Previous work on self-reconfiguring modular robots has concentrated primarily on designing hardware and developing reconfiguration algorithms tied to specific hardware systems. In this paper, we introduce a generic model for lattice-based self-reconfigurable robots and present several generic locomotion algorithms that use this model. The algorithms presented here are inspired by cellular automata, using geometric rules to control module actions. The actuation model used is a general one, assuming only that modules can generally move over the surface of a group of modules. These algorithms can then be instantiated onto a variety of particular systems. Correctness proofs of many of the rule sets are also given for the generic geometry; this analysis can carry over to the instantiated algorithms to provide different systems with correct locomotion algorithms. We also present techniques for automated analysis that can be used for algorithms that are too complex to be easily analyzed by hand.