Sim Comparison Table
| simulator | year | application | integrator | state | contact | friction solver | language | gradients |
|---|---|---|---|---|---|---|---|---|
| MuJoCo(DM) | 2015 | robotics | implicit Euler/RK4 | minimal | soft | Newton/PGS/CG | C | finite-difference |
| Drake | 2019 | robotics | implicit Euler/RADAU5 | minimal | soft/hard | LCP/Newton | C++ | gradient-bundle |
| ODE | 2001 | graphics | implicit Euler | maximal | soft/hard | LCP | C++ | |
| Bullet | 2006 | graphics | implicit Euler | minimal | soft/hard | MLCP | C/C++ | sub-gradient |
| DART | 2012 | robotics | implicit Euler/variational | minimal | hard | LCP | C++ | sub-gradient |
| ^ nimble | 2021 | " | " | " | " | diff LCP | ||
| Brax | 2021 | graphics | explicit Euler | maximal | soft | N/A | Python | sub-gradient |
| RaiSim | - | robotics | implicit Eutler | minimal | hard | bisection | C++ | - |
| Dojo | 2022 | robotics | variational | maximal | hard | NCP | julia | smooth gradient |
| IsaacSim | 2021 | robotics | - | - | - | - | C++ | - |
| Meta Option | - | - | - | - | - | - | - | - |
Notes:
Explicit euler takes system of equations and multiplies by dt
Brax might not be good for long horizon tasks for this reason
Less Feature Complete
ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
A Differentiable Physics Engine for Deep Learning in Robotics
Sources
Simulation Tools for Model-Based Robotics: Comparison of Bullet, Havok, MuJoCo, ODE and PhysX - Ezra, Tassa, Todorov
SimBenchmark | Physics engine benchmark for robotics applications: RaiSim vs. Bullet vs. ODE vs. MuJoCo vs. DartSim
Dojo: A Differentiable Simulator for Robotics - Taylor et. al