Jane Li. Assistant Professor Mechanical Engineering Department, Robotic Engineering Program Worcester Polytechnic Institute

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1 Jane Li Assistant Professor Mechanical Engineering Department, Robotic Engineering Program Worcester Polytechnic Institute

2 (4 pts) Derive Dynamic equations and state space representation for the system. (6 pts) Explain why a discrete spring may go unstable, and how to stabilize it. RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 2

3 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 3

4 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 4

5 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 5

6 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 6

7 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 7

8 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 8

9 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 9

10 Due to discretization Real contact force Moving into wall Moving out of wall RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

11 From the perspective of energy conservation Contact is stable when there is positive energy flow from human to wall Moving in: Moving out: RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

12 Energy applied to the wall when When moving in When moving out RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

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14 Virtual Wall RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

15 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

16 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

17 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

18 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

19 From the perspective of energy conservation RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

20 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

21 T = 0.05 sec Be = 50 Ns/m RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

22 Remote RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

23 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

24 T = 0.02 sec Be = 50 Ns/m Td = 1 time step RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

25 T = 0.02 sec Be = 50 Ns/m Td = 2 time steps RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

26 Remote RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

27 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

28 T = 0.02 sec Be = 50 Ns/m Td = 2 time steps Kvc = 20; Bvc = 0.4; RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

29 Stability controller Virtual contact Object dynamics Remote RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

30 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

31 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

32 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

33 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

34 Can you feel any force feedback for direct user contact? RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

35 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

36 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

37 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

38 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

39 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

40 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

41 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

42 Simulate the distributed control architecture for peer-to-peer networked haptic cooperation in Simulink Haptic device: mh = 10; bh = 25; Virtual object: m = 40; b = 25; Contact: Kvc = 2000; Bvc = 3; Virtual coupling for object: Kt = 2000; Bt = 300; Find a set of K_RDP and B_RDP such that the system is stable without delay Increase the delay until the system is unstable RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

43 Stability of a virtual wall Colgate, J. Edward, et al. "Implementation of stiff virtual walls in force-reflecting interfaces." Virtual Reality Annual International Symposium, 1993., 1993 IEEE. IEEE, 1993 Matlab Simulink S-function matlab-s-functions.html RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

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45 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

46 Reference: e_pdf/discretization.pdf A quick answer RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

47 Homogeneous solution Forced (particular) solution? RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

48 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

49 Compute A s eigenvalues and eigenvectors RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

50 When does this system go unstable? RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

51 A linear discrete-time system is asymptotically stable if and only if All eigenvalues have magnitude smaller than one RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

52 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

53 RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

54 Time domain S-transform Z-transform RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

55 Chapter 1-2 Send feedback in project group meeting Address the comments in your official proposal Chapter 3 Methodology Chapter 4 Preliminary result CAD design (printed out), algorithm simulation, implementation RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/

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Jane Li. Assistant Professor Mechanical Engineering Department, Robotic Engineering Program Worcester Polytechnic Institute

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