# Enhancing Autonomous Vehicle Navigation with a Clothoid-Based Lateral Controller
## 1 Introduction  
In the field of autonomous vehicle technology, the need for robust and precise navigation systems is crucial. Central to this pursuit is the refinement of lateral control mechanisms, which are critical in ensuring that vehicles can safely and efficiently navigate complex and dynamic environments. Lateral control, responsible for the vehicle's steering and trajectory following capabilities, is a fundamental aspect that directly influences safety, efficiency, and passenger comfort. As autonomous vehicles become increasingly prevalent, the demand for sophisticated lateral control strategies escalates. These systems must not only handle the intricate task of real-time decision making and path correction but also anticipate and adapt to unpredictable changes in road conditions and traffic dynamics. The introduction of a clothoid-based lateral controller represents a leap forward in this domain. Leveraging the mathematical properties of clothoids or Euler spirals promises to provide a control method with smoother transitions during lane changing, and hence, minimizing abrupt steering inputs and enhancing a vehicle's stability and passenger experience. This research delves into the optimization of such a controller, aiming to further bridge the existing gap in autonomous vehicle navigation through improved accuracy, reliability, and adaptability. Before addressing path tracking, the lateral control of a ground vehicle encompasses an essential aspect known as local path planning. Local path planning involves the generationof trajectories that connect the vehicle's current coordinates to its intended destination. Within this domain, a widely adopted and effective strategy for autonomous vehicle navigation is waypoint navigation. This approach leverages GPS technology to determine the vehicle's position and subsequently generates paths between the vehicle and its destination. Strategies are then devised to follow these generated paths (path tracking) and guide the vehicle to its intended endpoint. The following paragraphs delve into the literature and contemporary techniques relevant to path generation and tracking, collectively constituting waypoint navigation for autonomous vehicles. An early attempt to find the shortest paths between two known points was developed by [PERSON] in 1957 [1]. These paths, termed Dubins paths, represent the shortest curves connecting two points within a two-dimensional Euclidean plane. They adhere to curvature constraints and feature prescribed initial and terminal tangents. However, a limitation of Dubins paths lies in their constant curvature segments, which do not accurately model the variable curvature experienced by a moving vehicle. Another prevalent method for establishing trajectories between waypoints involves the use of splines [2], with cubic splines and B-splines being commonly employed. This thesis extends prior research by employing clothoids [3] for path generation, addressing issues related to steering profile smoothness and mitigating undesirable jerk in the steering wheel. This is achieved by ensuring continuity in curvature, a vital characteristic of clothoids [3,4]. Once a path has been generated, the subsequent challenge lies in guiding the vehicle along this path with minimal tracking errors and steering jerks [5]. Various control strategies, including pure pursuit [6, 7, 8, 9, 10], PID [11], and MPC [12, 13], etc., have been proposed to address this issue. Among the earliest path-tracking strategies introduced is the pure pursuit method, which involves fitting a semicircle through the vehicle's current configuration and a point on the reference path located ahead of the vehicle at a distance referred to as the lookahead distance. Carnegie Mellon University pioneered the application of this approach to a vehicle in 1985 [14]. Subsequently, numerous studies [7, 8, 9, 15] have further developed and enhanced this strategy, introducing their own variations.