Principle:Google deepmind Mujoco Composite Rigid Body
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Linear Algebra | 2025-02-15 |
Overview
Description: Composite rigid body inertia algorithm for efficient computation of the joint-space mass matrix.
Context: MuJoCo uses the composite rigid body algorithm (CRBA) during model initialization and forward dynamics to compute the joint-space inertia matrix, which is fundamental to both forward and inverse dynamics computations.
Theoretical Basis
The composite rigid body algorithm computes the joint-space mass matrix M(q) by traversing the kinematic tree from leaves to root. At each joint, the composite spatial inertia of the subtree rooted at that joint is accumulated. The (i,j) entry of M is then obtained by projecting the composite inertia through the joint motion subspaces. CRBA has O(n * d) complexity where n is the number of bodies and d is the depth of the kinematic tree, making it efficient for branched topologies typical in robotics.
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