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Terramechanics

Terramechanics – definition

Terramechanics is the engineering discipline that models the interaction between a vehicle running gear and deformable terrain. In mobile robotics, it explains how wheels generate traction, sink into soil, lose lateral stability, compact ground, and consume energy while driving on sand, gravel, mud, snow, or agricultural soil. The term is primarily associated with the analytical models developed by M. G. Bekker and later extended for off-road vehicles and planetary rovers.

For a wheeled UGV, terramechanics connects terrain properties with measurable vehicle behaviour. Relevant inputs include wheel geometry, wheel load, tyre or wheel material, soil cohesion, internal friction angle, shear deformation, and pressure-sinkage response. Relevant outputs include drawbar pull, rolling resistance, wheel slip, sinkage, and required motor torque.

Terramechanics is directly relevant to Leo Rover and Raph Rover when they operate outside smooth indoor floors. Leo Rover has a four-wheel differential-drive configuration and an IP55-rated chassis, but autonomous outdoor motion still requires terrain-aware sensor integration, state estimation, and navigation configuration. Raph Rover is intended for higher-payload applications, where increased mass and payload can substantially change wheel loading, sinkage, and traction requirements. Platform configuration details should be verified against the current Fictionlab technical documentation.

Core wheel-terrain interaction variables

Terramechanics does not treat terrain as a rigid surface. A wheel may deform the ground before it produces useful longitudinal force. This distinction matters when encoder odometry reports wheel rotation but the UGV has limited physical displacement.

The following variables are commonly used when evaluating a wheeled UGV on deformable terrain.

Parameter Meaning Practical UGV effect
Sinkage, z Vertical wheel penetration into terrain Increases rolling resistance and may reduce clearance.
Slip ratio, s Difference between wheel peripheral speed and vehicle speed Causes odometry drift and reduces traction efficiency.
Drawbar pull, DP Usable horizontal force available at the vehicle body Determines whether the rover can climb, tow, or overcome soil resistance.
Normal load, W Vertical load applied to a wheel Changes contact pressure, sinkage, and shear force.
Motion resistance, R Force opposing motion through terrain deformation and compaction Raises required wheel torque and electrical power demand.

For a driven wheel, longitudinal slip can be expressed as follows, where rω is wheel peripheral speed and v is measured forward vehicle velocity:

s = (rω - v) / max(rω, v)

A slip value near zero indicates agreement between wheel rotation and vehicle motion. It does not, by itself, prove accurate localisation because wheel radius, terrain compaction, and steering effects can also introduce error. Slip must be estimated using an independent velocity or position reference, such as visual odometry, LiDAR odometry, GNSS/RTK, or a motion-capture system.

Pressure-sinkage and traction models

The Bekker pressure-sinkage relationship is a common first-order model for a rigid wheel or plate pressing into soil. It relates normal pressure p to sinkage z and terrain parameters measured experimentally.

p = (kc / b + kφ) · z^n

In this model, kc is cohesive modulus, kφ is frictional modulus, b is wheel width, and n is the sinkage exponent. These parameters are terrain-specific. They should not be copied from an unrelated soil dataset without validation, because moisture, compaction, particle size, and wheel geometry affect results.

Traction is often modelled through a shear-stress relationship based on soil cohesion, normal stress, internal friction, and shear displacement. For UGV engineering, the model is useful for comparing wheel designs, payload distributions, and expected performance before field testing. It is less reliable when terrain has roots, rocks, discontinuities, deep ruts, or rapidly changing moisture.

Terramechanics in ROS 2 navigation

ROS 2 does not define a dedicated standard terramechanics message or a mandatory wheel-soil model. Instead, terramechanics affects the accuracy of state estimation and the assumptions used by the navigation stack. A rover that slips will publish wheel odometry that disagrees with its actual pose.

On Leo Rover or Raph Rover, a practical ROS 2 architecture usually combines wheel encoder data with one or more external references. The transform tree should follow ROS coordinate-frame conventions defined by REP 105.

  • sensor_msgs/msg/Imu provides angular velocity, linear acceleration, and orientation data when available.
  • nav_msgs/msg/Odometry can publish encoder-based odometry, visual odometry, or fused state estimates.
  • sensor_msgs/msg/NavSatFix carries GNSS position data, including RTK-derived fixes when supplied by the receiver driver.
  • geometry_msgs/msg/Twist or geometry_msgs/msg/TwistStamped carries velocity commands or measured velocities, depending on the interface.

The typical frame chain is map → odom → base_link. The odom frame remains locally continuous, while the map frame may be corrected by global localisation. REP 105 specifies these semantic roles. When slip is significant, fusing IMU and GNSS or visual/LiDAR odometry can reduce reliance on encoder-only motion estimates.

# Example concept for robot_localization EKF
ekf_filter_node:
  ros__parameters:
    two_d_mode: true
    publish_tf: true
    odom0: /wheel/odometry
    imu0: /imu/data
    odom0_config: [true, true, false,
                   false, false, true,
                   true, true, false,
                   false, false, true,
                   false, false, false]

This configuration is only a starting point. Covariance values, frame identifiers, sensor mounting orientation, timestamp quality, and GNSS handling must be configured for the actual hardware and terrain test procedure.

Field testing on Leo Rover and Raph Rover

A reproducible terramechanics test separates vehicle parameters from terrain parameters. The same route should be repeated with controlled payload, tyre pressure where applicable, speed command, and sensor configuration. Terrain changes caused by previous runs, including compaction and rut formation, should be controlled, recorded, or mitigated by using fresh test lanes. Tests should include a ground-truth reference when odometry accuracy is evaluated.

For Leo Rover, useful experiments include comparing encoder odometry with RTK GNSS or visual odometry on compacted soil, loose gravel, and short grass. For Raph Rover, payload-dependent tests are particularly important because a higher normal load may improve net drawbar pull under some conditions while also increasing sinkage and motion resistance.

  • Measure wheel speed, estimated body velocity, IMU acceleration, motor current, and ground-truth trajectory.
  • Record ROS 2 data with ros2 bag record for repeatable post-processing.
  • Compare commanded distance with independently measured distance to identify systematic slip.
  • Document terrain condition, moisture state, slope, wheel configuration, and payload mass for every run.
ros2 bag record /wheel/odometry /imu/data /gps/fix /tf /tf_static

Normative references and technical sources

Terramechanics models are engineering models rather than a single ROS or IEEE implementation standard. ROS frame semantics and message definitions should be taken from the applicable ROS documentation and REP documents.

See also