, virtual agents. The term behavior has many meanings. animal based on volition or instinct. It can mean the complex action of a human or other mechanical system, or the complex action of a chaotic system.
Action Selection: strategy, goals, planning

(Analogous to a

Hence the autonomous characters of this

It can mean the largely predictable actions of a simple In virtual reality and multimedia In this paper the term behavior

applications, it is sometimes used as a synonym for “animation.” is used to refer to the improvisational and lifelike actions of an autonomous character. The behavior of an autonomous character can be better understood by dividing it into several layers. follow. These layers are intended only for Figure 1 shows a division of motion A similar three layer hierarchy is clarity and specificity in the discussion that will

Steering:

path determination

Locomotion:

animation, articulation

Figure 1: A hierarchy of motion behaviors

behavior for autonomous characters into a hierarchy of three layers: action selection, steering, and locomotion. motor. Certainly other dissections are possible. described by Blumberg and Galyean [Blumberg 95], they call the layers: motivation, task, and Note that while the behavioral hierarchy presented here is intended to be widely applicable to motion behaviors, it is not well suited for other types of autonomous actions, for example the conversational behaviors of a “chatterbot” require a significantly different structure. Consider, for example, some cowboys tending a herd of cattle out on the range. wanders away from the herd. way. The trail boss tells a cowboy to fetch the stray. A cow

The cowboy

says “giddy-up” to his horse and guides it to the cow, possibly avoiding obstacles along the In this example, the trail boss represents action selection: noticing that the state of the The steering world has changed (a cow left the herd) and setting a goal (retrieve the stray). (approach the cow, avoid obstacles, retrieve the cow). behavior for the cowboy-and-horse team.

level is represented by the cowboy, who decomposes the goal into a series of simple subgoals A subgoal corresponds to a steering In general terms, these signals The horse Using various control signals (vocal commands,

spurs, reins) the cowboy steers his horse towards the target. implements the locomotion level. moves in the indicated direction. its skeleton.

express concepts like: go faster, go slower, turn right, turn left, and so on.

Taking the cowboy’s control signals as input, the horse This motion is the result of a complex interaction of the

horse’s visual perception, its sense of balance, and its muscles applying torques to the joints of From an engineering point of view, legged locomotion is a very hard problem [Raibert 91], [Hodgins 95], but neither the cowboy nor the horse give it a second thought.

This paper will focus on steering, the middle layer of the behavioral hierarchy. concrete foundation for the discussion of various steering behaviors. steering behaviors. Path-finding is a topic related to, but separate from, the subject of this paper. essentially solve mazes.

It will briefly

describe a simple model of the locomotion layer, but only in enough detail to provide a There will be some brief discussion of action selection, but primarily in the context of combining and blending basic

Path-finding

algorithms such as A* and Dijkstra's operate on networks (often representing grids) and Such a solution could serve as a specification to the steering An analogy might be to compare the written driving techniques described in this paper.

instructions for getting from one place to another with the act of driving the car along that route. For an excellent over view of path-finding see [Reese 99]. In order to understand the thrust of this work, it should be noted that the steering behaviors discussed here relate to “fast” motion: running versus crawling. turning acceleration. This is an informal notion, but is meant to suggest that the typical velocity of a character is large relative to its maximum As a result, the steering behaviors must anticipate the future, and take into account eventual consequences of current actions. Related Work Steering behaviors for autonomous characters draw on a long history of related research in other fields. Autonomous machines, servomechanisms, and control theory have their roots in The term cybernetics came from a the 1940s as described in Norbert Wiener’s 1948 book Cybernetics, or Control and communication in the Animal and the Machine [Wiener 48]. Greek word meaning steersman. During the late 40s neurophysiologist Grey Walter

constructed autonomous robotic turtles [Walter 50] which embodied several of the steering behaviors described here and were among the first machines to exhibit emergent life-like behavior. In the early 1980s Valentino Braitenberg extrapolated Walter’s prototypes into thought experiments about a series of fanciful “vehicles” with progressively more complex behaviors [Braitenberg 84]. David Zeltzer began applying techniques and models from artificial intelligence to animation applications [Zeltzer 83]. paper [Reynolds 87]. The list below of related research is divided into three general categories: robotics, artificial intelligence, and artificial life, although in some cases the distinction is somewhat arbitrary. Generally these works are oriented towards animation to some extent: they are located in the overlap between animation (or games, VR, and multimedia) and these three other fields. Work related to robotics. Rodney Brooks popularized the then-radical notion of building While originally inspired by ethological And in 1987, I created an animated behavioral model of bird flocks using techniques closely related to those presented in this

reactive controllers for robotic systems [Brooks 85].

(animal behavior) research, the work of Ron Arkin [Arkin 87, 89, 92] has centered on application of steering behaviors to mobile robots. Arkin’s research has paralleled much of the work presented in this paper, but his schema (perception›action mappings) are expressed in terms of potential field models as opposed to the procedural approach described here. avoidance) it leads to significantly different agent behavior. In

some cases this is a distinction without a difference, but in other cases (such as obstacle Marc Raibert and Jessica Hodgins

both began in legged robotics research and now both work in animation applications of physically realistic legged systems. In both cases, their work has touched on steering and Work by Zapata et al. Maja Mataric has path planning aspects of these systems [Raibert 91, 91b], [Hodgins 95]. momentum and other aspects of fast mechanical motion [Zapata 1992]. steering. Work related to artificial intelligence. Ken Kahn created an early system that generated animation of character motion from story descriptions [Kahn 79]. David Zeltzer [Zeltzer 83, 90] pioneered AI-based animation, popularizing the idea of abstract “task level” specification of motion. Gary Ridsdale [Ridsdale 87] created characters capable of improvising complex Steve motion, getting from A to B while avoiding static obstacles and other actors.

on steering controllers for fast mobile robots focused on strategies which had to deal with worked extensively in collective robotics [Mataric 93] and a central theme of this work is

Strassmann’s Desktop Theater work [Strassmann 1991] extended these notions to include handling of props and emotional portrayal. Mônica Costa’s agent-based behavioral animation work [Costa 90] allows a character to navigate around a house while reactively avoiding obstacles. Research on improvisational, dramatic characters, which touches on Barbara Hayes-Roth et al. [Hayes-Roth 96]. The 1987 boids model of flocks, herds, The following year related steering At the 1987 Artificial Life steering behavior, is ongoing at Project Oz (and now Zoesis) by Joseph Bates et al. [Bates 92] and at The Virtual Theater Project by

Work related to artificial life (and other fields).

schools and related group motion [Reynolds 87], decomposed this complex group behavior to three simple steering behaviors at the individual level. behaviors for obstacle avoidance [Reynolds 88] were presented.

Workshop Mitchel Resnick presented work on autonomous vehicles implemented in LEGO LOGO [Resnick 89] and Michael Travers demonstrated his AGAR Animal Construction Kit [Travers 89]. (See also more recent work by these authors [Resnick 93] and [Travers 94].) Steering behaviors were a key element in The Virtual Fishtank, a multiuser VR installation at The Computer Museum created by teams from MIT’s Media Lab and NearLife [Resnick 98]. Armin Bruderlin procedurally generated goal directed animation of human walking [Bruderlin 1989]. Randall Beer’s dissertation on an artificial cockroach [Beer 90] is noteworthy for the Central to this model are neural depth and complexity of its neuroethological model. analogs of steering behaviors described below.

implementation of several tropisms (such as chemotaxis and thigmotaxis) which are direct In [Wilhelms 90] Jane Wilhelms and Robert Thalmann et al. created Skinner investigate architectures for vehicle-like characters. vision as simulated with 3D rendering [Thalmann 90]. Panne 90].

behavioral animation characters who navigated down corridors and around obstacles using Michiel van de Panne created controllers for tasks like parallel parking of an automobile using state-space search [van de G. Keith Still has modeled large human crowds using a model of the steering Using a modified genetic algorithm, Karl Sims In work first reported at SAB94 and updated at behavior of each individual [Still 94].

simultaneously evolved brains and bodies for artificial creatures for various styles of locomotion and for goal seeking [Sims 94]. agents. SAB96 [Cliff 96], Cliff and Miller coevolved pursuit and evasion behaviors for predator and prey Xiaoyuan Tu et al. developed an elaborate and strikingly realistic model of the biomechanics, locomotion, perception, and behavior of fish in [Tu 94, 96] which included physically based locomotion, steering behaviors, and an ethologically based system for action selection. In [Blumberg 94] Bruce Blumberg described a detailed mechanism for complex

action selection and with Tinsley Galyean in [Blumberg 95] discussed the design for a VR character capable of both autonomous improvisation and response to external direction. One The application of these characters was in the ALIVE system [Maes 95] by Patties Maes et al.

Improv system by Ken Perlin and Athomas Goldberg [Perlin 96] also covers the gamut from locomotion to action selection, but uses a unique approach based on behavioral scripting and Perlin’s 1985 procedural synthesis of textures [Perlin 85] applied to motion. in interactive automobile driving simulators [Cremer 96]. inspired in part by an early draft of this paper. James Cremer and colleagues have created autonomous drivers to serve as “extras” creating ambient traffic Robin Green (of Bullfrog/EA) has developed a mature system for autonomous characters used in Dungeon Keeper 2 which was Dave Pottinger has provides a detailed discussion of steering and coordination for groups of characters in games [Pottinger 1999]. Locomotion Locomotion is the bottom of the three level behavioral hierarchy described above. locomotion layer represents a character’s embodiment. steering layer into motion of the character’s “body.” The

It converts control signals from the

This motion is subject to constraints

imposed by the body’s physically-based model, such as the interaction of momentum and strength (limitation of forces that can be applied by the body). As described above, a cowboy’s horse can be considered as an example of the locomotion layer. The rider’s steering decisions are conveyed via simple control signals to the horse who converts them into motion. The point of making the abstract distinction between steering and locomotion is to anticipate “plugging in” a new locomotion module. Imagine lifting the rider off of the horse and placing him on a cross-country motorcycle. behavior remain the same. signals (go faster, turn right, ...) into motion. the rider is unchanged. This suggests that with an appropriate convention for communicating control signals, steering behaviors can be completely independent of the specific locomotion scheme. practice it is necessary to compensate for the “agility” and individual locomotion systems. Although in different “handing characteristics” of The goal selection and steering All that has changed is the mechanism for mapping the control Originally it involved legged locomotion (balance, The role of

bones, muscles) and now it involves wheeled locomotion (engine, wheels, brakes).

This can be done by adjusting tuning parameters for a given

locomotion scheme (which is the approach taken in the steering behaviors described below) or by using an adaptive, self-calibrating technique (the way a human driver quickly adapts to the characteristics of an unfamiliar automobile). In the first case a steering behavior might determine via its a priori tuning that the character’s speed in a given situation should be 23 mph, in the second case it might say “slow down a bit” until the same result was obtained. The locomotion of an autonomous character can be based on, or independent from, its animated portrayal. balanced A character could be represented by a physically-based dynamically simulation of walking, providing both realistic animation and behavioral locomotion.

Or a character may have a very simple locomotion model (like described in the next section) to which a static (say a spaceship) or pre-animated (like a human figure performing a walk cycle) portrayal is attached. A hybrid approach is to use a simple locomotion model and an adaptive Finally, locomotion can be restricted to the motion animation model, like an inverse-kinematics driven walk cycle, to bridge the gap between abstract locomotion and concrete terrain.

inherent in a fixed set of pre-animated segments (walk, run, stop, turn left...) which are either selected discretely or blended together. A Simple Vehicle Model The approach taken in this paper is to consider steering behaviors as essentially independent from the underlying locomotion scheme. based on a simple idealized vehicle. A simple locomotion model will be presented in order This locomotion model will be to make the discussion of steering behaviors more concrete.

The choice of the term “vehicle” is inspired to some

degree by [Braitenberg 84]. It is intended to encompass a wide range of conveyances, from wheeled devices to horses, from aircraft to submarines, and (while certainly stretching the terminology) to include locomotion by a character’s own legs. of those. This vehicle model is based on a point mass approximation. On the one hand that allows a On the other The vehicle model described here is so simplistic and generic that it is an equally good (or equally bad) approximation to all

very simple and computationally cheap physically-based model (for example, a point mass has velocity (linear momentum) but no moment of inertia (rotational momentum)). real world. of inertia. hand, it cannot be a very compelling physical model because point masses do not exist in the Any physical object with mass must have a non-zero radius and hence a moment This use of an oversimplified non-physical vehicle model is merely for convenience

and intended to be “without loss of generality” — it should always be possible to substitute a more plausible, more realistic physically based vehicle model. A point mass is defined by a position property and a mass property. In addition, the simple vehicle model includes a velocity property. The velocity is modified by applying forces. Because this is a vehicle, these forces are generally self-applied, and hence limited. For example, a typical force which adjusts a vehicle’s velocity is thrust, generated by the vehicle’s own power plant, and hence limited in magnitude by the capacity of the power plant. (max_force). Most vehicles are characterized by a top speed. For the simple vehicle model, this notion is summarized by a single “maximum force” parameter Typically this limitation is due to the interaction between acceleration due to their finite thrust and the deceleration due to viscous drag, friction, or (in legged systems) the momentum of reciprocating parts. As an alternative to realistic simulation of all these limiting forces, the simple vehicle model includes a “maximum speed” parameter (max_speed). truncation of the vehicle’s velocity vector. This speed limit is enforced by a kinematic Finally, the simple vehicle model includes an (The terms

orientation, which taken together with the vehicle’s position form a velocity-aligned local coordinate space to which a geometric model of the vehicle can be attached. this local space.) Simple Vehicle Model: mass position velocity max_force max_speed orientation scalar vector vector scalar scalar N basis vectors localize and globalize will be used in this paper to connote transforming vectors into and out of

For a 3D vehicle model, the position and velocity vector values have three components and the orientation value is a set of three vectors (or a 3x3 matrix, or a quaternion). vectors or can be represented as a single scalar heading angle. The physics of the simple vehicle model is based on forward Euler integration. to the vehicle’s point mass. by the vehicle’s mass. At each For a 2D vehicle, the vectors each have two components, and the orientation value is two 2D basis

simulation step, behaviorally determined steering forces (as limited by max_force) are applied This produces an acceleration equal to the steering force divided Finally, the velocity is added to the old position: max_force) max_speed)

That acceleration is added to the old velocity to produce a new velocity,

which is then truncated by max_speed. steering_force acceleration velocity position = = = = truncate

truncate position

steering_force (velocity +

(steering_direction, / + mass acceleration,

velocity

The simple vehicle model maintains its velocity-aligned local space by incremental adjustment from the previous time step. vectors of the space. The local coordinate system is defined in terms of four vectors: a position vector specifying the local origin, and three direction vectors serving as the basis The basis vectors indicate the direction and length of coordinate units in These axes will be The descriptive (These correspond, of course, to X, Y and Z axes of each of three mutually perpendicular directions relative to the vehicle. referred to here as forward, up, and side. R .
3

But some people think up is obviously Y while some think it is obviously Z.

terms will be used in place of the Cartesian names for clarity.) In order to remain aligned with velocity at each time step, the basis vectors must be rotated into a new direction. (If velocity is zero the old orientation is retained.) Instead of using explicit rotations, the local space is reconstructed using a combination of substitution, approximation, and reorthogonalization. direction. We start with the new velocity and an approximation to the new up For example, the old up direction can be used as an approximation to the new up.

We use the vector cross product operation to construct the new basis vectors: new_forward new_side new_up = = = normalize = (velocity)

approximate_up cross

cross

normalize

(new_forward,

(new_forward,

(approximate_up) new_side)

approximate_up)

//

if

needed

The basic idea is that the approximate up is nearly perpendicular to the new forward direction, because frame-to-frame changes in orientation are typically small. The new side direction will be perpendicular to new forward, from the definition of cross product. The new up is the cross product of the perpendicular forward and side and so is perpendicular to each. The concept of “velocity alignment” does not uniquely specify an orientation. The degree of

freedom corresponding to rotation around the forward axis (also known as roll) remains unconstrained. Constructing the new local space relative to the previous one (by, for example, using the old up direction as the initial approximation to the new one) will ensure that the roll orientation at least remains consistent. Defining the “correct” roll value requires further heuristics, based on the intended use of the vehicle model. For a “flying” vehicle (like aircraft, spaceship, and submarines) it is useful to define roll in terms of banking. The basic idea of banking is to align the “floor” of the vehicle (-up axis) with the Conversely we want the up direction to apparent gravity due to centrifugal force during a turn.

align with the centripetal force that produced the maneuver.

In the presence of gravity, the So

down direction should align with the sum of turning acceleration and gravitational acceleration. We also want to add in the current orientation in order to damp out abrupt changes in roll. sum of: steering acceleration, gravitational acceleration, and the old up. For a “surface hugging” (wheeled, sliding, or legged) vehicle, we want to both constrain the vehicle’s position to the surface and to align the steering to implement banking in the simple vehicle model, the approximate up direction is a weighted

vehicle’s up axis to the surface normal. braking In

thrust

addition the velocity should be constrained to be purely tangential to the surface. These requirements can be easily met if the surface manifold is represented in such a way that an arbitrary point in space (corresponding to the old vehicle position) can be mapped to: (1) the The velocity can be

Figure 2: asymmetrical steering forces

nearest point on the surface, and (2) the surface normal at that point.

made tangent by subtracting off the portion normal to the surface. The vehicle’s position is set to the point on the surface, and the surface normal becomes its up axis. In this simple vehicle model, the control signal passed from the steering behaviors to the locomotion behavior consists of exactly one vector quantity: a desired steering force. realistic vehicle models would have very different sets of control signals. scalar quantities. More For example an

automobile has a steering wheel, accelerator and brake each of which can be represented as It is possible to map a generalized steering force vector into these scalar signals: the side component of the steering vector can be interpreted as the steering signal, the forward component of the steering vector can be mapped into the accelerator signal if positive, or into the brake signal if negative. due to engine thrust, as shown in Figure 2. Because of its assumption of velocity alignment, this simple vehicle model cannot simulate effects such as skids, spins or slides. its speed is zero. Furthermore this model allows the vehicle to turn when it allows undesirably large changes in orientation flee path

These mappings can be asymmetrical, for

example a typical automobile can decelerate due to braking much faster than it can accelerate

Most real vehicles cannot do this (they are “non-holonomic”) and in any case during a single time step. This problem can be

solved by placing an additional constraint on current change of orientation, or by limiting the lateral steering component at low speeds, or by simulating moment of inertia. seek path

velocity flee steering

seek

steering

Steering Behaviors This discussion of specific steering behaviors assumes that locomotion is implemented by the simple vehicle model described above, and is parameterized by a single steering force vector. Therefore the steering behaviors are described in

velocity (flee)

desired

velocity (seek)

desired

target

Figure 3: seek and flee

terms of the geometric calculation of a vector representing a desired steering force. clipped to max_force by the vehicle model. approximation to length as in [Ohashi 94].

Note that

generally the magnitude of these steering vectors is irrelevant, since they will typically be Note also that many of the calls to length and The terms “we” or “our” will sometimes be used to normalize functions in these formulations can be replaced by fast routines that use an indicate the first person perspective of the character being steered by a given behavior. Animated diagrams illustrating these behaviors can be found on the web at http://www.red.com/cwr/steer/ Seek (or pursuit of a static target) acts to steer the character towards a specified position in global space. the target. This behavior adjusts the character so that its velocity is radially aligned towards Note that this is different from an attractive force (such as gravity) which would The length of “desired velocity” could be

produce an orbital path around the target point. The “desired velocity” is a vector in the direction from the character to the target. application. max_speed, or it could be the character’s current speed, depending on the particular The steering vector is the difference between this desired velocity and the character’s current velocity, see Figure 3. desired_velocity quarry

target) future steering

*

=

max_speed

=

normalize -

(position velocity

-

desired_velocity

If a character continues to seek, it will eventually pass through the target, and then turn back to approach again. This produces motion a bit like a Contrast this moth buzzing around a light bulb.

now

pursuit

with the description of arrival below. evasion Flee is simply the inverse of seek and acts to steer the character so that its velocity is radially aligned away from the target. The desired velocity points in the opposite direction. Pursuit is similar to seek except that the quarry

Figure 4: pursuit and evasion

(target) is another moving character. future position. simulation step.

Effective pursuit requires a prediction of the target’s

The approach taken here is to use a simple predictor and to reevaluate it each For example, a linear velocity-based predictor corresponds to the assumption The position of

that the quarry will not turn during the prediction interval. While this assumption is often incorrect, the resulting prediction will only be in use for about 1/30 of a second. scaling its velocity by T and adding that offset to its current position. See Figure 4. The key to this implementation of pursuit is the method used to estimate the prediction interval T. Ideally, T would be the time until interception, but that value is unknowable because the quarry can make arbitrary and unpredictable maneuvers. corresponds to T=0). T could be assumed to be a constant, which while naive, would produce better pursuit than simple seek (which However for reasonable performance T should be larger when the A simple estimator of pursuer is far from the quarry, and small when they are nearby. a character T units of time in the future (assuming it does not maneuver) can be obtained by Steering for pursuit is then simply the result of applying the seek steering behavior to the predicted target location.

moderate quality is T=Dc where D is the distance between pursuer and quarry, and c is a turning parameter. A more sophisticated estimator can be obtained by taking into account the These two metrics can be expressed in terms of simple dot products (between unit forward vectors, and between the quarry’s forward and the offset to the pursuer’s position). Note that care must be taken to reduce T (e.g to zero) when the pursuer finds itself aligned with, and in front of, its quarry. Another approach to both seek and pursuit is based on the fact that when our character is on a collision course with a target, it will appear at a constant heading in our character’s local space. Conversely our character can steer toward interception by contriving to keep the target at a Figure 5: offset pursuit constant heading. Evasion is analogous to pursuit, except that flee is used to steer away from the predicted future position of the target character. Optimal techniques for pursuit and evasion exist in the field of control theory [Isaacs 65]. The versions given here are intended to be lightweight and are nonoptimal. In natural systems, evasion is often “intentionally” nonoptimal in order to be unpredictable, allowing it to foil predictive pursuit strategies, see [Cliff 96]. Offset pursuit refers to steering a path which passes near, but not directly into a moving target. Figure 6: arrival Examples would be a spacecraft doing a “fly-by” or an aircraft doing a “strafing run”: flying near enough to be within sensor or weapon range without colliding with the target. The basic idea is to dynamically compute a target point which is offset by a given radius R from the predicted future position of the quarry, and to then use seek behavior to approach that offset point, see Figure 5. To construct the offset point: localize the predicted target location (into our character’s local coordinate space) project the local target onto the character’s side-up plane, normalize that lateral offset, scale it by -R, add it to the local target point, and globalize that value. Arrival behavior is identical to seek while the character is far from its target. But instead of relative headings of pursuer and quarry, and whether the pursuer is generally ahead of, behind, or to the side of, the quarry.

moving through the target at full speed, this behavior causes the character to slow down as it approaches the target, eventually slowing to a stop coincident with the target, as shown in Figure 6. The distance at which slowing begins is a parameter of the behavior. This implementation is similar to seek: a desired velocity is determined pointing from the character towards the target. Outside the stopping radius this desired velocity is clipped to max_speed, inside the stopping radius, desired velocity is ramped down (e.g. linearly) to zero.

target_offset distance ramped_speed =

length = =

=

target

clipped_speed steering =

max_speed minimum =

(target_offset) *

-

position (distance / / slowing_distance) max_speed) * target_offset

desired_velocity

desired_velocity

(clipped_speed -

(ramped_speed, velocity

distance)

Real world examples of this behavior include a baseball player running to, and then stopping at a base; or an automobile driving towards an intersection and coming to a stop at a traffic light. Obstacle avoidance behavior gives a character A C the ability to maneuver in a cluttered environment by dodging around obstacles. avoidance and flee behavior. There is an Flee will always important distinction between obstacle cause a character to steer away from a given B location, whereas obstacle avoidance takes action only when a nearby obstacle lies directly in front of the character. For example, if a car was driving parallel to a wall, obstacle avoidance Figure 7: obstacle avoidance would take no corrective steering action, but flee would attempt to turn away from the wall, eventually driving perpendicular to it. The implementation of obstacle avoidance behavior described here will make a simplifying assumption that both the character and obstacle can be reasonably approximated as spheres, although the basic concept can be easily extend to more precise shape models. Keep in mind that this relates to obstacle avoidance not necessarily to collision detection. Imagine an airplane trying to avoid a mountain. Neither are spherical in shape, but it would suffice that the plane’s bounding sphere avoids the mountain’s bounding sphere. [Hubbard 96], and presumably for obstacle avoidance too. technique is described in [Egbert 96]. The geometrical construction of obstacle avoidance behavior bares some similarity to the offset pursuit behavior described above. It is convenient to consider the geometrical situation The goal of the behavior is to keep an imaginary The cylinder lies along the character’s forward An obstacle from the character’s local coordinate system. cylinder of free space in front of the character. A decomposable hierarchy of bounding spheres can be used for efficient representation of shapes for collision detection An unrelated obstacle avoidance

axis, has a diameter equal to the character’s bounding sphere, and extends from the character’s center for a distance based on the character’s speed and agility. further than this distance away is not an immediate threat. The obstacle avoidance behavior By localizing the center of each The local

considers each obstacle in turn (perhaps using a spatial portioning scheme to cull out distance obstacles) and determines if they intersect with the cylinder. spherical obstacle, the test for non-intersection with the cylinder is very fast.

obstacle center is projected onto the side-up plane (by setting its forward coordinate to zero) if the 2D distance from that point to the local origin is greater than the sum of the radii of the obstacle and the character, then there is no potential collision. Similarly obstacles which are For any fully behind the character, or fully ahead of the cylinder, can be quickly rejected.

remaining obstacles a line-sphere intersection calculation is performed.

The obstacle which

intersects the forward axis nearest the character is selected as the “most threatening.” Steering to avoid this obstacle is computed by negating the (lateral) side-up projection of the obstacle’s center. In Figure 7 obstacle A does not intersect the cylinder, obstacles B and C do, B is selected for avoidance, and corrective steering is to the character’s left. The value returned from obstacle avoidance is either (a) the steering value to avoid the most threatening obstacle, or (b) if no collision is imminent, a special value (a null value, or the zero vector) to indicate that no corrective steering is required at this moment. A final note regarding interaction of obstacle avoidance and goal seeking. Figure 8: wander our goal. Generally we only care about obstacles which are between us and The mountain beyond the airport is ignored by the airplane, but the mountain between the plane and the airport is very important. Wander is a type of random steering. and produces no sustained turns. One easy implementation would be to generate a It is “twitchy”

random steering force each frame, but this produces rather uninteresting motion. state and make small random displacements to it each frame. almost the same direction. another.

A more interesting approach is to retain steering direction Thus at one frame the

character may be turning up and to the right, and on the next frame will still be turning in The steering force takes a “random walk” from one direction to This idea can be implemented several ways, but one that has produced good results character. To produce the steering force for the

is to constrain the steering force to the surface of a sphere located slightly ahead of the next frame: a random displacement is added to the previous value, and the sum is constrained again to the sphere’s surface. The sphere’s radius (the large circle in Figure 8) determines the maximum wandering “strength” and the magnitude of the random displacement (the small circle in Figure 8) determines the wander “rate.” Another way to implement wander would be to use coherent Perlin noise [Perlin 85] to generate the steering direction. Related to wander is explore (where the goal is to Figure 9: path following exhaustively cover a region of space) and forage (combining wandering with resource seeking). See [Beer 90] and [Tu 96] for more details. Path following behavior enables a character to steer along a predetermined path, such as a roadway, corridor or tunnel. This is distinct from constraining a vehicle rigidly to a path like a

train rolling along a track.

Rather path following behavior is intended to produce motion such In the implementation described here, The path is then a “tube” or The

as people moving down a corridor: the individual paths remain near, and often parallel to, the centerline of the corridor, but are free to deviate from it. a path will be idealized as a spine and a radius. The spine might be represented as a spline

curve or a “poly-line” (a series of connected line segments).

“generalized cylinder:” a circle of the specified radius, swept along the specified spine. staying within the specified radius of the spine.

goal of the path following steering behavior is to move a character along the path while If the character is initially far away from the path, it must first approach, then follow the path. To compute steering for path following, a velocity-based prediction is made of the character’s future position, as discussed above in regard to obstacle avoidance behavior. on the path spine. The predicted If this projection future position is projected onto the nearest point See Figure 9. distance (from the predicted position to the wall following

nearest on-path point) is less than the path radius, then the character is deemed to be correctly following the path and no corrective steering is required. Otherwise the character is veering away To from the path, or is too far away from the path.

steer back towards the path, the seek behavior is used to steer towards the on-path projection of the predicted future position. Figure 10: wall following, containment Like in obstacle A avoidance, a null or zero value is returned is returned if no corrective steering is required. path can be followed without regard to direction, or in a specified direction (from A to B or from B to A) by adjusting the target point along the path in the desired direction. Variations on path following include wall following and containment as shown in Figure 10. Wall following means to approach a “wall” (or other surface or path) and then to maintain a certain offset from it [Beer 90]. For a discussion of offset goals, see offset pursuit above. Containment refers to motion which is restricted
S F

to remain within a certain region.

Path

following is a type of containment where the allowable region is a cylinder around the path’s spine. Examples of containment include: fish To implement: first swimming in an aquarium and hockey players skating within an ice rink. predict our character’s future position, if it is inside the allowed region no corrective steering is necessary. Otherwise we steer towards the This can be accomplished by allowed region.

V

using seek with an inside point (for example, we Figure 11: flow following can project the future position to the obstacle surface, and then extend this offset to obtain a

target point) or we can determine the intersection of our path with the boundary, find the surface normal at that point, and then use the component of the surface normal which is perpendicular to our forward direction as the corrective lateral steering. Flow field following steering behavior provides a useful tool for directing the motion of characters based on their position within an environment. It is particularly valuable in some production teams because it allows motion specification to be made without use of programming and so can used by the art staff directly. future In the case of game production this

person might be a “level designer” and in animation production they might be a “scene planner” or “layout artist.” In flow field following behavior the character steers to align its motion with the local tangent of a flow field (also known as a force field or a vector field). The flow field defines a mapping from a location in space to a flow vector: imagine for example a floor with arrows painted on it. Such a

future

now

now

map, typically representing the floor plan of an environment, can be easily created by an artist with a special purpose “paint” program which allows them to draw the desired traffic flow with a paint brush. The implementation of flow field

Figure 12: unaligned collision avoidance

following is very simple. sampled at that location. and the desired velocity.

The future position of a character is estimated and the flow field is This flow direction (vector F in Figure 11) is the “desired velocity” and

the steering direction (vector S) is simply the difference between the current velocity (vector V)

Unaligned collision avoidance behavior tries to keep characters which are moving in arbitrary directions from running into each other. Consider your own experience of walking If all nearby across a plaza or lobby full of other walking people: avoiding collisions involves predicting potential collisions and altering your direction and speed to prevent them. characters are aligned, a less complicated strategy can be used, see separation below. angle To implement this as a steering behavior, our character considers each of the other characters and determines (based on current velocities) when and where the two will make their nearest approach. A potential for collision exists if the nearest approach is in the future, and if the distance between the characters at nearest approach is small enough (indicated by circles in Figure 12). The nearest of these potential collisions, if any, is determined. The character then steers to avoid the site of the predicted collision. It will steer laterally to turn away from the

distance

Figure 13: neighborhood

potential collision. It will also accelerate forward or decelerate backwards to get to the indicate site before or after the predicted collision. In Figure 12 the character approaching from the right decides to slow down and turn to the left, while the other character will speed up and turn to the left. The next three steering behaviors: separation, cohesion, and alignment, relate to groups of characters. In each case, the steering behavior Characters As determines how a character reacts to other characters in its local neighborhood. Figure 14: separation outside of the local neighborhood are ignored.

shown in Figure 13, the neighborhood is specified by a distance which defines when two characters are “nearby”, and an angle which defines the character’s perceptual “field of view.” Separation steering behavior gives a character the ability to maintain a certain separation distance from others nearby. This can be used to To prevent characters from crowding together.

compute steering for separation, first a search is made to find other characters within the specified neighborhood. This might be an exhaustive search of all characters in the simulated world, or Figure 15: cohesion might use some sort of spatial partitioning or caching scheme to limit the search to local characters. For each nearby character, a repulsive force is computed by subtracting the positions of our character and the nearby character, normalizing, and then applying a 1/r weighting. (That is, the position offset vector is
2

scaled by 1/r .)

Note that 1/r is just a setting that

has worked well, not a fundamental value. These repulsive forces for each nearby character are summed together to produce the overall steering force. See Figure 14.

Cohesion steering behavior gives an character Figure 16: alignment the ability to cohere with (approach and form a group with) other nearby characters. 15. See Figure Steering for cohesion can be computed by The steering

finding all characters in the local neighborhood (as described above for separation), computing the “average position” (or “center of gravity”) of the nearby characters. force can applied in the direction of that “average position” (subtracting our character position from the average position, as in the original boids model), or it can be used as the target for seek steering behavior.

Alignment steering behavior gives an character the ability to align itself with (that is, head in the same direction and/or speed as) other nearby characters, as shown in Figure 16. Steering for alignment can be computed by finding all characters in the local neighborhood (as described above for separation), averaging together the velocity (or alternately, the unit forward vector) of the nearby characters. This average is the “desired velocity,” and so the steering vector is the difference between the average and our character’s current velocity (or alternately, its unit forward vector). its neighbors. Flocking behavior: in addition to other applications, the separation, cohesion and Figure 17: leader following alignment behaviors can be combined to produce the boids model of flocks, herds and schools [Reynolds 87] (see also [Tu 94], [Tu 96] and [Hodgins 94]). flocking (see Combining Behaviors below). before summing them. In some applications it is sufficient to simply sum up the three steering force vectors to produce a single combined steering for However for better control it is helpful to first normalize the three steering components, and then to scale them by three weighting factors As a result, boid flocking behavior is specified by nine numerical parameters: a weight (for combining), a distance and an angle (to define the neighborhood, see Figure 13) for each of the three component behaviors. Leader following behavior causes one or more character to follow another moving character designated as the leader. Generally the followers want to stay near the leader, without In addition, if there is more than one follower, they The arrival crowding the leader, and taking care to stay out of the leader’s way (in case they happen to find them selves in front of the leader). want to avoid bumping each other. The implementation of leader following relies on arrival (The offset distance might optionally In addition This steering will tend to turn our character so it is aligned with

behavior (see above) a desire to move towards a point, slowing as it draws near. target is a point offset slightly behind the leader. increases with speed.)

If a follower finds itself in a rectangular region in front of the leader, it See Figure 17.

will steer laterally away from the leader’s path before resuming arrival behavior. the followers use separation behavior to prevent crowding each other.

Finally, here are quick sketches of some other steering behaviors that fit into the same general category as those described in more detail above. Interpose steering behavior attempts to put its character between two other moving characters, for example a soccer player trying to block a pass between two members of the opposing team. The general approach is similar to pursuit described above: predict the future position of the two other characters, determine a target point by interpolating between the future positions, and use seek to steer toward the target point. Related to leader following and pursuit, we could shadow our quarry by The arrival This can be approaching and then using alignment to match their speed and heading.

behavior described above can be considered a constraint on position and speed. and/or to meet these constraints at a given time.

extended to simultaneously constrain orientation (to produce docking), or a non-zero velocity, Hide behavior involves identifying a target

location which is on the opposite side of an obstacle from the opponent, and steering toward it using seek. Combining Behaviors The individual steering behaviors described above serve as building blocks for more complex patterns of behavior. words of a story. They are components of a larger structure, like notes of a melody or Unless an autonomous character exists in In order to make interesting and life-like behaviors we need to select among,

and blend between, these individual components. single steering behavior. Combining behaviors can happen in two ways.

an very simple world, it would seldom make sense for the character to continually execute a

A character may sequentially switch between For example, imagine caribou This event triggers a

behavioral modes as circumstances change in its world. discrete behavioral switch. flee from the predators.

grazing in a meadow when suddenly they sense wolves approaching.

All thoughts of grazing are forgotten as the caribou herd turns to These discrete changes

There is no tendency to mix these behaviors: a caribou will not slow

down while running from a wolf in order to grab another bite of food. hierarchy discussed in the Introduction. [Tu 94], [Tu 96] and in [Blumberg 94].

of behavioral state take place at the action selection level, the top of the three level behavioral There is a extensive discussion of action selection in

On the other hand, some kinds of behaviors are commonly blended together, effectively acting in parallel. For example, as the caribou flee through the forest, they blend evasion and obstacle avoidance together to allow them to escape from the wolves while dodging trees. A caribou cannot afford to ignore either component behavior, it must always be moving in a direction that both takes it away from the wolf and avoids collisions with trees. blending occurs at the middle steering level of the behavioral hierarchy. Blending of steering behaviors can be accomplished in several ways. The most straightforward is simply to compute each of the component steering behaviors and sum them together, possibly with a weighting factor for each of them. behaviors) could be much harder to combine.) (Note that steering vectors are especially easy to blend, other kinds of behaviors, producing other kinds of values (e.g. conversational This simple linear combination often works well, but has at least two shortcomings: it is not the most computationally efficient approach, and despite adjusting the weights, component behaviors may cancel each other out at inopportune times. The computation load can be decreased by observing that a character’s momentum serves to apply a low-pass filter to changes in steering force. So rather than compute several steering components each simulation step and average them together, we could instead select one steering component to compute and apply each frame, and depend on momentum (and perhaps some explicit damping of acceleration) to blend them together. The problem of components canceling each other out can be addressed by assigning a priority to components. (For example: first priority is obstacle avoidance, second is evasion ...) The steering controller first checks to see if obstacle avoidance returns a non-zero value (indicating a potential collision), if so it uses that. behavior, and so on. Otherwise, it moves on to the second priority This behavioral

A hybrid of these techniques that the author has found useful is “prioritized dithering”: with a certain probability the first priority behavior is evaluated, and if it returns a non-zero (non-null) value that will be used. Otherwise (if the behavior returns zero, or it was skipped over due to the random selection) the second priority behavior is considered, and so on. In [Reynolds 87] a blending scheme called “prioritized acceleration allocation” was used with the boids flocking model. behaviors. The basic idea was that by adjusting their magnitude, higher priority behaviors could decide whether or not to leave any steering force for use by lower priority In the course of several reimplementations of boids over the years, a simple linear When combining flocking with combination of the component behaviors has proved sufficient. been used successfully. Conclusions This paper defined “autonomous character” in terms of autonomous agents and improvisational action. and locomotion. behaviors. It presented a decomposition of the task of constructing motion behaviors for autonomous characters into a three level hierarchy of: action selection, steering, It has defined a minimal implementation of the locomotion level in terms of a It has then presented a collection of simple, common steering “simple vehicle model.”

other behaviors such as obstacle avoidance, both simple summing and prioritized dither have

(Including: seek, flee, pursuit, evasion, offset pursuit, arrival, obstacle

avoidance, wander, path following, wall following, containment, flow field following, unaligned collision avoidance, separation, cohesion, alignment, flocking, and leader following.) Finally it has described some techniques for blending these simple steering behaviors together. Acknowledgments The techniques described in this paper have been developed over the last twelve years, for many different projects, at several companies. of all the companies and coworkers involved. I wish to acknowledge the helpful cooperation Specifically I wish to thank the following people At Sony Computer Entertainment America: At

for managerial support and technical collaboration.

Phil Harrison, John Phua, Attila Vass, Gabor Nagy, Sky Chang, and Tom Harper. Raghavachary, and Mike Ullner.

DreamWorks Feature Animation: Dylan Kohler, Bart Gawboy, Matt Arrott, Lance Williams, Saty At SGI’s Silicon Studio: Bob Brown, Leo Blume, Roy At Electronic At Symbolics Finally, Hashimoto, and especially my behavioral animation colleague Xiaoyuan Tu. Arts: Luc Barthelet, Steve Crane, Kelly Pope, Steve Sims, and Frank Giraffe. loving thanks to my wife Lisa and our children Eric and Dana. autonomous, I hope I steer the kids in the right direction. characters! References
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