Fast and Reliable Gradients for Deformables Across Frictional Contact Regimes

Abstract

Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional contact remains the "elephant in the room." Current frameworks often avoid contact singularities via non-Markovian position approximations or heuristic gradients. This lack of mathematical consistency distorts gradients, causing optimization stagnation or failure in complex frictional contact and large-deformation scenarios. We introduce our unified fully GPU-accelerated differentiable simulator, which establishes a rigorous theoretical paradigm through: Long-Horizon Consistency: enforcing strict Markovian dynamics on a coupled position-velocity manifold to prevent gradient collapse; Unified Contact Stability: employing a mass-aligned preconditioner and soft Fischer--Burmeister operator for smooth frictional optimization; Robust Material Identification: resolving FEM singularities via a derived "Within-block Commutation" condition. Our experiments demonstrate our solver efficacy in bridging the Sim-to-Real gap, delivering precise, low-noise gradients in contact-rich tasks like dexterous manipulation and cloth folding. By mitigating the gradient instability issues common in conventional approaches, our framework significantly enhances the fidelity of physical system identification and control.

Figures (13)

• Figure 1: Differentiation graph: gradients are obtained by implicitly differentiating the converged system in Equation \ref{['eq:dynamics']} and solving an adjoint linear system.
• Figure 2: The smoothed Fischer-Burmeister function transforms a hard complementarity problem (left, not differentiable at $(0,0)$) to a smoothed one (right), providing a reliable gradient for different branch switching.
• Figure 3: Starting from zero applied force, we optimize a horizontal force to pull the Munchlax toward the target position (violet). The proposed heuristic gradient enables a successful transition from the sticking regime to the sliding (kinetic) friction regime.
• Figure 4: Starting from an initial guess of $E = 1\times 10^{5}$ and $\nu = 0.2$ (left), we perform system identification on a curtain undergoing gravity-induced deformation. Owing to the accuracy and robustness of the proposed gradients, the optimizer is able to simultaneously recover both parameters and converges to values close to the ground truth ($E = 1\times 10^{4}$, $\nu = 0.3$, right).
• Figure 5: Gradient-based of stiffness (top) and Poisson's ratio (down) in contact-free settings. We recover volumetric stiffness and Poisson’s ratio across linear and nonlinear elastic models, demonstrating that the proposed gradients capture long-range elastic coupling and nonlinear parameter sensitivities.