# Path Planning Based on Obstacle-Dependent Gaussian Model Predictive Control for Autonomous Driving
## 1 Introduction
For example, the continuous geometry curve-based method can be performed using spline curves [13], bezier curves [14], and polynomial curves [15]. However, these methods also have a limitation because they do not perform optimal path planning in terms of relative speed. The fourth method is the risk-based approach, which consists of repulsive forces to avoid collision and attractive forces to reach the goal. Therefore, when accurate information on the roads and surrounding obstacles is available to recognize, it is an effective method to generate a trajectory without causing an obstacle collision. Because the risk-based approach method does not contain vehicle dynamics, it cannot guarantee experimentation in real vehicles. Examples include the artificial potential field (APF) [11], which updates the peripheral information in the driving conditions of the expressway; then, the algorithm works. There are also attempts to imitate a way of the person as a way of defining risk, such as Driver's Risk Field [16] and humans motor response [17]. While theses approaches to path planning through obstacle avoidance provide good results in many applications, there are some major drawbacks to the trade-off between essential computational resources and solution optimization. Many of the commonly used path planning methods rely heavily on extensive simulation testing because there is no formal stability analysis and verification methodology. Therefore, it is desirable to formalize the path planning problem as a low complexity problem. In the Model Predictive Control (MPC) path planning, a path is found to solve a constrained optimal control problem over a finite time horizon. A cost function is minimized subject to constraints, including vehicle dynamics, design and physical constraints, and additional constraints introduced to avoid collision with surrounding vehicles. The constrained optimal control problem is solved in the receding horizon, i.e., at every time step, the problem is formulated over a shifted time horizon based on newly available sensor measurement information. The main advantage of resorting to such a formulation is that collision avoidance is guaranteed, provided that the optimization problem is feasible. However, collision avoidance constraints for trajectory planning are generally non-convex, limiting the feasibility and uniqueness of the solution to the optimization problem. Researchers rely on techniques such as piecewise-linear model [18], Gaussian process-based approach [19], convexification [20], and machine learning [21; 22; 23] to address the issue. Local path planning is a high-resolution low-level planning that operates by generating a path using a limited time and space boundary [24]. These algorithms make a finite set of trajectories that follow a waypoint provided by a global path planner, avoiding obstacles detected by the sensor. The discrete scheme of this trajectory is optimized by the integration of differential equations in vehicle dynamics [25]. Typically, the bug algorithm, a local path planning algorithm, works based on sensors without information on the map [26]. These algorithms make a straight line in the direction of the target point provided by the global path planner and then move along the line and encounter an obstacle. The algorithm detects the obstacle and moves around it. After moving around it, the algorithm finds the nearest point to the target point and moves back to the target point. Another example of local path planning is the tentacle method [27]. This method creates a path by selecting only one of several vehicle trajectories depending on the obstacle location and uses the local path planning method for global path planning. Because this method does not consider moving people or moving vehicles, it is currently used as path smoothing. The aforementioned global path planning method limits the information from the entire map in the outdoor case where the map information is needed.