## 4 Materials and Methods
### Model Overview  
Figure 2 demonstrates the overview of our pedestrian path-planning model. The model consists of two components:  
1. _Path-planning training._ This component instructs the agent to learn the basic navigations and collision avoidance within the environment using reinforcement learning. The details of the component are presented in Section 5.
2. _Point-of-conflict (POC) prediction._ This component simulates the agent's prediction of the collision with the obstacle. The process of prediction updates the input of the path-planning components and is handled before the planning process. Section 6 explains the prediction model in detail.  
For a reinforcement learning model, the design of the environment plays an important role. An environment that is similar to the real-world environment is usually unsuitable, as its complexity often leads to multiple problems. First of all, generally, the agent is not able to earn efficiently in a complex environment. For example, if there are many obstacles within the environments, they would create an extensive number of different states, leading  
Figure 2: Overview of the pedestrian path-planning model.  
to a considerably noisy training environment. To learn in an environment like that could be difficult for the agent, as the training would be quite unstable. There is also the overfitting problem. This means the agent could learn to navigate in the training environment, but its knowledge could not be transferred into unfamiliar environments.  
This also partially corresponds to the human cognitive system. In the human cognitive system, the environment reflected in the human brain is usually a distorted topology of the real-world environment. Instead of using an entire map of the environment for local path-planning, only a portion of the visible environment is collected, depending on the cognitive system's planning horizon. As a result, in real life, pedestrians usually accomplish the path-planning process within a short distance from the current location to a determined destination. Once that location is reached, another path-planning process is carried out to a new location.  
For that reason, our environment is designed to have a fixed area size, and also there is only one obstacle that may exist inside. A complex environment would be scaled down or divided into multiple parts, depending on the situation. There are several methods to realize this. For instance, in a study by [PERSON] et al. (2017), the agent would treat each component navigation part as its sub-goal when planning the route to a certain location. This would greatly help stabilize the training process while still is able to expand its applicability to new environments.  
Consequently, our environment is modeled as illustrated in Figure 3. The area of the environment is \(22\) meters by \(10\) meters. The position of the agent is randomized between the coordinates \((-5,-12)\) and \((5,-12)\). The agent's current destination is randomized between the coordinates \((-5,10)\) and \((5,10)\).  
The navigation path from the agent's position to its current destination consists of \(10\) component nodes whose coordinates' y values are predefined. The x coordinates of these nodes correspond to \(10\) outputs of the neural network. This will be presented in more detail in Section 5.2.