  This paper addresses the multi-faceted problem of robot grasping, where
multiple criteria may conflict and differ in importance. We introduce a
probabilistic framework, Grasp Ranking and Criteria Evaluation (GRaCE), which
employs hierarchical rule-based logic and a rank-preserving utility function
for grasps based on various criteria such as stability, kinematic constraints,
and goal-oriented functionalities. GRaCE's probabilistic nature means the
framework handles uncertainty in a principled manner, i.e., the method is able
to leverage the probability that a given criteria is satisfied. Additionally,
we propose GRaCE-OPT, a hybrid optimization strategy that combines
gradient-based and gradient-free methods to effectively navigate the complex,
non-convex utility function. Experimental results in both simulated and
real-world scenarios show that GRaCE requires fewer samples to achieve
comparable or superior performance relative to existing methods. The modular
architecture of GRaCE allows for easy customization and adaptation to specific
application needs.
