Measure yaw rate by integrating heading, not by averaging body-frame angular velocity - the two differed 15x
heading-integral-not-body-rate.For any secular rate (turn gain, drift), integrate the world-frame angle over the window; never average instantaneous body-frame rates during oscillatory motion - and when code comments warn about a measurement, believe them before re-measuring.
Symptom
Two measurements of the same turn gain disagreed by a factor of ~15: time-averaged body-frame omega_z gave -0.05 while the sim2sim harness's heading-angle integration gave +0.473.
Context
The harness code comment had already documented and predicted the failure: during gait the torso oscillates (body-frame omega_z std up to 0.7); projecting world angular velocity onto a swaying body axis and then averaging biases the estimate systematically - "实测体系均值 −0.04 而实际在以 +0.15 转" (measured body-frame mean -0.04 while actually turning at +0.15). The author's own -0.05 measurement was declared void and the training machine's 1.58/2.45 turn gains confirmed valid.
Change
Measurement doctrine fixed: yaw rate for evaluation = net heading change by integration over the window; instantaneous body-frame rates are unusable for averaged directional statistics during legged gait.
Outcome
Subsequent friction sweeps and turn-gain accounting were all conducted in the heading-integral currency, making cross-simulator comparisons (MuJoCo vs Isaac 1.04/1.02) meaningful.
Mechanism
Averaging a vector quantity expressed in an oscillating frame couples the frame's oscillation into the mean (a rectification bias); the heading integral is computed in the world frame where the gait oscillation integrates to ~zero, leaving the secular component.
Applies when
- measuring turn gain, heading drift, or any secular angular rate
- a body-frame-averaged statistic disagrees with trajectory-level truth
- writing evaluation code for oscillating platforms
“我用体坐标系 ωz 的时间均值测,得 −0.05;sim2sim 用航向角积分,得 +0.473。差 15 倍。… 步态中躯干摇晃(体系 ωz std 可达 0.7),把世界角速度投到摇摆的体轴上再取均值会系统性偏掉 … 结论:偏航率必须用航向积分,体系瞬时角速度取均值不可用。”