Principle:Google deepmind Mujoco PGS Solver
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Numerical Methods | 2025-02-15 |
Overview
Description: Projected Gauss-Seidel (PGS) iterative solver for resolving constrained dynamics with box and friction cone constraints.
Context: PGS is a widely used constraint solver in physics engines. MuJoCo provides it as an alternative to the Newton solver, particularly useful for problems where per-constraint projection is beneficial or for comparison purposes.
Theoretical Basis
PGS is a block coordinate descent method that iterates over individual constraints, solving each one analytically while holding others fixed, then projecting the result onto the feasible set (friction cone or box constraint). Each sweep visits all constraints once, updating the constraint force vector in place. Convergence is linear and depends on the spectral properties of the constraint matrix. While slower than Newton's method per iteration, PGS iterations are cheaper and the method is more robust to ill-conditioned systems. PGS is also straightforward to warm-start using constraint forces from the previous timestep.
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