Torque

Torque – definition

Torque is the rotational effect of a force about an axis. In mobile robotics, torque determines whether a drive wheel can accelerate the UGV, climb a slope, overcome rolling resistance, or maintain motion while carrying a payload. Its SI unit is the newton metre (N·m). Although torque and energy share the same base dimensions, torque is expressed as N·m and must not be treated as a joule.

For a force applied at a distance from an axis, torque is defined by the vector product:

τ = r × F

Its magnitude is:

|τ| = r · F · sin(θ)

where τ is torque in N·m, r is the lever-arm distance in metres, F is force in newtons, and θ is the angle between the force and the lever arm. For a wheel rolling without slip, the tangential traction force can be approximated as F = τ / r, where r is the effective wheel radius.

The BIPM SI Brochure lists the newton metre as the unit used for moment of force. In a UGV drivetrain, torque is relevant at several levels: motor shaft, gearbox output, wheel axle, and wheel-ground contact.

Torque in differential-drive UGV platforms

Leo Rover (four-wheel skid-steer) and Raph Rover (Ackermann steering) use mobile ground-robot architectures in which drive torque is converted into longitudinal wheel force. The controller must provide enough torque at each side of the drivetrain to meet the required traction force without exceeding motor, driver, gearbox, or battery limits.

For a differential-drive vehicle, the left and right sides generate independent tractive forces. Their difference produces yaw motion, while their sum produces forward or reverse motion. The required wheel torque increases with robot mass, slope angle, wheel radius, rolling resistance, acceleration target, and payload.

A simplified longitudinal-force model is:

F_required = m·a + m·g·sin(α) + C_rr·m·g·cos(α)

The approximate total wheel torque requirement is then:

τ_wheels = F_required · r

This calculation is a first-order sizing method. It does not include transient current limits, drivetrain backlash, wheel slip, uneven terrain, or losses caused by steering resistance in four-wheel skid-steer configurations.

Parameter	Meaning	Engineering relevance
Continuous torque	Torque that can be sustained without exceeding thermal limits.	Used for sustained driving, hill climbing, and payload transport.
Peak torque	Short-duration torque available under current and thermal constraints.	Relevant during acceleration, obstacle crossing, and recovery from stall.
Stall torque	Torque at zero shaft speed, normally associated with maximum motor current.	Not a continuous operating point. Prolonged stall can overheat motors and drivers.
Gear reduction ratio	Ratio between motor input speed and gearbox output speed.	Raises output torque while reducing output rotational speed.
Wheel radius	Effective rolling radius under load.	Larger wheels require more axle torque for the same traction force.

Motor torque, gearbox torque, and power

Motor torque is not identical to wheel torque. A gearbox increases torque approximately in proportion to its reduction ratio, but mechanical efficiency reduces the available output value. A practical approximation is:

τ_output = τ_motor · G · η

where G is the gear reduction ratio and η is drivetrain efficiency. Torque must also be evaluated together with rotational speed. Mechanical power is:

P = τ · ω

where P is power in watts and ω is angular velocity in radians per second. A UGV may have adequate low-speed torque but insufficient power to maintain higher speed under load. Conversely, a high-speed drivetrain can lack the wheel torque required for uneven terrain.

Motor datasheets should therefore be read as torque-speed curves rather than as a single torque value. Current limits, supply voltage, driver protection thresholds, gearbox ratings, and battery voltage sag affect the usable operating region.

Torque representation in ROS 2

ROS 2 commonly represents joint effort through standard messages and ros2_control hardware interfaces. In the ROS coordinate and units convention, REP 103 specifies SI units. Rotational effort is therefore expressed in N·m.

The sensor_msgs/msg/JointState message contains an effort array aligned with its name array. It can report measured or estimated joint effort, depending on the motor controller and feedback hardware. The official ROS 2 message definition is available in the sensor_msgs documentation.

For controlled hardware, ros2_control defines standard command and state interfaces, including position, velocity, and effort. A torque command interface is useful only when the motor driver supports current or torque control and exposes that capability through the hardware interface.

joint_state_broadcaster:
  type: joint_state_broadcaster/JointStateBroadcaster

drive_controller:
  type: diff_drive_controller/DiffDriveController
  left_wheel_names: [left_front_wheel_joint, left_rear_wheel_joint]
  right_wheel_names: [right_front_wheel_joint, right_rear_wheel_joint]

The configuration above describes wheel joints for a differential-drive controller. It does not itself enable torque control. The available command interfaces must match the firmware and ros2_control hardware implementation. See the ros2_control documentation for controller and hardware-interface requirements.

Torque considerations for Leo Rover and Raph Rover

On Leo Rover, drive torque is mainly relevant when adding payloads, operating on ramps, using larger or higher-grip wheels, or tuning acceleration limits in ROS 2 navigation. Leo Rover is a four-wheel differential-drive platform, so wheel slip and skid-steering resistance can increase the torque required during turns. Its documented hardware and ROS 2 integration details should be verified against Leo Rover technical documentation before changing motor-control parameters.

Raph Rover is intended for applications requiring a larger payload capacity. For this class of UGV, torque budgeting should include payload centre of mass, terrain slope, wheel-ground friction, battery discharge behaviour, and the mechanical load on the drivetrain. Higher payload does not automatically mean that maximum acceleration or climbing performance remains unchanged.