1. M.S. Thesis Presentation
MIDDLE EAST TECHNICAL UNIVERSITY
Aerospace Engineering Department
M.S. Thesis Presentation on
Steering of Redundant Robotic Manipulators and Spacecraft Integrated Power and Attitude Control-Control Moment Gyroscopes
Presentation By : Alkan Altay
Thesis Supervisor : Assoc. Prof. Dr. Ozan Tekinalp

2. Presentation Outline Redundant Actuator Systems
IPAC-CMG Systems
Robotic Manipulators
Mechanical Analogy
Steering of Redundant Actuators
Inverse Kinematics Problem & Solutions
Blended Inverse Steering Logic
Thesis Work and Results
Robotic Manipulator Simulations
IPAC-CMG Cluster & IPACS Simulations
Conclusion & Future Work
2/34

3. Integrated Power and Attitude Control System (IPACS)
A Variable Speed CMG That Stores Energy
IPAC – CMG Cluster
IPACS
3/34

4. Due to spin acceleration
Integrated Power and Attitude Control - Control Moment Gyroscope (IPAC-CMG)
A CMG variant, whose flywheel spin rate is altered by a motor/generator
Due to spin acceleration
Due to gimbal velocity
4/34

5. IPAC-CMG Cluster Single IPAC-CMG, single direction
At least 3 IPAC-CMGs for 3-axis attitude control
PYRAMID CONFIGURATION
1 redundancy
Nearly spherical momentum envelope with β= deg,
5/34

6. Robotic Manipulators
An actuator system composed of joints and series of segments
Tasked to travel its end-effector on a certain trajectory
Redundancy Applied To Increase Motion Capability
Mechanically analog to CMG cluster
6/34

7. The Mechanical Analogy
Total Ang. Mom.
Position
IPAC-CMG Momentum
Link Length
Torque
End Effector Velocity
Steering Problem
7/34

8. Inverse Kinematics Calculations  Steering Laws
Steer the actuator through the desired path
Calculate the angular speed of each actuator
Invert a rectangular matrix ?
What if singular ?
Steering Laws For Redundant Systems
Minimum 2-Norm Solution
Singularity Avodiance Steering Logic
Singularity Robust Inverses ?
8/34

9. Moore Penrose Pseudo Inverse (Minimum 2-Norm Solution)
Minimum normed vector; the solution that requires minimum energy
Singularity is a problem
Most steering laws are variants of this pseudo inverse
OTHER SOLUTIONS :
Singularity Avoidance Steering Logic
Singularity Robust Inverse, Damped Least Squares Method
Extended Jacobian Method, Normal Form Approach, Modified Jacobian Method
9/34

10. The proper desired quantity is injected through this term
Blended Inverse
Satisfy two objectives; realize the desired path in desired configuration
PROBLEM
SOLUTION
and Q and R are symmetric positive definite weighting matrices
where,
The proper desired quantity is injected through this term
Pre-planned
Steering
10/34

11. Robotic Manipulator Simulations
3-link planar robot manipulator dynamics :
Direct Kinematical Relationship
Steering Logic
11/34

12. Robotic Manipulator Simulations (Test Case I)
AIMS :
Repeatability performance of B-inverse on a routinely followed closed path
Tracking performance of B-inverse, when supplied with false
12/34

13. Robotic Manipulator Simulations (Test Case I –MP-inverse Results)
13/34

14. Robotic Manipulator Simulations (Test Case I –B-inverse Results)
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15. Robotic Manipulator Simulations (Test Case II)
AIM :
The singularity avoidance performance of B-inverse
MP-inverse drives the system close to an escapable singularity at [ x1 , x2 ] = [-2 , 0 ]
Escapable Singularity
15/34

16. Robotic Manipulator Simulations (Test Case II –MP-inverse Results)
16/34

17. Robotic Manipulator Simulations (Test Case II –B-inverse Results)
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18. Robotic Manipulator Simulations (Test Case II – Results)
Escapable Singularity Simulations
Steering with MP-inverse
Steering with B-inverse
18/34

19. Robotic Manipulator Simulations (Test Case III)
AIM :
Singularity transition performance of B-inverse
The path passes an inescapable singularity at [ x1 , x2 ] = [ 0 , 0 ]
Inescapable Singularity
19/34

20. Robotic Manipulator Simulations (Test Case III –MP-inverse Results)
20/34

21. Robotic Manipulator Simulations (Test Case III –B-inverse Results)
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22. Robotic Manipulator Simulations (Test Case III – Results)
Inescapable Singularity Simulations
Steering with B-inverse
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23. IPAC-CMG Cluster Simulations
Rate Command to each IPAC-CMG
Torque and Power Commands
Realized Torque and Power
STEERING ALGORITHMS
IPAC-CMG Cluster
AIMS :
Investigate the performance of IPAC-CMG cluster
Investigate the performance of B-inverse
23/34

24. IPAC-CMG Cluster Simulations
Two different simulation models are employed to steer IPAC-CMG cluster
Generic simulation model
( used in MP-inverse simulations )
B-inverse simulation model
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25. IPAC-CMG Cluster Simulations
Torque Command
Power Command
Min Ang.Mom.of each IPAC-CMG [Nms]
7.7
IPAC-CMG Flywh. Spin Interval [kRPM]
15 – 60
Initial Flywheel Spin Rates (kRPM)
[40, 40, 40, 40]
Initial Gimbal Angles (deg)
[0, 0, 0, 0]
25/34

26. IPAC-CMG Cluster Simulations – MP-inverse Results
Torque & Angular Momentum Realized
Energy and Power Profiles
Gimbal Angle History
Flywheel Spin Rates
Singularity Measure
26/34

27. IPAC-CMG Cluster Simulations – B-inverse Results
Torque Error & Ang. Mom. Profile
Energy and Power Profiles
Singularity Measure
Gimbal Angle History
Flywheel Spin Rates
27/34

28. IPACS Simulations 28/34 Spacecraft Inertias [ kgm2 ] [15, 15, 10]
Initial Orientation of S/C [deg]
[0, 0, 0]
IPAC-CMG Flywh. Spin Interval [kRPM]
Initial Flywheel Spin Rates [kRPM]
[39, 40, 41, 42]
Initial Gimbal Angles [deg]
[-75, 0, 75, 0]
28/34

29. Spacecraft IPACS Simulation Model
IPACS Simulations
Spacecraft IPACS Simulation Model
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30. IPACS Simulations
Attitude Command
Power Command
30/34

31. IPACS Simulations – MP-inverse Results
Torque and Angular Momentum History
Energy and Power Profile
Attitude Profile
Gimbal Angles
IPAC-CMG Flywheel Spin Rates
Singularity Measure
31/34

32. IPACS Simulations – B-inverse Results
Torque Error and Ang.Mom. Profile
Gimbal Angles
Attitude Profile
IPAC-CMG Flywheel Spin Rates
Energy and Power Profiles
Singularity Measure
32/34

33. Conclusion B-inverse is employed in robotic manipulators :
Singularity Avoidance
Singularity Transition
Repeatability
IPACS is discussed :
Comparison to Current Technologies
Algorithm Construction
Theoretical Performance
B-inverse is employed in IPACS :
In IPAC-CMG Clusters & S/C IPACS
Singularity Avoidance & Multi Steering
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34. Future Work B-inverse in highly redundant robotic mechanisms
Detail Design of IPAC-CMG
Capabilities of B-inverse
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35. Singularity in Robotic Manipulators and CMG Systems
Physically, no end effector velocity (torque) can be produced in a certain direction
Controllability in that direction is lost.
Mathematically, Jacobian Matrix loses its rank.Thus;
det(J)= 0 ( or det(JJT)=0 )
Singularity Measure m=det(JJT)
J-1 ( or (JJT)-1 ) becomes undefined
#/30

36. Singularity Avoidance Steering Logic
Particular Solution
Homogeneous Solution
Addition of null motion, n, in the proper amount (determined by γ)
12/40

37. Singularity Robust Solutions
Singularity Robust Inverse :
k =
for m > mcr
k0(1-m/m0)2 for m < mcr
Disturbs the pseudo solution near singularities to artificially generate a well –conditioned matrix
Increases the tracking error, causes sharp velocity changes around singularities
Another example may be the Damped Least Squares Method
13/40

38. Singularity Robust Solutions
New generation of solutions, offering accurate and smooth singularity transitions, not mature yet
Extended Jacobian Method
Normal Form Approach
Modified Jacobian Method
Extends the jacobian matrix with additional functions, creating a well –conditioned one, belonging to a “virtual” system
square matrix
singularity
Proposes to transform the kinematics to its quadratic normal form, employing equivalence transformation, around singularities
Proposes to replace the linearly dependent row of Jacobian Matrix, to remove the singularity, with a derivative of a configuration dependent function 
14/40

39. Thesis Objectives Blended Inverse on Redundant Robotic Manipulators
Spacecraft Energy Storage & Attitude Control
IPAC-CMG based IPACS
Blended Inverse on IPAC-CMG clusters
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40. Spacecraft Energy Storage and Attitude Control
Rotating flywheels for smooth attitude control
Spacecraft store & drain energy periodically.
Electrochemical Batteries
vs.
Flywheel Energy Storage Systems (FES)
Integrate energy storage & attitude control
4/40

41. Blended Inverse
How to select ?
Pre-planned Steering
11/40