Brooks Butler, Electrical and Computer Engineering, Ph.D

Title: Collaborative Safe Formation Control for Coupled Multi-Agent Systems

The safe control of multi-robot swarms is a challenging and active field of research, where common goals include maintaining group cohesion while simultaneously avoiding obstacles and inter-agent collision. Building off our previously developed theory for distributed collaborative safety-critical control for networked dynamic systems, we propose a distributed algorithm for the formation control of robot swarms given individual agent dynamics, induced formation dynamics, and local neighborhood position and velocity information within a defined sensing radius for each agent. Individual safety guarantees for each agent are obtained using rounds of communication between neighbors to restrict unsafe control actions among cooperating agents through safety conditions derived from high-order control barrier functions (CBFs). One application of this algorithm is to the control of drone swarms in forest fire surveillance where drones are to automatically maximize sensor coverage of a designated area while simultaneously avoiding no-fly areas.

Yue Cao, Electrical and Computer Engineering, Ph.D

Title: Ground Manipulator Primitive Tasks to Executable Actions Using Large Language Models

Layered architectures have been widely used in robot systems, where planning and execution functions often operate in separate layers. Despite their widespread use, there still lacks a straightforward way to transit from high-level tasks in the planning layer to low-level motor commands in the execution layer. To address this gap, we introduce a novel approach that utilizes large language models (LLMs) to ground the robot primitive tasks to low-level actions. Our focus is on manipulator interaction control tasks. We designed a program-function-like prompt based on the task frame formalism. In this way, we enable LLMs to generate position/force set-points for hybrid control.

Demetrius Gulewicz, Mechanical Engineering, M.S.

Title: Non-Linear Model Predictive Control of a Hybrid Thermal Management System

Hybrid thermal management systems (hybrid TMS) in their most basic form consist of a component that generates heat, and a device that expels that heat. A thermal energy storage device (TES) can be added to improve system performance. In addition, model predictive control (MPC) has been shown to be effective and robust in the optimal control of many systems, including TMS. While many have proposed controllers for hybrid TMS, many approximations are usually made to ensure computational feasibility. We propose a single step controller (as opposed to a hierarchical approach) that enforces the TES nonlinear phase change dynamics. In addition, our prediction model is a high state system, containing 77 states. After synthesizing the controller, we also show experimental results of the MPC implemented on a testbench.

Wenjian Hao, Aeronautics and Astronautics Engineering, Ph.D

Title: Deep Koopman Learning of Nonlinear Time-varying Systems

This work presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

S M Nahid Mahmud, Aeronautics and Astronautics Engineering, Ph.D

Title: Adaptive Distributed Framework for Safety-critical Multi-agent Optimal Control Systems

The ability to complete additional tasks without redesigning the optimal control system from the beginning provides significant flexibility in real-life applications. To facilitate this adaptability feature, tunable parameters are often included in the dynamical model and/or objective function of the system. While an approach known as Pontryagin Differentiable Programming (PDP) has been proven effective for tuning single and multi-agent optimal control systems, previous studies have overlooked safety challenges such as inter-agent constraints inherent in multi-agent systems. Inspired by PDP, this study proposes an adaptive distributed framework for multi-agent safety-critical optimal systems where a network of agents cooperatively optimizes tunable parameters to minimize the sum of their loss functions while ensuring safety. The main idea of the proposed framework relies on integrating barrier function and gradient descent-based distributed optimization with a gradient generator that captures the optimal performance as a function of the parameter in the feedback loop tuning the parameter for each agent. Theoretical and simulation results are obtained to verify this proposed adaptive distributed framework for safety-critical multi-agent optimal control systems.

Nicolas Miguel, Aeronautics and Astronautics Engineering, Ph.D

Title: Stochastic Formulations for Barrier Function-based Collision Avoidance

The use of barrier functions to provide provably safe collision guarantees in the field of optimal control is a recent advancement. Taking advantage of the properties of set invariance provided by barrier function formulations, control barrier functions (CBF) can be utilized as safety filters to ensure safety-critical control. Additionally, when formulated as quadratic programs, CBFs provide faster real-time implementation, more flexibility, and improved constraint handling over typical optimal control methods.

Stochastic CBFs arise from the need to guarantee performance of CBFs even in stochastic environments, where Gaussian noise can cause the system to take unsafe actions. We investigate the application of Stochastic CBF methodology into collision-cone based barrier functions, and discuss future directions of theoretical research in the field.

Ayush Rai, Aeronautics and Astronautics Engineering, Ph.D

Title: Closed-loop Neighboring Extremal Optimal Control Using HJ Equation

This study introduces a method to obtain a neighboring extremal optimal control (NEOC) solution for a broad class of nonlinear systems with non-quadratic performance indices by investigating the variation to a known closed-loop optimal control law caused by small, known variations in the system parameters or in the performance index. The NEOC solution can formally be obtained by solving a linear partial differential equation similar to those arising in an iterative solution procedure for a nonlinear Hamilton-Jacobi equation. Motivated by numerical procedures for solving such an equation, we also propose a numerical algorithm based on the Galerkin algorithm that uses basis functions to solve the underlying Hamilton-Jacobi equation. This approach allows the determination of the minimum performance index as a function of both the system state and parameters and extends to allow the determination of the adjustment to an optimal control law given a small adjustment of parameters in the system or the performance index, effectively by computing the derivative of the law with respect to those parameters. The validity of the claims and theory is supported by numerical simulations.

Kaichang Shi, Aeronautics and Astronautics Engineering, Ph.D

Title: Differential Game of Two Pursuers and One Superior Evader

My work focuses on a pursuit-evasion differential game involving two slow pursuers and a fast evader, considering capture radius. The Cartesian Oval (CO) is implemented to represent game parameters accurately. Depending on the gap type, pursuers have a capture guarantee or both pursuers and evader have their own optimal strategy from nash equailibrum. Sub-obtimal strategies for both pursuer side and evader side are proposed as well, which will significantly reduce the computational cost of finding the nash equilibrium point of the game for optimal strategies. The study concludes that improved cooperation using reachable region analysis enhances capture success, challenging the optimality of prior strategies.

Yuezhu Xu, Industrial Engineering, Ph.D

Title: Learning Dissipative Neural Dynamical Systems

Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In general, imposing dissipativity constraints during neural network training is a hard problem for which no known techniques exist. In this work, we address the problem of learning a dissipative neural dynamical system model in two stages. First, we learn an unconstrained neural dynamical model that closely approximates the system dynamics. Next, we derive sufficient conditions to perturb the weights of the neural dynamical model to ensure dissipativity, followed by perturbation of the biases to retain the fit of the model to the trajectories of the nonlinear system. We show that these two perturbation problems can be solved independently to obtain a neural dynamical model that is guaranteed to be dissipative while closely approximating the nonlinear system.

Haoyang Zheng, Aeronautics and Astronautics Engineering, Ph.D

Title: A Langevin Diffusion Process Perspective on Multi-Armed Bandits

Langevin diffusion processes refer to a class of stochastic processes driven by Brownian motion. They have been widely used in various sampling tasks in machine learning. I will discuss with Langevin diffusion, gradient Langevin algorithms, and how this powerful tool can be used in the analysis and implementation of reinforcement learning algorithms (Thompson sampling). In particular, I will go over two topics: sampling from gradient Langevin diffusion with Markov Chain Monte Carlo, and its application in multi-armed bandits. More information can be found here.