The walk phase machine structurally cannot express flight - rebuild the representation for duty < 0.5, teach flight with a mask tax, never a cliff bounty
phase-machine-structural-limits.When a new gait changes the contact pattern's structure, audit whether the phase/mask representation can express it and rebuild the representation if not; teach the new contact pattern with graded mask-mismatch pressure and count it in acceptance with artifact-proof definitions (minimum segment length), never with cliff bounties.
Symptom
Running requires both feet airborne, but the walk-era phase machine switches legs by the sign of sin(phase) - with duty < 0.5 the two swing windows must OVERLAP during flight, which a sign-switching representation cannot express at all.
Context
The run phase machine was re-architected rather than patched: per-leg phases (left = phi, right = phi+0.5 mod 1) with leg_phase < duty defining stance, aligned to the walk sin convention at duty=0.5 so the machines agree where their domains overlap. Flight is taught by the SAME mechanism that once cured foot-dragging, direction reversed: in the two planned flight windows the contact mask is (0,0) and feet_contact_number_duty charges -0.3 per foot still on the ground - a mild ~0.16/step tax, deliberately NOT a cliff: "悬崖式腾空奖励诱发跳跃 hack,v4-clearance 家族老课文". The reference shape (half-sine bump over swing progress) is zero at window boundaries by construction, eliminating the clearing-window that the C4 probe measured to cost 13-19% on non-sinusoidal references. The shape self-check ("零代价选项是什么") was run on three behaviors: standing pays ref everywhere (known cmd=0 stepping risk, booked), walking pays only the flight-window tax, proper running collects full marks.
Change
New rewards.py run section (leg_phase_duty / stance_mask_duty / ref_run / clearance_run / contact_duty) with the walk versions untouched byte-for-byte; flight acceptance metric defined with a segment-length floor (>=40 ms to count) so numeric contact flicker cannot fake flight.
Outcome
Flight became expressible and taught by a calibrated mild pressure; the walk lineage's phase code stayed frozen as its own contract.
Mechanism
A phase representation defines which contact patterns exist in the reward's vocabulary; duty cycling below 0.5 introduces states (double-flight) outside a half-period sign convention's language, so no weight tuning can teach them. And rare desirable events taught by cliff-shaped bounties invite hacks (jumping in place); the graded mask tax prices the planned pattern without creating a jackpot.
Applies when
- extending a walking stack to running/jumping (duty < 0.5)
- a desired contact pattern never appears despite reward increases
- defining flight/contact acceptance metrics
“duty<0.5 时摆动窗 (1−duty)T > T/2,两腿摆动窗在腾空段重叠 —— sin 符号切腿的机制结构上表达不了"双脚同时在空中"。… feet_contact_number_duty 对"还踩着地"持续 −0.3/脚 —— 与 walk 治拖地同一机制,方向相反。不腾空的税 ~0.16/步 … 梯度温和不构成悬崖(悬崖式腾空奖励诱发跳跃 hack,v4-clearance 家族老课文)。”