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Optimal Control Theory

Solving the HJB equation for a simple system in order to find the optimal control law. Making small perturbations to this control law and seeing the cost increase.

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Investigation of using indirect numerical optimization methods, based on Pontryagin's Minimum Principle.

Localization and Mapping

Demonstration of the Extended Kalman Filter (EKF) being used in Simultaneous Localization and Mapping (SLAM).  Both a one-dimensional and two-dimensional simulation with differential drive model. Also includes robot/landmark uncertainty over time for each simulation.

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Miscellaneous

My friends and I worked together to make art for our living room wall! With materials that were relatively cheap, this project was a really way to explore the intersection of art and electronics.

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