# Design and Experiments of Autonomous Path Tracking Based on Dead Reckoning
## 1 Introduction
Although MPC has exhibited good performance in many applications, heavy computation remains a challenge with real-time applications, particularly nonlinear MPC, and this controller type may face optimization failure if the initial values are improper [19]. In an autonomous driving scenario, a vehicle must know where it is currently located and how it is moving in the environment. Autonomous driving uses several localization techniques, such as a global positioning system (GPS)/inertial measurement unit (IMU)-based technique, a camera-based technique, a radar-based technique, a Lidar-based technique, and an ultrasonic-based technique [20]. For example, the work of Mechlab used LiDAR for the detection of lane marks and localization in autonomous driving [21]. Although the majority of these techniques are quite successful in providing accurate positioning, a large amount of data must be processed in real time, which is computationally demanding, and in some cases, sensors may be unable to provide localization information, such as GPS in tunnels or an indoor environment. In addition, in extreme cases when severe occlusions occur and the majority of localization sensor systems fail to work, the vehicle must be able to accurately assess its dynamical motion. Therefore, dead reckoning has become an indispensable technology in autonomous driving, as it can provide the vehicle with a certain degree of accurate positioning and navigation where other sensors cannot. [PERSON] et al. [22] analyzed the error sources in land vehicle dead reckoning with differential wheel speeds, finding the limiting factors for dead reckoning accuracy during ordinary driving to be primarily unmodeled roll dynamics and surface unevenness. [PERSON] et al. [23] proposed a method able to accurately calibrate the parameters without knowing the ground truth using Rauch-Tung-Striebel smoothing to create an accurate dead reckoning system. [PERSON] et al. [24] proposed a trained deep neural network for learning car speeds using inertial sensors for dead reckoning navigation. [PERSON] et al. [25] proposed a novel approach to inertial-only dead reckoning for wheeled vehicles based on deep neural networks for the dynamic adaptation of the parameters of a Kalman filter. In response to the use of dead reckoning and simple control methods for achieving accurate trajectory tracking, two problems remain with methods that have been proposed in the current literature:  
1. Among all the dead reckoning methods, the differential drive model is a more common localization method, but it is generally applied to mobile robots, and relatively few papers have applied it and tested it in vehicular situations. For example, [PERSON] et al. [26] used the differential drive model combined with Lidar for indoor trajectory tracking for mobile robots, while [PERSON] et al. [27] proposed a velocity-based dynamic model for differential drive mobile robots, again for indoor robots, and [PERSON] et al. [28] also proposed a similar method. The common feature shared by these papers is that the mobile robots are small with only one wheel in the front guide wheel, meaning that their experimental results do not reflect the performance of differential drive methods in real vehicles. Therefore, applying and evaluating this method for its performance in autonomous vehicles is necessary. 2. In the available pure pursuit path tracking literature, most studies have used localization sensors such as GPS, demonstrating unsatisfactory tracking accuracy. For example, [PERSON] et al. [29] used a modified pure pursuit for achieving unmanned driving, but the tracking error reached 1.2 m, while [PERSON] et al. [30] used a pre-built map and LiDAR for localization and pure pursuit for trajectory tracking, but the tracking trajectory still showed a large deviation from the set trajectory in the results. Therefore, whether the adoption of pure pursuit autonomous path tracking without localization sensors can achieve better tracking accuracy than these studies is an issue that is worthy of further study.