1. Optimal Base Placement of Robot Manipulators
with applications
Mohammadali Aghakhani Lonbani

2. Purpose of work 2
Problem:
Best base pose for the
Manipulators around the operating
area to have maximum easiness in
End-Effector movement
Motivation:
• Keeping the robot’s End-
effector away from workspace
boundaries and minimizing
robot reconfigurations.
• Existence of joints limits and
physical obstacles around the
Robot

3. 1. Optimum Performance: Based on performance Indices (P.I.), e.g.
Manipulability Index, etc. [1, 2]
2. Orientability: The Orientation of the End-Effector on a target point is
investigated [3]
3. Reachability: Impelling the W.S. to embrace predefined target points
[4]
3
Robot Base Placement

4. 4
Definition: The performance index of a robotic mechanical system is
a scalar quantity that measures how well and how much smooth the
system behaves regarding force and motion transmission.
Application: Design, Synthesis and Control
Performance Indices
• Manipulability index (Yoshikawa 85)
• Local Conditioning Index [5] LCI =
𝜎 𝑚𝑖𝑛
𝜎 𝑚𝑎𝑥
• Isotropy index [6] Δ =
𝑚
𝜆1×𝜆2×⋯×𝜆 𝑚
𝜆1+𝜆2+⋯+𝜆 𝑚
𝑚
w = det(𝐽 × 𝐽 𝑇) = 𝜎1 × ⋯ × 𝜎 𝑛
𝐽 = Jacobian matrix
𝜎 𝑛 = 𝑠𝑖𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝐽 𝑚𝑎𝑡𝑟𝑖𝑥
𝑣𝑒 =
𝑝 𝑒
𝜔 𝑒
= 𝐽 𝑞 . 𝑞

5. “Optimal Base placement of the Da Vinci System based on the
Manipulability Index” [1]
𝑤 = det(𝐽. 𝐽 𝑇)
𝑋 = {𝜃 𝑏, 𝑃𝑥, 𝑃𝑦, 𝑡1, 𝜃2, 𝜃3, 𝜃4, 𝜃5, 𝜃6}
𝑋∗ = arg(𝑚𝑎𝑥 𝑋 𝑚𝑖𝑛𝑖 𝑚𝑎𝑥 𝜃7−12
𝑤𝑖 𝑋, 𝜃7−12 )
5
Base Placement by P.I.
1. No collision detection
2. The problem of different joint
types and dimensions during
calculations

6. Orientability
• Service Sphere concept
To take different orientations, the tip is
pivoted at a target point, then the
spherical wrist rotates around that point
on a surface of an imaginary sphere
which is called the service sphere, and
the region that the tool sweeps in is called
service region.
6
"Atlases of orientability for robotic manipulator arms“[3]

7. Reachability 7
Impelling the WorkSpace from 𝑂0 to 𝑂1
to reach the target points.
Robot W.S.
“On the placement of open-loop robotic manipulators for reachability”[4]

8. 8
Optimization Problem
O. F.
Constraints
“On the placement of open-loop robotic manipulators for reachability”[4]
Workspace rotation and translation
Boundaries rotation and translation
Reachability

9. 9
Hammond, F. L., and Kenji Shimada 2009
Example

10. Base placement of KUKA lwr for the neurosurgical
application
10
a. Location of the target area with
respect to the robot base space
(left pics)
b. Penalizing area to degrade the
approach of the base to the not
permitted zone (right pic)

11. Solution of the simulation 11
The spectrum of manipulability
index values from top view
The spectrum of manipulability
index values from side view

12. Solution of the simulation 12
The spectrum of manipulability values from top
view with respect to the patient body

13. [1] Moulianitisb, I. et. al. "Optimal Base placement of the Da Vinci System based on the
Manipulability Index” proceeding of the RAAD, 22nd International Workshop on
Robotics in Alpe-Adria-Danube Region, Portoroz, Slovenia, (2013).
[2] Hammond, F. L., and Kenji Shimada. "Improvement of kinematically redundant
manipulator design and placement using torque-weighted isotropy measures." In
Advanced Robotics, 2009. ICAR 2009. International Conference on, pp. 1-8. IEEE,
2009.
[3] Abdel-Malek, Karim, and Harn-Jou Yeh. "Atlases of orientability for robotic
manipulator arms" international journal of robotics and automation 15, no. 4 (2000):
189-205.
[4] Yang, et. al. "On the placement of open-loop robotic manipulators for reachability"
Mechanism and Machine Theory 44, no. 4 (2009): 671-684.
[5] Yoshikawa, Tsuneo. "Manipulability of robotic mechanisms" The international journal
of Robotics Research 4, no. 2 (1985): 3-9.
[6] Salisbury, J. Kenneth, and John J. Craig. "Articulated hands force control and
kinematic Issues." The International Journal of Robotics Research 1, no. 1 (1982): 4-
17.
[7] Kim, Jin-Oh, and Pradeep K. Khosla. "Dexterity measures for design and control of
manipulators." In Intelligent Robots and Systems' 91.'Intelligence for Mechanical
Systems, Proceedings IROS'91. IEEE/RSJ International Workshop on, pp. 758-763.
IEEE, 1991.
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14. 14