Simulation Instability

A physics simulation diverging numerically — the robot twitches violently, objects fly apart, and the state turns into NaN or huge numbers.

Simulation instability (often called blow-up) is a common failure mode in physics simulation: the velocities and accelerations the integrator computes each step keep growing until they become NaN (not a number) or astronomically large, which shows up on screen as a robot shaking violently, parts flying off, or an object that penetrated another getting launched away. Common causes include too large a simulation timestep, joint PD gains (the stiffness and damping of position control) set too stiff, unreasonable mass or inertia values, objects that start out interpenetrating, or too few constraint-solver iterations. MuJoCo's documentation explicitly warns that too large a timestep makes simulation unstable; the engine checks every step whether acceleration is NaN or exceeds a limit, and if so, issues a warning and resets the simulation automatically by default. In massively parallel reinforcement learning, the NaN values from just one environment can contaminate an entire batch of training data, so problem environments usually need to be detected and reset individually.

ExampleIn MuJoCo, increasing the timestep while also setting joint stiffness very high can make a robot arm shake violently within a few steps and its state turn into NaN; MuJoCo reports a bad-acceleration (BADQACC) warning and automatically resets the simulation.

Also called

Blow-up, Numerical Instability, NaN Explosion, Simulation Blow-up

Related

Simulation Timestep · Numerical Integrator (Semi-implicit Euler / RK4) · Constraint Solver · Interpenetration · Solver Iteration Count (Position / Velocity Iterations) · MuJoCo (Multi-Joint dynamics with Contact)

Sources

MuJoCo Documentation: Computation - Numerical integration
MuJoCo Documentation: XML Reference (option/flag autoreset)