Principle:Google deepmind Mujoco Analytical Derivatives
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Optimization | 2025-02-15 |
Overview
Description: MuJoCo computes analytical derivatives of the full dynamics equation with respect to states and controls. These exact gradients enable efficient gradient-based optimization and control without relying on numerical approximation.
Context: Analytical derivatives are essential for trajectory optimization, model-based reinforcement learning, and system identification. MuJoCo differentiates through the entire forward dynamics pipeline, including smooth dynamics, constraint forces, and actuator models.
Theoretical Basis
Analytical derivatives of rigid body dynamics involve differentiating the equations of motion:
- Smooth dynamics: Derivatives of M(q) * qacc = f(q, qvel, ctrl) with respect to state and control variables
- Contact derivatives: Differentiation through the constraint solver using implicit function theorem techniques
- Chain rule composition: The full derivative is assembled by composing partial derivatives through each stage of the simulation pipeline
Analytical derivatives are exact (up to floating-point precision) and significantly faster than finite-difference approximations for high-dimensional systems.
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