# Path Planning Based on Obstacle-Dependent Gaussian Model Predictive Control for Autonomous Driving
## 1 Introduction  
Autonomous driving refers to a technology that determines the driving situation through sensors and drives to the destination without driver intervention. Autonomous driving in the future is expected to increase traffic efficiency and driver convenience, and enhance traffic safety. Most traffic accidents and fatalities occur during lane changes and overtaking [1]. Such accidents greatly injure human life, and autonomous driving remains an important task for full commercialization in the current technology regarding path planning safety. Adaptive cruise control [2], lane-keeping assist [3], and automated emergency braking [4] of advanced driver assistance systems (ADAS) technologies have positive effects on driving safety [5]. Recently, Advanced driver assistance systems (ADAS) use advanced detection sensors, global positioning systems (GPS), and video equipment to recognize situations while driving, judge the situation, and control the car. Therefore, companies, such as Google and Tesla, are working on fully autonomous driving without human intervention [6]. However, it is still difficult to research the technology of fully autonomous driving. Therefore, this paper suggests determining how a vehicle should behave concerning surrounding vehicles as an obstacle avoidance path planning problem. Path planning is a technology that enables mobile robots or vehicles to move autonomously. With the advancement of technology, research on avoiding obstacles without human intervention has been actively conducted in the field of autonomous driving [7]. The path planning research area is divided into global path planning, which generates a path using the information from the entire map, and local path planning, which generates a path using sensors. Global path planning is a low-resolution high-level planning that determines the map information before the vehicle runs, creates a path, and then operates. Frequently used global path planning algorithms include sampling-based approaches [8], search-based approaches [9], continuous geometric curve-based methods [10], and artificial dislocation field approaches [11]. The sampling-based approach is a method that quickly searches the space by selecting a random point in each sample and creating a path continuously by extending it in the random point direction. Because the algorithm relaxes the completeness requirement, it has the advantage of being able to relatively quickly find a path that is possible from the start to the target point, even with a high-dimensional state space. Therefore, the destination can be reached safely without problems at a local minimum based on probability. The Rapidly exploring Random Tree (RRT) and RRT* algorithms [8] are typical examples of the sampling-based approach method. However, the sampling-based approach methods have a limitation in finding the best path: the disadvantage of unnecessary costs in computation and inefficiency. The second method is the search-based approach method. The biggest feature of this algorithm is searching for a heuristic-based search as the graph-based method. After the graph is generated, the path is searched from the start to the target point at the minimum cost. The optimum path can be found faster using the correct heuristic function. Examples include the Dijkstra algorithm and A* algorithm [9]. However, the computation amount is limited due to the large graph and complexity of the environment. If the environment changes after determining the shortest path, it is difficult to respond quickly. Therefore, the algorithm works well in low-speed applications but has a limitation in high-speed driving. The third method, the continuous geometry curve-based method, is an optimized path planning algorithm that uses the spline function used in various mobile robot fields. The search and sample methods described above do not include vehicle dynamics; thus, optimal path planning cannot be performed. However, this method is based on vehicle dynamics and many studies on path smooth algorithms [12].