Mathematical Foundations for Robotics,

A major component of robotics is concerned with the representation and manipulation of physical objects. The design of computer algorithms to interact with these representations and to carry out task planning raises many mathematical and computational issues that are not well understood. This article explores some of these issues and outline areas where mathematical development is needed to support a robotics effort. Task level planning is an important aspect of robotics. What is needed is the ability to communicate a task to a robot at the level of insert peg in hole and have the detailed instructions such as open gripper, move to location x, rotate gripper, etc. be automatically generated by a computer. To do this requires solving many problems. First, one must be able to automatically deduce a grip positions that will not interface with the desired task. Then one must develop an approach strategy that will insure gripping even in the presence of some uncertainty of position. Finally one must be able to plan motion.