Justin Koeln

Joshua Ortiz, Alyssa Vellucci, Justin Koeln et al.

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.

Shilin You, Gael Luna, Juned Shaikh et al.

We present an algorithm for planning trajectories that avoid obstacles and satisfy key-door precedence specifications expressed with a fragment of signal temporal logic. Our method includes a novel exact convex partitioning of the obstacle free space that encodes connectivity among convex free space sets, key sets, and door sets. We then construct an augmented graph of convex sets that exactly encodes the key-door precedence specifications. By solving a shortest path problem in this augmented graph of convex sets, our pipeline provides an exact solution up to a finite parameterization of the trajectory. To illustrate the effectiveness of our approach, we present a method to generate key-door mazes that provide challenging problem instances, and we perform numerical experiments to evaluate the proposed pipeline. Our pipeline is faster by several orders of magnitude than recent state-of-the art methods that use general purpose temporal logic tools.