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Biped Robot Balance Lab: ZMP, Capture Point and Evolution

A generic 7-link humanoid walks in the sagittal plane. Joint torques come from a PD servo that tracks a Linear Inverted Pendulum (LIPM) plan; an evolution strategy tunes the plan.

Scenarios

Robot and world

Controller and learning

Policy

train with the push below

Generations25

Population 20, each candidate walks for 8 simulated seconds; fitness = distance walked minus fall, flight and energy penalties.

Fitness per generation (best and mean). Dashed line: hand-tuned design in this world.

Live telemetry

Everything is drawn relative to the centre of mass (0 line). Teal band: support polygon (foot soles in contact). Amber: ZMP. Blue dashed: capture point. A stable step keeps amber inside teal.

Numerical checks

Experiment: one-step capture after a shove

Question: after a sudden shove that gives the standing robot extra speed Δv, where must it put its foot to stop? The LIPM answer is the capture point ξ = x + v/ω carried forward to touchdown, ξ(T) = p + (ξ₀ - p)e^ωT.

Dots: where the foot of the full rigid-body robot actually landed. Dashed line: capture point predicted by the LIPM. Band: landings that still put the capture point under the foot.

The science