Motion Planning for Character Animation and Computer Games

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Motion Planning for Character Animation and
Computer Games

• Luv Kohli
• COMP290-058
• October 13, 2003

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Outline

• Planning Motions with Intentions
• Dynamic Autonomous Agents Game Applications
• Better Group Behaviors in Complex Environments
  using Global Roadmaps

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Planning Motions with IntentionsY. Koga, K.
Kondo, J. Kuffner, Jean-Claude Latombe
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Motion with Intention?

• A motion driven by the intent to accomplish some
  task
• Non-predictable
• Not described by laws of physics

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Task-based Animation

• Animation of figures automatically computed by
  motion planner
• Animator concentrates on creating imaginative
  graphics instead of moving figures realistically

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Manipulation Planning

• Subset of task-based animation
• Automatic generation of human/robot arm motions
  to complete manipulation tasks
• Contrast with passive system (e.g. ball falling)
  arms move with the intention of completing some
  task

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Problem

• Find a collision-free path for arms to grasp and
  then carry a moveable object from an initial
  location to a goal location
• Known as multi-arm manipulation planning problem
• Must account for the ability of arms to change
  grasp (ungrasp/regrasp) of the object

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Planner

• Input
• Geometry of the environment
• Initial and goal configurations of the moveable
  object and arms
• Set of potential grasps of the moveable object
• Inverse kinematics of the arms

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Some definitions (1)

• Stable space (Cstable) set of all legal
  configurations in Cfree where the object is
  statically stable
• Grasp space (Cgrasp) set of all legal
  configurations in Cfree where one or several arms
  rigidly grasp the object such that they have
  sufficient torque to move it. Cgrasp ? Cstable

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Some definitions (2)

• 2 basic types of paths
• Transit path defines arm motions that do not
  move the object
• Transfer path defines arm motions that move the
  object
• Manipulation path - alternate sequence of transit
  and transfer paths that gets from the initial
  position to the goal

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Composite configuration space
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Planning approach (1)

• Each path is a subtask of the total task
• Two-stage approach
• Generate series of subtasks to achieve goal
• Plan transit or transfer paths for each subtask
• Example grab object, carry it to an intermediate
  location, change grasp, carry object to goal
  location, ungrasp

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Planning approach (2)

• Planning a series of subtasks and converting them
  into legal paths is difficult
• Compromise plan a sequence of transfer tasks
  that are guaranteed to be completed into transfer
  paths
• Transit tasks are immediately defined
• Assumes legal transit path exists for each
  transit task

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Grasp restrictions

• To simplify the selection of transfer tasks, a
  finite grasp set is predefined
• Each grasp describes a rigid attachment of the
  end-effector(s) of one or several arms with the
  object

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Generating transfer tasks (1)

• A path Tobj that moves the object from its
  initial to its goal configuration is created
• The planner attempts to use the same grasp or set
  of grasps for as long as possible
• Tobj is computed using RPP (Randomized Path
  Planner)

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Generating transfer tasks (2)

• RPP generates Tobj as list of adjacent
  configurations in a fine grid placed over Cobj
• Original RPP only checks that each inserted
  configuration is collision-free
• Use a modified RPP verifies that the object can
  be grasped using a grasp from the grasp set

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Generating transfer tasks (3)

• grasp assignment - associates an element of the
  grasp set and the identity of the grasping arm(s)
• The planner enumerates all grasp assignments at
  the initial configuration
• Keeps a list of valid grasp assignments (no
  collisions)
• This list is associated with initial configuration

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Generating transfer tasks (4)

• Before inserting a new configuration, prune the
  list of grasp assignments which are now invalid
• If the list is empty, reset it to contain all
  possible grasp assignments (as in the initial
  configuration)

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Generating transfer tasks (5)

• The same grasp using different arm postures is
  considered a separate grasp assignment
• Each arm has a non-obstructive configuration
• The object must be held at all times during
  regrasps

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Generating transit paths (1)
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Generating transit paths (2)

• Difficulty arises when an ungrasp/regrasp is
  required between two transfer tasks
• In some cases, an intermediate grasp may be
  required
• Break the transit task into smaller transit
  subtasks such that no two arms have the same
  grasp at the same time

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Human-Arm Kinematics

• Model based on two results from neurophysiology
• Arm and wrist posture mostly independent of each
  other problem can be decoupled
• Arm posture for pointing determined by simple
  sensorimotor transformation model used to
  determine shoulder and elbow joint angles

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Arm posture

• Arm described by four parameters
• ?, ?, ?, ? - elevation and yaw of upper arm and
  forearm respectively
• Wrist position (or hand frame) expressed in
  spherical coordinates
• Azimuth ?, elevation ?, radial distance R

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Transformation model (1)

• The sensorimotor transformation model suggests
  that the parameters for arm posture are
  approximated by a linear mapping from the hand
  frame coordinates
• ? -4.0 1.10R 0.90?
• ? 39.4 0.54R 1.06?
• ? 13.2 0.86? 0.11?
• ? -10.0 1.08? 0.35?

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Transformation model (2)

• If the resulting values are legal, then determine
  the wrist joint angles
• Otherwise enter a tuning phase to adjust the
  values until they are legal

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Transformation model (3)

• Wrist joint angles found using standard IK
  techniques. If values are not legal, then closest
  are chosen and improved in final adjustment step
• Final adjustment step constrained optimization

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Natural motion

• Results compared to neurophysiological
  naturalness constraints fit fairly well
• Dynamics not considered this is OK according to
  neurophysiology
• Modulation in elevation and yaw in upper arm and
  forearm close to sinusoidal, and techniques
  experimental values match well

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Results

• Each human arm has 7 DOF, 19 for each hand
• Robot has 6 revolute joints and 3 DOF for
  end-effector
• Grasp set contained 289 grasps, and grasp
  assignment lists of up to 2600 elements
• (show video)

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Dynamic Autonomous Agents Game ApplicationsS.
Goldenstein, E. Large, D. Metaxas
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The problem

• Want to model autonomous agents in game-like
  environments
• Real-time
• Dynamic targets and obstacles in the environment

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Why?

• Useful for
• Simulations
• Games
• VR
• Want agents to exhibit certain behaviors without
  user intervention

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How?

• Make use of dynamical systems theory
• Express intelligent behaviors using systems of
  differential equations
• Two distinct dynamic systems are combined
• Movement dynamics controls agent movement
  (heading, velocity)
• Task dynamics controls agent behavior

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Heading direction (1)

• Movement defined by 2D vector representing
  agents heading angle and forward speed
• Heading angle computed via
• f is a nonlinear function and env represents the
  state of the environment

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Heading direction (2)

• Each element of the environment can attract or
  repel an agent
• Attractors and repellers are located at the zero
  crossings of f (critical/fixed points)
• Attractor (target) modeled as
• ? is angle of targets location relative to
  agents location, and a is constant parameter
  (generally set as 1)

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Heading direction (3)

• Obstacles (e.g. enemies or hazards) are distinct
  entities
• Fire-pits, for example, are clearly more
  dangerous than a large wall.

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Heading direction (4)

• Different repellers created using multiplication
  of three functions
• Ri type of repeller
• Wi angle-based influence

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Heading direction (5)

• Di distance-based influence
• Repeller (obstacle) modeled as
• Resulting influence from obstacles

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Heading direction (6)

• Heading angle obtained using
• wtar and wobs are weights obtained through the
  task dynamics system
• The noise term n allows the system to escape from
  unstable fixed points

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Example 1
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Example 2
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Velocity

• Simplest possibility constant velocity, but
  potential for many collisions
• Instead, have agent move faster when no objects
  are near and slower in a crowded area
• rmin distance to closest obstacle,d1 safety
  distance, t2c time to contact

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Task dynamics (1)

• Individually, attractors and repellers work well,
  but their sum might yield problems
• Instead of a direct sum, use weights determined
  by a second dynamical system that runs at a more
  refined time scale

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Task dynamics (2)

• The second system is modeled as
• ?1, ?2, ?12, and ?21 are parameter functions to
  be designed
• wtar and wobs are computed based on the
  computation of the fixed points in this system
  (.wtar .wobs 0)

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Stability analysis (1)

• This system when chosen arbitrarily may not
  converge to a fixed point, so a stability
  analysis is required
• This is done using a classical nonlinear
  dynamical system stability analysis
• It is determined that the system has four
  critical points (0,0), (0,?1), (?1,0), (?A1,
  ?A2), where

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Stability analysis (2)
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Stability analysis (3)

• Based on this information the parameter functions
  can be computed (see paper)

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Better Group Behaviors in Complex Environments
using Global RoadmapsO. Burchan Bayazit,
Jyh-Ming Lien, Nancy Amato
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References

• Y. Koga, K. Kondo, J. Kuffner, J.L. Latombe,
  Planning Motions with Intentions. Proceedings of
  SIGGRAPH 94, ACM SIGGRAPH, 1994, 395-408.
• Goldenstein, S., Large, E., and Metaxas, D.
  Dynamic Autonomous Agents Game Applications.
  Computer Animation, 1998.
• O. Burchan Bayazit, Jyh-Ming Lien, Nancy M.
  Amato, Better Group Behaviors using Global
  Roadmaps. Proceedings of the 8th International
  Conference on the Simulation and Synthesis of
  Living Systems (Alife02), December 2002, pp.
  362-370.