Principle:Google deepmind Mujoco Kinematics
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Robotics | 2025-02-15 |
Overview
Description: Forward kinematics computation and spatial algebra operations for transforming between body frames and computing motion quantities.
Context: MuJoCo computes forward kinematics as the first stage of the simulation pipeline, transforming generalized coordinates (joint angles) into Cartesian positions and orientations for all bodies, geoms, and sites in the kinematic tree.
Theoretical Basis
Forward kinematics traverses the kinematic tree from root to leaves, composing spatial transforms at each joint to obtain the global pose of each body. Spatial algebra (6D vectors combining linear and angular quantities) provides a compact and efficient framework for these computations. Key operations include quaternion multiplication for orientation composition, spatial velocity propagation using the recursive Newton-Euler formulation, and Jacobian computation that maps joint velocities to Cartesian velocities. The spatial utilities also provide operations for cross products, coordinate frame transformations, and inertia transformations between frames.
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