Six-Legged Walker

What is modelled

The gait engine of the 3D page, ported to flat ground: each leg has a phase offset and swings for the part of the cycle that the gait leaves, while the other feet stay planted in the world. Tripod uses duty factor 0.64, ripple 0.83 and wave 0.86. At each moment the convex hull of the planted feet is the support polygon, and the stability margin is the shortest distance from the centre of mass to its edge, negative if the centre is outside. The page adds the static load each stance foot carries and the joint torques needed to carry it.

Equations

• Leg phase φi = (f t + oi) mod 1; swing when φi ≥ β (duty factor β).
• Allowed speed min(0.85, 0.95 · stride · cadence) m/s; foot touchdowns of one leg are v / f apart.
• Leg position r = c + l1 cos θ1 + l2 cos(θ1 + θ2), y = l1 sin θ1 + l2 sin(θ1 + θ2) with c = 0.28, l₁ = 0.78, l₂ = 0.98 m.
• Static joint torques τ = JT F with F = m g / n_stance: femur F (r - c), knee F (r - c - l1 cos θ1).

Checks run in the page

• 400 random foot targets through inverse and forward kinematics.
• Duty factor and the fewest legs on the ground for each gait over 10 s.
• Distance between successive touchdowns against speed over cadence.
• Jacobian torque by finite differences against force times lever arm, and the margin function on a unit square.

Honest simplifications

The motion is kinematic: there is no leg or body dynamics, no ground friction limit, no leg mass or motor model, the centre of mass is the body origin, and the terrain is flat. The torque is a static estimate with the weight shared equally among the stance legs; real robots share load unevenly and need extra torque to accelerate. Numbers show how the geometry behaves and are not a design for a particular machine.

• Compare Tripod, Ripple and Wave: slower gaits keep more legs down and a larger margin but allow less speed.
• Choose Turning tripod and watch the support polygon rotate against the footprints.
• Raise the body mass and see the joint torques grow in proportion.