Search for: All records

Motivated by robust dynamic resource allocation in operations research, we study the Online Learning to Transport (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw connections between online learning, optimal transport, and partial differential equations through an insight called the minimal selection principle, originally studied in the Wasserstein gradient flow setting by Ambrosio et al. (2005). This allows us to extend the standard online learning framework to the infinite-dimensional setting seamlessly. Based on our framework, we derive a novel method called the minimal selection or exploration (MSoE) algorithm to solve OLT problems using mean-field approximation and discretization techniques. In the displacement convex setting, the main theoretical message underpinning our approach is that minimizing transport cost over time (via the minimal selection principle) ensures optimal cumulative regret upper bounds. On the algorithmic side, our MSoE algorithm applies beyond the displacement convex setting, making the mathematical theory of optimal transport practically relevant to non-convex settings common in dynamic resource allocation. 

This work presents a unique approach to the design, fabrication, and characterization of paper-based origami robotic systems consisting of stackable pneumatic actuators. These paper-based actuators (PBAs) use materials with high elastic modulus-to-mass ratios, accordion-like structures, and direct coupling with pneumatic pressure for extension and bending. The study contributes to the scientific and engineering understanding of foldable components under applied pneumatic pressure by constructing stretchable and flexible structures with intrinsically nonstretchable materials. Experiments showed that a PBA possesses a power-to-mass ratio greater than 80 W/kg, which is more than four times that of human muscle. This work also illustrates the stackability and functionality of PBAs by two prototypes: a parallel manipulator and a legged locomotor. The manipulator consisting of an array of PBAs can bend in a specific direction with the corresponding actuator inflated. In addition, the stacked actuators in the manipulator can rotate in opposite directions to compensate for relative rotation at the ends of each actuator to work in parallel and manipulate the platform. The locomotor rotates the PBAs to apply and release contact between the feet and the ground. Furthermore, a numerical model developed in this work predicts the mechanical performance of these inflatable actuators as a function of dimensional specifications and folding patterns. Overall, we use stacked origami actuators to implement functionalities of manipulation, gripping, and locomotion as conventional robotic systems. Future origami robots made of paper-like materials may be suitable for single use in contaminated or unstructured environments or low-cost educational materials.