Forward and Inverser kinematics of mobile robot

Calculation of Angular Displacement from RPM and Time Interval

$$v = r \omega$$

$$rpm = \frac{v \cdot 60}{2 \pi r}$$

where:

• v is the velocity of the wheel
• r is the radius of the wheel
• ω is the angular velocity (motorVelocity) of the wheel
• rpm is the revolutions per minute of the wheel
• π is the revolutions per minute of the object

Step 1: Convert RPM to Angular Velocity

To calculate the motor’s angular displacement, we first need to convert the rotational speed from RPM to angular velocity in radians per second.

The formula for converting RPM to angular velocity is:

$$omega= RPM×\frac{2 \pi}{60}$$ or, $$omega = RPM×0.1047$$

After calculating the angular velocity, we divide by the gear ratio to adjust for the gearing system. The final formula for motor velocity is:

$$motorVelocity=\frac{RPM×0.1047}{gearRatio}$$

For the left and right motors, respectively:

$$LeftmotorVelocity=\frac{LeftRPM×0.1047}{gearRatio}$$ $$RightmotorVelocity=\frac{RightRPM×0.1047}{gearRatio}$$

gear ratio might be (30:1, 20:1, 60:1, ....)

Step 2: Calculate Angular Displacement

Once we have the angular velocity, the next step is to calculate the angular displacement. Angular displacement refers to how far the motor has rotated during a given time interval.

The formula for angular displacement is:

$$θ = ω×Δt$$

Thus, the formulas for the left and right motor angular displacements are:

$$leftAngularDisplacement = leftMotorVelocity×Δt$$ $$rightAngularDisplacement = rightMotorVelocity×Δt$$

where:

• θ is the angular displacement
• Δt represents the time interval (delta_seconds).