A training-side rate limit anchored on the last commanded target is an integrator inside the balance loop - two unrelated lineages converged to the same 34-43% re-fall rate, a soft penalty could not fix it, and the bandwidth arithmetic said safety and standing could not coexist
slew-anchor-is-an-integrator.If you constrain actions in training, anchor the constraint on the measured state, not on the previous command - a limiter with memory adds lag inside the balance loop; and when two different lineages converge to the same failure rate, treat the cause as structural and stop adding soft penalties.
Symptom
With the rate limit moved into training (V1), policies either could not stand up or stood up and kept falling again: the stand oscillated, fell and climbed back, 34-43% of the time.
Context
V1.0-B (user decision: explore new postures from scratch, hard constraint in training): target <- prev + clip(target - prev, +/-S*dt) at the TIGHT rates, anchored on the last issued target like the bridge. Four runs: v1_0 from scratch 0.8% - every category righted under the limit, then knelt (the limit also damped the exploration that had escaped the seated basin in V0); v1_0c continued from R3.1 99.8% get-up but 36-43% re-fall and knee jitter 0.604 rad/s; v1_0p with a pull-assist curriculum (56 N -> 0, fully withdrawn) 39.1% unassisted, re-fall 34-42%; v1_0w with a windup-gap penalty 25.4%, re-fall 18-43%. Removing the limiter from v1_0p gave 0.0%: the policy had co-adapted with it.
Change
The rate-limit route was declared dead after four runs and the line was re-rooted on a beta-anchored action space (V2, user approval required).
Outcome
V2.0's first acceptance at full authority already showed re-falls of 0-1% (V1: 34-43%), the structural bet paying off before any tuning.
Mechanism
Anchored on the previous command, a saturated policy becomes a rate controller - one more integrator in the loop - and active balance through that lag oscillates, while a kneeling sit needs no active control and is stable. The arithmetic: kp 30 needs 0.4 rad of error for 12 N*m; at 4 rad/s that takes 0.1 s, half the pendulum time constant sqrt(0.38/9.8) ~ 0.2 s; keeping standing bandwidth needs S of at least ~8 rad/s, within 20% of the 10 rad/s velocity limit - no bound at all. Anchoring on the measured angle (q + beta*a) makes the full kp*beta authority available in one step, with no memory, and caps the impact at the same time.
Applies when
- adding rate limits, slew limits or target filters to a policy's action path
- a policy stands but oscillates and re-falls after a constraint was added
- different lineages or curricula land on the same failure signature
“v1_0p(拉力课程):会站(prone 79.9%),再摔 34~42% —— **两条完全不同 血统、不同学习路径,收敛到同一失败率**。 … 动作饱和时它退化为 速率控制 = 环内多一个积分器;主动站姿平衡穿过该滞后必振荡(v1_0 的跪坐不需 主动控制,所以稳)。对照:**HoST 的 β 锚在当前实测 q,无记忆、无积分器**”