Transcript Swing Dancing and Multi

Swing Dancing and Multi-agent
Coordination
Sommer Gentry
Eric Feron
MURI Meeting March, 2002
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
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
Lindy Hop (1935)
Connection State
determines which
actuators on the
follower’s motion
are available to leader
Tuck turn
Closed
Sendout
Pullthrough
Right hand
Underarm
Circle
Sling
Whip
Crosshand
Decentralized Hybrid Controller
Connection state change request
Connection Automaton
κ
For fixed κ
Desired (xf , yf , θf )
Leader
P
K
(xf , yf , θf )
Forces (κ)
Follower
P
K
Decentralized hybrid control
• Connection state
– {closed, right hand, two hands, crosshand, no hands}
• (xl , yl , θl ), (xf , yf , θf ) are leader’s and follower’s
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 leader’s force signals to
select a sequence of moves
Controlled switching surfaces
• Two hands
one hand
– no restrictions
• One hand
closed
– close enough: (xl - xf)2 + (yl - yf)2 < C
– facing each other: 90 < θl - θf < 180
– on the correct side: (cos θl)xl < (cos θl)xf
(sin θl) yl > (sin θl) yf
Follower’s 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
Leader’s problem
• Given a movement from a shared dance
vocabulary, design a lead that
– is unambiguous
– doesn’t render the movement impossible for
either the leader or the follower
– minimizes some physical criterion (jerk for
example)
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/(socalswing|swingoutdc)
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
A follower is not a ton of bricks
F
/
m
= a
=
and if on the expected beat, coded properly in derivative
.
F
= follower motion
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 1930’s and 1940’s
is treasured by dancers and could be studied
• Example: sugar push video
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
Sugar Push
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, Yeadon’s model gives inertial properties
of the
segments of the
body
(M, Ix, Iy, Iz)
• Stadia: trunk segments
• Truncated cones:
arm, leg segments
SD/FAST results
• SD/FAST software computed the inverse
dynamics given time histories of the joint
angles and the follower’s inertial properties
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
Sugar push connection force
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
Time (secs)
4.
0
3.
7
3.
5
3.
2
3.
0
2.
7
2.
5
2.
2
2.
0
1.
7
1.
5
1.
3
1.
0
0.
7
0.
5
0.
3
0.
0
Force (N)
Sugar pushes versus swingouts
30
25
20
15
10
5
0
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
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]
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.”
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
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
Questions? Ideas?
5th Place American Showcase 2001