Simple Temporal Networks (STNs) were introduced by Tsamardinos (2002) as a means of describing graphically the temporal constraints for scheduling problems. Since then, many variations on the concept have been used to develop and analyze algorithms for multi-agent robotic scheduling problems. Many of these algorithms for STNs utilize a flexibility metric, which measures the slack remaining in an STN under execution. Various metrics have been proposed by Hunsberger (2002); Wilson et al. (2014); Lloyd et al. (2018). This thesis explores how adequately these metrics convey the desired information by using them to build a reward function in a reinforcement learning problem.

The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tools to solve and test the obstacle avoidance problem through mathematics.