Customized Effectors for Stable Robotic Grasping

Overview

We shall introduce three types of effectors (Fig. 1), that is, robotic hands, which can grasp every object modeled as a polyhedron, in a stable manner. The effectors simply have a planar, cylindrical, or spherical surface for contacting objects; in fact, a wider range of shapes can be used (this result will be published in the near future).

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Fig. 1: Effectors with a planar, a cylindrical, and a spherical surface, respectively.

Immobilizing Objects

The effectors can immobilize every object modeled as a polyhedron: an immobilized object can neither translate nor rotate. Fig. 2 shows three types of immobilizing grasps with at most three such effectors; the collection of the grasps is complete in the sense that every polyhedron can be immobilized by at least one of the grasps. For more details, see our paper.

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Fig. 2: Three types of immobilizing grasps that can immobilize all polyhedral objects, with the three types of effector surfaces (planar, cylindrical, or spherical).

Caging Objects

The effectors can cage every object modeled as a polyhedron: a caged object cannot escape from the grip of the effectors. Fig. 3 shows three types of cages with two such effectors; see how they are related to the immobilizing grasps in Fig. 2.

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Fig. 3: Three types of cages. Each cage is formed by a pair of the effectors.

In the cages of Fig. 3, the effectors are contacting the objects; however, the effectors do not have to make contacts. Suppose that the two effectors, in each panel of Fig. 3, are allowed to move in such a way that they relatively translate along the axis shown in each panel. Then the upper bound of the distance between the two effectors that does not break the cage can be obtained in an analytical (Fig. 4) or empirical (Fig. 5) manner.

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Fig. 4: (a) For the second type of the cages, shown in the middle panel of Fig. 3, consider a right circular cone that can be inscribed in the pyramid. (b) If δ<h and δ+d<a, then the cone (and thus the original object) is caged by the two effectors.

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Fig. 5: (a) For the third type of the cages, shown in the right panel of Fig. 3, consider a smaller tetrahedron that can be inscribed in the original tetrahedron. (b) When the distance between the two cylindrical effectors was 0.35m, an RRT-based motion planning algorithm failed to find a path for the tetrahedron to escape from the grip of the effectors. The object is thus caged (up to the completeness of the motion planning algorithm) by the effectors 0.35m apart.

Fig 4, 5 suggest that we can quantify the capability of an effector pair in terms of caging objects in a standardized manner, which can also be thought of as a grasp quality measure.

Stable Grasping

The effectors were used as the modular end-effectors of the manipulator show‌n in Fig. 6. The manipulator grasps an object by executing a two-stage algorithm: preshaping (caging the object) followed by squeezing (decreasing the distance between the end-effectors). Click here for a video. The distance between the end-effectors can be thought of as a Lyapunov function. We thus physically guarantee Lyapunov stability in grasping by the physical contour of the effectors.

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Fig. 6: Whole-arm grasping by a modular manipulator.

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