One of the grand challenges in planning is tying together high-level global planners with low-level local planners, often called behaviors or control laws. Global planners provide provable guarantees but are often too abstract to respect the details and dynamics afforded by local planners, which in turn lack provable guarantees. The proposed work aims to get the best of both worlds: inhereting the provable completeness of global planners while respecting the local details and dynamics with local planners. The real challenge is: how does one tie together the high-level and low-level aspects of a planner. The proposed work takes a topological approach towards addressing this problem, addressing three focused problems -- planning in narrow corridors with probabilistic methods, defining hybrid control laws for navigating and mapping tasks, and sensor-based exploration of highly articulated bodies. The broad impact of this work lie in path planning for non-Euclidean configuration spaces and developing control laws for those spaces, as well as further develop a LEGO robotics lab module.
