Recently, robots have played an increasingly helpful role in navigation, mapping, remote manipulation, and many other dynamic applications. As capabilities continue to advance, robots with many joints offer the potential to execute more nuanced, sophisticated tasks than simpler mechanisms. However, the curse of dimensionality can place prohibitive costs in time and resources in order to control and refine such behaviors. In this work, we investigated the role of system geometry in addressing these challenges. Geometric mechanics offers a framework to generalize intuitive features, like friction and inertia, into broad categories of robots that experience the same functional forms relating momentum, internal shape motions, and body motions. We focused on friction-dominated robots, where we could see that the vanishing role of momentum reduces the dynamics from a second order to a first order system. Subsequent architectural simplifications in behavior modeling, planning, and control resulted in robots that were capable of rapidly self-modeling and optimizing useful behaviors. We demonstrated on a simulated robotic snake that during joint failure, the system was able to adapt more quickly when it was equipped with more motorized joints. In this case, dimensionality was an asset, rather than a liability. Additionally, we demonstrated that the methods use no prior knowledge about system kinematics by building a robot made of tree branches. This system was able to optimize a library of primitives for navigation, training on less than 12 minutes of experimental data. Finally we showed that these methods can extend to both soft robots and systems with momentum. This defense will cover our findings concerning the practical applications of data-driven geometric mechanics.