A theory of information invariance that includes sensors and computation is suggested. The author's results generalize the work of M. Blum and D. Kozen (1978). Detailed yet abstract models of physical autonomous mobile robots are considered together with generalizations and variations on compasses and orientation sensors. A generalized and stratified theory of the power of such sensory-computational devices is developed. It is hoped that information invariants can serve as a framework in which to measure the capabilities of robot systems, to quantify their power, and to reduce their fragility with respect to assumptions that are engineered into the control system or the environment. The authors believe that the equivalences that can be derived between communication, internal state, external state, computation, and sensors, can prove valuable in determining what information is required to solve a task, and how to direct a robot's actions to acquire that information to solve it.< >