# Path Planning Based on Obstacle-Dependent Gaussian Model Predictive Control for Autonomous Driving
## 1 Introduction
The concept of local path planning is required to compensate for the limitations of global path planning [24]. In most autonomous driving currently under research, maps are created through sensors. Then, path planning is conducted without information on the entire map. Many current path planning studies have used global path planning as local path planning [28; 29; 30; 31]. Therefore, this paper focuses on the local path planning method of autonomous vehicles based on a predefined global path. Autonomous driving requires the ability to maintain lanes and speed while overtaking front vehicles. In the driving environment, lanes are divided into solid lines and dotted lines, as shown in Figure 1. The Ego vehicle \(E\) must be controlled to avoid a dangerous collision with the surrounding vehicle \(S_{k}(k=1,\cdots,q)\), where \(q\) is the number of surrounding vehicles. The APF algorithm [32] described in Section 1 explains the results of effectively conducting path planning with attractive and repulsive forces differently from other algorithms. However, due to the many parameters used for control, it is difficult to determine the optimal control. Thus, [PERSON] et al. [33] experimented using the ODG potential field (PF), the improved version of the APF algorithm. The ODG PF algorithm uses the Obstacle-Dependent Gaussian (ODG) model, which expresses the presence of an obstacle measured by the sensor as a risk using a Gaussian function [33]. It is confirmed that path planning is more stable than APF through the experiment while having fewer parameters. However, as the ODG PF does not contain vehicle dynamics, the experimental results show unstable control, which is limited in real vehicle models. Figure 1: Autonomous driving environment. We propose a risk model-generalized ODG model to create a path that incorporates the vehicle risk rather than removing the MPC constraints on collision avoidance. The proposed algorithm calculates the optimal path using MPC, and in this process, the cost function includes the proposed risk model that expresses the risk information of the obstacle detected by the sensor. Due to the characteristics of the proposed algorithm, it tends to react quickly to obstacle information detected by the sensor and avoid the obstacle. As a result, stable driving is possible with a quick response to an obstacle vehicle, and a quick response creates a low lateral acceleration. Therefore, we propose an optimal controller that integrates the proposed risk model and MPC to solve the computational problem and enable stable obstacle avoidance path planning. The main contributions of this paper are as follows:  
1. We proposed a general ODG-based risk model to apply for vehicles and lanes to define the risk of driving. 2. We combined the general ODG-based risk model and MPC, and the proposed algorithm responds to avoid obstacles quickly. Due to this tendency, the proposed method provides safe control and minimizes vehicle shake. 3. The proposed method can control the vehicle for the obstacle avoidance process in real-time, and it has been confirmed through experiments. This paper is organized as follows. Section 2 discusses related work, introducing the ODG model and the MPC function. Section 3 defines the proposed method using the proposed risk model and MPC. Section 4 presents an experiment using mobile robots similar to vehicle dynamics and the experimental results of propose method. Section 5 summarizes and concludes. In addition, the nomenclature and variable definition are given in Nomenclature, respectively.