# Physics-Based Vehicle Simulation Using PD Servo
## 1 Introduction  
In computer graphics, most of the object simulation techniques can be broadly classified into two categories: example-based and physics-based simulation. The example-based techniques utilize an object's movements tracked by a camera sensor. For example, a motion capture system is popular to generate high-quality motion data from a live subject. However, simulating an object's dynamics requires a large size of motion database in advance, which is expensive and laborious to build from a scratch using the capture systems [1; 2]. On the other hand, the physics-based techniques analyze given motion, estimate physics rules, and generate simulation results from previously learned rules. Compared to example-based techniques, they require less nor any existing data to simulate object's dynamics; hence, they are more suitable to generate the interactive scenes like car accidents.  
Most research in the computer animation field have focused on generating more natural and responsive motion of manlike objects such as virtual characters. Besides the characters in a scene, moving objects such as vehicles are widely used to describe the scene contents. However, there have been little research works and tools for the vehicle scene generation. For example, [PERSON] et al. suggested a method of simulating various kinds of vehicles, not only cars but also other transportation such as helicopters and boats [3]. While considering environmental conditions, their system controls a single vehicle moving along a given route. [PERSON] et al. [4] introduced a large-scale traffic simulation by running vehicles on a highway with side roads [4]. Similarly, [PERSON] et al. and [PERSON] et al. proposed a large-scale traffic simulation which drives cars among the towns through complex roadways and crossroads [5; 6]. [PERSON] et al. [7] demonstrated a system to simulate a car with a simple structure [7]. In these approaches, a simplified car model is used for traffic simulation, which is notsuitable to generate detailed traffic scenes where an individual vehicle responses to surrounding objects or other vehicles.  
In this paper, we introduce a novel system for physics-based vehicle simulation from input trajectory. The proposed system approximates the physical movements of a real vehicle using a proportional derivative (PD) servo which estimates proper torques for wheels and controls a vehicle's acceleration based on the conditions of the given trajectory. To avoid expensive simulation calculation, the input trajectory is segmented and compared to the optimized trajectories stored in a path library. Based on the similarity of the curve shape between the input and simulated trajectories, an iterative search method is introduced to generate a physically derivable trajectory. For an interaction with other objects in the virtual environment, the surface of the vehicle is subdivided into several parts and deformed individually by external forces. As demonstrated in the experimental results, such a dynamic and responsive simulation is useful to create diverse traffic scenes with multiple vehicles. The overall simulation process is fully automated and designed for a general user who is not familiar with the dynamic properties of moving vehicles.  
The rest of this paper is organized as follows: Section 2 introduces related works in vehicle simulation. Section 3 describes virtual vehicle model designed for our simulation. In Section 4, the optimization process for input trajectory is detailed while Section 5 presents vehicle model deformation by external forces. We demonstrate the experimental results in Section 6 and conclude the paper with limitations in Section 7.