Contact-Aware Morphology Optimization Via Physically Consistent Differentiable Simulation

Optimizing robot morphology and behavior remains an open challenge, primarily because hardware parameters affect system and contact dynamics, and naive parametrization can yield physically inconsistent designs and unreliable gradients. We propose a simulation-based co-design approach for gradient-based morphology optimization through intermittent contact by expressing inertial quantities, collision geometry, and contact forces as smooth functions of bounded hardware parameters. This parametrization preserves physical consistency across admissible designs and enables trajectory-level differentiation through contact transitions. The methodology is simulator-agnostic and is instantiated in a JAX-based differentiable simulator to leverage accelerator execution and automatic differentiation. We validate the approach by optimizing a single-leg morphology to reach a target jump height under torque limits. Controlled studies further assess correctness: synthetic system identification recovers ground-truth parameters to numerical precision, cross-engine calibration against MuJoCo reaches MSE below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-5}$</tex-math></inline-formula>, and second-order derivatives match finite differences. Compared to genetic algorithms, gradient-based optimization is substantially faster but more sensitive to initialization, while remaining computationally practical for co-design.