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Grasping Objects with Environmentally Induced Position Uncertainty

Figure 1

Graphical illustration of grasp analysis with directional position uncertainty.

(A) The critical aspect of grasping an object with position uncertainty is the control of the contact surfaces of the index finger and thumb (rectangular patches). These surfaces must be moved along paths that will make appropriate contact with the object at any of its possible locations (gray transparent cylinders). Appropriate contact involves the concept of force-closure (see materials and methods). Upper inset: Force-closure grasping representation. Assume that a reach trajectory results in two contact points of the index finger (A) and the thumb (B) on the surface of the cylinder c_i. This trajectory produces force-closure grasping because the line segment (AB) is located between the two friction cones defined by the contact points A and B. Based on the Coulomb's law, two contact points produce force-closure when the component of the contact forces at these points in the direction of the surface normals () exceeds the coefficient of friction μ times the tangential components. The friction cones are determined by the vector and , where (.) corresponds to subscript th and f for the thumb and the index finger, respectively. Note that u refers to the surface tangents. Lower inset: Graphical representation of the fingers' contact surface approach for grasping a cylindrical object with directional position uncertainty. The thumb and the index finger contact surfaces are displayed as line segments with local position r and normals u. For visualization reasons, we present only the characteristics of the index finger, whereas the characteristics of the thumb is similar to the index finger, but with the subscript th. The gray circles describe the possible cylinder locations based on the object's position distribution, which is illustrated as ellipse with center x and major and minor axes , respectively. Given a possible cylinder location c_i, the reach trajectory will produce force-closure if the line segment defined by contact points of the thumb and the index finger surface on the cylinder surface, is between the two friction cones at the two contact points. Note that (w, d) corresponds to the local contact coordinates of the index finger (with subscript f) and thumb (with subscript th) (see materials and methods section). (B) Effects of approach direction in the probability of producing force-closure for ideal (dashed lines) and noisy (solid lines) approaches for 0 deg (gray) and 45 deg (black) covariance orientations. Noisy approaches were generated by adding noise to both approach direction (variance = 4.5 deg²) and fingers orientation (variance = 2.5 deg²).

doi: https://doi.org/10.1371/journal.pcbi.1000538.g001