Manipulation%20Planning

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Manipulation Planning
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• In 1995 Alami, Laumond and T. Simeon proposed
• to solve the problem by building and searching a
  manipulation graph.

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• The problem

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• The problem
• Constraints
• The movable objects cannot move by itself.
• The movable objects cannot be left alone in
  unstable positions.

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• The problem
• We consider the composite configuration space of
  the robot and all movable objects CS CSR x
  (CSA x CSB x)
• Where CSR is the configuration space of the robot
• and CSA, CSB, are the configuration spaces of
  the
• movable objects.

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• The composite C-space CS

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• The composite C-space CS

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• The composite C-space CS

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• The composite C-space CS

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• We obtain a manipulation-path (solid blue
  line) between two configurations in the composite
  C-space.
• Not any path (like the dotted ones) in the free
  space is a manipulation path.

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• A manipulation path
• Satisfies the physical constraints of the problem
• Consists of alternation of
• Transit Path
• Transfer Path

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• Transit Path The robot moves from its current
  configuration, to any configuration that enables
  
• the part to grasping an object.
• Transfer Path The robot carries the grasped
  object
• to its desired goal configuration.

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• A manipulation path
• Satisfies the physical constraints of the problem
• Consists of alternation of
• Transit Path
• Transfer Path

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• Few more definitions
• PLACEMENT the subspace of free CS containing
• all valid placements for all objects, i.e.
  placements
• which respect the physical constraints.
• In PLACEMENT
• Not in PLACEMENT

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• Few more definitions
• G-connectivity 2 configurations of free(CS) are
  
• g-connected if they are connected by a transfer
  path.

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• Few more definitions
• GRASP the subspace of free(CS) containing the
  configurations which are g-connected with a
• configuration of PLACEMENT.

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• The case of discrete PLACEMENTS and GRASPS for
• several movable objects

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• The case of discrete PLACEMENTS and GRASPS for
• several movable objects
• Consider a robot R and two moveable objects A and
  B.
• Let p1A , p2A , ? CSA and p1B , p2B , ? CSB
  the valid placements for A and B respectively.

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• The case of discrete PLACEMENTS and GRASPS for
• several movable objects
• Consider a robot R and two moveable objects A and
  B.
• Let p1A , p2A , ? CSA and p1B , p2B , ? CSB
  the valid placements for A and B respectively.
• Let GA1 , GA2, and GB1 , GB2, be finite number
  of
• possible grasps for A and B.

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• The case of discrete PLACEMENTS and GRASPS for
• several movable objects
• For a given start and goal position in the
  composite
• C-space CS CR x CA x CB, obtain a manipulation
  
• path by building and searching a manipulation
  graph.

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT

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• GRASP
• PLACEMENT
• GRASP n PLACEMENT

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT
• Building the edges
• Nodes are linked by transit edges or transfer
  edges.

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT
• Building the edges
• Nodes are linked by transit edges or transfer
  edges.
• A transit edge exists between two nodes if they
  belong to the same transit state C(_, pAi, pBj).

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• Transit State

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT
• Building the edges
• Nodes are linked by transit edges or transfer
  edges.
• A transit edge exists between two nodes if they
  belong to the same transit state C(_, pAi, pBj).

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT
• Building the edges
• Nodes are linked by transit edges or transfer
  edges.
• A transit edge exists between two nodes if they
  belong to the same transit state C(_, pAi, pBj).
• A transfer edge can be build between two nodes if
  they belong to the same transfer state C(GAi , _,
  pBj) or C(GBi , pAj ,_).

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• Transfer State

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• Building the manipulation graph
• Building the nodes
• Nodes of the graph is the set
• GRASP n PLACEMENT
• Building the edges
• Nodes are linked by transit edges or transfer
  edges.
• A transit edge exists between two nodes if they
  belong to the same transit state C(_, pAi, pBj).
• A transfer edge can be build between two nodes if
  they belong to the same transfer state C(GAi , _,
  pBj) or C(GBi , pAj ,_).

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• The manipulation graph looks like

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• The manipulation graph looks like

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• The manipulation graph looks like
• Finally graph search is done to find a
  manipulation path.

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• Implementation
• Manipulation Task Planner
• Builds the manipulation graph and searches a
  manipulation path using A Algorithm.
• Motion Planner
• Computes the edges of the graph.

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• Extension from discrete to infinite set of
  grasps
• Now the discrete configurations of the set
• GRASP n PLACEMENT is replaced by connected
  components of GRASP n PLACEMENT obtained
• by its cell decomposition.

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• To end with