Caging Planar Objects with a Three-Finger One-Parameter Gripper

Thi s puper eztcn,ds the caging theory of R i m o n and Bluke [ill for. orre-parameter two-finger grippers t o orwparame tar three-finger grippers. T h e caging theory describes lroui the f ingers of a robot gripper can be placed uroumd u n object so tha t it cannot escape. A s the fiingers close f r o m such a configuration, the f reedom of the object t o move is gradually restricted, unti l , in the absence of f r ic t ion , it is completely immobilized by the f ingers u t an immobilizing grasp. T h e ex tens ion of the cagirq theory t o three-fingered grippers i s impor tunt because conuex objects cannot be caged by two,finger grippers. T h e computa t ion of the set of caging fo rmat ions requires the identif ication of both the twocmd three-finger frictionless grasps. These grasps correspond to critical points of the opening parameter in the gripper's configuration space. There are two m a i n problems here. Firstly, a method is needed t o compu te the critical po in ts of the opening parameter an the three-finger contact space. Th i s is complicated by the fac t tha t this space m a y have more tha t one connected cofmponent. T h e second problem is how t o associate the immobilizing grasps wi th punctures . In this paper we solve both these problems, presenting e f i c i en t algor i thmic solu,tions.