Object caging under imperfect shape knowledge

One of the ultimate challenges in robotics is to manipulate an arbitrary object without knowing its exact shape beforehand. The shape is rather acquired on the spot via using a laser range scanner, structure from multiple views; therefore, maybe only partially observed and corrupted by a certain degree of noise. We propose an algorithm to identify available failsafe strategies capable of preventing an object from escaping from the fingers, i.e. caging, even if its shape is partially and/or inaccurately observed. This algorithm extends the previously proposed one that characterizes all caging sets via a maximal dispersion control but, instead of taking a single polytope P exactly representing the object as input, it takes two polytopes: P⁺ and P^- containing P and contained in P, respectively. The algorithm characterizes all possible formations of fingers that guarantee to cage any polytope P such that P^- ⊆ P ⊆ P⁺ as long as the dispersion (i.e. looseness) of the fingers´ formation is kept under a critical value called the maximal dispersion. This allows us to gracefully handle uncertainty of acquired shapes and quickly identify robust solutions in case of simplified shapes.