MANIPULATION PLANNING UNDER CONTINUOUS GRASPS AND PLACEMENTS

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MANIPULATION PLANNING UNDER CONTINUOUS GRASPS AND
PLACEMENTS
T. Simeon, J Cortes, A Sahbani, JP Laumond

• By,
• Arjun. K. Arumbakkam

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A 6 dof Robotic Manipulator performing pick and
place of the Rod inside the Cage.
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Manipulation Planning Problem

• Configuration space of Robot
• Crob
• Configuration space of Object
• Cobj
• Composite Configuration Space
• Cspace Crob x Cobj
• Free space
• Csfree ? Subset of Cspace

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Manipulation Constraints

• Solution is a constrained path is Csfree.
• Solution path consists of
• Transit path ? Only the robot moves and the
  Object is static.
• Transfer path ? Object is static relative to the
  robot. Robot is moving around.

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Hierarchical subdivision of Problem

• Planner divides search space into several
  components
• CSpace
• Placement Space ? CP
• Grasp Space ? CG

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Structure of the Manipulation Roadmap
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Problem definition

• To find a path connecting two configurations in
  CG U CP, given P and G.

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Earlier manipulation planners

• Required Inputs from the user
• Finite set of Stable Placements of Movable
  Object.
• Finite set of Possible Grasps of Movable Object.

Hence, they were known as Planners for Discrete
cases
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What is new in this planner ?

• Deals with continuous sets of P and G.
• CG CP is defined as a continuous domain, which
  is basically the manifold that corresponds to the
  robot grasping the movable object on a stable
  placement.
• Utilizes REDUCTION PROPERTY of the manipulation
  graph.

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Manipulation Graph

• Is a Search space
• Nodes correspond to small connected components of
  CG CP .
• These nodes are connected using alternating
  Transit and Transfer paths.

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Visibility road map computed in CG CP and two
placements in two different connected components
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Connections using Transfer and Transit paths

• When a direct collision free path between q1
  and q2 in CG CP cannot be made then
• qi (gi, pi)
• A connection is attempted by the planner if
• There is a transfer path from (g1,p1) to (g1,
  p2) followed by a transit path from (g1, p2) to
  (g2, p2) and vice versa.

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Probabilistic Algorithm for path planning

• The connected components in CG CP are
  computed.
• Connectivity of these subsets is determined using
  Transit and Transfer paths (reduction technique).
• This approach allows for continuous sets in the
  manipulation problem.

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• I.e. several classes of possible continuous
  grasps are entered as Gi.
• Gi is defined by a Transformation matrix Tgi and
  a set of parameters/ q_grasp, varying in an
  interval.
• Same thing applies for possible continuous
  placements (defined by)
• Transformation matrix and q_place (x, y, Q)

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Virtual closed chain system and a feasible CGCP
motion.
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Manipulation planning Algorithm

• Incrementally constructs a manipulation graph
  (MG), until it exceeds MAX_NTRY nodes or finds a
  solution.
• Primarily consists of four subroutines
• EXPAND_GRAPH(MG)
• EXPAND_IN_GP(MG)
• EXPAND_USING_REGRASPING(MG)
• EXPAND_USING_TRANSFER(MG)

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References

• A Probabilistic Algorithm for Manipulation under
  continuous grasps and placements, by
• A. Sahbani, J Cortes, T. Simeon
• A Manipulation planner for pick and place
  operations under continuous grasps and
  placements, by
• T. Simeon, J. Cortes, A Sahbani, JP Laumond
• JC Latombe Robot Motion Planning