In our work we present a collection of distributed algorithms for the locomotion of rectangular and histogram-shaped square-lattice-based modular robots, on free ground and in the presence of obstacles. Each algorithm presented is accompanied with a correctness proof, a complexity analysis, and a direct implementation in a simulator, that allows the direct observation of the effect of the rules over different systems and obstacles. . The goal of this project is to develop geometric algorithms, both centralized and distributed for modular robotic systems. The algorithms should make the system reconfigure, move on a substrate, and solve other geometric tasks. Some algorithms can be specifically designed to current protoptypes, while others can be generic in the sense that they can be applied to a set of prototypes. The framework is restricted to lattice-based modular robots