Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamics

Modern differentiable physics engines often force a trade-off between simulation accuracy, gradient reliability, and computational cost. Tape-based engines (like MJX) require very small timesteps to maintain stability and suffer from memory usage that grows linearly with the number of timesteps. Surrogate models avoid these memory issues but often lose the geometric details necessary for accurate contact and friction modeling. The authors ask: can we build a GPU-accelerated simulator that resolves hard contacts accurately while maintaining O(1) memory per timestep for gradient computation?

Ostrich addresses this by combining a non-smooth Newton solver with the Implicit Function Theorem (IFT). The simulator uses a backward-Euler integrator to resolve hard contacts and friction within each timestep. By applying the IFT to the converged residual of the Newton solver, the authors compute gradients via an adjoint method that reuses the forward Schur complement. This design decouples the gradient memory requirements from the number of internal solver iterations, allowing for stable simulation at much larger timesteps (h ~ 0.1 s) than traditional penalty-based methods.

Ostrich demonstrates significant improvements over existing differentiable simulators like MJX and Newton Semi-Implicit. In a pallet-traversal task, Ostrich maintains sim-to-real accuracy at timesteps up to 50 times larger than those required by MuJoCo. In control-synthesis experiments, Ostrich achieved a 100% success rate, whereas baselines struggled with gradient reliability and convergence. Furthermore, Ostrich scales to 8,192 parallel worlds on a single GPU, sustaining 29 times the optimization throughput of checkpointed MJX baselines. The authors also successfully demonstrated trajectory optimization over complex triangle-mesh terrain, a task that typically forces other engines to either restrict geometry or face severe memory and convergence limits.