Jane Li Assistant Professor Mechanical Engineering Department, Robotic Engineering Program Worcester Polytechnic Institute
(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
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 3
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 4
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 5
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 6
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 7
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 8
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 9
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 10/11/2017 10
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 10/11/2017 11
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 10/11/2017 12
Virtual Wall RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 14
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 15
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 16
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 17
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 18
From the perspective of energy conservation RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 19
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 20
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 10/11/2017 21
Remote RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 22
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 23
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 10/11/2017 24
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 10/11/2017 25
Remote RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 26
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 27
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 10/11/2017 28
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 10/11/2017 29
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 30
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 31
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 32
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 33
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 10/11/2017 34
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 35
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 36
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 37
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 38
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 39
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 40
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 41
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 10/11/2017 42
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 https://www.mathworks.com/help/simulink/sfg/writing-level-2- matlab-s-functions.html RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 43
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 45
Reference: http://users.wpi.edu/~zli11/teaching/rbe595_2017/lectureslid 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 10/11/2017 46
Homogeneous solution Forced (particular) solution? RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 47
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 48
Compute A s eigenvalues and eigenvectors RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 49
When does this system go unstable? RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 50
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 10/11/2017 51
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 52
RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 53
Time domain S-transform Z-transform RBE 595 Synergy of Human and Robotic Systems Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10/11/2017 54
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 10/11/2017 55