(Solved): 1) Derive the mobile kinematics,K, of a car-like robot with Ackermann steering as given below, where ...

1) Derive the mobile kinematics,K, of a car-like robot with Ackermann steering as given below, where the controls are forward speed (advance control) v and heading direction turning speed (turn control) ?, and l.

2) Derive the inverse mobile kinematics for the same robot (represent the control of the car in terms of the target car motion), and compute the matrix with l = 0.25 m.

 

Derive the mobile kinematics, \( K \), of a car-like robot with Ackermann steering as given below, where the controls are forward speed (advance control) \( v \) and heading direction turning speed (turn control) \( \omega \), and \( l \). (5 points) \[ \dot{q}=\left[\begin{array}{c} \dot{\phi} \\ \dot{x} \\ \dot{y} \\ \dot{\psi} \end{array}\right]=K\left[\begin{array}{c} v \\ \omega \end{array}\right] \] 2. Derive the inverse mobile kinematics for the same robot (represent the control of the car in terms of the target car motion), and compute the matrix with \( l=0.25 \mathrm{~m} \). (5 points)