Vikram Ramanathan

Vikram Ramanathan

G2 Applied Mathematics PhD Candidate

Portfolio

Methods in Extending RL to LQR Adaptive Control: A Survey

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Learning-theoretic work on extending fundamental RL algorithms to LQR Adaptive Control has recently (over the last decade) received more attention. Inspired by the significant progress made independently in RL and adaptive control, this fusion of approaches shows significant promise with potential applications in robotics, plant operations, and game theory (to name a few). This survey is intended to provide the reader with an overview of the recent algorithms and significant theoretical results obtained in extending RL to LQR Adaptive control. This study is done with regards to the benchmark discrete-time, infinite-horizon LQR with unknown dynamics. Regret analyses are presented, and detailed discussions that compare and contrast the methods are provided.

Lagrange Multipliers in Fenchel Duality

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In this paper, we present the equivalence of Fenchel and Lagrangian duality. Then, for the problems of concave maximization and convex minimization, we show that the Lagrange multiplier is indeed equal to a particular constant used in Fenchel duality.

Online On-Device MCU Transfer Learning

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This project develops a method to improve the performance and flexibility of microcontroller (MCU) on-device binary image classification (MobileNetV1) by implementing online on-device transfer learning. Given the necessary energy, memory and compute efficiency, training deep networks on MCUs seems far-fetched and near impossible. Instead, online transfer learning is an implementable edge learning mechanism that can make use of the feature detection capabilities of a well-trained frozen base model without having to gather/store/access large datasets and parameter values on device.

COVID Safety Rating Project

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This project was developed with my long-time friend, Sai Kasam, as a fun summer project. It is a community driven rating system that helps evaluate the, (1) Social Distancing, (2), Communications (from/at the location), (3) Use/Availability of Personal Protective Equipment (PPE) at most public areas/locations/businesses in the world. These individual scores are averaged to get the final location’s overall COVID Safety Score. All functionality in this website can be accessed with just a few clicks. By entering a place into the search bar above, you can access the location’s rating, read other user reviews, and rate the location if you have an experience you would like to share.

Improved Swerve Drive Design with Suspension

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My senior design team designed a swerve drive module for one of the robots I personally worked with for my research (affectionately named “Scrat”). Scrat is a non-holonomic, pseudo- omnidirectional robot designed to traverse laboratory floors to detect alpha radiation contamination. This project was inspired by Scrat’s several design issues: poor tire traction, no suspension, poor encoder resolution, and large gear backlash. In light of these issues, the team’s goal was to design, test, and manufacture a new wheel module with an accurate steer system and functional suspension while remaining within a $3,000 budget. We made detailed CAD models, a full BOM with references to vendors, detailed assembly instructions, and a 3D simulation. Unfortunately, the actual machining and assembly of the module was not possible because of the COVID-19 pandemic. However, this design has been successdully implemented.

Self-Powered Flow Rate Sensor

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The purpose of this project was to design a self-powered flow velocity sensor. The sensor is different from state-of-the-art implementations of flow rate sensing in that the mechanical design is not only smaller but also optimized for a larger range of flow velocity measurements. The sensor is also able to rectify input voltage signals, charge a battery, power an Arduino and have the ability to be calibrated easily. While this sensor is designed for civil applications (plumbing and piping systems), the mechanical design could be very easily altered to accommodate for flow sensing in water bodies (rivers, ocean currents, etc).

Stealthy Path Planning

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This was a toy problem that investigated the development of a stealthy search algorithm that minimizes exposure of the object under consideration to ‘areas of consequence’ on the grid. Areas of consequence could range from capture zones in games to operational range of missiles and mines. In this solution, I elected to use a cost minimizing algorithm, specifically, A* search with a custom-made heuristic. This heuristic evaluates the minimum Euclidean distance to an obstacle on the grid from the node under study and then subtracts it from the Euclidean distance to the destination node. The result is assigned to the priority of the node in the priority queue used in the A* search.

FRACTRAN

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Programmed an interpreter to play around with FRACTRAN, Conway’s Turing-complete esoteric programming language.