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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
Koopman Basics
Published:
In this blog post, we introduce the Koopman operator, a powerful mathematical framework that transforms nonlinear systems into a linear perspective by focusing on observable functions rather than raw state variables.
Navigating Safely: Following the Path of Density
Published:
Robots today are more than machines; they’re companions, assistants, and explorers. For these robots to safely navigate dynamic and cluttered environments—like a robot vacuum avoiding toys or a delivery drone dodging pedestrians—they need a clear understanding of their surroundings. One powerful tool they use is density functions, a mathematical framework to represent safe and unsafe areas while guiding them safely toward their goals.
Operator Magic: Transforming Robotics Through Operator Theory
Published:
Science often gives us tools to make sense of the seemingly chaotic. Whether it’s predicting the weather, designing self-driving cars, or programming robots to navigate dynamic environments, these tools help us uncover the hidden order in complex systems. One such tool is the Koopman operator, a mathematical concept that transforms how we understand the evolution of dynamic systems.
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publications
Safe Navigation Using Density Functions
Published in IEEE Robotics and Automation Letters, 2023
This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere navigation with safety and stability guarantees.
Recommended citation: Andrew Zheng*, Sriram S. K. S. Narayanan*, Umesh Vaidya (2023). "Safe Navigation Using Density Functions." IEEE Robotics and Automation Letters.
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Off-Road Navigation of Legged Robots Using Linear Transfer Operators
Published in Modeling Estimation and Control Conference, 2023
This paper presents the implementation of off-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the off-road environment, we lift the navigation problem into the density space using the Perron-Frobenius (P-F) operator. This allows the problem formulation to be represented as a convex optimization.
Recommended citation: Joseph Moyalan, Andrew Zheng, Sriram S. K. S. Narayanan, Umesh Vaidya (2023). "Off-Road Navigation of Legged Robots Using Linear Transfer Operators." Modeling Estimation and Control Conference (2023) . (best paper award)
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SE(3) Koopman-MPC: Data-driven Learning and Control of Quadrotor UAVs
Published in Modeling Estimation and Control Conference, 2023
In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system.
Recommended citation: Sriram S. K. S. Narayanan, Duvan Tellez-Castro, Sarang Sutavani, Umesh Vaidya (2023). "Off-Road Navigation of Legged Robots Using Linear Transfer Operators." Modeling Estimation and Control Conference (2023) .
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Safe Navigation in Dynamic Environments using Density Functions
Published in arXiv, 2024
This work uses density functions for safe navigation in dynamic environments. The dynamic environment consists of time-varying obstacles as well as time-varying target sets. We propose an analytical construction of time-varying density functions to solve these navigation problems. The proposed approach leads to a time-varying feedback controller obtained as a positive gradient of the density function.
Recommended citation: Sriram S. K. S. Narayanan, Joseph Moyalan, Umesh Vaidya (2024). "Safe Navigation in Dynamic Environments using Density Functions." submitted to IEEE Transactions on Automatic Control Letters.
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teaching
ME 3330 (Junior lab)
Junior Lab, Clemson Unviersity, Mechanical Engineering, 2023
During my PhD, I served as the lead Teaching Assistant (TA) for ME 3330, a junior-level Mechanical Engineering lab focused on data acquisition and control. The lab is designed around project-based learning, featuring seven modules: filters, thermal sensors, accelerometers, strain gauges, fluids, HVAC systems, and heat exchangers.
PID Playground
Micro teaching lesson, Clemson Unviersity, Mechanical Engineering, 2024
I developed this micro teaching lesson incorporating active learning techniques as an introductory lecture to PID control. it provides students with hands-on experience with MATLAB/Simulink for system simulation and controller design. By the end of the course, students will be able to design, analyze, and implement a PID controller to meet specified performance criteria in engineering applications.