Principle:Google deepmind Mujoco Constraint Solving
| Knowledge Sources | Domains | Last Updated |
|---|---|---|
| Google DeepMind MuJoCo | Physics Simulation, Numerical Methods | 2025-02-15 |
Overview
Description: Iterative constraint solver algorithms including Projected Gauss-Seidel (PGS), Newton's method, and Conjugate Gradient (CG) for resolving contacts and joint limits.
Context: After contact detection and constraint formulation, MuJoCo uses one of several iterative solvers to find constraint forces that satisfy complementarity conditions, friction cone constraints, and joint limits simultaneously.
Theoretical Basis
MuJoCo formulates constraints as a convex optimization problem and offers multiple solver backends. PGS iterates over individual constraints, projecting each onto its feasible set. The Newton solver uses second-order information for faster convergence on smooth problems. CG solves the underlying linear system using conjugate gradient iterations. All solvers operate on the constraint-space system A*f = b subject to box or cone constraints, where A is the constraint Jacobian projected mass matrix, f is the constraint force vector, and b encodes the desired constraint correction. The choice of solver affects convergence speed and accuracy.
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