Mobile Robot Control based on Car-like Robots

Description

➢ Inputs: u1 (throttle control), phi (steering control)
➢ Outputs: x, y, theta

We cannot drive the robot to move at the speed (vxd, vyd) along the rear wheel axis direction as side slip is not possible.
➢ Similar to DD robot, we can set a new reference point to overcome this issue.
➢ New Reference Point (xr, yr):

Control of Car-like Robots

The new reference point (xr, yr) (the red spot in the figure). Note the new reference point is along the central line of the robot with a length from the old reference point for d.

The kinematics of the reference point can be obtained as

Define u2=u1*tan(phi), the above equations become

In matrix form,