Grasp Quality Improvement with Particle Swarm Optimization

(PSO) for a Robotic Hand Holding 3D Objects

Venkataramani Rakesh

, Utkarsh Sharma

, Murugan S

, Venugopal Srinivasan

and Thondiyath Asokan

Robotics & Remote Handling Section, Indira Gandhi Centre for Atomic Research, Chennai-603 102, India

Department of Engineering Design, Indian Institute of Technology Madras, Chennai-600 036, India

Keywords: Grasping, Robot Hand, Synthesis, Particle Swarm Optimisation (PSO), Grasp Quality.

Abstract: Automated grasp planning for robotic hands is a complex problem when compared with the ease with which

human hands grasp objects. Research in robotic grasp synthesis attempts to find novel ways in which a

stable grasp can be achieved reliably. In this work, we present a grasping methodology that achieves

optimized force closure grasps on 3D irregular objects. 3D objects in the form of polygonal meshes are

parameterized to 2D shapes in order to reduce the search space by constraining robotic hands finger tips to

be in contact with the objects surface. We use a Particle Swarm Optimization (PSO) based framework to

optimize an initial grasp. The scheme has been validated on test-case 3D objects represented with surface

tessellation for a 5-fingered DLR robotic hand.

1 INTRODUCTION

Robotic arms are one of the most common

applications in automation and intelligence based

systems. The robot arm is usually a serial link

manipulator, and is provided with a parallel jaw

gripper fitted as the end effector. Parallel jaw

grippers suffer major disadvantages, while handling

objects to be handled with arbitrary shapes and

uneven surfaces (Shimoga, 1996). Better robot

grasping abilities are assured by fitting robotic arms

with end effectors, which are adept at matching

human hand-like motions. The research in the field

of robot grasping tries to address three different

issues viz. existence, analysis and synthesis of

grasps. The study of robot hands and grasping are

sharply differentiated from the design of fixtures and

industrial grippers, which have extensive usage

currently. Moreover, grasping research (especially

synthesis) is devoted to generating schemes to find

the best possible location to hold the object.

The design of the 3-fingered robot hand (Mason

and Salisbury, 1985) largely initiated the tone for

research in the field along with studies on

prehension (Asada, 1979). The notion of grasp

quality was introduced in order to provide a metric

for successful grasps, (Ferrari and Canny, 1992).

This was defined as the radius of the largest wrench

space ball, centered at the origin, which can just fit

within the unit grasp wrench space. Mathematical

analyses were also presented by comparing various

metrics (Mishra, 1995).

Grasp synthesis problems are tackled using

analytical and empirical methods in literature and

using a few other different grasp quality measures

were also reviewed (Suárez et al., 2006).

Analytical grasp synthesis studies are based on a

combination of geometric, kinematic and dynamic

formulations. Modeling and solving problems by

this approach is computationally intensive. The

earliest works (Lakshminarayana, 1978) specify

sufficient conditions of form closure of 2-D and 3-D

objects. Thereafter, necessary conditions for 4-finger

force closure grasps were published (Ponce et al.,

1997).

Empirical methods give emphasis to techniques

co-relating object features with robot hand. A case in

example (Li et al., 2007) uses 3-D models of the

object for shape matching with samples from a

database of grasps. Another offshoot of this thread

uses learning algorithms (Romero et al., 2008)

where grasp images are searched for fundamental

matching with the one demonstrated.

It is interesting to note that robotics research in

grasping also leans on the study of an elaborate

taxonomy of human grasps (Cutkosky, 1989). As

Rakesh, V., Sarma, U., S, M., Srinivasan, V. and Asokan, T.

Grasp Quality Improvement with Particle Swarm Optimization (PSO) for a Robotic Hand Holding 3D Objects.

DOI: 10.5220/0005959901850191

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 2, pages 185-191

ISBN: 978-989-758-198-4

185

mentioned, in the introduction, the pinnacle of grasp

perfection would need to exploit designs based on

anthropomorphism (even partially) in order to mimic

the human hand (Biagiotti et al., 2004).

As a natural consequence, due to the complexity

of such hands, attempts are made to reduce the search

spaces (Li et al., 2003). In analytical methods, the

complexity is reduced by accounting for the

constraints formed by the coupling of various finger

joints. The Barrett Hand Grasper uses such interlink

transmissions reducing the total number of actuators

(Townsend, 2000). Grasp synthesis algorithms are

often handicapped by the limitation of the input

representation of the objects and/or the semantics of

the required tasks. This naturally introduces errors in

the object registration/approximation by the grasp

planner. Hence the synthesis strategy should fortify

itself by generating a broad set of contact locations

which in essence would lead for a robust grasp.

Independent Contact Regions (ICR) provided leeway

in the finger positioning (Nguyen, 1988).

Efforts are also directed in empirical methods

towards the simplification of 3-D shapes by planar

representation (Morales et al., 2006). A similar

work (Aarno et al., 2007) utilizes representations

based on 3-D contours.

The problem of grasp scheme generation is

exacerbated by the infinite types of objects to be

handled by numerous hand shapes/designs. Hence,

there is an ever-present incentive to devise novel

schemes for grasp synthesis which provide quality

grasps elegantly.

2 PROBLEM OUTLINE

The objective of the present work is to find quality

grasps on 3D objects. The grasps are synthesized for

the robotic DLR/HIT Hand II model. The DLR/HIT

Hand II has been jointly developed by DLR (German

Aerospace Center) and HIT (Harbin Institute of

Technology). The objects, for which the grasps are

evolved, are represented with surface tessellation.

2.1 Grasp Planner Inputs

A triangular tessellation mesh has been used for the

objects used for the trial experiments to generate

grasp and validate the scheme. The density of the

tessellation set, Ω, determines the detail with which

the object features are represented. The points on the

object surface are provided with position vectors, p

with respect to the centre of mass (C.M) of the

object and the unit normal vector, n

of the

corresponding triangle.

2.2 Wrenches and Contact

The robot hand finger-tip on the object surface

generates a force on the object at the surface point.

A corresponding torque with respect to the C.M. is

also created. The concatenation of this force-torque

vector represents the associated wrench, ω

applied

by the finger-tip on the object surface at a location

denoted by i. A Coulomb friction model has been

assumed, in the present work, for point contact

between the finger-tip and the object. In order to

assure that there is no slippage between the object

and the robot hand at the finger-tips, it is necessary

that the applied contact force vector should lie

within the friction cone. The friction cone is

linearized with an 8-sided pyramid. The coefficient

of friction used is taken as 0.4

2.3 Grasp Quality Optimization

In the current work, the quality of the grasp is

improved by particle swarm optimization (PSO), a

heuristic method, which performs a global search.

The global search is performed over the object

surface points with a view to increase the grasp

quality. Hence, the objective function, for the

current work, is the grasp quality.

The grasp quality objective function, for

optimization, is formed with a component which uses

the condition number of the hand Jacobian, H. A

better quality (of this component) for the grasp

indicates a better manipulability of the grasped object

by the hand. This is expressed as the ratio of the

maximum and minimum singular values of H i.e.

(H) (Shimoga, 1996). The best quality for this

component i.e the best value possible is 1. In addition

to this factor, a variation of the criterion of largest ball

(Ferrari and Canny, 1992) grasp quality is used here,

which is the radius of the largest ball, ρ, within the

convex hull formed by the wrenches, irrespective of

the reference (Teichmann, 1996). The expression for

the grasp quality, Q, as a combination with these two

components, with normalization, is expressed as,

Q =

–

1000[1/n

(H)])

(1)

2.4 Particle Swarm Optimization

The implementation of the PSO, in the current work,

utilizes combination of the pattern-search method

with the traditional PSO global search algorithm

(Vaz et al., 2007).

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

186

The individual finger-tips of the five-fingered

robot hand touch the object on the surface points. An

initial FC grasp is generated using trial and error.

The finger-tip contact points on the object’s surface

are then mapped to the 2d parameterized surface as

discussed in the section 3. These set of five points

along with hands position and orientation, formed as

a vector are taken as one of the initial population

member where others are chosen randomly. The

parameterized surface is chosen as the solution space

over which the PSO searches for the solution. The

linear equations of the boundaries of the 2d

parameterized surface are taken as the lower and

upper bounds for the solution space.

The swarm size for the PSO is taken as 42. The

social and cognition parameter values are both 0.5.

The initial and final inertia weights are 0.9 and 0.4

respectively. A maximum function evaluation of

10,000 is provided as the stopping criterion for the

optimization method.

3 MESH MAPPING

The object surface has a specific discrete set of

points, available to the planner, on which the grasp

search can be conducted. This simple and efficient

procedure, though adequate can be further mapped

to a modified surface which allows a thorough and

continuous search by the use of mesh

parameterization (Floater et al., 2005, and Hormann

et al., 2007).

Figure 1: The 2D parameterizations of the surface

tessellations for the 3D Objects used for validating the

grasp synthesis schema (a) Rectangular parallelepiped. (b)

Duck.

The 3D object surface mesh is parameterized to

an equivalent 2D surface. A triangle constituting a

unit of initial tessellation set, Ω, is removed. This

creates an equivalent homeomorphic disc from the

remaining surface of the 3D object.

In order to ensure and enable a continuous search

region on the object surface, Barycentric co-

ordinates are used. The 3D objects for the

experimental trials, in this work, are shown in Figure

1 (Rakesh et al., 2015) along with the corresponding

2D mesh parameterizations. The search for quality

grasps are carried out on a rectangular parallelepiped

and a duck as the 3D objects as shown and is

described in the subsequent sections.

4 EXAMPLE CASE-STUDIES

A DLR robot hand with five fingers has been used

on two objects within the MATLAB frame-work for

testing the synthesis of the quality grasps as

discussed hitherto. The objects consist of 3D models

of a rectangular parallelepiped and a duck as shown

in Figure 1. The parallelepiped surface consists of

1879 tessellation triangles. On the other hand, the

duck is represented with moderate surface

tessellation of 2055 triangles.

Figure 2: The DLR hand used for the case-studies.

The DLR robot hand, shown in Figure 2, consists

of five fingers. For each fingers, the segments l

55 mm. The segments l

and l

are equal and

represent a length of 25 mm each. The

abduction/adduction movement is represented by θ

at the base of each finger and the in-plane degree-of-

freedom (DOF) for the joint at the same location is

denoted by θ

. Hence, the base of each finger

consists of 2-DOF joint. The subsequent in-plane

Grasp Quality Improvement with Particle Swarm Optimization (PSO) for a Robotic Hand Holding 3D Objects

187

finger joint rotations are denoted by θ

and θ

which

are equal to each other, in the present case.

The skeletal connectivity diagram of the DLR

hand is shown in Figure 3. The inverse kinematics

relations for the fingers are detailed in the Appendix.

Figure 3: The skeletal connectivity diagram for the DLR

hand used for the case-studies.

The Syngrasp frame-work (Malvezzi et al., 2013)

within the MATLAB programming environment has

been used to implement the scheme, on a personal

computer with Intel i3, 2.2GHz processor.

4.1 Case-study: Rectangular

Parallelepiped

The DLR robot hand is initialized with a grasp as

shown in Figure 4 for the rectangular parallelepiped.

The initial grasp quality is 11.08.

Figure 4: The initial grasp of the DLR hand on the

rectangular parallelepiped.

The optimized grasp with a final grasp quality of

26.38 is generated as shown in Figure 5.

Figure 5: The final grasp of the DLR hand on the

rectangular parallelepiped.

The iteration progress during the optimization for

increasing the grasp quality is given in Figure 6.

Figure 6: The increase in the grasp quality for the DLR

hand and the rectangular parallelepiped.

The total time take for the optimization run is 47.6 s.

4.2 Case-study: Duck

The duck model with a moderate tessellation value

of 2055 triangles forms the second sub-case for the

test studies in this work.

The initial grasp with a quality of 13.036 is

shown in Figure 7.

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188

Figure 7: The initial grasp of the DLR hand on the duck.

On implementing the PSO for increasing the

grasp quality the final grasp generated is shown in

Figure 8.

Figure 8: The final grasp of the DLR hand on the duck.

The total time taken for improving the grasp

quality to 21.85 for the duck is 90 s.

Figure 9: The increase in the grasp quality for the DLR

hand and the duck model.

The progress of the iterations is shown in Figure

5 CONCLUSIONS

The current work has formulated a scheme for grasp

quality optimization with a robot hand for test case

objects, based on PSO. The routine performs fairly

well over a simple model like parallelepiped and

also a comparatively complex geometrical model of

duck. The reasonably fast run-times show the

efficacy of the formulation for generating quality

grasps quickly. Using an analytical method for

computing inverse kinematics of the hand

contributes to the lower times in grasp computation.

It is difficult to process complex objects

analytically with the objective of automation in

grasp synthesis. Moreover, in most of the applicable

cases the computational times are disparagingly

high. In this context, the current work has suitably

validated the synthesis of quality grasps in a virtual

environment. The applicability of the method on a

simulated test bench helps to eliminate expensive

hardware trials and manufacturing cycles, while

reducing the implementation costs. Hence, the current

work has been a successful endeavour for quality

grasp synthesis and optimization, as a generalized

planner for a different of objects, using PSO.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the

encouragement provided by Dr. A. K. Bhaduri,

Director, Metallurgy & Materials Group, Indira

Gandhi Centre for Atomic Research, during this

study.

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APPENDIX

The inverse kinematics for a particular finger can be

derived geometrically. Analogous relations are valid

for each of the fingers. It may be noted that

adduction/abduction movement (θ

) about the finger

base gives rotation about the Y-axis. At a specific

abduction/adduction angle (θ

) the in-plane

configuration of the finger is shown in Figure 10

along with the corresponding relevant nomenclature.

Figure 10: Geometical method to for the inverse

kinematics to find

and θ

(= θ

)

The finger-tip position is at E, and the base of

the finger starts from A, which coincides with the

origin of the rectangular co-ordinate system at (0,0).

For the inverse kinematics, the finger-tip position at

E (x

, y

), is knows in terms of the co-ordinate

values.

Here,

AB =

= 55 mm ; BD =

= 25 mm = DE

and AE =

(A.1a)

∠CBD = ∠FDE

(A.1b)

Hence, ∠ABD = ∠BDE

(A.1c)

Since, BC = -

/(2Cos σ) so,

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190

AC =

/(2Cos

)

;

CE =

/(2Cos

)

(A.2)

In ΔACE,

= A

+ C

- 2 AC.CE.Cos (2σ – π

)

(A.3)

Taking only the negative solution as

meaningfully realizable, we have, Substituting Cos σ

= x and using (A.1a) and (A.2), in the above

equation, we have

(2x

)

+(2x

)

+2(2x

)

. (2x

)

.( 2

-1

)

(A.4)

The solution for the above bi-quadratic

equation yields the value of x as

x = ±[-

{

)

–9(

)

(

)

-4

(

)

}

+ (

)

)]

.(4.

)

(A.5)

Taking only the negative solution as

meaningfully realizable, we have,

σ = Co

x thereby,

= π -

(A.6)

ΔACE,

α = -(CE.

)/AE

Using (1a) and (2), in the above equation, we

have

α =

[{

σ(2Cos

-1)

}

]

(A.7)

Thence,

∠EAX+ α

(A.8)

where , ∠EAX = tan

-1

)

(A.9)

Grasp Quality Improvement with Particle Swarm Optimization (PSO) for a Robotic Hand Holding 3D Objects

191