Before training a one-leg stand, the accounts and a probe showed the default gains could not hold it at all - kp 20 needs 0.39 rad of error to carry the static roll moment, more than the whole adduction range - so per-joint gains came first, and thermal limits set the session length
single-support-gain-authority-probe.Before training a posture that loads one joint statically, compute the steady tracking error load/kp and the series stiffness against m*g*h, and prove with a simple hand-written controller that the posture can be held under the deployment gains - change the gains first if it cannot; then size session length from the thermal account.
Symptom
The one-leg line (standing on one foot, the other folded back, no hopping) had to decide whether the existing gain profile could hold single support before any reward was designed.
Context
Hardware accounts (9.792 kg, COM 0.234 m high, 170 x 80 mm feet, legs 80% of the mass): moving the COM over one foot needs 107 mm of shift and the 20 deg hip-roll adduction range gives 131 mm - geometrically enough. The static frontal moment is 7.8-9 N*m, within RS02's 17 N*m - torque is enough. But at kp 20 carrying 7.8 N*m needs 0.39 rad of tracking error, more than the entire adduction range, and the real robot had already shown it: commanded +0.17, actual -0.04 (0.21 rad droop) under load, 0.0008 rad hanging - load, not the motor. A probe (probe_oneleg.py) then showed open-loop PD cannot hold single support on physics grounds, so the criterion became "an equilibrium exists and a hand-written 4-gain COM feedback can hold it": single-support roll stiffness is hip and ankle in series and must exceed m*g*h_com = 22.5 N*m/rad; ankle kp 12 in series with hip kp 80 gives only 10.4 (open loop 16/16 fell), ankle 60 with hip 80 gives 34.3 (52% margin).
Change
A per-joint gain profile (rl_oneleg: hip_roll kp 80, ankle_roll kp 60, the rest as rl_default) - which needed per-joint gain support in robot.yaml, the bridge, deploy and the trainer's actuator groups - decided before training. Thermal account: single support makes hip_roll the dominant heat load (about 7.8 N*m against a 7 N*m continuous rating), so acceptance and demos run in segments of at most 60 s with a temperature check.
Outcome
Under rl_oneleg the hand-written feedback held six cells cleanly for 6 s (hip_roll steady torque 2.1-3.4 N*m, half the thermal budget); under rl_default the same feedback on the same cells fell 0/4. The trained V0 policy then passed its 40-cell acceptance.
Mechanism
With PD position control, the steady error needed to carry a static load is load/kp; when that error exceeds the joint's range the posture is unreachable whatever the policy does, and series compliance between joints lowers the effective stiffness below the gravity stiffness that single support demands.
Applies when
- single-support, crouched or one-arm-load postures on PD actuators
- a joint "droops" under load on hardware but tracks well when hanging
- deciding whether a new skill needs its own gain profile
“但 kp=20 时撑住 7.8 N·m 需要 **0.39 rad 跟踪误差 > 整个内收行程**。真机已实测: 命令 +0.17 实际 −0.04（droop 0.21 rad），悬挂时 0.0008 rad——是负载不是电机。 … 单支撑滚转是 hip/ankle **串联**刚度，必须 > m·g·h_com = 22.5 N·m/rad；ankle kp12 串 hip80 只有 10.4（开环 16/16 全摔），60 串 80 = 34.3（裕 52%） … **rl_default 同反馈同格 0/4 全摔**（增益档必要性对照）”