Abstract. Reconfigurable manipulators can be very advantageous in dexterity-demanding tasks such as space operations. This paper presents the modeling, control and simulation of a robotic reconfigurable manipulator. The manipulator benefits from passive cylindrical joint design for its links which allows it to change the link parameters. The robot enters the reconfiguration phase in two steps; first, it forms a closed kinematic chain or in other words docks its end-effector to a fixed point in order to increase the constrained DOFs. Second, it releases the built-in locks of its cylindrical joints to enable the reconfiguration of the links. Then, the reconfiguration process is performed by using the proper control method. After achieving the desired configuration, the cylindrical joints are locked again, the end-effector is released and robot enters the operation mode. This paper only focuses on the reconfiguration process of a 6-DOF manipulator with two lockable passive cylindrical joints. See the paper here: http://link.springer.com/chapter/10.1007/978-3-642-40849-6_11

1. Modeling, Control and Simulation
of a 6-DoF Reconfigurable Space Manipulator
with Lockable Cylindrical Joints
Pooya Merat1, Farhad Aghili2, Chun-Yi Su1,
1 Concordia
University, Montreal, QC, Canada,
2 Canadian Space Agency, St-Hubert, QC, Canada,
{p_merat, cysu}@encs.concordia.ca,
farhad.aghili@asc-csa.gc.ca
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2. Reconfigurable Robots

Benefits of reconfigurable robots
vs. non-reconfigurable robots:



Extra dexterity
Adaptation for different tasks
Modular reconfigurable robots


Such as M-Tran III (Murata, S. et al)
No robust docking mechanism
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Murata, S. et al

3. Reconfigurable Manipulator with Lockable Cylindrical Joints

Lockable Cylindrical links



Normally locked (released only
during reconfiguration)
When released adds 2 extra DoF (one
linear and one rotational) to the
manipulator.
Reconfiguration process
(a,b) Grasping a fixed point by endeffector.
(c,d) Releasing the first cylindrical joint
and reconfiguration of first link while
second link is locked.
(e) Locking the first cylindrical joint and
releasing the second cylindrical joint and
reconfiguration of second link.
(f) Locking the second cylindrical joint
and releasing the end-effector.
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4. Reconfigurable Manipulator with Lockable Cylindrical Joints

Benefits


Use of no extra actuators and sensors
for the reconfiguration process.
Ability to reduce the arm lengths.
Ideal for space applications


High lunch cost/extra weight
Limited place for a
manipulator on launch vehicle
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Two hinges: used to
fold the Canadarm II
before placing on
launch vehicle.
But they have to be
unfolded manually
by astronauts.

5. In this paper…

Modeling, control and simulation



6-DoF reconfigurable manipulator with
two cylindrical joints
During reconfiguration phase
Reconfiguration process



Single reconfiguration phase
Using 6 actuators
Achieving 4 desired outputs (two link
lengths and two link twist angles)
End-effector is docked to a fixed point to
reduce the system DoF and to allow the
reconfiguration of the cylindrical joints
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Cylindrical
Joint #1
Cylindrical
Joint #2

6. Modeling Process

Modeling of the unconstrained (open chain) manipulator

Mq V

.
Use of projection operator for modeling of constrained system.

Calculation of the jacobian of constrained equation in joint space
B
B
PEE0
PEE
A
.
0.
B
B
q
OEE
OEE0

Calculation of projection matrix.
P

I
A A.
Constrained system equation would be:

M C q P(

V ) CC q .
MC
CC
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M
PM

MA A .
( PM )T .

7. Simulation and Control

Error Compensation


Integration during simulation results in accumulative error of q (joint

variables) and q .
Iterative formula for compensation of q error.
~
~
δq
A (q ) ( q )
~ ~
q q δq
Corrected q


Iterative formula for compensation of q (joints velocity) error.
~


δq
A (q)A( q)q
~ ~
 

q q δq

Corrected q
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8. Overall Control process
d
Desired
configuration
Reconfiguration
Control
Control
mode
Reconfigurable
Robot
Desired
trajectory
d
, d
Motion
Control
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, 

9. Simulation and Control

Control law
Paa1 Pab K d 
Kp(
d
) g
g .
Torques at active joints

Estimation of passive joints

No sensor at passive DoF
ˆ

ˆ
K
Q( , ˆ )  AT ( , ˆ ) K
( , ˆ).
ˆ dt .

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WT KW .

10. Reconfiguration Control Diagram
Estimated
position of
passive joints
Estimated
velocity of
passive joints
Control torque
(I
ˆ

Kd

ˆ
Kp
d
AT K
T
Ppp ) 1 Pap
g
g
( , ˆ)
Desired
passive joints
position
Effect of
gravity on
passive joints
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Reconfigurable
Robot
Paa1 Pap
Effect of
gravity on
active joints

11. Validation of the Model

Monitoring total energy of the system
(ideally
K

1 T


q Mq .
2
Conditions




constant total energy)
Duration = 10 seconds
Simulation time-step = 5ms
Initial kinetic energy (K) = 0.032 J
Result after monitoring

Standard deviation of kinetic energy (K) = 0.000024e J
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12. Unfolding Scenario of a Reconfigurable Space Manipulator
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13. Simulation Results
Cylindrical joints lengths
Cylindrical joints twists
Active Joint angles
Active joint torques
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14. Conclusion

Modeling, control and simulation methods
of a 6-DoF manipulator
Single phase reconfiguration of both cylindrical joints

Future works



Singularity avoidance during reconfiguration
Obstacle avoidance
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15. Thank you
for your attention
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