Swing Dancing and Multi-agent Coordination

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Swing Dancing and Multi-agent Coordination

• Sommer Gentry
• Eric Feron
• MURI Meeting March, 2002

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And a 5, 6, a 5-6-7-8

• About swing dancing
• High-level cooperative motion planning
• Experimental work Connection force estimates
  from video via inverse dynamics

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Why Swing Dancing?

• Sports biomechanics studies abound for
  gymnastics, swimming, pole vaulting, etc.
• Swing dancing is a partnered form of movement
  necessitating shared momentum
• Could be a setting for novel cooperative maneuver
  studies
• unknown environments
• constrained resources and communication
• leader and follower structure

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Lindy Hop (1935)
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Connection State determines which actuators on
the followers motion are available to leader
Tuck turn
Pullthrough
Closed
Right hand
Sendout
Underarm
Circle
Crosshand
Sling
Whip
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Decentralized Hybrid Controller
Connection Automaton
Connection state change request
?
For fixed ?
Leader
P
Desired (xf , yf , ?f )
-
K
Forces (?)
(xf , yf , ?f )
Follower
P
K
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Decentralized hybrid control

• Connection state
• closed, right hand, two hands, crosshand, no
  hands
• (xl , yl , ?l ), (xf , yf , ?f ) are leaders and
  followers position on floor and facing angle
• Leader choreographs dance in real-time
• Leader knows desired follower trajectory
• Hypothesis leader imparts force, but can not
  cause the complete motion of the follower
• Follower knows a lexicon of swing dance moves
• Hypothesis follower interprets leaders force
  signals to select a sequence of moves

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Controlled switching surfaces

• Two hands one hand
• no restrictions
• One hand closed
• close enough (xl - xf)2 (yl - yf)2 lt C
• facing each other 90 lt ?l - ?f lt 180
• on the correct side (cos ?l)xl lt (cos ?l)xf
  (sin ?l) yl gt
  (sin ?l) yf

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Followers problem

• Given the lead as an input, decide what movement
  to do
• model imperfect or noisy leads (late leads,
  over-forceful turns, etc.)
• uncover or learn strategies for robust following

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Leaders problem

• Given a movement from a shared dance vocabulary,
  design a lead that
• is unambiguous
• doesnt render the movement impossible for either
  the leader or the follower
• minimizes some physical criterion (jerk for
  example)

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Dancers tune their connection

• A few quotes from swing dancers
• When I dance with a new partner, I try to feel
  whether he wants to counterbalance me and try to
  judge how much he can take.
• Is she a light or heavy follow? Is she matching
  my counterbalance or I hers? Is she supporting
  her own weight? Or as a follow is he a strong
  lead or do I need to think about what he's trying
  to get me to do? Does he pull me too hard on
  swingouts or is he clear and minimal in his
  leads?
• I have seen some footage of late 30s and early
  40s L.A. style Lindy and it relies on lots of
  counter-balance and traveling steps.
• Source www.delphiforums.com/(socalswingswingoutd
  c)

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Force / trajectory control

• Dancers use counterbalance force
• leader and follower holding hands both shift
  center of gravity back slightly the resulting
  static force is connection, or counterbalance
• counterbalance enables faster spins and travel
• Movement is also initiated by force
• How is force that requests increased
  counterbalance distinguished from force that
  requests follower to move forward? Preliminary
  data suggest move forward is coded in the first
  derivative of force

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A follower is not a ton of bricks
acceleration
F / m a
and if on the expected beat, coded properly in
derivative
.
F
follower motion
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Force estimates from video

• Acquire estimate of the connection force between
  dancers in video
• Active marker systems (Optotrak) exist, but here
  I used standard video recording frames
• Lindy hop is a historical dance form
• uninstrumented video from 1930s and 1940s is
  treasured by dancers and could be studied
• Example sugar push video

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Inverse Dynamics

• Given inertial properties and a time history of
  the motion of a system, generate force/torque
  histories for that system
• Tabulate motion history from video frames

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Sugar Push
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Inertial properties of a human

• Yeadon, M.R. "The simulation of aerial movement -
  II. A mathematical inertia model of the human
  body." J. Biomechanics 23, pp 67-74
• From lengths and circumferences of body segments,
  Yeadons model gives inertial properties of the
  
  segments of the body
  (M, Ix, Iy, Iz)
• Stadia trunk segments
• Truncated cones
  arm, leg segments

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SD/FAST results

• SD/FAST software computed the inverse dynamics
  given time histories of the joint angles and the
  followers inertial properties

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Measured connection force
Tek-scan sensor system captured connection
forces between leader and follower
Thanks to Dr. Patricia Schmidt of the MIT
Manned Vehicle Lab
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Sugar push connection force
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Conclusions from first stage

• Video, via inverse dynamics, might be used to
  generate estimates of connection force
• The pattern of connection force for a particular
  maneuver is consistent with some noise that is,
  a sugar push lead has a certain nominal force
  pattern with some bounded variation

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Sugar pushes versus swingouts
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Representing dance leads quantitatively

• Push and pull should be distinguished
• Some moves involve leads which push and pull
  while hands move
• Right and left hands are not always symmetric
• Which foot the follower is on changes the meaning
  of a lead

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Relevant work

• Physical interaction between human and a bipedal
  humanoid robot Realization of human-follow
  walking, A. Takanishi et al 1999 IEEE Conf.
  Robotics and Automation
• Controlling formations of multiple mobile robots,
  J.P. Desai, J. Ostrowski, V. Kumar 1998 IEEE
  Conf. Robotics and Automation
• Robust hybrid control for autonomous vehicle
  motion planning, E. Frazzoli, M. Dahleh, E. Feron
  LIDS-P-2468

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Relevant work

• Optimal robot motions for physical criteria, J.E.
  Bobrow et al, Journal of Robotic Systems 18(12),
  2001
• One view of a motion program is as a
  concatenation of simpler motion primitives. The
  compiler's role then is to optimize this sequence
  of motion primitives with respect to some
  performance criterion. In this sense the motion
  compiler can be viewed as a choreographer - it
  pieces and blends a sequence of crude basic
  motions into a fluid and artistic dance.

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Graceful motion is optimized

• Planning of joint trajectories for humanoid
  robots using B-spline wavelets, A. Ude, C.
  Atkeson, M. Riley IEEE Conf. Robotics and
  Automation 2000
• regularization by
  minimizing amplitude
  of acceleration or jerk

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Big Picture

• What is the perfomance measure being optimized by
  expert swing dancers?
• objectively judge dance performances
• Characterize swing dance lead and follow
• lead is not just a signal but also makes the
  movement physically possible or impossible
• Ultimate goal might be to create a control
  strategy for a robot that can swing dance
• control multi-agent systems with a leader and
  follower(s) in collision-free coordinated motion

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Questions? Ideas?
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5th Place American Showcase 2001