Planning robot grasping motions in the presence of uncertainty

1 I . Introduction 2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 I1 . Task Mechanics and Notation 9 Friction Cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 I11 . Pushing with One Plane 14 Where Will the Plane Touch First? . . . . . . . . . . . . . . . . . . . 16 How Will the Polygon Rotate? . . . . . . . . . . . . . . . . . . . . . 17 Summary . One-Plane Pushing . . . . . . . . . . . . . . . . . . . . 26 IV . Squeezing with Two Planes 28 Squeezing Notation m d the Squeezing Space . . . . . . . . . . . . . . . 30 Where Can the Squeezing Planes Contact the Polygon? . . . . . . . . . . 31 . . . . . . . . . . . . . . 34 What Polygon Orientations Wedge in an Undesirable Configuration? . . . . 38 Combining Seek Lines and Avoidance Regions . . . . . . . . . . . . . . 41 How Can We Include Pushing Information? . . . . . . . . . . . . . . . 43 Objective A . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Objective B . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Objective C . . . . . . . . . . . . . . . . . . . . . . . . . . 47 . . . . . . . . . . . . . . . . . . . 48 Which Contact Pairs Provide a Stable Grasp? Summary Two-Plane Squeezing V . When Simple Squeezing Faile 50 The Offset-Grasp . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 The Push-Grasp . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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