FIRMGrasp: A Friction-Informed Risk Margin for Robust Grasp Synthesis

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.