Research

Optimal Transport Based Reachability

Optimal transport provides an alternative way to sample from the reachable set of a control set. In left, a standard randomized sampling based approach to sample gets concentrated on the attractor of the system. In the right, an optimal transport based approach provides a sample efficient approach to uniformly sample from the reachable set.

Diffusion Based Planning and Control

We use denoising diffusion from machine learning to construct controllers of stabilizing a point in a domain with obstacles.

Coverage of Compact Manifolds by Nonholonomic Robots

How does one get a swarm of agents spatially cover a non-convex space, using local interaction rules only? Using mean-field PDE techniques one can construct coordination strategies for swarms that are globally asymptotically stabilizing to any target probability distribution. What's more? The strategies are identity free; robots don't have to able to remember each other's faces or names, thus reducing their massive sensing burden in classical multi-agent control techniques. Though if your robot forgets your name, get your money back! (Paper)

Herding Agents To Target Distributions using a Leader

This study poses the herding problem as one of controlling a swarm using a leader. By using a leader that locally influences swarm agents through repulsion, we show that it is possible to steer the swarm to arbitrary probability  distributions. Gulp! Keep this research away from mean Ph.D. advisors. (Paper)

Optimal Transport of Particle in Double Gyre Flow