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Differential Drive Robot Angular Velocity

Calculates the rotational (turning) velocity of a differential-drive mobile robot from the difference in its wheel velocities and wheelbase width.

Written by the Vorzep Team

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Differential Drive CalculatorRobot Angular Velocity

ω = ( vR − vL ) / L
ω = angular velocity (rad/s)  ·  vR = right wheel speed (m/s)  ·  vL = left wheel speed (m/s)  ·  L = wheel separation (m)
⟹ Solve⟷ω, vR, vL, L
rad/s
m/s
m/s
m
L = distance between left and right wheels
Please fix the errors above.
Solve for:
Presets:
Angular Velocity—
—
ω: —vR: —vL: —L: —
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Angular Velocity Magnitude—
Slow (< 1 rad/s) Moderate (1–3 rad/s) Fast (3–6 rad/s) Very Fast (> 6 rad/s)
ω = (vR − vL) / L  ·  Positive ω = counter‑clockwise rotation. Units: rad/s, m/s, m.
omega = (v_right - v_left) / L
Differential Drive Robot Angular Velocity

Variables

SymbolQuantityUnit
omegaRobot angular velocityrad/s
v_right, v_leftVelocities of the right and left wheelsm/s
LDistance between the two wheels (wheelbase)m

What it means

The angular velocity (ω) of a differential drive robot is proportional to the difference in wheel speeds divided by the distance between wheels (L). This formula is the counterpart to linear velocity. It is used to compute the robot’s turning rate, which is essential for heading estimation and for generating turning motions. In odometry, it integrates to yield orientation change. In control, it is used for trajectory tracking and point‑to‑point navigation. Understanding this is critical for designing and programming differential drive robots.

Worked example

Differential Drive Angular Velocity – Two Detailed Examples

Real‑World
Scenario: A differential drive robot has wheel speeds v_right = 1 m/s, v_left = 0 m/s, and wheelbase L = 0.5 m. The angular velocity ω = (v_right - v_left) / L = (1 - 0) / 0.5 = 2 rad/s. The robot rotates clockwise at 2 rad/s. This is used to control the robot's heading during turns, which is essential for autonomous navigation and obstacle avoidance.
ParameterValue
v_right (m/s)1
v_left (m/s)0
L (m)0.5
1ω = (1 - 0) / 0.5 = 2 rad/s
Result 2 rad/s ✓ Rotation rate
Scenario: A robot with v_right = 3 m/s, v_left = 1 m/s, and L = 0.4 m has ω = (3 - 1) / 0.4 = 2 / 0.4 = 5 rad/s. This high angular velocity indicates a sharp turn. The robot controller uses this to calculate the turning radius and adjust the wheel speeds to follow a desired path smoothly, avoiding sudden jerks that could destabilise the robot.
ParameterValue
v_right3
v_left1
L0.4
1ω = (3 - 1) / 0.4 = 5 rad/s
Result 5 rad/s ✓ Sharp turn
Insight: The angular velocity of a differential drive robot depends on the difference in wheel speeds and the wheelbase. A larger difference or smaller wheelbase results in a faster turn.

Common mistakes

  • Differential drive angular velocity: ω = (v_right − v_left) / L – where L is the wheelbase (distance between wheels).
  • Sign: Positive rotation counter‑clockwise (right wheel faster).
  • Units: v in m/s, L in m → ω in rad/s.
  • Wheelbase: Measured between the contact points of the wheels – not the robot width.
  • Assumes: No slipping and the robot is in a planar motion.

Applications

Differential drive robot angular velocity, ω = (v_right − v_left)/L, where L is the wheelbase, relates the difference in wheel speeds to the turning rate. This is critical for controlling the robot's orientation. Engineers use this to calculate the required wheel speed commands for desired turning rates, enabling smooth turns and path following. In odometry, it updates the heading angle. This formula is also used in more complex kinematic models for non‑holonomic robots. By combining linear and angular velocity control, robots can follow arbitrary trajectories. Understanding this relation is essential for mobile robot navigation and control.

  • Heading control and turning for mobile robots
  • Path generation for curved trajectories
  • Odometry heading updates for localisation
  • Implementation of control laws for autonomous vehicles
  • Simulation and analysis of mobile robot dynamics