Control Systems Design for Autonomous Vehicles: Mathematical Approaches to Path Planning and Trajectory Tracking

Abstract

Self-driving cars are a big change in the way people get around. They promise to make transportation safer, more efficient, and more convenient. Strong control system design, which includes path planning and trajectory tracking, is a key part of how they work. This essay looks at mathematics methods that are important for reaching these goals. The path planning problem is to find a way to get from where you start to where you want to go while taking into account natural and changing limits. Different methods, like geometric algorithms, optimization techniques, and statistical approaches, are used to find lines that don't collide and maximize things like time, energy, and comfort. Trajectory tracking, on the other hand, is the process of sticking to the planned path even when there are problems or unknowns. Model predictive control, feedback linearization, and adaptive control are some of the control methods that are used to make sure the car stays stable and follows the path that is wanted. One of the hardest parts of controlling a driverless car is balancing the different goals of planning a path and following its current path in real time. Because of this, we need to create combined control systems that can smoothly handle the planning and performance steps while taking into account how the surroundings and car state change over time. Also, the rise of linked and self-driving cars opens the door to joint control methods, in which cars talk to each other and work together to improve safety and traffic flow. Vehicle-to-vehicle contact is used by cooperative route planning algorithms to coordinate moves and avoid crashes, which makes the system more reliable and efficient as a whole.