Under continuous 3-axis uniform sampling, pure straight-line walking is a zero-measure event the policy never trained
zero-measure-commands-need-mode-sampling.Enumerate the exact command points users will actually issue (straight, stop, in-place turn) and give each explicit probability mass via mode sampling with off-axes pinned to zero - never assume a continuous sampler covers its measure-zero subsets.
Symptom
"The robot drifts even in sim when told to walk straight" persisted across reward tunings - because with commands drawn as vx in [0.15,0.5] x vy ~ U(+/-0.2) x wz ~ U(+/-0.6), the event vy=0 AND wz=0 has probability zero: pure straight-line walking was never sampled even once.
Context
Restart evidence item #3: "纯直行是零测度点 … 'sim 里直行就漂'是分布的 必然,不是 reward 没调好" - the drift metric was legitimately drowned by commanded turning (v11's own comment self-documented this). The structural fix is discrete mode sampling: a custom ModeVelocityCommand that first draws a mode by share (stand/forward/back/turn/side/mixed), then draws values only on that mode's axes with all others pinned to exact zero - which is also what preserves single-variable discipline in the C ladder (native 3-axis uniform "采不出'离散模式桶' … 把 C1~C4 的单变量纪律直接毁掉"). The mixed mode later got an ellipsoid constraint rather than a cube for the same reason in reverse - corner combinations of a cube are unrepresentative extremes.
Change
Command generation moved from independent per-axis uniforms to mode-bucket sampling with pinned-zero off-axes (plus 20% rel_standing); acceptance likewise evaluates per mode.
Outcome
Straight-line behavior became a trained, testable mode instead of a measure-zero hope; the C ladder could add one mode per rung with provable isolation.
Mechanism
A policy optimizes expected reward under the command distribution; events of probability zero contribute nothing to the objective, so exact-zero-command behaviors (straight walk, stand, in-place turn) are only learned if the sampler gives them mass. Product-of-uniforms distributions concentrate mass on mixtures and give none to the pure behaviors users actually command.
Applies when
- a "simple" command (straight, stop) underperforms mixtures in sim
- designing command distributions for velocity-tracking tasks
- a ladder needs per-mode isolation for attribution
“纯直行是零测度点:最终 command 为 vx∈[0.15,0.5] × vy∈U(±0.2) × wz∈U(±0.6) 连续均匀,vy=0∧wz=0 从未被专门采样 —— "sim 里直行就漂"是分布的必然,不是 reward 没调好 … Isaac 原生 UniformVelocityCommand 是三轴各自 uniform,采不出"离散模式桶"”