Research
Mixed Integer Linear Programming
Can we find a better solution when agents plan their trajectories online?
Signal temporal logic (STL) is a useful framework for encoding mission specifications, and solving an optimization problem subject to constraints derived from agent dynamics and mission specificati...
Morse Theory for Optimization
Can we find some gradient-like vector field on a manifold such that we can follow some flow to get to a minimizer?
This research focuses on establishing theoretical guarantees and developing algorithms that identify gradient-like vector fields, and studying the behavior of gradient-based algorithms on general m...
Applied Sheaf Theory
Can heterogeneous agents perform heterogeneous mixture coordination tasks?
This research applies sheaf theory and algebraic topology (cohomology) to develop algorithms that converge under bounded and unbounded delays for distributed coordination problems with local and gl...
Safety Critical Systems
Can agents achieve their goals without collisions?
Robot safety guarantees can come at the cost of slower navigation. For example, autonomous delivery robots often encounter situations where they become hopelessly stuck and require human assistance...
Communication/Computation Constrained Autonomy
Can agents solve problems when there are communication and computation delays present?
This research focuses on finding theoretical guarantees for algorithms to converge under bounded and unbounded delays for convex and non-convex optimization problems. As multi-agent systems grow, ...
Topological Motion Planning
Can we use robot geometry and perception data to plan faster and smarter?
Classical motion planners often treat the robot and its environment as abstract geometric objects, ignoring rich structure available from the robot’s geometry and perception data. This leads to slo...