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This paper discusses some techniques for directing the paths of objects moving around an environment, normally towards specified goals, such that they do not collide with either static obstacles or other moving objects. Most of these techniques apply equally well to motion in three-dimensional space or on two-dimensional surfaces. The intended application is the control of motion of geometrical models in simulated environments, such as in the production of computer animation. Similarly, they are useful in certain types of simulation studies for engineering applications, such as modeling the flow of machines and people around each other on a factory floor. Some of the techniques are applicable to control of the motion of real physical objects such as robotic vehicles.

It is possible to pre-specify paths around a static environment. Indeed, this is by far the most common technique for describing motion for animation. A series of control points is specified which describe a splined curve in space. The object is moved along the curve at a scripted rate. For simple, well-defined motion this is probably the most convenient and direct technique for controlling the animation.