Foot dragging is an attractor, not a low amplitude - and joint damping is the mode switch, adjustable at deploy time

Symptom

s2e_pd-1400's swing height "median 12.1 mm" hid a perfect bimodal distribution: 20 seeds split into a drag mode (2.6-4.9 mm) and a step mode (19.3-24.0 mm) with NOT ONE seed in between - the median sat in the empty gap, and "swing debt -11 mm" really meant "50% probability of falling into the drag attractor".

Context

Two designed experiments closed the mechanism. Test A (nominal plant, 40 seeds): step 42% / drag 58% / middle 0 - at nominal gains, initial conditions alone pick the mode, both modes 100% survivable. Test B (fixed init, kp x kd grid): kd is the mode SWITCH - at kd 1.3 all surviving cells step (13-22 mm), at kd 0.7 nearly all drag (2.7-4.3), only at kd 1.0 does init get a vote; kp >= 1.2 is dangerous (5/6 falls). Global verification at kd x1.3 (20-seed, delay 2): survival 20/20 at ZERO cost, step share 42 -> 80%, swing median 12.1 -> 18.4 mm, slip record low 334, thicker tilt margin - costs: vx 85 -> 78%, saturation +5 pp. A Pareto sweep then priced the knob: step share 42/72/75/88/82/90 across kd 1.00-1.30 with a linear vx tax of -2.3 pp per 0.1 kd - the basin gain is fully collected at kd 1.20 ("1.30 是 over-damping 纯多付税"). Mechanism: low damping leaves a landing micro-oscillation / ground-slide channel the policy can exploit to drag; damping plugs the channel.

Change

Deployment lever adopted: kd-scale 1.20 (conservative 1.15) as the legitimate successor to the power-0.8 crutch ("前者削幅度保稳,后者堵 拖地通道换步态,且不牺牲存活"); training-side prescription: move the DR band to nominal-1.2 x (0.9,1.1) = [1.08,1.32], deleting the [0.7,1.0) drag-teaching zone - a contract-level change requiring digest re-baselining, gated on measuring the real robot's actual kd dispersion first.

Outcome

The kd surgery rung (s2e_kd) delivered basin 8 -> 11/20, slip 405 -> 331, vx 81 -> 85% with no out-of-band fragility (below-band check 20/20) - "拐杖烧进分布的正确姿势", explicitly contrasted with the failed s1g amplitude version: this one changes the plant family the policy has seen, that one changed the execution mapping the policy would have to relearn.

Mechanism

The gait's swing behavior is a bistable dynamical system whose basin boundaries are set by plant parameters; a policy trained across a kd band that includes the drag basin has learned to inhabit it. Shifting the deployed (and then trained) damping moves the system into the step basin without touching the policy - a plant-side fix for what looked like a training deficiency.

Applies when

• a gait quality metric splits into distinct modes across seeds
• deciding between more training and a gain/damping change
• converting a deployment crutch into a training-distribution change