Mathematics in Caging of Robotics
This work addresses a foundational gap in robotics for researchers, but it is incremental as it builds on prior studies without introducing a new method.
The paper tackles the problem of mathematically defining caging for general geometric objects and robots, showing that caging difficulty is related to combinatorial problems and wire puzzles.
It is a crucial problem in robotics field to cage an object using robots like multifingered hand. However the problem what is the caging for general geometrical objects and robots has not been well-described in mathematics though there were many rigorous studies on the methods how to cage an object by certain robots. In this article, we investigate the caging problem more mathematically and describe the problem in terms of recursion of the simple euclidean moves. Using the description, we show that the caging has the degree of difficulty which is closely related to a combinatorial problem and a wire puzzle. It implies that in order to capture an object by caging, from a practical viewpoint the difficulty plays an important role.