This project is supposed to provide a control system testing environment for a four wheeled vehicle. It uses a real time dynamic simulation of a "bicycle" model, as well as a realistic tire model. The simulation and the controller are two separate threads, communicating with each other through a server in a Publisher-Subscriber scheme, which is meant to emulate a ROS system.

PID control demonstration

MPC control demonstration

Pink dots represent the path points predicted by the optimizer. It doesn't work that well, because the COBYLA optimizer isn't really suited for this kind of application. This performance was only obtained after simplifying the MPC itself, e.g. embedding kinematic constraints in the cost function; otherwise it wouldn't work at all. Interfacing with IPOPT could probably solve this issue.

Following equations represent the "bicycle" vehicle model in which two front and two rear wheel are turned into a one front and one rear wheel, with disregard to the roll of the vehicle. Such simplification gives accurate results while also being relatively easy to implement. The model equations are integrated using the RK4 method

Symbols explained:

• psi - yaw angle in the global frame
• omega - yaw rate
• Iz - Inertia about the centre of rotation of the vehicle around the z axis
• Lf - length from the front of the vehicle to the center of gravity
• Lr - length from the rear of the vehicle to the center of gravity
• delta - steering angle
• vx, vy - longitudinal and lateral velocity in vehicle reference frame
• X, Y - vehicle coordinates in the global reference frame
• If, Ir - inertia of the front and rear tyre along the axis of rotation
• Rf, Rr - radius of the front and rear tyre
• Tf, Tr - torque on the front and rear wheel from the engine

The whole paper describing the tyre model and all it's variables and constants can be found here "Analytical Modeling of Driver Response in Crash Avoidance Maneuvering Volume II: An Interactive Tire Model for Driver/Vehicle Simulation"