Toward An Analytic Theory of Intrinsic Robustness for Dexterous Grasping

Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp robustness refers to the ability to resist external disturbances after grasping an object. In contrast, this work studies robustness to intrinsic sources of uncertainty like object pose or geometry affecting grasp planning before execution. To do so, we develop a novel analytic theory of grasping that reasons about this intrinsic robustness by characterizing the effect of friction cone uncertainty on a grasp's force closure status. As a result, we show the Ferrari-Canny metric -- which measures the size of external disturbances a grasp can reject -- bounds the friction cone uncertainty a grasp can tolerate, and thus also measures intrinsic robustness. In tandem, we show that the recently proposed min-weight metric lower bounds the Ferrari-Canny metric, justifying it as a computationally-efficient, uncertainty-aware alternative. We validate this theory on hardware experiments versus a competitive baseline and demonstrate superior performance. Finally, we use our theory to develop an analytic notion of probabilistic force closure, which we show in simulation generates grasps that can incorporate uncertainty distributions over an object's geometry.

PONG: Probabilistic Object Normals for Grasping via Analytic Bounds on Force Closure Probability

Classical approaches to grasp planning are deterministic, requiring perfect knowledge of an object's pose and geometry. In response, data-driven approaches have emerged that plan grasps entirely from sensory data. While these data-driven methods have excelled in generating parallel-jaw and power grasps, their application to precision grasps (those using the fingertips of a dexterous hand, e.g, for tool use) remains limited. Precision grasping poses a unique challenge due to its sensitivity to object geometry, which allows small uncertainties in the object's shape and pose to cause an otherwise robust grasp to fail. In response to these challenges, we introduce Probabilistic Object Normals for Grasping (PONG), a novel, analytic approach for calculating a conservative estimate of force closure probability in the case when contact locations are known but surface normals are uncertain. We then present a practical application where we use PONG as a grasp metric for generating robust grasps both in simulation and real-world hardware experiments. Our results demonstrate that maximizing PONG efficiently produces robust grasps, even for challenging object geometries, and that it can serve as a well-calibrated, uncertainty-aware metric of grasp quality.

FRoGGeR: Fast Robust Grasp Generation via the Min-Weight Metric

Many approaches to grasp synthesis optimize analytic quality metrics that measure grasp robustness based on finger placements and local surface geometry. However, generating feasible dexterous grasps by optimizing these metrics is slow, often taking minutes. To address this issue, this paper presents FRoGGeR: a method that quickly generates robust precision grasps using the min-weight metric, a novel, almost-everywhere differentiable approximation of the classical epsilon grasp metric. The min-weight metric is simple and interpretable, provides a reasonable measure of grasp robustness, and admits numerically efficient gradients for smooth optimization. We leverage these properties to rapidly synthesize collision-free robust grasps - typically in less than a second. FRoGGeR can refine the candidate grasps generated by other methods (heuristic, data-driven, etc.) and is compatible with many object representations (SDFs, meshes, etc.). We study FRoGGeR's performance on over 40 objects drawn from the YCB dataset, outperforming a competitive baseline in computation time, feasibility rate of grasp synthesis, and picking success in simulation. We conclude that FRoGGeR is fast: it has a median synthesis time of 0.834s over hundreds of experiments.