Swerve drive

Top linear speed, drive-base radius and maximum rotation rate of a swerve drive.

Inputs

Drive motor

12 V vendor specs; see the motor database.

Gear reduction

Drive reduction, e.g. 6.75 for SDS MK4i L2.

Wheel diameter

Trackwidth (module centre to centre)

Wheelbase (module centre to centre)

Speed factor

Real top speed as a share of free speed.

Result

Top linear speed

4.256

Maximum rotation rate: 10.42
Free speed: 15.51
Drive-base radius: 0.4086
Time for a 180° turn: 0.3016

How it’s calculated

Formula

v_\text{max} = k \, \frac{\omega_\text{free}}{R} \, \frac{d}{2}

r = \sqrt{(t/2)^2 + (b/2)^2}, \qquad \omega_\text{max} = \frac{v_\text{max}}{r}

With your numbers (converted to SI units)

v_\text{max} = 0.9 \times \frac{628.3\,\text{rad/s}}{6.75} \times 0.0508\,\text{m} = 4.256\,\text{m/s}

r = \sqrt{(0.2889\,\text{m})^2 + (0.2889\,\text{m})^2} = 0.4086\,\text{m}

\omega_\text{max} = \frac{4.256\,\text{m/s}}{0.4086\,\text{m}} = 10.42\,\text{rad/s}

What it means

Every module can reach the same top speed. When the robot spins in place, the modules sit on a circle of radius r, so the fastest spin is when they all run at top speed tangent to that circle. Use v_max and ω_max as the limits in your drive code, and desaturate wheel speeds when a combined command asks for more.

Assumptions

Modules at the corners of a rectangle centred on the robot’s centre of rotation.
Translation and rotation share the same module speed limit.

Learn the concepts behind this on resources.simbotics.org · All formulas