Jane Li

Assistant Professor

Mechanical Engineering Department, Robotic Engineering Program

Worcester Polytechnic Institute

• (2 pts) How to ensure games for rehabilitation can be played by a wide range of stroke patients?

• (4 pts) Name one assistive strategy which are not found in the multi-joint exoskeletons

• (4 pts) Why is it helpful for LL exoskeleton to provide knee joint stability reinforcement? And how to provide it?

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 2

• How to make games playable for a broad range of stroke patients?

• Assume no use of hands

• Simple games should support multiple methods of user input

• Calibrate to the patient’s motion range

• Direct and natural mappings are necessary

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 3

• Devices for hip, knee and ankle

• Fundamentally different joint functions

• Assistive strategies unique to single-joint device

• Muscle stiffness control, proportional EMG control

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 4

• Gravity compensation

• Feedforward movement assistance during swing

• Knee joint stability reinforcement during stance

•

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 5

• Prepare for understanding the stability control in teleoperation and haptics

• Dynamic system and feedback control

• Stability of continuous and discrete systems

• This is a vey brief introduction

• ES 3011. CONTROL ENGINEERING I – undergrad

• RBE 502. ROBOT CONTROL – grad

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 6

• Feedback Systems: An Introduction for Scientists and Engineers, 2nd Edition, by KJ Astrom and R. M. Murray

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 7

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 10

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 11

• Causes for unstable systems?

• Determine whether a system is stable or not?

• Design a stability controller?

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 12

• Dynamic system

• A system whose behavior changes over time, often in response to external stimulation or forcing

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 14

Open-loop Closed-loop

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 15

• Feedback allows a system to be

• Resilient to external disturbances

• Insensitive to variations of internal elements

• Feedback may

• Create dynamic instabilities (oscillations or “runaway”)

• Introduce sensor noise into the system

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 16

• In engineering context

• The use of algorithms and feedback to produce desired system behavior

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 17

• Cruise control of vehicle

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 18

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 19

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 20

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 21

Past FuturePresent

• How to model this system?

• Time Domain

• ODE

• State space

• Frequency Domain

• Laplace transform

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 22

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 23

ODE – How to solve?

• Let be a solution,

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 24

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 25

• Two distinct real roots:

• General solution

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 26

• Two complex conjugate roots

• Euler formula

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 27

• General solution

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 28

• Repeated real root

• General solution

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 29

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 30

Solutions have negative real parts

• Let be a solution with initial condition

• A solution is stable if other solutions that start near stay close to

• A solution is asymptotically stable if all the nearby solutions converge to this stable solution for large time

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 31

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 32

Solution format?

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 33

Over

Under

Critical

All asymptotically stable

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 34

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 35

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 36

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 37

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 38

• Lyapunov function

• An energy-like function

• Nonnegative function

• Always decreases along trajectories of the system dynamics

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 39

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 40

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 41

dynamics matrix Control matrix

sensor matrix Direct term

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 42

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 43

Stability Criterion?

• Any linear system? Choose a new coordinate system

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 44

Stability Criterion = A’s eigenvalues have negative real parts

• Stability is a property of system dynamics

• Instability of a continuous system

• Due to the introduction of feedback

• How to determine the stability of a dynamic system?

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 45

• Shared virtual object

• PD controller for position coherency

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 46

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 47

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 48

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 49

• For the above systems

• Derive dynamic equations

• Derive state space representation

• m = 1, b=0.4, K=5000 N/m, choose a set of b(s) for stability and instability

• No network delay (Td = 0)

10/2/2017RBE 595 – Synergy of Human and Robotic Systems – Instructor: Jane Li, Mechanical Engineering Department & Robotic Engineering Program - WPI 50