Formula & Calculator
Robot Turning Radius
Calculates the radius of the curved path a mobile robot follows given its linear and angular velocity.
Interpretation
R = v / ω. Radius of the circular path followed by the robot during a turn. Used in motion planning and trajectory generation.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R | Turning radius | m |
| v | Linear (forward) velocity | m/s |
| omega | Angular (turning) velocity | rad/s |
What it means
The turning radius R is the radius of the circle traced by the robot’s centre when moving with linear velocity v and angular velocity ω. For a differential drive robot, it is determined by the ratio of speeds. This parameter is used in path planning to generate arcs, in obstacle avoidance, and in control to ensure smooth turns. A small R means a tight turn. Understanding the turning radius helps in designing robot motion to navigate confined spaces and to avoid collisions.
Worked example
Robot Turning Radius – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| v (m/s) | 1 |
| ω (rad/s) | 2 |
| Parameter | Value |
|---|---|
| v | 3 |
| ω | 1 |
Common mistakes
- Turning radius: R = v / ω – the radius of curvature of the robot’s path.
- Sign: R is positive for left turns (if ω>0) – direction matters.
- Units: v in m/s, ω in rad/s → R in m.
- Infinite radius: If ω = 0, the robot goes straight (R → ∞).
- Instantaneous centre of curvature: The robot rotates about the ICC located at distance R from the centre.
Applications
Robot turning radius, R = v/ω, determines the radius of the circular path followed by a differential drive robot given its linear and angular velocities. This is used in trajectory planning and control to assess manoeuvrability and to generate smooth paths. Engineers use it to check if the robot can make a required turn within available space, to avoid obstacles, and to compute path curvature. By adjusting the speed ratio, they can control the turn radius. This relation is also used in autonomous driving algorithms. Understanding turning radius is essential for mobile robot navigation and for designing safe and efficient paths.
- Path planning and obstacle avoidance
- Manoeuvrability assessment for mobile robots
- Trajectory generation for curved paths
- Autonomous parking and navigation in tight spaces
- Simulation of wheeled vehicle dynamics
Frequently Asked Questions
The turning radius R is the radius of the circular path the robot follows when moving at a constant speed and turning rate. It is given by R = v / ω, where v is the linear velocity and ω is the angular velocity.
Applying the formula when angular velocity is zero, where the turning radius is infinite (a straight line), not zero. Some may incorrectly think R = 0 when ω = 0.
R = (L/2) · (v_right + v_left) / (v_right – v_left). This follows from R = v/ω. If v_right = v_left, the denominator is zero, giving infinite radius (straight line).
The minimum turning radius is achieved when one wheel is stopped (e.g., v_left = 0), giving R = L/2. For a spin‑in‑place (v_right = –v_left), the radius is zero (turn in place).
The turning radius limits the robot's ability to follow sharp curves. In path planning, constraints like minimum turning radius are used to generate feasible trajectories (Dubins curves, Reeds‑Shepp curves).
Curvature κ = 1/R. A smaller radius means higher curvature (sharper turn).
Path planning, vehicle dynamics, and control design for mobile robots.
For a desired radius R and speed v, ω = v/R. Then solve for v_right and v_left using the inverse differential drive equations.
Slip causes the actual turning radius to differ from the commanded one. This is why odometry alone is insufficient for accurate navigation; sensor fusion (e.g., IMU) is needed.
The formula R = v/ω is general. For a specific robot, the relationship between wheel speeds and v,ω must be known. The track width L determines the mapping.