Modelling robot manipulators with multivariate B-splines

In programming robot manipulators to carry out a wide variety of tasks it w ould be desirable to create a CAD system in which these tasks can be progra mmed at the task level, leaving the fine-grained detail of path planning an d collision detection to the system. This paper describes the theoretical b ackground to such a system, by providing a model in which robot motions are represented using multivariate B-splines, a standard representation for fr ee-form shapes in the CAD environment. The paper also describes algorithms which take this representation and apply it to collision detection and path -planning.