Pranav Rajbhandari

The geodesic complexity of a length space $X$ quantifies the required number of case distinctions to continuously choose a shortest path connecting any given start and end point. We prove a local lower bound for the geodesic complexity of $X$ obtained by embedding simplices into $X\times X$. We additionally create and prove correctness of an algorithm to find cut loci on surfaces of convex polyhedra, as the structure of a space's cut loci is related to its geodesic complexity. We use these techniques to prove the geodesic complexity of the octahedron is four. Our method is inspired by earlier work of Recio-Mitter and Davis, and thus recovers their results on the geodesic complexity of the $n$-torus and the tetrahedron, respectively.

Bio-inspired design is often used in autonomous UAV navigation due to the capacity of biological systems for flight and obstacle avoidance despite limited sensory and computational capabilities. In particular, honeybees mainly use the sensory input of optic flow, the apparent motion of objects in their visual field, to navigate cluttered environments. In our work, we train a Reinforcement Learning agent to navigate a tunnel with obstacles using only optic flow as sensory input. We inspect the attention patterns of trained agents to determine the regions of optic flow on which they primarily base their motor decisions. We find that agents trained in this way pay most attention to regions of discontinuity in optic flow, as well as regions with large optic flow magnitude. The trained agents appear to navigate a cluttered tunnel by avoiding the obstacles that produce large optic flow, while maintaining a centered position in their environment, which resembles the behavior seen in flying insects. This pattern persists across independently trained agents, which suggests that this could be a good strategy for developing a simple explicit control law for physical UAVs.

With the increasing number of autonomous platforms in everyday life, forming coordinated teams of agents becomes vital. To solve this, we propose BERTeam, an algorithm inspired by Natural Language Processing. BERTeam trains a transformer-based deep neural network to select from a population of agents. It can integrate with coevolutionary deep reinforcement learning, which evolves a diverse set of players to choose from. We evaluate BERTeam in Marine Capture-The-Flag, and find it learns non-trivial team compositions that outperform unknown opponents. In this setting, we find that BERTeam outperforms MCAA, another team selection algorithm.

When researching robot swarms, many studies observe complex group behavior emerging from the individual agents' simple local actions. However, the task of learning an individual policy to produce a desired group behavior remains a challenging problem. We present a method of training distributed robotic swarm algorithms to produce emergent behavior. Inspired by the biological evolution of emergent behavior in animals, we use an evolutionary algorithm to train a 'population' of individual behaviors to produce a desired group behavior. We perform experiments using simulations of the Georgia Tech Miniature Autonomous Blimps (GT-MABs) aerial robotics platforms conducted in the CoppeliaSim simulator. Additionally, we test on simulations of Anki Vector robots to display our algorithm's effectiveness on various modes of actuation. We evaluate our algorithm on various tasks where a somewhat complex group behavior is required for success. These tasks include an Area Coverage task and a Wall Climb task. We compare behaviors evolved using our algorithm against designed policies, which we create in order to exhibit the emergent behaviors we desire.