Wheel-soil interaction follows classical Bekker/Wong terramechanics, the model used to design real planetary-rover wheels (Lunar Roving Vehicle, MER, Curiosity). Two coupled equations govern it:
Sinkage (Bekker): z0 = ( W / (kc/b + kφ) )^(1/n)
Shear stress (Janosi-Hanamoto):
τ(j) = (c + σ·tanφ) · (1 − e^(−j/K))
where W is load per wheel, b the wheel width, kc/kφ/n the soil's pressure-sinkage moduli, c the cohesion, φ the internal friction angle, σ the contact pressure, j the shear (slip) displacement across the contact patch and K the shear deformation modulus.
Slip ratio: s = (ωr − v) / (ωr), ωr = commanded wheel surface speed, v = actual rover speed
Traction: F(s) = [c + σ·tanφ]·A · (1 − e^(−sL/K)) summed over all wheels
Net acceleration is traction minus the gravity component along the slope (mg·sinθ) and soil compaction resistance, divided by rover mass. On loose regolith and steep grades, traction saturates before it can balance gravity — the wheels keep spinning (slip → ~100%) while ground speed drops toward zero, exactly the "high-centering / excess slip" failure real rover drivers plan around.
- Throttle — commanded wheel surface speed ωr; higher throttle does not guarantee more traction if the soil can't supply it.
- Slope — increases the gravity component the wheels must overcome.
- Soil preset — swaps c, φ, K, kc, kφ between loose dust, compacted regolith and rock, changing both sinkage and the traction-vs-slip curve.
- Suspension — the rocker-bogie mode lets each wheel independently track terrain height while the chassis pose approximates the linkage's "half-angle" load-equalizing behaviour; rigid-axle mode holds the chassis fixed to the front axle only, so mid/rear wheels lose ground contact over bumps — this is a geometry demo and does not itself change the traction numbers above.