Mirror augmentation over an asymmetric default injects systematic error - symmetrize the default first and verify the transform bit-exact
mirror-augmentation-needs-symmetric-default.Before enabling any symmetry augmentation, make every constant inside the observation encoding exactly symmetric, and validate the mirror transform against forward kinematics to machine precision - an unverified augmentation is a new error source, not a regularizer.
Symptom
Mirror data augmentation was about to be added while both default poses (standing_pose, walk nominal_pose) were asymmetric - stale hand-tuned compensations from before a ground re-calibration, with hip_yaw differing 2.40 deg between sides and the foot soles actually tilted (pitch 2.88/1.35 deg, roll -2.47/+0.25 deg).
Context
The observation encodes joint_pos_rel = q - default. Under mirroring q_l -> -q_r, the relation (q-default)_l -> -(q-default)_r holds only if default_l = -default_r; with an asymmetric default, augmentation produces observation pairs that are NOT mirror images, i.e. "default 不对称时做镜像增强会引入系统性错误,比不做还糟" (worse than not doing it). The fix: adopt model geometric zero as standing default (MuJoCo FK verified: sole pitch/roll exactly 0, asymmetry 0.00 deg) and a symmetric crouch for walk (hip -0.25/knee -0.5/ankle -0.25 satisfying hip - knee + ankle = 0 to keep soles flat). The mirror transform itself was verified bit-exact before use: pseudovector vs polar-vector sign patterns (ang vel [-1,1,-1], gravity [1,-1,1], cmd [1,-1,-1]), joint swap-and-negate; FK check that left-foot pose under q equals the mirror of right-foot pose under mirror(q), measured error 0.00e+00.
Change
Defaults symmetrized first (with init heights recomputed by FK), stand policy retrained on the new default so both policies share one default; augmentation enabled only after the FK mirror test passed.
Outcome
stand_v1 achieved exact left/right pairing (l_knee -0.1013 / r_knee +0.1013), six-pair asymmetry 0.0 deg, height fluctuation 7 -> 1 mm, 33% less mean |action|.
Mechanism
Augmentation asserts an equivariance of the observation encoding; any asymmetric constant inside the encoding (the default) breaks the asserted symmetry, so the augmented data teaches a false invariance. Verifying the transform against FK geometry tests the assertion end to end, independent of the training stack.
Applies when
- adding mirror/symmetry augmentation to locomotion training
- defaults or trims were hand-tuned per side at any point
- observations are expressed relative to a default pose
“观测里 joint_pos_rel = q − default。镜像下 q_l → −q_r,要让 (q−default)_l → −(q−default)_r 成立,必须 default_l = −default_r。default 不对称时做镜像增强会引入系统性错误,比不做还糟。… 位置误差与姿态矩阵误差实测均为 0.00e+00。”