What Robots Can Do: Robot Programs and Effective Achievability

In this paper, we propose a definition of goal achievability: given a basic action theory describing an initial state of the world and some primitive actions available to a robot, including some actions which return binary sensing information, what goals can be achieved by the robot? The main technical result of the paper is a proof that a simple robot programming language is universal, in that any effectively achievable goal can be achieved by getting the robot to execute one of the robot programs. The significance of this result is at least two fold. First, it is in many ways similar to the equivalence theorem between Turing machines and recursive functions, but applied to robots whose actions are specified by an action theory. Secondly, it provides formal justifications for using the simple robot programming language as a foundation for our work on robotics.