The Compass That Steered Robotics

Robotics researchers will be aware of Dexter Kozen’s contributions to algebraic algorithms, which have enabled the widespread use of the theory of real closed fields and polynomial arithmetic for motion planning. However, Dexter has also made several important contributions to the theory of information invariants, and produced some of the most profound results in this field. These are first embodied in his 1978 paper

On the Power of the Compass

, with Manuel Blum. This work has had a wide impact in robotics and nanoscience.

Starting with Dexter’s insights, robotics researchers have explored the problem of determining the information requirements to perform robot tasks, using the concept of

information invariants.

This represents an attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity.

In this vein, several measures have been proposed [14] to measure the information complexity of a task: (a) How much internal state should the robot retain? (b) How many cooperating robots are required, and how much communication between them is necessary? (c) How can the robot change (side-effect) the environment in order to record state or sensory information to perform a task? (d) How much information is provided by sensors? and (e) How much computation is required by the robot? We have considered how one might develop a kind of “calculus” on (a) – (e) in order to compare the power of sensor systems analytically. To this end, information invariants is a theory whereby one sensor can be “reduced” to another (much in the spirit of computation-theoretic reductions), by adding, deleting, and reallocating (a) – (e) among collaborating autonomous robots. As we show below, this work steers using Dexter’s compass.