Principle:Google deepmind Mujoco Control Noise Generation

Knowledge Sources	Ornstein-Uhlenbeck Process MuJoCo
Domains	Benchmarking, Stochastic_Processes, Control
Last Updated	2026-02-15 06:00 GMT

Overview

Pattern for generating temporally correlated control signals using an Ornstein-Uhlenbeck process for realistic simulation benchmarking.

Description

Control Noise Generation produces smooth, temporally correlated actuator commands for benchmarking purposes. Rather than using independent random noise at each step (which creates unrealistically jerky motion), an Ornstein-Uhlenbeck (OU) process generates signals that mean-revert with controllable rate and amplitude. This results in more realistic actuation patterns that exercise the full dynamics of the model including contacts.

The Halton quasi-random sequence is used instead of pseudo-random numbers to ensure reproducible and evenly distributed noise.

Usage

Use in benchmarking scripts to generate realistic control inputs that exercise the full simulation pipeline including contacts and constraint solving.

Theoretical Basis

The Ornstein-Uhlenbeck process is a mean-reverting stochastic process:

$d x_{t} = - θ x_{t} d t + σ d W_{t}$

In the discrete MuJoCo implementation:

$θ$ corresponds to ctrl_noise_rate
$σ$ corresponds to ctrl_noise_std
$d W_{t}$ uses Halton sequence values mapped through the inverse normal CDF

Related Pages

Implemented By

Implementation:Google_deepmind_Mujoco_CtrlNoise_Pattern

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Principle

Implementation

Heuristic

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