# Mathematical Model for Differential Drive Robot¶

## System Definition¶

In this lab, we formulate a mathematical model for Woodbot in Fig. 1, a differential drive 2-wheel robot.

Figure 1: Hardware for the lab series.

Figure 2: The Woodbot schematic and dimensions.

The robot physical dimensions are defined as in Fig. 2.

## Kinematics Model¶

### State Definition¶

What state is necessary to represent the robot in 2D space?

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### Kinematics Model¶

The 4 patterns of differential drive robot forward and tun motions are illustrated as following. Here we are assuming that the center of rotation is at point O.

Hint

Think about how the robot translational and angular velocity are affected based on change in two wheel velocities. Consider some tribial cases such as one of the wheel is stopped and velocities are negative (reversed).

The relationship between wheel angular velocity and wheel tangential velocity is illustrated as follows.

Thus, under no slip condition, the robot translational velocity and angular velocity can be described as:

Note

No slip condition simplify the robot model since we don't need to consider frictions or dynamics of the robot.

This is why we derive kinematics (1st order) model

We can illustrate Markovian system the robot next state given the current state and input:

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Which now can be expressed in a 1st order system model (kinematics model).