Simulation of Vehicle Collisions in Real Time

Typical vehicle simulations require numerical integration at an integration time step no larger than 0.01 seconds, usually less than half that time. This does not leave enough time to carry out the complex calculations required for detailed collision calculations in real time. This paper presents a method that strikes a compromise, which, although not carrying all the detail necessary for very accurate collision calculations, allows useful simulations to proceed in real time. The method has three parts: collision detection, estimation of the momentum transfer expected to result from the collision, and application of forces to provide the desired momentum transfer. The method uses a common scene graph for collision detection, which allows the system to work with most of the common scene database formats without the need of specialized preprocessing. All of the collision detection and response calculations employ open-source code and are designed to work well at speeds required by real-time vehicle simulation. Examples based on the VDANL vehicle dynamics simulation illustrate the utility of the methodology. INTRODUCTION Our interest in collision in real time follows from our interest in driving simulation, which demands real time calculations. References [1,2,3,4] present descriptions of a several driving simulators. Reference [5] describes four components common to all driving simulators: • A simulation of the physics of the vehicle model and the road surface • A simulation of the surrounding environment • Video and audio displays to display state output to the operator • Input control devices for the operators Reference [6] discusses these components of vehicle simulation and adds two additional components, collision interaction and networking management, for a collaborative driving simulation application. This paper focuses on simulating vehicle collisions in real time. The motivation is to allow driving simulations to continue in the face of glancing impacts with barriers rather than distract the user by going through the barrier or by causing the simulation to stop. There are two key challenges, detecting that a collision has occurred, and computing the effects of the collision. BACKGROUND Detailed collision simulation has been an active area of research since the 1960’s. Various lumped mass spring models were presented in the early 1970’s [7,8] as a method to evaluate crashworthiness of vehicles in a more cost effective way. In 1973 McHenry [9] presented the Simulation Model of Automobile Collisions (SMAC) computer program as a tool for accident reconstruction. All of these methods were intended to simulate somewhat detailed collision events, and in the accident reconstruction cases, were often used in an iterative way to match physical evidence. They were not concerned with real time performance. In 1983 Macmillan [10] presented rigid body impulse response calculations specifically for vehicle collisions. The method assumed the pre and post collision velocities at the impact point were governed by a coefficient of restitution. This method of calculation is appealing for real-time simulation because of the simplicity and speed of the calculations. Hahn [11] in 1988 presented rigid body impulse response calculations for more general rigid bodies in computer animations. About that same time Moore and Wilhelms [12] discussed the topics of collision detection and collision response. They presented two response methods, a spring based penalty method and an impulse based solution. The impulse method was typically faster to compute, especially in violent collisions, and had an added benefit in that the resulting system of equations need only be solved once per collision instead of every time step as required by the spring based methods. This paper implements the impulse methods given by Macmillan and presents a method based on the loss of kinetic energy during the collision. Both these response methods give reasonable looking results in real-time. While this paper focuses on collision response calculations, it will also demonstrate that the real-time performance is highly dependent on the collision detection algorithm speed. Lin [13], Jiménez [14], and Kim [15] have provided recent surveys of collision detection methods. The following sections address the issues of real-time collision detection and response and address the challenge of real time implementation. COLLISION DETECTION Typically collisions are detected by searching a database of collidable objects to find the interference. If a collision is detected, the collision point and collision plane normal are saved to enable calculation of the resulting response. There are several ways to perform the detection operation [13, 14, 15]. We selected Open Scene Graph [17] to perform collision detection against a visual scene graph database. This option provides a great deal of flexibility in database formats while still maintaining ample computation speed. In addition, Open Scene Graph is free, open source, and can run on several computer platforms. Other methods may have faster detection speeds, particularly with databases containing a high number of polygons, but often they require specialized file formats and substantial preprocessing [15]. To test for a collision against the scene graph, the vehicle is represented as a set of line segments that generate a horizontal 2D rectangular plate around the vehicle at the CG height. For each integration time step, the bounding rectangle is tested against the scene for intersections. Figure 1 shows the front-right corner of the bounding rectangle intersecting with a wall. A collision is detected when any segment intersects an object. To enable calculation of the vehicle response to the collision, simple algorithms typically require specification of the point of force application and the direction of the force. Here we find the point of application of the force by taking the midpoint of the line of interference between the two objects. As an example, in Figure 2 the point of application would be the midpoint of the line segment a-b. Since we are concerned in this paper with flexible vehicle bodies hitting rigid barriers, the collision plane normal will be the surface normal of the rigid barrier.