Rigid Body Car Driving Simulation

Cooper FindleyChuck Moyes

Mark Wang

Overall Idea Implement OpenGL 3D car driving simulation in

C++ Libraries used: SDL, GLEW, SOLID, SDL_ttf,

SDL_image, SDL_mixer, Armadillo Emphasis: Realistic Physics

Rigid Body Dynamics Simulation Erleben “Velocity-Based Shock Propagation for Multibody Dynamics

Animation”

CS 5643: Physically Based Animation for Computer Graphics

Euler numerical integration

Collision detection, response, tangential Coulomb friction, resting contact

Projected Relaxed Gauss-Seidel solver

ODE's “Hinge-2” Joint Constraint

Other Possibilities:

Impulse, Penalty methods

for contact 4th Order RK integrator, Time-Corrected Verlet method

Car Physics Model Short, et al. “Simulation of Vehicle Longitudinal Dynamics”

Beckman “Physics of Racing Series”

Monster “Car Physics for Games”

Longitudinal Forces

Engine Force (torque curve as function of RPM) Resistance Forces: Fluid dynamic air drag (proportional v²),

Rolling resistance (C_rr), Brake Forces Lateral Forces

Pacejka tire model (continued) Slip angle, slip ratio

Gear Box Model

Gear ratios, differential ratio Automatic shifter logic

Pacejka Tire Model

Lateral Longitudinal

Torque Curves (V8 Engine)

First gear g1 2.66Second gear g2 1.78Third gear g3 1.30Fourth gear g4 1.0Fifth gear g5 0.74Sixth (!) gear g6 0.50Reverse gR 2.90Differential ratio xd 3.42

Torque Modely = c + b*x + b*x^2TMax = 528.7 + 0.152*R − 0.0000217R^2

Brake ModelT_brake = p*K*min(1, omega/alpha)

Automatic Gear Box Shift Map

Time-Permitting

Work on suspension/weight distribution by modeling mass-spring-dashpot system for each tire

Work on advanced wheel-body joint constraints using Jacobian (as seen in ODE)

A height-map terrain engine using the ROAM level of detail algorithm for driving over bumpy terrain

The use of a special input device such as a Logitech steering wheel controller with force feedback

A more advanced force-based model of the car physics as discussed in Beckman’s articles

A full-fledged racing game using the simulation engine