Generalizable Friction Coefficient Estimation via Material Embedding and Proxy Interaction Modeling

Accurately estimating object mass and friction is fundamental to reliable robotic manipulation. While interactive perception is powerful, most approaches rely on specialized hardware like force/torque sensors, limiting scalability. This paper introduces PhyPush, a physics-guided Transformer that estimates an object's mass and friction coefficient using only end-effector velocity from a single push, data readily available on standard robotic arms. By incorporating Newton's second law and the Coulomb friction model through a physics-guided loss, the model improves physical consistency and generalizes to unseen objects and surfaces. Across diverse setups, PhyPush consistently achieves highly accurate estimations in challenging out-of-domain conditions. In simulation, it reduces error by over 10% compared to a baseline with privileged force data, while in real-world experiments, it successfully zero-shot transfers from simulation to outperform a purely data-driven baseline.

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

Classical grasp quality metrics assume one deterministic friction coefficient and therefore cannot assess whether a grasp maintains force closure across plausible friction values. We present FIRMGrasp, a family of grasp quality metrics that incorporates friction uncertainty through Conditional Value-at-Risk (CVaR). At confidence level $β$, we evaluate the force-closure margin at the mean of the adverse friction tail. This evaluation defines the risk-adjusted margin $\varepsilon^{(β)}$, the inscribed-ball radius of the corresponding grasp wrench space. We prove that $\varepsilon^{(β)}$ varies monotonically with $β$, remains differentiable in the grasp parameters, and certifies that any grasp with $\varepsilon^{(β)} > 0$ achieves force closure with probability at least $β$. Across 1,599 LEAP Hand and Allegro Hand grasps, $\varepsilon^{(β)}$ identifies friction-sensitive grasps that receive high nominal Ferrari-Canny scores, and 53% of the nominally force-closed grasps lose closure in the adverse friction tail. The nominal margin ranks a successful grasp above a failed grasp with probabilities of only 0.53 in the shake test and 0.67 in the pick test, whereas $\varepsilon^{(β)}$ achieves 0.63 and 0.78. At an adverse friction coefficient of 0.2, 70% of grasps with positive $\varepsilon^{(β)}$ withstand a simulated lift and lateral pull, compared with 25% of grasps with positive nominal margin and nonpositive $\varepsilon^{(β)}$. We also synthesize grasps with positive $\varepsilon^{(β)}$ for the RealHand L6 and LEAP Hand, both of which retain the object during adverse-friction lifts. In MuJoCo trials with the RealHand L6, 95% of grasps that establish contact and have positive $\varepsilon^{(β)}$ retain the object at the same adverse friction coefficient.