An exponential kernel on instantaneous velocity punishes gait oscillation - track the cycle average
cycle-average-tracking-for-gait-quantities.Reward velocity tracking on gait-cycle averages (or filtered values), not instantaneous samples, whenever the desired behavior oscillates at stride frequency; widening the kernel does not fix a variance penalty.
Symptom
Even while the robot genuinely sidewalked (verified after the metric fix), the Isaac-side tracking reward sat on the ignore-floor: true sidewalk scored 0.178 vs 0.189 for ignoring the command - the reward was mildly punishing the desired behavior.
Context
Sidewalking is inherently oscillatory: per-frame vy std was 0.177 while the tracking kernel width was sigma = 0.15, applied to the instantaneous value. A kernel-width scan showed widening sigma 0.15 -> 0.50 still loses (-0.14 -> -0.07): "指数核惩罚的是方差，而侧步天生带方差" (the exponential kernel penalizes variance, and side-stepping inherently carries variance). Modeling with measured parameters: replacing instantaneous vy with the mean over one gait cycle (0.5 s) flips the margin decisively (true sidewalk 1.888 vs ignore 1.281, +0.607), half-cycle is neutral (+0.006), two cycles adds nothing more. Explicitly flagged as extrapolation pending Isaac-side implementation. This also vindicated a previously dismissed external note (sigma too small) - right conclusion, different mechanism than claimed (variance, not gradient).
Change
Proposed fix recorded: change the tracked quantity from instantaneous vy to a one-gait-cycle running average; widening sigma alone rejected by the scan.
Outcome
Diagnosis complete and quantified; the C4 product shipped via feed-forward before the reward change was implemented, so the cycle-average fix remained a verified-by-model, not-yet-trained change.
Mechanism
E[exp(-(v-c)^2/sigma^2)] decreases with Var(v) even when E[v] = c exactly; a gait's phase-locked oscillation guarantees variance at the stride frequency, so instantaneous tracking rewards structurally prefer standing still at the command mean. Averaging over exactly one cycle removes stride-frequency variance while preserving command-following error.
Conflicts
The cycle-average fix itself is model-extrapolated ("⚠️ 这一条是外推，须在 Isaac 侧实装并复量后才能当结论") - the diagnosis is measured, the remedy untested in training at the time of writing.
Applies when
- tracking rewards for lateral/turn/any oscillation-carrying velocity
- a verified behavior scores below the ignore-floor
- choosing sigma for exp-kernel tracking terms
“侧走时 vy 的逐帧摆幅 std = 0.177，而 track_lin_vel_y_exp 核宽 σ = 0.15，且作用在瞬时值上 … 真侧走（均值 66%，振荡 ±0.18）0.178 | 完全无视指令 0.189 … 真侧走的得分比无视指令还低。… σ 从 0.15 放到 0.50，侧走仍然吃亏 … 把跟踪目标从瞬时 vy 换成一个步态周期（0.5 s）的平均 vy：… 1.888 vs 1.281”