In [Don4], 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 paper, we answer in the affirmative. We do so by using the general methods of [Don4] analyzing information invariants. We discuss several measures for the information complexity of the task: (a) How much internal state should the robot retain? (b) How many cooperating agents 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? 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 (a) - (e) among collaborating autonomous agents. We add a resource to (a) - (e) and ask: (f) How much information is provided by the task mechanics? By answering this question, we hope to develop information invariants that explicitly trade-off resource (f) with resources (a) - (e). The protocols we describe here have been implemented in several different forms, and we will show a video reporting on experiments to measure and analyze information invariants using a pair of cooperating mobile robots for manipulation experiments in our laboratory.