Abstract --- Graspless manipulation is easily interfered by external disturbances because the manipulated object is not completely held by a robot hand and supported by an environment such as a floor. Thus it is important to ensure the manipulation is executed robustly against some disturbances. In our works, we have proposed a rigid-body-based analysis of indeterminate contact forces for quasi-static graspless manipulation, and also joint torque optimization for robotic hands. The joint torques of the robot is determined in consideration of some robustness of manipulation against disturbances, which include changes or estimation errors of friction. In the analysis of contact forces in quasi-statics, we consider a kinematic constraint on static friction to exclude infeasible sets of frictional force, with considering treatment of kinetic friction. We also propose new objective functions for computing optimal joint torques in both static and quasi-static graspless manipulation. Some numerical samples of both applications are shown to verify our proposed methods.

1. Joint Torque Optimization for Quasi-static Graspless Manipulation
*S. Makita and Y. Maeda
Proposal
 Rigid-body-based analysis of quasi-statics
 Constraint on static and kinetic friction
 Optimization of joint torques that keep robustness
against disturbances
Constraint on static frictional forces
Kinetic friction is NOT constrained
Virtual sliding
always occur at
the contact points
in actual sliding
pushing sliding tumbling pivoting
Based on virtual motion of rigid-body
Joint Torque Optimization
Maximizing the margin between each friction cone and
contact force in it
Numerical examples
<Support a ball> <Slide a cuboid>
(virtual
sliding)
**valid**
Invalid frictional forces
(Invalid combination)
Valid frictional forces
(Valid combination)
(virtual
sliding)
**invalid**
(non-selected)
(Actual sliding)
and virtual sliding
(Virtual sliding) **invalid**
(always selected)
[3D view] [2D view]
Surface of friction cone
Approximated
friction cone Contact point
Contact force
Margin

2. Joint Torque Optimization for
Quasi-static Graspless
Manipulation
S. Makita (Sasebo National Coll. of Tech.)
Y. Maeda (Yokohama National Univ.)

3. Proposal
◦ Rigid-body-based analysis of quasi-
statics
◦ Constraint on static and kinetic friction
◦ Optimization of joint torques that keep
robustness against disturbances
3
Overview

4. Non-grasp and non-lift
Graspless (nonprehensile) manipulation
4
pushing
sliding
tumbling
pivoting

5. Kinetic friction occurs
5
In quasi-static manipulation
pushing
sliding
tumbling
pivoting

6. Applied in the direction opposite to
sliding or intention to slide
6
Frictional forces
Pushing
(Sliding)
(Kinetic friction)
Pushing
(Intention
to slide)
(Static friction)
***in rigid-body analysis***

7. Based on virtual motion of rigid-body
◦ (Intention to slide -> virtual sliding)
7
Constraint on static frictional forces
Virtual sliding
Friction force
Valid frictional force
(Valid combination)
Invalid frictional force
(Invalid combination)

8. Its direction is always determined by
actual sliding
8
Kinetic friction
Pushing
(Sliding)
(Kinetic friction)

9. How to apply the constraint on static
friction in quasi-static manipulation
9
Question
Pushing
(Sliding)
(Kinetic friction)
Can the static friction occur?

10. Feasible combination of virtual sliding
10
Constraint on static frictional forces
(virtual
sliding)
**valid**
Invalid frictional forces
(Invalid combination)
Valid frictional forces
(Valid combination)
(virtual
sliding)
**invalid**
(non-selected)

11. Consider virtual sliding
11
Kinetic friction is NOT constrained
(actual
sliding)
Valid frictional forces?
(Valid combination of forces?)
Valid frictional forces
(Valid combination)
(actual
sliding)
(non-selected)(virtual sliding) **valid**

12.  Combination of only static friction
-> Invalid
 Combination of static and kinetic
friction
-> Valid?
12
Unreasonable results

13. Virtual sliding does not occur at the
contact points in actual sliding
13
False: Ignorance of contact points
(Actual sliding)
(non-selected)
(virtual sliding) **valid?**

14. Virtual sliding always occur at the
contact points in actual sliding
14
Consideration of virtual sliding
(Actual sliding)
and virtual sliding
(Virtual sliding) **invalid**
(always selected)

15. Determined by actual sliding
(not affected by virtual sliding)
15
Direction of kinetic friction
(Actual sliding)
and virtual sliding
(virtual sliding) **invalid**
Kinetic friction

16. 16
In 3D scenes (Inappropriate case)
Valid friction force
Valid friction force?
Pushing
Actual sliding
Virtual sliding
Friction force

17. 17
In 3D scenes (Improved method)
Valid friction force
Invalid friction force
Pushing
Actual sliding
Virtual sliding
Friction force

18. 
18
Constraint on static friction
Selection matrix
Virtual motion
of the body
Virtual motion
of the robot
Virtual sliding of
the contact points

19. 
19
Non-selected contact points

20. 
20
Direction of static friction
Direction of virtual sliding
Static frictional forces
Selection matrix choosing
contact points in actual sliding

21. 
21
Indeterminate contact forces
* Force Equilibrium
* Jacobian and joint
torques
* No frictional forces
* Constraint on static
friction

22. Joint Torque Optimization
22

23. Objective
◦ To apply appropriate contact forces to the
manipulated object
◦ To make the object robust against some
external disturbances
23
Joint Torque optimization

24. Maximizing the margin between each
friction cone and contact force in it
24
Basic idea of robustness
[3D view] [2D view]
Surface of friction cone
Approximated
friction cone Contact point
Contact force
Margin

25. A margin between the contact force
and the base face
25
Definition of margin (1)
25[2D view]
Surface of friction cone
Contact point
Contact force
Margin

26. A margin between contact force and
each side face
Definition of margin (2)
26[2D view]
Surface of friction cone
Contact point
Contact force
Margin

27. Margin (2) CANNOT be defined at the
contact points in actual sliding
27
Kinetic friction along friction cone
27[2D view]
Kinetic frictional force
Contact point
Contact force
Minimum margin is always ZERO

28. Maximizing margins to resist against
as large changes of disturbances as
possible
28
Algorithm 1
Maximize
Maximize
Disturbances

29. 
29
Algorithm 1
* Indeterminate
contact forces
* Margin 1
* Margin 2
* Torque limitation

30. Minimizing joint torques that
equilibrates contact forces with given
disturbances
30
Algorithm 2
Minimize
Minimize
Disturbances

31. 
31
Algorithm 2
* Indeterminate
contact forces
* Margin 1
* Margin 2
* Torque limitation

32. Numerical examples
32

33. 33
Case: Robot fingers support a ball
45 [deg]
(P2)
P1
P3
x
y
z
Joint 1
Joint 2

34. 
34
Calculation results

35. 35
Case: Robot fingers pinch a cuboid and slide it
45 [deg] x
y
z
P2
P1
P3
(P4)P5
P6
Joint 1
Joint 2

36. 
36
Calculation results (keep stationary)

37. 
37
Calculation results (slide upward)

38. 
38
Calculation results (slide downward)

39. Why optimal joint torques in sliding
case are larger than those in stationary
case?
39
Discussion

40. Kinetic friction is always applied to the
object as the maximum frictional force
Static frictional forces tend to be small
for considering margin (2).
40
Discussion

41.  Rigid-body-based analysis of indeterminate
contact forces in quasi-static graspless
manipulation is proposed
 Modified constraint on static friction can be
applied to the cases where kinetic friction exists
 Torque optimization based on the margins of the
friction cone for quasi-static manipulation is
proposed
41
Conclusion

42.  Motion planning and control of quasi-
static graspless manipulation
42
Future works