Motion Planning

1
World space physical space, contains robots
and obstacles Configuration set of independent
parameters that characterizes the position of
every point in the object In 3D space, 6 numbers
required to describe configuration of rigid body
(3 for position, 3 for orientation). For a
manipulator, the parameters are the state of
each one of its joints (e.g. a 2-link PUMA only
rotational joints manipulators configuration
needs 2 parameters to be described) Degrees of
freedom (dof) of an object number of
parameters specifying a configuration
2
gt6-dof manipulators in 3D space belong to the
class of redundant manipulators, more flexible,
free to use extra dof as wish to solve MP (Motion
Planning) problem
3
Configuration space (Cspace) set of all
configurations Free space (Cfree) set of
allowed (feasible) configurations Obstacle space
(Cobstacle) set of disallowed configurations
Cspace Cfree Cobstacle
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• Path of an object
• curve in the configuration space
• represented either by
• Mathematical expression, or
• Sequence of points
• Trajectory
• Path assignment of time to points along the
  path
• Motion Planning (MP), a general term, either
• Path planning, or
• Trajectory planning

5

• Path planning
• design of only geometric (kinematic)
  specifications of the positions and orientations
  of robots
• Trajectory planning
• path planning design of linear and angular
  velocities
• Path planning lt Trajectory planning
• at path planning, dynamics of robots unimportant
  or neglected
• path planning also used as first step in design
  of trajectories

6

• Static motion planning
• obstacle info known a priori
• motion of robot designed from given information
• Dynamic motion planning
• partial obstacle info available (e.g. visible
  parts)
• Initial planning based on the available
  information
• Follows planned path, discovering more obstacle
  info
• Updates internal representation of environment
• Replans path
• Continued till goal accomplished
• Most papers in MP, up to 1992, deal with static
  case

7

• Generalized movers problem
• given
• Robot with d degrees of freedom (dof)
• In an environment with n obstacles
• Find path
• collision-free
• connecting current (start) configuration to
  desired (goal) one

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• Completeness (classification of MP algorithms)
• Exact
• usually computationally expensive
• may determine bounds of a problems complexity
• Heuristic
• ained at genertating a solution in a short time
• may fail to find solution or find poor one at
  difficult problems
• important in engineering applications
• Resolution complete (discretization)
• Probabilistically complete (probabilistic
  completeness ?1)

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• Scope (classification of MP algorithms)
• Global
• take into account all environment information
• plan a motion from start to goal configuration
• Local
• avoid obstacles in the vincinity of the robot
• use information about nearby obstacles only
• used when start and goal are close together
• used as component in global planner, or
• used as safety feature to avoid unexpected
  obstacles not present in environment model, but
  sensed during motion

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• MP formulation
• Configuration space (Cspace space of all
  possible motions)
• Object representation (robot and objects config.
  obstacles)
• Select motion planning approach (suitable to
  problem)
• Skeleton, Cell decomposition, Potential field,
  Mathematical programming / optimization
• Use search method(s), to find a solution path
• Local optimization of motion (get shorter and
  smoother path)
• smoother no sharp corners not have to use
  very low speed

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• Search methods
• Depth-first (not the shortest)
• Breadth-first / brushfire (shortest path,
  examines large part)
• Hill climbing / Best-first / Hypothesize and test
  (blind-alley trap, long time)
• A (minimum cost / shortest path, pruning)
• Bi-directional (combine with any algorithm,
  narrow channels)
• Dijkstras shortest-path for graphs (most
  efficient)
• Random search / simulated annealing (random,
  long time)
• MP -gt find connected sequence of feasible
  configurations between start and goal ones

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Best explained using a grid S Start
configuration G Goal configuration Dark
Infeasible configurations Parent configuration
-gt child configuration Each child has at max one
parent (avoid cycles/loops)
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• Selection of search method
• If criterion for selecting good moving direction,
  use best-first rather than depth-first or
  breadth-first
• If easy problem (free space wide, many motion
  solutions, any solution adequate, not optimal
  one), use depth-first or best-first
• If shortest path desired, use A or Dijkstras
  algorithm
• Massively parallel computation ? breadth-first
  effective
• Bidirectional search whenever possible. Move from
  cluttered to open space, harder to achieve a
  configuration in cluttered space
• If many MP with different start/goal, compute
  spatial representation ahead
• If one MP problem, do partial representation,
  refine iteratively (ICORS)
• Environment slow change, updating scheme, no
  recomputation