Delay Randomization Widens the Delay Margin of Learned Humanoid Motion Trackers

Learned humanoid controllers are usually trained in one simulator and then checked in a second one before they go near hardware. We ask what that check says about command delay. We train motion-tracking policies for a 24-joint humanoid on five motions taken from monocular video and test them in an independent CPU MuJoCo harness, which we first verify against the training model. Every policy completes its motion in at least 26 of 30 episodes under the training randomization. With 40 ms of constant command delay, however, survival drops to 15% on average (0% - 45%), and the delay margin is only 20 - 30 ms. Randomizing the delay during training (0 - 50 ms) lifts survival at 40 ms to 95% on average (75% - 100%) and moves the margin to 50 - 70 ms. A control arm trained for the same number of extra iterations without delay does not improve, so the gain comes from the randomization itself. This holds for all five motions with three training seeds each, and a policy trained in PhysX behaves the same way. The price is slightly looser tracking (0.02 - 0.06 rad on four motions) and, for the most dynamic motion, less robustness to other perturbations. We also show that the first sim-to-sim gap we saw came from the harness, a missing floor and a wrong timestep, and not from the physics engines. The 0 - 20 ms delay ranges common in locomotion training lie inside the margin an unrandomized tracker already has. The benefit comes from randomizing beyond it, so the range should be set from the robot's measured latency, and delay margin belongs next to other sim-to-sim metrics.