Embedded Files
Flow Matching based Control
Flow matching is a versatile approach to turn a collection of open-loop trajectories into a feedback controller. Here, we use RRT* to construct a noising process that explores the space efficiently around the obstacles, and the time-reversal gives a closed-loop plan that navigates the system around obstacles. The idea is to treat feedback control as a "denoising problem" in the sense of diffusion models.
Geometry Preserving Neural Network Architectures
Encoding geometry in neural network architectures has wide applications, from robots' configuration spaces to safety. We study differential geometric and variational ways to enforce constraints by design. Should one apply constraint enforcing augmentations between every layer, or is augmentation at the final layer sufficient? And which kind of augmentation should we use?
Optimal Transport Based Reachability
Optimal transport provides an alternative way to sample from the reachable set of a control system. Above, a standard randomized sampling based approach to sample gets concentrated on the attractor of the system. Bottom, an optimal transport based approach provides a sample efficient approach to uniformly sample from the reachable set.
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