Koopman Basics
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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.
Blog posts
2024
Navigating Safely: Following the Path of Density
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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
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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.