Transcript Computational Motor Control: Redundancy and Invariance

Computational Motor Control:
Redundancy and Invariance
Guigon, Baraduc, and Desmurget,
J. Neurophysiol., 2007
Question
• The brain deals with the task
of controlling complex
redundant biomechanical
system in the presence of
noise
• We use oversimplified models
that can explain experimental
results
– Understand the brain using a
limited set of computational
principles
Discussion
• What is the purpose of models?
• How complicated a model needs to be?
– What does it needs to explain?
– Where do we stop to increase complexity?
• Does a model needs to be physiologically
plausible?
– Do we need to be able to map the boxes to physiology
• Does the model needs to be biomechanically
veridical?
– Can we learn something from the attempt to control a
robotic linkage without any muscles?
Good model
• For understanding:
– As simple as possible
– Explains phenomena
– Consistent with reasonable chunk of previously
existing data
– Provides testable predictions
• Refutable
• For using in application:
– Useful
– Improves performance
Take home
• A model based on a limited set of
computational principles can explain:
– Kinematic redundancy
• Bernstein (1967, but actually 1929)
– Motor equivalency
• Lashley (1933)
– Scaling of movement duration with amplitude
• Speed accuracy tradeoff (Fitts, 1954)
Model principles
①Separation
– Static v. dynamic commands are computed separately
• Not separation between movement and posture
②Optimal Feedback Control
– A solution to ill-posed problem obtained by
minimizing cost function
– Includes a state estimator (state not observable, and
noisy)
Model principles cont.
③Maximum efficiency
– Cost function: centrally generated signals that
generate dynamic forces
– Constraint function: boundary conditions at ti and tf
④Constant effort
– Important when movement time is not specified
– A set of instructions is equivalent to effort level
– Movement with different amplitudes, directions, or
loads are executed with the same effort
General sketch of the model
Assumption about muscles and
neurons
• Muscle
– Generates forces when stimulated
– Linear spring
– Low pass filter
– Generates joint torques
• Neurons
– One neuron innervates all muscle
– Receives a unique and specific control signal
Model
• N-link robotic manipulator
• 2N muscles
• Dynamics
• Optimal controller
Model cont.
• Constant effort principle
– Find the optimal E for given movement A and D
– For a given E, deduce A or D if not specified
• Parameters were chosen (arbitrary?) and not
fitted to any particular data set
Results – kinematic redundancy
Pelegrini and Flanders, 1996
Novice
10mm
Nisky et al, in preparation
Expert
Results – terminal posture
independent of velocity
Soechting and
Lacquaniti, 1981
Results – difference between up
and down movements
Appear without adding gravity into the model!
Papaxanthis et al., 2003
Results – grasping movements
Desmurget et al., 1996
Results – grasping movement
High start
Low start
Desmurget et al., 1998
Results – kinematic invariance
Without a desired trajectory -> emergent property (???)
Target distance
Gordon et al., 1994
Results – kinematic invariance
Nisky et al, in preparation
Results – invariance with
inertial loads
Making models more complex
• Muscular redundancy
• Nonlinear Hill-type
muscle
• Muscle synergies
• Changed patterns of
activation, but not
kinematics
Conclusion
• Solution to the degrees of freedom problem
should
– Explain how a solution determined
– Explain why it is different at each time
• Principles
– Optimal feedback control
– Maximum efficiency
– Separation principle – necessary for realistic solution
in nonlinear dynamics case
– Constant effort added for completeness in case
amplitude/duration are not defined
Limitations
• Nonsymmetric velocity profiles
• Effects of instructions on slope of
amplitude/duration scaling
• Model invariant to rotation about shoulder
joint
• Joint limits
• Other limitations that we can think about
Different Separation Principles
• Equilibrium Point Hypothesis:
– Reciprocal activation v. Coactivation of antagonist
muscle
• Internal Models
– Inverse model v. feedback control
• This work
– Dynamic v. static
Discussion
• Sober and Sabes paper
interpretation
– Sober and Sabes suggest
perfect control from
imperfect initial position
estimation
– Guigon et al. suggest
imperfect control from true
hand position