Computation of Force Closure Grasps from Finite Contact Point Set Nattee Niparnan Advisor: Dr. Attawith Sudsang

General Outline The story so far: robotic grasping The story so far: robotic grasping What lies behind us: literature review What lies behind us: literature review Where shall we go: the problem Where shall we go: the problem Who walk along the same road: related work Who walk along the same road: related work Problem Detail Problem Detail Grasping Basic Grasping Basic How do we reach the goal: attack point How do we reach the goal: attack point Boring stuffs work plan, objective, scopes, benefit

Robotic Grasping To hold an object firmly To hold an object firmly Prevent motion of an object Prevent motion of an object

State of the Art

Ultimate Goal of Grasping Sense the object Sense the object Calculate grasping position Calculate grasping position Initiate a grasp Initiate a grasp

Grasping Components Task Model Algorithm Hand Model Purpose of grasp Power grasp Dexterous grasp Tool-specific grasp Physical of hands Power Degree of Freedom Hand property Grasp Planning Where to grasp Objective Function Grasping constraints Grasp Planning Algorithm

Example: Grasping a Hammer Task: Moving a Hammer Task: Moving a Hammer Maximize stability Maximize stability Task: Using a Hammer Task: Using a Hammer Maximize head speed Maximize head speed Hand: Parallel Jaw Gripper Hand: Parallel Jaw Gripper Hand: 4-fingered Hand Hand: 4-fingered Hand

Grasp Planning Algorithm Algorithm Object to be grasped Grasping Configuration Input Output

What comes before us 80’s200690’s Grasping Definition Hanafusa Asada ’77, ’79 Ohwovoriore ‘80 Salisbury ’82 Asada By ’85 Nguyen ’88, ’89 Existence of Grasps Lakshminarayara ’78 Mishra et al. ’87 Markenscoff et al. ’ Reuleaux Grasping Quality Li Sastry ’88 Kirkpatric et al. ’90 Ferarri Canny ’92 Trinkle ’92 Grasp Planning Ponce et al. ’95 Lui ’99 – ’05 Li et al ’03 Zhu Wang ’03 Sumov

Hand Model Utah/MIT Dextrous Hand Barrette HandDLR Hand II Robonaut Hand

Task Model

Grasping Objective Function Tolerance Minimize effect Tolerance Minimize effect StabilityAccuracy Objective Function Kirkpatric et al Ferrari Canny Ponce et al Lui et al Ponce et al. Nguyen Ding et al

Conventional Grasping Objective Function Hand Model Objective Function Task Model Customized algorithm

Issues No generally good grasp!!! No generally good grasp!!! No general task model No general task model No general hand model No general hand model Different measurement and constraints Different measurement and constraints Object modeling Object modeling Modeling accuracy Modeling accuracy

Object Modeling Modeling accuracy Modeling accuracy Polygon Polygon Linear Linear Low accuracy Low accuracy Curve Curve High cost of curve fitting High cost of curve fitting Nonlinear Nonlinear High Accuracy High Accuracy Contact points Contact points High number of contact points High number of contact points Almost the same accuracy of curve Almost the same accuracy of curve Practical Practical Polygon Curve Contact Point

Where shall we go New grasp planning framework New grasp planning framework Hand Model Task Model Generalized Algorithm Take no a priori knowledge Use Contact Points (Model-less)

Where shall we go Instead of finding one best grasp Instead of finding one best grasp Just find “firm” grasps Just find “firm” grasps Find lots of grasps Find lots of grasps Use no a priori knowledge of Task/Hand Use no a priori knowledge of Task/Hand Let task model and hand model choose appropriate grasp Let task model and hand model choose appropriate grasp Using contact points Using contact points Model-less input Model-less input a large number of input a large number of input

Is It Hard? Consider one single “firm grasp” problem in Polygonal model Consider one single “firm grasp” problem in Polygonal model Computational intensive Computational intensive Linear Programming / Ray Shooting / Point Inclusion Linear Programming / Ray Shooting / Point Inclusion Multiple grasping solution? Multiple grasping solution? Almost unobtainable until recently Almost unobtainable until recently With contact point model? With contact point model? Polygon  around faces Polygon  around faces Contact Point  around 1000 contact points Contact Point  around 1000 contact points Much more computational extensive Much more computational extensive

Challenge SPEED!!! SPEED!!!

Usage of the Result Given Task/Hand Given Task/Hand enumerate solution to find the best one enumerate solution to find the best one O(n) O(n) Result is associated to the object Result is associated to the object Normal use usually involve multiple step Normal use usually involve multiple step Regrasp Regrasp

Problem Statement: First Draft Given a set of contact points Given a set of contact points Find Find As many good grasps as possible As many good grasps as possible In a short time In a short time

Naïve Approach one single “firm grasp” problem one single “firm grasp” problem Still is an active topic Still is an active topic Lui ’99 – ’05 Li et al ’03 Zhu Wang ’03 Borst et al ’03 Zhu et al ’04

Naïve Approach Finding all solutions Finding all solutions Combinatorial Problem Combinatorial Problem 1000 points 4 fingers Must check O(N 4 ) Search space

Who walk along the same road Contact point input Contact point input Wallack Canny ‘94 Wallack Canny ‘94 Brost Goldberg ‘96 Brost Goldberg ‘96 Wang ‘00 Wang ‘00 Multiple solutions Multiple solutions 04 van der Stappen ‘04 Multiple solutions & Contact point Input Multiple solutions & Contact point Input None... None...

Problem Detail

Grasping Basic Force Closure Force Closure Formal definition of firm grasp Formal definition of firm grasp “Hand can influence the object such that any external disturbance can be nullified” “Hand can influence the object such that any external disturbance can be nullified”

Influence of a hand via contact points between a hand and an object via contact points between a hand and an object Described by Described by Contact positions ( r ) Contact positions ( r ) Contact directions ( n ) Contact directions ( n )

Influence of a Contact Point Force (contact direction) Force (contact direction) Force vector ( f ) Force vector ( f ) Torque (contact position & direction) Torque (contact position & direction) Torque vector ( r x f ) Torque vector ( r x f )

Wrench To combine force and torque into one component To combine force and torque into one component Easier to describe Easier to describe Wrench = force vector concatenates with torque vector Wrench = force vector concatenates with torque vector w = ( f, r x f ) w = ( f, r x f ) Model a contact point by a wrench Model a contact point by a wrench Space Dimension Force Dimension Torque Dimension Wrench Dimension 2D2D1D3D 3D3D3D6D

Wrench Example

Force Closure in terms of Wrenches External disturbance can also be written as a wrench External disturbance can also be written as a wrench Contact points can exert Contact points can exert Their respective wrenches Their respective wrenches Also positive combinations of the wrenches Also positive combinations of the wrenches Force Closure = any wrench can be expressed by a positive combination of contact point wrenches Force Closure = any wrench can be expressed by a positive combination of contact point wrenches Grasping Hand Contact Points Forces &Torques Wrenches

Problem Transformation Equivalence Equivalence Wrenches achieve force closure Wrenches achieve force closure Wrenches positively span R 6 (or R 3 ) Wrenches positively span R 6 (or R 3 ) A Convex hull of wrenches contains the origin A Convex hull of wrenches contains the origin Grasping Hand Contact Points Forces &Torques Wrenches Force Closure? Positively Spanning ? The origin inside CH?

Positively Spanning any vector can be expressed by a positive combination of given vectors any vector can be expressed by a positive combination of given vectors

Point in Convex Hull The origin is strictly inside the convex hull of contact point vectors The origin is strictly inside the convex hull of contact point vectors In the interior of the convex hull In the interior of the convex hull

Contact Model (Friction) With friction With friction One contact point is associated with many wrenches One contact point is associated with many wrenches

Check Point Grasping problem is Grasping problem is A mathematical problem A mathematical problem A computational geometry problem A computational geometry problem Emphasize on deriving of an efficient algorithm for reporting several solutions from contact point input Emphasize on deriving of an efficient algorithm for reporting several solutions from contact point input

Problem Configuration Object Model RoleContact Model Finger Contact point Curved object Polygon Optimizer Classifier Frictionless Frictional 3 fingers (2D) 4 fingers (2D,3D) 2 fingers n fingers 7 fingers (3D)

The Problem: Revisited Input: A set of contact points Input: A set of contact points Output: A set of grasping solutions Output: A set of grasping solutions Combinatorial problem Combinatorial problem Algorithm Contact Points as wrenches Sol 2D Frictional (3 fingers) 2D Frictionless (4 fingers) 3D Frictional (4 fingers) 3D Frictionless (7 fingers)

How do we reach the goal Exploit multiple solution nature of the problem Exploit multiple solution nature of the problem Try to use pre-computation Try to use pre-computation Sorting, searching, suitable data structure, etc. Sorting, searching, suitable data structure, etc. Problem reformulation Problem reformulation Reduce dimension of wrench space Reduce dimension of wrench space

Work Plan Study the works in the related fields Study the works in the related fields Preliminary works on a heuristic algorithm Preliminary works on a heuristic algorithm Study a reformulation of the problem Study a reformulation of the problem In-depth study of grasp planning algorithms In-depth study of grasp planning algorithms Perform extensive comparison of various grasping condition Perform extensive comparison of various grasping condition Develop algorithms Develop algorithms Comparison Comparison Publish a journal article Publish a journal article Prepare and engage in a thesis defense Prepare and engage in a thesis defense

Recent Works Fast Computation of 4-Fingered Force-Closure Grasps from Surface Points. Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp , Fast Computation of 4-Fingered Force-Closure Grasps from Surface Points. Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp , Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Object. Proc. of the IEEE International Conf. on Robotics and Automation, pp , Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Object. Proc. of the IEEE International Conf. on Robotics and Automation, pp , A Heuristic Approach for Computing Frictionless Force-Closure Grasps of 2D Objects from Contact Point Set. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 A Heuristic Approach for Computing Frictionless Force-Closure Grasps of 2D Objects from Contact Point Set. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Algorithm. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Algorithm. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, Fingered Force-Closure Grasps from Surface Points using Genetic Algorithm. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, Fingered Force-Closure Grasps from Surface Points using Genetic Algorithm. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006

Objective To develop efficient algorithms that report several force closure grasps from a set of finite contact points To develop efficient algorithms that report several force closure grasps from a set of finite contact points

Scope of the Research Considers force closure grasping in both 2D and 3D in friction and frictionless case Considers force closure grasping in both 2D and 3D in friction and frictionless case Derived algorithms must work faster than an enumerative approach that uses the fastest computation Derived algorithms must work faster than an enumerative approach that uses the fastest computation Performance measurement can be either an actual running time (in case of a heuristic algorithm) or a complexity analysis (in case of a complete algorithm) Performance measurement can be either an actual running time (in case of a heuristic algorithm) or a complexity analysis (in case of a complete algorithm)

Scope of the Research 2D Frictional (3 fingers) 2D Frictionless (4 fingers) 3D Frictional (4 fingers) 3D Frictionless (7 fingers) Compare with the best known “single solution” algorithm Evidence of superiority Proof of complexity analysis Running Time Comparison Evidence of superiority Proof of complexity analysis Running Time Comparison Evidence of superiority Proof of complexity analysis Running Time Comparison Evidence of superiority Proof of complexity analysis Running Time Comparison

Expected Contribution Having algorithms that report several force closure grasps from a set of discrete contact points. Having algorithms that report several force closure grasps from a set of discrete contact points.

Thank You Comments are heartily welcomed

Coulomb Friction fnfn f t = uf N a = tan -1 (u)

DLR Hand Sensor per each finger Sensor per each finger 3 joint position sensors: 3 joint position sensors: 3 joint torque sensors: 3 joint torque sensors: 3 motor position/speed sensors: 3 motor position/speed sensors: 1 six-dimensional finger tip force torque sensor: 1 six-dimensional finger tip force torque sensor:finger tip force torque sensorfinger tip force torque sensor 3 motor temperature sensors: 3 motor temperature sensors: 3 sensors for temperature compensation: integrated sensors 3 sensors for temperature compensation: integrated sensors