A Mathematical Introduction to Robotic Manipulation 輪講 第五回.pdf
- 1. 2021-09-10 ZHANG QI Section 5 Multifingered hand kinematics
- 2. 02 Grasp Statics CONTENTS 03 Force closure 01 Introduction to grasping
- 4. Introduction to grasping Traditional robot manipulator Large arm + Simple gripper Drawbacks: 1. Small range movement is not effective. 2. For a given gripper, only a small class of objects can be grasped. Example 1 Example 2 Robot writing: Need to move whole arm Difficult to grasp Multifingered hand
- 6. Introduction to grasping Multifingered hand Advantages: 1. Can grasp a large class of objects. 2. Solve the fine motion problem. Disadvantages: 1. Must study the kinematics and dynamics of mechanical systems with contact constraints. 2. freedom increase the difficulty of planning.
- 7. Properties of grasping The ability to resist external forces: Given a wrench applied to an object, we wish to apply contact forces which generate an opposing wrench. The ability to dextrously manipulate the object: Move the object in a way compatible with the desired task
- 9. Grasp Statics Contact models: Frictionless point contact Point contact with friction Friction cone area: Soft-finger contact Friction cone:
- 10. Grasp Statics
- 11. 2.2 The Grasp map :wrench transformation matrix: maps contact wrenches to object wrenches = 𝐺𝑖𝑓𝑐𝑖 :force exerted by a single contact can be written in object coordinates
- 12. 2.2 The Grasp map Total wrench: Grasp map = 𝐺𝑓𝑐 Definition 5.1. Representation of a grasp
- 13. 03 Force closure
- 14. 3 Grasping system Enveloping grasp Fingertip grasp Graspless manipulation
- 15. 3 Force closure Fig. 1. Examples of force closure grasps in 2D and 3D.
- 16. 3 Force closure Definition: If a grasp can resist any applied wrench, we say that such a grasp is force-closure. Key feature: Existence of internal forces
- 17. 3 Force closure——Force-Direction Closure Definition of Internal forces: Existence of a strictly internal force is a necessary condition for a grasp to be force-closure. Force closure Not Force closure A set of planar wrenches W can generate force in any direction if and only if there exists a three tuple of wrenches (W1 , W2, W3) whose respective force directions f1, f2, f3 satisfy: 1. Two of the three directions f1, f2, f3 are independent. 2. A strictly positive combination of the three directions is zero: αf1 + βf2 + γf3 = 0.
- 18. 3 Force closure——Force-Direction Closure A set of planar wrenches W can generate force in any direction if and only if there exists a three tuple of wrenches (W1 , W2, W3) whose respective force directions f1, f2, f3 satisfy: 1. Two of the three directions f1, f2, f3 are independent. 2. A strictly positive combination of the three directions is zero: αf1 + βf2 + γf3 = 0.
- 19. 3 Force closure——Finding Force-Closure Grasps Two Opposing Fingers: COROLLARY 3 Two point contacts with friction at P and Q form a planar force-closure grasp if and only if the segment PQ, or QP, points strictly out of and into the two friction cones respectively.at P and Q
- 20. 3 Force closure——Finding Force-Closure Grasps Force-closure grasps with three hard-finger contacts.
- 21. 3 Convexity conditions for force-closure grasps For a grasp consists only of frictionless point contacts, the grasp map is: The following statements are equivalent: Convexity theory
- 22. 3 Form closure 2D 3D At least 4 frictionless point contact At least 7 frictionless point contact
- 23. 3 Contact with friction to judge force-closure Solve the equation below: Problem: FC is non-linear Simplify FC 𝑒1 𝑒2 𝑒3 𝑣𝑠 Vector of sth edge Contact force: where
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