A computational model of arm trajectory modification using dynamic movement primitives

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MOTIVATION
A COMPUTATIONAL MODEL OF ARM TRAJECTORY
MODIFICATION USING DYNAMIC MOVEMENT PRIMITIVES
Peyman Mohajerian, Heiko Hoffmann, Michael Mistry, Stefan Schaal
Computer Science, Neuroscience, and Biomedical Engineering, University of Southern California,
Los Angeles, CA 90089-2520 & ATR Computational Neuroscience Laboratories, Kyoto, Japan
http://www-clmc.usc.edu/
References:
Flanagan J. R., Ostry D. J., Feldman A. G .(1993) Control of trajectory modifications in target-directed reaching. J Mot Behav 25:140-52.
Henis E., Flash T. (1995) Mechanisms underlying the generation of averaged modified trajectories. Biol Cybern, 72, 407-419.
Hoff B., Arbib M. (1992) A model of the effects of speed, accuracy and perturbation on visually guided reaching. In: Caminiti R (ed) Control of arm movement in space: neu-
rophysiological and computational approaches. Springer-Verlag, Berlin, pp 285–306
Hoff B., Arbib M. (1993) Models of trajectory formation and temporal interaction of reach and grasp. J Mot Behav 25:175-192.
Ijspeert, J. A., Nakanishi, J.;Schaal, S. (2002). Movement imitation with nonlinear dynamical systems in humanoid robots, International Conference on Robotics and Automa-
tion (ICRA2002).
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METHODS
DISCUSSION
Introduction:
An open issue in the neural control of movement is how humans generalize a previously
learned behavior to new or altered situations. One method to investigate this is the double-
step target displacement protocol which shows how an unexpected upcoming new target
modifies an ongoing discrete movement.
Hypothesis for online goal adaptation:
+ Second movement is superimposed on the first movement (Henis and Flash, 1995)
+ First movement is aborted and the second movement is planned to smoothly connect
the current state of the arm with the new target (Hoff and Arbib, 1992)
+ Second movement is initiated by a new control signal that replaces the first move
ment‘s control signal, but does not take the state of the system into account
(Flanagan et al., 1993)
+ Second movement is initiated by a new goal command, but the control structure stays
unchanged, and feed-back from the current state is taken into account
(Hoff and Arbib, 1993)
Goals:
Show that online correction and the observed target switching phenomena can be
accomplished by changing the goal state of an on-going Dynamic Movement Primitive
(DMP), without the need to switch to different movement primitives or to re-plan the
movement.
This poster addresses using DMPs as a parsimonious movement
generalization paradigm to investigate online movement correction
RESULTS
Experimental Setup:
• Endpoint tracking using Newton Lab Color Vision System at 60 Hz.
• Psychtoolbox software with MatLab for generating 3D anaglyph visual stimuli.
Procedure:
Starting from a visually displayed start point, subjects perform reaching movement to a
given target point. Subjects were instructed to immediately move to the target as soon as
it was displayed. In 50% of the trials, the target suddenly switched to a new target. The
interstimulus interval (ISI) between the onset of the first and second target was varied
between 30, 50, 100 and 200ms across blocks. Each subject performed four blocks (80
trials), presented in a randomized way. Model Equations based On Dynamic Movement
Primtiives:
Subject #1 ISI: 30 ms Subject #1 ISI: 50 ms Subject #1 ISI: 100 ms Subject #1 ISI: 200 ms
Subject #2 ISI: 30 ms Subject #2 ISI: 50 ms Subject #2 ISI: 100 ms Subject #2 ISI: 200 ms
Subject’s view of the display monitor. In the lower left is the sphere for the
initial end-effector position, in the upper right is the position of the primary
target (in the middle) and the two secondary targets orthogonal to it.
Obviously at any point in time subjects can only see one of the spheres.
View of the experimental setup. A subject is pointing at
the initial target while the two cameras are tracking the
green sphere that he is holding. The cubic foam with the
green ball on top is used during calibration of the cameras
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Minimum Jerk Movement
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Optimized Minimum Jerk
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Optimized Minimum Variance
Analytical Minimum Jerk
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Optimized Minimum Torque
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Minimum Torque Movement
Dynamic Movement Primitives are a general representation for kinematic movement planning with learnable linear parameters . The parameters can be acquired, e.g., from
imitation learning, but also from general optimization frameworks, as shown in the plot above. In these plots. we simulated a 1 DOF linear movement system with mass, stiffness,
and damping parameters. The parameters were optimized according to different criteria that were suggested in the literature, e.g., minmum jerk, minimum torque change,
and minimum endpoint variance (Flash and Hogan 1985; Uno et al. 1989; Harris and Wolpert 1998).
data, original goal
data, goal switch
Our model
Flash model
Trajectories of the goal directed movement for two subjects for different ISI values, averaged across all trials. In both
subjects as the ISI increases the initial direction of the movement moves toward the first target.
Our model is comparable to Flash‘s, but a straight movement is not sufficient to distinguish between models. We will
extend our experiment to more complex target switches, and also more complex movements (e.g., like a spiral).
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On the left trial by trial and the averaged trajectories for one of the subject for ISI value of 30 ms.
On the right, averaged velocity profile for the same set of data. Bell shaped velocity characteristic is preserved during target switching.
averaged original goal
a trial, original goal
averaged, switching
a trial, switching
x- position, v- velocity
- start position, g- goal position
- similar to spring constant
- damping term, critically damped
- gaussian basis function with
center and heights of ,
-phasic variable between 0 to 1
-time constant