bekker_wheel_sinkage — DRIVE `roverslip` op

• Data kinds: scalar × table × any → scalar

• Call: import fullseye as fs; fs.ledger.bekker_wheel_sinkage(load, wheel, soil, form: 'str' = 'classic') -> 'float' (to call the implementation directly, import roverslip; roverslip.bekker_wheel_sinkage(load, wheel, soil, form: 'str' = 'classic') -> 'float'; from the registry, opsdrive.get("bekker_wheel_sinkage"))

• GPU: none (CPU reference implementation only)

Usage

Bekker's approximate formula for the sinkage of a rigid wheel [m]. The contact is approximated by the parabola z(x) = z₀ − x²/D; shear is not included.

load is the vertical load on one wheel [N], D = 2r, k = k_c/b + k_φ. The load is W = b k sqrt(D) z₀^(n+1/2) · I(n), I(n) = ∫₀¹ (1 − t²)ⁿ dt. form = "classic": Bekker's textbook formula z = [3W / ((3 − n) b k sqrt(D))]^(2/(2n+1)). This is We put I(n) ≈ (3 − n)/3 as (1 − t²)ⁿ ≈ 1 − n t², which is strict only for n = 1 (for n = 1.9, I is about 32% (underestimates and therefore gives subsidence approximately 17% deeper). form = "parabolic": Keep the same parabola and strictly use I(n) = √π Γ(n+1) / (2 Γ(n + 3/2)). small subsidence Converges to the numerical integration of wheel_sinkage (no grounding on the rear side, τ = 0) at (z ≪ D).

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_rover_slip_risk_path — py -3.11 examples/poc_rover_slip_risk_path.py

Ops the type connects to (they accept `scalar` as input)

spin_from_marker_sequence · carla_transform_matrix · carla_pose_to_world · carla_camera_pose · carla_xy_yaw · carla_scene_load · town_chain · osm_parse

Same category (`roverslip`)

bekker_pressure · wheel_forces · wheel_sinkage · wheel_traction_curve · slope_slip_curve · ground_shift_track · odometry_slip · slip_gp_fit

*Provenance: roverslip.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

bekker_wheel_sinkage — DRIVE roverslip op