The UH-LSU-TAMU Undergraduate Mathematics Research Conference is a forum for sharing the results of undergraduate research activities in mathematics. This annual event rotates between the University of Houston (UH), Louisiana State University (LSU), and Texas A&M University (TAMU).

We create a lively environment wherein students present research and discuss mathematics. Such activities help prepare students for graduate study, positions with research laboratories, or employment in the industry.

The 2024 conference will be fully in-person. There will be no virtual component.

Plenary Talk

as

Boyang Zhang, Duke University 

Title: Control through Constraint: with Applications to Multi-Robot Systems

Abstract: As autonomy and AI continue to shape our future, multi-robot systems are increasingly central to a wide array of applications, from autonomous transportation and delivery to search and rescue operations. However, real-world deployment of these systems faces a range of challenges, such as nonlinearity, time variability, external disturbances, actuator limits, and inaccuracies in modeling, measurement, and estimation. These  critical aspects, however, are either simplified or overlooked in existing methods.

In this talk, I will introduce a new control paradigm designed to tackle these challenges inherent in multi-robot systems. Distinct from the literature, my multi-robot control results from solving a constrained optimization that does not involve a cost function, a time horizon, or any linearization. The stability, structure (centralized or decentralized), and performance (e.g., deadlock resolution) of the control are achieved exclusively through the design of constraints. I will demonstrate the effectiveness of my constraint-based control with three examples: the coordinated navigation of a swarm of double integrators, the navigation and collision avoidance of high-speed wheeled mobile robots, and the unified control of position and orientation for fully nonlinear quadrotor UAVs. The present control is computationally simple and efficient, with a decentralized control computation time in an order of ten microseconds for these examples. 

Organizers

as

• Wencai Liu (Texas A&M University) A

• Daniel Onofrei (University of Houston)

• William Ott (University of Houston)&M University)

• Stephen Shipman (Louisiana State University)

• Andrew Török (University of Houston)

• Fan Yang (Louisiana State University)

• Matthew Young (Texas A&M University)

Support 

• Department of Mathematics,  Texas A&M University