Solving Polynomials with Computers

Abstract

When we think of a robot, many of us conjure up a science-fiction image of a two-legged, two-armed ma chine with lightbulbs for eyes, vaguely resembling a human being. In science fiction, robots are super-competent at mechanical tasks but unable to master the more difficult problems people have to deal with?good versus evil, honesty versus deception, the nature of self-awareness. For the time being, however, the reality of robots is quite different, because our first assumption is a fallacy: Robots are not super-com petent mechanically. In fact, it is outra geously difficult to make a robot that can perform some of the simplest mo tions that we take for granted. For an example, draw a square on your back halfway between your shoulders. Even though you cannot see your hand, you instinctively sense where it is going. Not so a robot. It can sense only the angles formed by its joints; if it needs to know where its hand is, it has to figure it out mathe matically. It can solve the forward kinematic problem?if I make an an gle 61 with my shoulder and an angle