Assignment Question -

A tricycle-like mobile robot is shown in Figure 1. There are usually two different types of mechanisms used to manoeuvre a tricycle. The first type uses the front wheel for both the steering and driving actions, while the second type uses the front wheel as the steering wheel and back wheels as driving wheels. The axial distance d is 0.5 (m).

Build and simulate the kinematic model of this robot

1. Derive kinematic equations for both types of mobile robots.

2. Using SIMULINK (a MATLAB toolbox) to build the kinematic models of the robots and simulate and demonstrate the behaviour of the vehicle subject to:

i. Constant driving velocity and a constant steering angle.

ii. Constant driving velocity and a linearly changing steering angle.

iii. Linearly changing driving velocity and linearly changing steering angle.

It is assumed that the maximum driving velocity is ± 1.5 m/s, the maximum driving acceleration is ± 0.8 m/s², the maximum steering angle and steering velocity are ±p/4 rad, and ± 0.3 rad/s, respectively.

3. The robots are required to follow a trajectory shown in Figure 2. Plan the driving acceleration and steering velocity profiles for the front wheel steering and back wheel driving robot so that the robot will follow the path. Apply the same control profile to the front wheel steering and front wheel driving robot. Is the outcome the same? Explain why.

4. Present at least the following results in your report:

• Compare the results obtained from the two models and discuss the meaning of the results.
• Show that the robots are moving along the predefined path.
• Calculate the minimum radius of curvature of the circle the vehicle can drive around. Confirm this with simulation results.