Study 02 of 03

From simulation to smoother robot motion

The normalized-residual policies combine higher feature rank with roughly 3× lower joint jitter in simulation, and that smoothness advantage persists on a physical Spot. We also compare representations and control smoothness across simulated quadrupeds and a humanoid.

What we measure

We evaluate deployment using two hardware measurements: the high-frequency ratio of the joint control signal (jitter) and center-of-mass linear velocity tracking RMSE. Both are recorded on the physical Spot at 50 Hz, using the same scripted sagittal velocity profile as in simulation.

In simulation, the normalized-residual family produces smoother control while matching or improving tracking. On hardware, the deep MLP shows substantial degradation in both jitter and tracking, while SimBa maintains low jitter and tracking error. These observations establish co-occurrence, not a direct causal link between effective rank and smoothness.

Spot joint jitter and velocity tracking RMSE in simulation and on hardware, plus cross-robot jitter
(a) Spot joint control jitter % and (b) center-of-mass linear velocity tracking RMSE (m/s) in simulation (faded bars) and physical hardware deployment (solid bars) across MLP and SimBa. (c) Simulation-only cross-robot control jitter across Spot (12-DoF), ANYmal-D (12-DoF) and H1 (19-DoF biped).
Global feature effective rank for MLP versus SimBa across three robots
Global feature effective rank for MLP versus SimBa across all three robots. SimBa has a consistent Δ ≈ 20 higher rank. Bars show mean ± spread over runs; the difference also appears on perceptive rough terrain.
The Boston Dynamics Spot used for the real-world experiments. Inference runs in ONNX runtime on an external desktop over Ethernet.
ANYmal-D, perceptive rough terrain, 32 parallel environments.
Unitree H1, 19-DoF biped, rough terrain.

Hardware results

QuantitySimBa-XXL (8.45M)MLP-XXL (1.89M)
Hardware jitter, HFR %0.64 [0.61, 0.66]3.28 [0.56, 6.00]
Hardware tracking RMSE, m/s0.066 [0.064, 0.067]0.176 [0.086, 0.265]
Tracking-error reduction62.7%Baseline

Evaluation covers 10 policy configurations, 81,313 logged steps, and 193 steady-state forward strides. Control runs at 50 Hz with 2–5 ms end-to-end latency. Intervals are 95% bootstrap confidence intervals.