Path following control - D7039E-E7032E/Project-Report GitHub Wiki

Introduction

The robot will navigating by generating a path that it should follow to avoid obstacles and reach it's destination. The purpose of this control is to steer the robot so it follow this path.

Method

The control makes the car follow the line by steering the robot such that the point P in figure 1 is always above the path. The control system will achieve this by changing speed relation between the wheels on the robot, making it turn.

Figure 1

System

To simplify the system, some assumptions were made. Because the robot is equipped with strong motors and wheels with good grip, the assumption was made that the robot will not lose it's grip. The system is also assumed to have a near perfect step response. With these assumption the system will be static, only changing when moved by actuator.

systeI Figure 2

By making the final assumption that the target point T, in figure 2, is stationary then we can introduce a new variable d as in equation 1.

Asume Equation 1

Then the system can be represented in a state space model seen in equation 2, where Wmax is the maximum rotation speed of the robot.

system Equation 2

Control rule

Because the system is of first order, by using the assumptions from previous section, the optimal controller will be a P controller, as seen in equation 3.

rule Equation 3

the variable p, in equation 3, will be chosen in simulations for optimal performance.