Abstract
   Given the escalating presence of autonomous mobile robots in industries like agriculture, manufacturing, and shipping, it is essential to develop and improve planning and optimization methods for agents navigating diverse environments. This dissertation addresses the enduring areas of interest in computer science and automation, namely path planning and path optimization. Firstly, it proposes a deterministic shortcut-based smoothing method that achieves user-specified termination conditions based on solution quality, overcoming key difficulties observed in traditional random-based shortcut determination. Secondly, it introduces a new path optimization scheme based on convex optimization of piecewise quadratic Bézier paths. This method addresses C1 continuity and a target minimum clearance to obstacles while minimizing path length and maximum curvature. This method is versatile and suitable for a variety of path planning applications in robotics and autonomous vehicles. Lastly, this dissertation introduces a multi-agent lane optimization scheme that extends the previous method to adapt specifically to non-intersecting path collections, which are referred to as lanes. The approach is based on a priority-based lane processing algorithm that addresses the dependencies between the lanes, consistently produces lanes which adhere to the specified constraints. 
   

Biography
   Maryam Khazaei is a PhD Candidate in Electrical Engineering and Computer Science at the University of California Merced. She has been advised by Professor Marcelo Kallmann and Professor Sungjin Im. Maryam Khazaei received the Outstanding Teaching Award at University of California Merced. Her research interests are in Algorithms, Muti-agent Path Optimization and Path Planning. Her research focuses on path smoothing and optimization methods for animation, simulation, robotics, and data analytics. She received a Master of Science degree in Applied Mathematics from University of Colorado Denver and Bachelor of Science degree in Applied Mathematics from Iran University of Science and Technology.