Workspace Optimization - for Autonomous Mobile...

Workspace Optimizationfor Autonomous Mobile Manipulation

May 25, 2015

Giacomo Marani

West Virginia Robotic Technology CenterWest Virginia University

USA

26

WorkspaceOptimization

Giacomo Marani

1Introduction

Autonomous MobileManipulation

Kinematic control

Resolved motion ratecontrol

Task priority

Task Reconstruction

TR applications

Workspaceoptimization

Implementation

Experimental results withSAUVIM

Conclusions

Acnowledgements

West Virginia RoboticTechnology Center

Introduction

Many tasks related to robotic space intervention, such assatellite servicing, require the ability of acting in an unstructuredenvironment through autonomous mobile manipulation.

When introducing levels of autonomy in robotic intervention,several issues appear repeatedly.

The full cycle of an autonomous intervention is here presentedthrough a case study in underwater robotics, a project calledthe Semi-Autonomous Underwater Vehicle for Intervention Mis-sions1.

1SAUVIM began in 1997 at the University of Hawaii at Manoa, under Prof.Junku Yuh. The project was funded by the Office of Naval Research over a 10year period and administered by Dr. J. Yuh, S.K Choi and G. Marani.

26


Giacomo Marani

Introduction

2Autonomous MobileManipulation

Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements


IntroductionAutonomous Mobile Manipulation

I Issue 1: Target area navigation.One of the most important aspects in autonomy is theenvironment perception. The best solution is determinedby several factors, including task and environment.

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



I Issue 2: Vehicle positioning. An autonomous servicermust be capable of performing workspace optimization, cor-recting the vehicle position for maximizing the manipulabil-ity of the arm during its operations.

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



I Issue 3: Arm control system. Cope with many issuescommonly seen in robotics (kinematic singularities, colli-sions, joint limit, motor saturation, etc).

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



I An autonomous robotic system must be able to intelligentlycope all the above situations to successfully complete thegiven mission, whenever possible.

26


Giacomo Marani

Introduction


6Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements


Kinematic control

Autonomous manipulation system:

I performs intervention tasks with limited human supervision;

I the human operator should be able to control the manipu-lation process with only high-level commands;

I the robot determines what joint trajectories need to be fol-lowed for successfully achieving goals.

26


Giacomo Marani

Introduction


Kinematic control

7Resolved motion ratecontrol

Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements


Kinematic controlResolved motion rate control

Resolved Motion Rate Control (RMRC) is a local method forsolving inverse kinematics problems. Given a generic task r =

f (q), it uses the Jacobian J of the forward kinematics to de-scribe a change in the end-effector position:

δr =∂f∂q

δq = J (q) δq (1)

In RMRC we compute δq for a given δr and q by solving theabove linear system. The solution, in the general form, is2:

δq = J+ (q) δr +(In − J+ (q)J (q)

)y (2)

where J+(q) is the Moore-Penrose pseudo-inverse of J(q), y

is an arbitrary vector and In indicates an identity matrix.

2Y. Nakamura: Advanced Robotics: Redundancy and Optimization, AddisonWesley, 1991

26


Giacomo Marani

Introduction


Kinematic control


8Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements


Kinematic controlTask priority

Nakamura introduced the inverse kinematics taking into accountof the priority of the subtasks:

Task 1(Priority 1)

r1 = f1 (q)

Task 2(Priority 2)

r2 = f2 (q)

Inverse kinematics with priority

δq = J1+δr1 + J+

2

(δr2 − J2J1

+δr1), J2 = J2

(In − J1

+J1)

26


Giacomo Marani

Introduction


Kinematic control


9Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



Example with:

I Task 1 (higher priority): Cartesian position of the end-effector

I Task 2 (lower priority): orientation of the end-effector

26


Giacomo Marani

Introduction


Kinematic control


10Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



The direct implementation of the task priority in its original form

δq = J1+δr1 + J+

2

(δr2 − J2J1

+δr1)

(3)

presents difficulties due to physical and mathematical singulari-ties:

I Kinematic singularities: loss of rank of J1 and J2.

I Algorithmic singularities: loss of rank of J2 with J1 and J2

of full rank

26


Giacomo Marani

Introduction


Kinematic control


Task priority

11Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements


Kinematic controlTask Reconstruction

To solve the previous problem we use the concept of Task re-construction.The basic idea in task reconstruction is to circumscribe singular-ities by moving, when approaching to them, on a hyper-surfaceswhere the distance index (measure of manipulability ) remainsconstants.

Desired trajectory

Reconstructed trajectory

Singular Configuration0mom =

mom m=

Figure: Conceptual diagram of Task Reconstruction

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



Task reconstruction processI Phase 1: definition of a distance index

In case of singualities avoidance, the "distance from singular-ities" index is given by the measure of manipulability (MOM),introduced by Yoshikawa:

µ (J) =√

det (JJT ). (4)

µ (J) takes a continuous non-negative scalar value and becomesequal to zero only when the Jacobian matrix is not full rank.

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



Task reconstruction process

I Phase 2: application3

δq = J+ (q)TR (J ,m (q) , δr) (5)

where:

TR (J ,m (q) , δr) =(Im − k1nmnm

T ) δr + k2nm

nm =

(∂m(q)∂q J+

)T∥∥∥∂m(q)∂q J+

∥∥∥k1 =

1 − sign (δr · nm)

2km (m,m,m)

k2 = Kr km

(m,

m2,

m2

)(6)

3Marani, G, Yuh, J., Introduction to Autonomous Manipulation, SpringerTracts in Advanced Robotics

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



Task reconstruction process

0m q

m q m

1 m mk r n n

r

pr

mn

Reconstructed

trajectory

Desired

trajectory

Figure: Geometric interpretation of the task reconstruction concept

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



Task reconstruction exampleI Cartesian position has priority over orientation

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



TR advantages:

I Fewer tuning parameters (mainly the distance limit)

I The performance is then simply affected by the choice ofthe lower limit.

I Based on a real-time evaluation of the measure of manip-ulability, this method does not require a preliminary knowl-edge of the singular configurations

I Can be regarded as a dynamic priority-changing algorithm.

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



TR advantages:I Fewer tuning parameters (mainly the distance limit)



I Can be regarded as a dynamic priority-changing algorithm.

26


Giacomo Marani

Introduction


Kinematic control


Task priority


TR applications


Implementation


Conclusions

Acnowledgements



TR advantages:I Fewer tuning parameters (mainly the distance limit)



I Can be regarded as a dynamic priority-changing algorithm4.

4J. Kim, G. Marani, W. K. Chung, J. Yuh: Kinematic Singularity Avoidancefor Autonomous Manipulation in Underwater, The Fifth ISOPE Pacific/AsiaOffshore Mechanics Symposium, Daejeon, Korea, November 17-20, 2002

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

17TR applications


Implementation


Conclusions

Acnowledgements


Kinematic controlTR applications

With a different choice of the distance index, the TR algorithmcan be applied also to:

I collision avoidance

I joint limits avoidance

I workspace optimization

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

18TR applications


Implementation


Conclusions

Acnowledgements



Collision avoidanceI Index: "minimum distance between all objects"

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

19TR applications


Implementation


Conclusions

Acnowledgements



Joint limits avoidance. Index:

P (q)∆=

n∏i=1

Np (qi), Np (qi) = 1 −(

2 (qi − qi,min)

(qi,max − qi,min)− 1

)2

Example with imposed joint limits (0, π/2) to elbow and wrist:

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications

20Workspaceoptimization

Implementation


Conclusions

Acnowledgements


Workspace optimization

The whole vehicle-navigation system is regarded as unique openchain with multi-degrees of freedom joint

I joint 1 is a 6 DOFjoint

I joints 2 through 8 are1 DOF rotational

1� �

3

2

4

5

6,7,8

e� �

0� �

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


21Implementation


Conclusions

Acnowledgements


Workspace optimizationImplementation

Goal:I target optimally positioned within the dexterous arm

workspace.

Implementation:

I TR index: measure of manipulability of the whole chain

I Task r1 (3 DOF): Cartesian position of Link 8 (the end-effector)

I Task r2 (3 DOF): Orientation of Link 8 (the end-effector)

I Task r3 (3 DOF): Position (x and y ) and orientation (aroundz) of the vehicle (hovering condition)5

5In our implementation, the hovering condition is achieved by setting to zerothe time derivative of the third manipulation variable

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation

22Experimental results withSAUVIM

Conclusions

Acnowledgements


Workspace optimizationExperimental results with SAUVIM

ResultI The vehicle position is autonomously changed only when

needed, to increase the manipulability of the arm:

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



0 5 10 15 20 25 30 35 40 45 500.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Time (sec)

mom

(J1)

Measure of manipulability of J1 (linear)

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

Acnowledgements



0 5 10 15 20 25 30 35 40 45 500.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time (sec)

mom

(J2)

Measure of manipulability of J2 (angular)

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


25Conclusions

Acnowledgements


Conclusions

I Robotic systems capable of operating autonomously in un-structured environments will need this type of complete so-lution strategy.

I Many issues appear repeatedly in autonomous robotic ma-nipulation (of all areas):

I target area navigationI vehicle positioningI arm control systems

Giacomo Marani, Junku Yuh:Introduction to Autonomous ManipulationSpringer Tracts in Advanced Robotics

26


Giacomo Marani

Introduction


Kinematic control


Task priority

Task Reconstruction

TR applications


Implementation


Conclusions

26Acnowledgements


ConclusionsAcnowledgements

The research relative to the SAUVIM project was conducted atthe Autonomous Systems Laboratory (University of Hawaii). Itwas sponsored by ONR (N00014-97-1-0961, N00014-00-1-0629,N00014-02-1-0840, N00014-03-1-0969, N00014-04-1-0751).

Special thanks are given to all the people who participate to theSAUVIM development, including Giuseppe Casalino (DIST, Uni-versity of Genoa, Italy), the Dept. of Mechanical Eng., PohangUniversity of Science and Technology, with Prof. Wan KyunChung, and Dr. Aaron Hanai of the university of Hawaii.

Thank you

Workspace Optimization - for Autonomous Mobile...

Documents

Transcript of Workspace Optimization - for Autonomous Mobile...