On the Efficient Computation of Independent Contact Regions for - PowerPoint PPT Presentation

On the Efficient Computation of Independent Contact Regions for Force Closure Grasps Robert Krug, Dimitar Dimitrov, Krzysztof Charusta and Boyko Iliev Learning Systems Lab Center for Applied Autonomous Sensor Systems Örebro University, Sweden robert.krug@oru.se Robert Krug IROS 2010 1 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Robert Krug IROS 2010 2 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with one finger Robert Krug IROS 2010 2 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with one finger If each finger is placed within its respective region . . . . . . certain grasp properties are preserved Robert Krug IROS 2010 2 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with one finger If each finger is placed within its respective region . . . . . . certain grasp properties are preserved Robert Krug IROS 2010 2 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with one finger If each finger is placed within its respective region . . . . . . certain grasp properties are preserved Robert Krug IROS 2010 2 / 21

Independent Contact Regions (ICR) Impossible to position the fingers of a grasping device precisely at the desired contact locations Representation of a grasp as a set of regions Each region is associated with one finger If each finger is placed within its respective region . . . . . . certain grasp properties are preserved Robert Krug IROS 2010 2 / 21

Outline Motivation 1 2 Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches The Algorithm: Step - by - Step 3 Benchmark 4 Contributions & Outlook 5 Robert Krug IROS 2010 3 / 21

Motivation Outline Motivation 1 2 Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches The Algorithm: Step - by - Step 3 Benchmark 4 Contributions & Outlook 5 Robert Krug IROS 2010 4 / 21

Motivation Motivation In general such regions are not unique ⇒ the computation methods reflect application/assumptions. Robert Krug IROS 2010 5 / 21

Motivation Motivation In general such regions are not unique ⇒ the computation methods reflect application/assumptions. Our approach is based on geometric reasoning [Pollard, 1994] Efficient algorithm for ICR-computation on discretized objects Robert Krug IROS 2010 5 / 21

Motivation Motivation In general such regions are not unique ⇒ the computation methods reflect application/assumptions. Our approach is based on geometric reasoning [Pollard, 1994] Efficient algorithm for ICR-computation on discretized objects Given a prototype force-closure grasp Robert Krug IROS 2010 5 / 21

Concept Outline Motivation 1 2 Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches The Algorithm: Step - by - Step 3 Benchmark 4 Contributions & Outlook 5 Robert Krug IROS 2010 6 / 21

Concept Preliminaries Preliminaries Grasp → set of contact points G = [ p 1 , ··· , p N ] T Grasp contact forces f s are bounded Robert Krug IROS 2010 7 / 21

Concept Preliminaries Preliminaries Grasp → set of contact points G = [ p 1 , ··· , p N ] T Grasp contact forces f s are bounded Mapping of contact forces ⇒ contact wrenches � f s � τ s = ( p s × f s ) , w s = τ s Robert Krug IROS 2010 7 / 21

Concept Preliminaries Preliminaries Grasp → set of contact points G = [ p 1 , ··· , p N ] T Grasp contact forces f s are bounded Mapping of contact forces ⇒ contact wrenches � f s � τ s = ( p s × f s ) , w s = τ s Planar grasp ⇒ 3D - wrench space 3D grasp ⇒ 6D - wrench space Robert Krug IROS 2010 7 / 21

Concept Grasp Wrench Space Grasp Wrench Space (GWS) Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp Robert Krug IROS 2010 8 / 21

Concept Grasp Wrench Space Grasp Wrench Space (GWS) Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . . Robert Krug IROS 2010 8 / 21

Concept Grasp Wrench Space Grasp Wrench Space (GWS) Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . . . . . can be countered by a convex combination of grasp wrenches Robert Krug IROS 2010 8 / 21

Concept Grasp Wrench Space Grasp Wrench Space (GWS) Hypothetical 2D - contact wrenches for a 4-fingered frictionless grasp A disturbance wrench like this . . . . . . can be countered by a convex combination of grasp wrenches All possible convex combinations ⇒ GWS Mirror image of all resistible disturbance wrenches Robert Krug IROS 2010 8 / 21

Concept Task Wrench Space Task Wrench Space (TWS) Consider a given prototype grasp . . . . . . and knowledge about possible disturbances Robert Krug IROS 2010 9 / 21

Concept Task Wrench Space Task Wrench Space (TWS) Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Robert Krug IROS 2010 9 / 21

Concept Task Wrench Space Task Wrench Space (TWS) Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy Robert Krug IROS 2010 9 / 21

Concept Task Wrench Space Task Wrench Space (TWS) Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy Robert Krug IROS 2010 9 / 21

Concept Task Wrench Space Task Wrench Space (TWS) Consider a given prototype grasp . . . . . . and knowledge about possible disturbances TWS ⇒ space of wrenches to counter given disturbances Obviously some redundancy Approximate the Task . . . . . . by shifting hyperplanes parallely Robert Krug IROS 2010 9 / 21

Concept Visibility - Convex Hulls Visibility Well known from computational geometry Facet f is visible from x ⇒ x lies in the half-space of f not containing the centroid Robert Krug IROS 2010 10 / 21

Concept Visibility - Convex Hulls Visibility Well known from computational geometry Facet f is visible from x ⇒ x lies in the half-space of f not containing the centroid If x 1 “sees” the same facets as x . . . . . . replacement preserves the original convex hull Robert Krug IROS 2010 10 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Robert Krug IROS 2010 11 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Robert Krug IROS 2010 11 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task Robert Krug IROS 2010 11 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task Robert Krug IROS 2010 11 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task Robert Krug IROS 2010 11 / 21

Concept Admissible Wrenches Admissible Wrenches Changing grasp contact points means changing grasp wrenches Define search spaces utilizing the visibility concept Every grasp with wrenches in each search space . . . . . . guarantees the task find wrenches inside the search spaces ⇒ corresponding contact points form the ICR Robert Krug IROS 2010 11 / 21

The Algorithm: Step - by - Step Outline Motivation 1 2 Concept Preliminaries Grasp Wrench Space Task Wrench Space Visibility - Convex Hulls Admissible Wrenches The Algorithm: Step - by - Step 3 Benchmark 4 Contributions & Outlook 5 Robert Krug IROS 2010 12 / 21

The Algorithm: Step - by - Step Step 1: Defining the wrench spaces EXAMPLE: Discretized Ellipse Robert Krug IROS 2010 13 / 21

The Algorithm: Step - by - Step Step 1: Defining the wrench spaces EXAMPLE: Discretized Ellipse Initial grasp G = [ p 1 , ··· , p 3 ] T Robert Krug IROS 2010 13 / 21