Title: Robust Real-Time Solvers for Generalized Nash Equilibria in Constrained Differential Dynamic Games

Date: Thursday, December 4th, 2025

Time: 3PM to 5PM ET

Location: Montgomery Knight 325 or via Zoom https://gatech.zoom.us/j/3944839121?omn=91088115333 

Zhiyuan Zhang

Robotics Ph.D. Student

Guggenheim School of Aerospace Engineering

Georgia Institute of Technology

Committee:

Dr. Panagiotis Tsiotras (advisor) – Guggenheim School of Aerospace Engineering, Georgia Institute of Technology

Dr. Kyriakos Vamvoudakis – Guggenheim School of Aerospace Engineering, School of Electrical and Computer Engineering, Georgia Institute of Technology

Dr. Yongxin Chen– Guggenheim School of Aerospace Engineering

, Georgia Institute of Technology

Dr. Glen Chou –  School of Cybersecurity & Privacy, Georgia Institute of Technology

Dr. Sarah Li – Guggenheim School of Aerospace Engineering

, Georgia Institute of Technology

Abstract:

In a traditional robotic application, a robot works in a dedicated work area designed for a single robot, isolated from other robots and human operators. Now, robots often operate in a dynamic and collaborative environment shared by other robots and human agents.  This shift in application scenario highlights the safety, efficiency, and robustness of planning and control in the vicinity of other interactive agents.

Constrained Differential Dynamic Game (CDDG) is a natural multi-agent extension of the single-agent optimal control problem. Through coupled state constraints and cost functions, CDDG captures the interaction between agents. Generalized Nash Equilibrium (GNE) is a standard solution concept of a CDDG. State-of-art methods solve for the necessary conditions of GNE and have achieved promising practical performance. However, these methods are vulnerable to non-equilibrium saddle points, lacking guarantees of convergence to a true GNE.

This proposal aims to fill two closely related gaps in the existing body of work on CDDG. First, enhance first-order methods for DDG by developing an efficient numerical method to verify true GNE using inertia-controlling factorization. Second, develop efficient GNE solvers guaranteed to find GNE instead of saddle points, leveraging the Local Symplectic Surgery method and the Follow-the-Ridge method. In addition, we propose to evaluate the performance of these methods in comprehensive simulation benchmarks and in physical experiments with the BuzzRacer autonomous race car platform and the Crazyflie quadcopter platform.