Modelling robot manipulators with multivariate B-splines

In programming robot manipulators to carry out a wide variety of tasks it would be desirable to create a cad system in which these tasks can be programmed at the task level, leaving the ne-grained detail of path planning and collision detection to the system. This paper describes the theoretical background to such a system, by providing a model in which robot motions are represented using multivariate B-splines, a standard representation for free-form shapes in the cad environment. The paper also describes algorithms which take this representation and apply it to collision detection and path-planning.