Dojo:

A differentiable physics engine for robotics

Taylor Howell and Simon Le Cleac'h

Dojo prioritizes

physical accuracy

and

differentiability

what is Dojo and what can it do?

doesn't

MuJoCo/Drake/Bullet/Brax

already do that?

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

popular simulators

https://leggedrobotics.github.io/SimBenchmark/

https://github.com/dojo-sim/Dojo.jl

  • send us your Github username to be added to Dojo organization
  • star the repository (please!)
  • maximal-coordinates representation
  • variational integrator
  • higher-fidelity contact model
  • custom interior-point solver
  • smooth gradients

Dojo

maximal-coordinates representation

z^{(i)} = (p^{(i)}, v^{(i)}, q^{(i)}, \omega^{(i)})
Linear-Time Variational Integrators in Maximal Coordinates. J. Brudigam and Z. Manchester.
Linear-Time Contact and Friction Dynamics in Maximal Coordinates using Variational Integrators. 
J. Brudigam and Z. Manchester.
Linear-Quadratic Optimal Control in Maximal Coordinates. J. Brudigam and Z. Manchester.

Altas' sparsity pattern

variational integrator

Newton:

F = ma
m(p_+ -2p +p_-)/h - hmg = 0
Discrete mechanics and variational integrators. J. E. Marsden and M. West.

variational integrator

Euler:

J\dot{\omega} + \omega \times (I \omega) = \tau

energy and momentum conservation

Dzhanibekov effect

astronaut

Simulation Tools for Model-Based Robotics: Comparison of Bullet, Havok, MuJoCo, ODE and PhysX. 
T. Erez, Y. Tassa, and E. Todorov.

energy and momentum conservation

contact model

impact

\gamma \geq 0 \quad \quad \phi(z) \geq 0 \\ \gamma \circ \phi(z) = 0
An Implicit Time-Stepping Scheme for Rigid Body Dynamics with Inelastic Collisions and Coloumb Friction. D. E. Stewart and J. C. Trinkle.

impact

Dojo

MuJoCo

contact model

friction

On unilateral constraints, friction and plasticity. J. J. Moreau.

friction cones

approximation

exact

friction cones

Subtitle

interior-point solver

gradients

gradients

gradients

implicit-function theorem

Lezioni di analisi infinitesimale. U. Dini.

trajectory optimization

Dojo: success

MuJoCo: success

Dojo: success

MuJoCo: failure

examples

trajectory optimization

optimized with iterative LQR

reinforcement learning

Subtitle

augmented random search to train static linear policies

reinforcement learning

augmented random search v. augmented gradient search

system identification

ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representations. 
S. Pfrommer, M. Halm, and M. Posa.

system identification

learning via quasi-Newton method

geometry

friction coefficient

ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representations. 
S. Pfrommer, M. Halm, and M. Posa.

system identification

Dojo gradient

system identification

real-to-sim

project ideas

  • space-debris collection
  • adaptive time-stepping
  • GPU/ADMM simulation
  • contact-implicit MPC
  • Dojo + NeRF
  • meta-meta learning
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