Mecanum Robot

What is modelled

Each mecanum wheel pushes along a line at 45 degrees to the robot axis. Combining four of these forces yields forward, sideways and yaw motion independently.

Equations

• Inverse kinematics: ωFL = (vx - vy - (lx+ly)ω)/r and the matching pattern for FR, RL, RR.
• Wheel force: Fi = clamp(Kp (ucmd - ui), ±μ m g/4) along the roller line.
• Body dynamics: m a = Σ Fi di, I α = Σ ri × Fi.
• Best forward acceleration: amax = μ g / √2.

Checks run in the page

• Strafing needs the wheel pattern (-,+,+,-).
• Measured launch acceleration against μ g/√2.
• A circle of radius v/ω closes after one revolution.
• Inverse and forward kinematics round trip, and the controller reaches the command.

Honest simplifications

Rollers are perfectly free, load is shared equally over the four wheels (no weight transfer), there is no motor torque or battery limit and no lateral roller friction. Real mecanum rollers cause vibration and slip when the floor is uneven.

• "Diagonal on ice": wheels hit the friction limit (red) and the robot lags its command.
• "Spin in place" shows that yaw uses all four wheels at once.
• Raise the mass and watch the acceleration limit stay the same (it depends only on mu).