Information invariants for distributed manipulation

In Donald (1995), we described a manipulation task for cooperating mobile robots that can push large, heavy objects. There, we asked whether explicit local and global communication between the agents can be removed from a family of pushing protocols. In this article, we answer in the affirmative. We do so by using the general methods of Donald (1995), analyzing information invariants. We discuss several measures for the information complexity of the task: (I) How much internal state should the robot retain? (2) How many cooperating agents are required, and how much communication between them is necessary? (3) How can the robot change (side effect) the environment to record state or sensory information for performing a task? (4) How much information is provided by sensors? and (5) How much computation is required by the robot? To answer these questions, we develop a notion of information invariants. We develop a technique whereby one sensor can be constructed from others by adding, deleting and reallocating I) through 5), among collaborating autonomous agents. We add a resource to measures I) through 5) and ask: 6) How much information is provided by the task mechanics? By answering this question, we hope to develop information invariants that explicitly tradeoff resource 6) with resources I) through 5). The protocols we describe here have been implemented in several different forms, and we report on experiments to measure and analyze information invariants using a pair of cooperating mobile robots for manipulation experiments in our laboratory.