the bump model: speed-accuracy tradeoffs and velocity profiles of aimed movement robin t. bye...
TRANSCRIPT
The BUMP model: Speed-accuracy tradeoffs and
velocity profiles of aimed movement
Robin T. Bye ([email protected])PhD student in neuroengineeringSchool of Electrical Engineering & TelecommunicationsUniversity of New South Wales Sydney Australia
Research seminar at NTNU, 27 September 2007
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Presentation outline
What is neuroengineering? Invariants in aimed movements
Speed-accuracy tradeoffs Velocity profiles
The BUMP model Simulation experiments Summary Q & A
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What is neuroengineering?
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What is neuroengineering?
Emerging interdisciplinary field of research Electrical/computer engineering
Control systems, signal processing, neural networks, etc. Neural tissue engineering Computational/experimental neuroscience Materials science Clinical neurology Nanotechnology Other areas
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What is neuroengineering?
Goal: “Reverse-engineer” the nervous system How does it function? How can we modify it? What can we learn from the brain?
Bidirectional inspiration: humans vs. external world Existing and potential human improvements inspired by
external world: Bionic limb “Mind control” through brain-computer interface
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What is neuroengineering?
“Pacemaker” for cerebral palsy, stuttering, lesions Cochlea implant
External world improvements inspired by the human CNS
Robotics and control systems Information processing and coding algorithms, e.g.
neural networks face recognitioning systems
Example of bionic arm presented next...
7Bionic arm schematic. Adapted from the Washington Post (2006).
8Claudia Mitchell's bionic arm. Adapted from CNN report: Lady with bionic arm (2006).
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Reverse-engineering the brain
The nervous system is a “black box”
Cannot take the brain apart and put it together again! Second-best:
Medical imaging, e.g. fMRI → “grey” box? Given inputs, deduce black box system from outputs
Input (instruction) Output (response)
System (CNS)
?
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Reverse-engineering the brain
Control systems approach Mathematical description of signals and systems Applicable in modelling human movements The CNS (black box) is a system
Movement instruction → response execution E.g. lift a glass, say “Aaaah”, or move from A to B Response may reveal properties of the CNS control
system Deviation from desired response? Common characteristics across responses?
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Invariants in aimed movements
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Invariants in aimed movements
Common response characteristics across subjects, tasks, and environments constitute invariants
E.g. increased movement variance with increased speed, single-peaked velocity profile, approximately straight line trajectory, response timing, etc.
Why do invariants occur? Intrinsic properties, e.g. transmission times,
biomechanical system, external world influences Response planning strategies in CNS
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Useful measures of aimed movements
Quantitative measures of aimed movements Movement time T Target distance D Target width W Endpoint error measures, e.g.
Absolute error |E| or square error E² (why not signed (negative) errors?)
Standard deviation S or variance S²
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1D movement task
Start
Centre of target
Overshoot region
Undershoot region
W
D
m1
m2
m3
m4Four possible movements:m1 misses target (too short)m2 undershoots centre of targetm3 overshoots centre of targetm4 misses target (too long)
E1
E2
E3
E4
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1D movement invariants in this presentation
Speed-accuracy tradeoffs Logarithmic tradeoff (Fitts' law) Linear tradeoff
Velocity profiles Asymmetrical (left-skewed) profile Symmetrical profile
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Speed-accuracy tradeoff
Facts from experiments and common experience: Faster movement leads to less accuracy High accuracy requires slower movement
If it exists, what is the mathematical function?
Error
Movement time*
f(x) = ?
* For a fixed distance, speed is inversely related to movementtime
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Logarithmic tradeoff
Reciprocal tapping experiment by Fitts (1954) Observe T for fixed combinations of D and W Count number of target hits during period of time Move fast while hit rate at least 95%
Fitts' reciprocal tapping task. Adapted from Fitts (1954).
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Fitts' logarithmic law
T increases with greater target distance D T increases with smaller target width W
Fitts' law: T = a + b log2(2W/D)
Index of difficulty: Id = log
2(2W/D)
Linear form of Fitts' law : T = a + b Id
a
bId
Movement time T
Index of difficulty Id
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Fitts' law
A “Newton's law” for human movements? Holds for extraordinary amount of paradigms:
People: Kids, adults, elderly, mentally challenged, drugged, ... Manipulators: Joystick, mouse, keyboard, foot pedal, ... Environments: On land, under water, in aircraft flights, ... Other: Discrete movements, without visual feedback, vision
through microscope, ...
However, fails for timed movements! Inclusion of temporal goal → linear tradeoff
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Linear tradeoff
Discrete tapping experiment, Schmidt et al. (1979) ≈ Fitts-like experiment + temporal goals (desired T) Result: Standard deviation S of endpoint varies
linearly with average movement speed D/T Linear law: S = a + bD/T
a
bD/T
Standard deviation S
Average movement speed D/T
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Linear tradeoff
Holds for variety of time-matching tasks, including single tapping tasks saccadic eye movements wrist rotations other time-matching tasks (see Zelaznik, 1993, for
review)
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Other tradeoffs?
Many have been suggested: Other logarithmic or linear laws Power laws Delta-lognormal law
Some may fit better for particular experiments Sometimes “academic” improvement Fitts' and Schmidt's laws de facto tradeoffs
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Velocity profiles
Aimed movements usually have single-peak velocity profiles for
almost any limb single- and multi-joint movements different environments different inertial loads different movement speeds target sizes, shapes, and distances (see Plamondon, 1997,
for review)
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Velocity profiles
Symmetrical profiles ballistic movements (≈ 100 ms duration) movements with temporal goals
Velocity
Time (ms)1000 50
Velocity
Time (ms)1500 300
Ballistic movement 300 ms timed movement
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Velocity profiles Asymmetrical (left-skewed) profiles
Non-ballistic movements incorporating feedback Movements with spatial constraints only Skewness increases with movement time (Beggs &
Howarth, 1972)
Velocity
Time (ms)0
Velocity
Time (ms)0 300
150 ms movement 300 ms movement150
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Summary
Spatially constrained movements The goal is to minimise endpoint error Results in logarithmic speed-accuracy tradeoff (Fitts' law) Results in asymmetrical (left-skewed) velocity profiles
Spatially + temporally constrained movements The goal is to minimise endpoint error and make
movement in prespecified duration Results in linear speed-accuracy tradeoff Results in symmetrical velocity profiles
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The BUMP model
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Modelling movement
Why make models? Imitate human movements
Improve robotic applications Predict human behaviour
Extend knowledge about CNS Model consistent with human data? If so, provides explanation of how the CNS may operate (if it is
biologically-feasible) If not, proves how the CNS may not work!
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Some influential models
Deterministic iterative-corrections model (Crossman & Goodeve, 1963)
Impulse-variability model (Schmidt et al., 1979) Minimum jerk model (Flash & Hogan, 1985) Stochastic optimised-submovement model (Meyer et
al., 1988) Minimum torque-change model (Uno et al., 1989)
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Adaptive model theory (AMT)
The BUMP model is part of AMT Neuroengineering account of movement control Fusion of adaptive control theory and neuroscience Addresses major human movement science issues
e.g. intermittency, redundancy, resources, nonlinear interactions (see Neilson & Neilson, 2005, for review)
Three systems for information processing Biologically-feasible neural network solution
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Three processing systems
Sensory analysis (SA) system Response planning (RP) system (this presentation) Response execution (RE) system Operate independently and in parallel: The CNS can
simultaneously Plan appropriate response to a stimulus (RP system) Execute response to an earlier stimulus (RE system) Detect and store a subsequent stimulus (SA system)
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Intermittency SA and RE systems operate continuously RP system operates intermittently
System is refractory while operating on “chunks” of info Fixed planning time interval to plan a response trajectory Planning time interval T
p = 100 ms
Leads to repeating SA-RP-RE sequences: BUMPs Movement consists of concatenated submovements
Each submovement has a fixed duration of 100 ms
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Basic Unit of Motor Production (BUMP)
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Response planning system
Planning in terms of sensory consequences E.g. in an airplane, the pilot plans in terms of the
consequences of moving the joystick rather than the hand movements controlling the joystick
Redundancy problem Infinite trajectories to move from A to B
which one to choose? Yet, trajectories usually have invariants
E.g. straight-line trajectory, single-peaked velocity profile
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Response selection Adding constraints to a movement task limits
possible trajectories Optimal control: use a cost function for trajectories Choose particular trajectory that minimises cost Common cost functions:
Movement time Movement distance or its derivatives
velocity, acceleration (energy), jerk, snap Torque or torque-change
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Minimum acceleration approach
Choosing acceleration as cost criterion to minimise results in
minimum acceleration/energy trajectory optimally smooth trajectories trajectories that are S-shaped symmetrical velocity profiles (peak half-way)
Rationale: Equivalent to minimising metabolic energy Computationally easier than jerk
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Planning in accelerated time
Optimal trajectory R* generated every Tp = 100 ms
Duration of R* may be of much longer duration!
Optimal S-shaped trajectory R* with 500 ms duration. The trajectory moves the response from a standstill position at zero to a standstill position at unity. During movement, only the first 100 ms are executed. Then, an updated R* replaces the old one. Again, only 100 ms are executed. This series of submovementsrepeats until the target is reached.
Optimal S-shaped trajectory
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Variable horizon control
Duration of R* is called prediction horizon Variable horizon control = ability to vary duration of
R* at RP intervals Strategies for varying the horizon:
Receding horizon control Fixed horizon control Others may exist
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Receding horizon control
The duration of R* remains constant The prediction horizon recedes when approached
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Fixed horizon control R* planned to a point ahead fixed in time and space The prediction horizon decreases as the fixed
horizon is approached
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Inaccuracies in movement
Movements never perfect - why? Inaccurate internal models of
external system (joystick, bicycle) muscle control system, biomechanical system
Noise in the CNS Broadband signal-dependent noise Standard deviation increases with size of motor
command Remedy: Intermittent error corrections
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Intermittent error corrections
Receding horizon control.Each optimal R* has a duration of 100 ms.Ri* = desired responseRi = actual responseEi = error (undershoots)Note: Errors can equallywell overshoot target.
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Simulation experiments
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Simulator description
Implemented using MATLAB and Simulink Every component is biologically-feasible Simulations of step movements (discrete point-to-
point 1D movements) employing variable horizon control
Receding horizon control Fixed horizon control
Stochastic noise added to motor commands
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Simulation results Receding horizon control, 500 ms movement
Logarithmic speed-accuracy tradeoff
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Simulation results Receding horizon control, 500 ms movement
Asymmetrical (left-skewed) velocity profile
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Simulation results Fixed horizon control, 100-500 ms movements
Linear speed-accuracy tradeoff
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Simulation results Fixed horizon control, 500 ms movement
Symmetrical velocity profile
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Receding horizon control
Coe cient of ffidetermination R² as a measure of goodness of fit for the best fit exponential and linear functions W = D × 2−λt and T = aId + b, respectively, for 10 cm step movements employing receding horizon control and prediction horizons Th = {100, 200, . . . , 1000} ms.
Table of goodness of fit
Logarithmic tradeoff: Goodness of fit
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Receding horizon control
Level of asymmetry in velocity profiles for 10 cm step movements using receding horizon control given by the ratio of duration of positive and negative acceleration.
Table of levels of asymmetry
Asymmetrical profile: Level of asymmetry
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Fixed horizon control
Groups of fixed horizon control step movements of varying initial prediction horizons and movement distances and their corresponding correlation coe cientffi R2 as a measure of goodness of fit for the best linear function We = a D/T + b. Th is the initial prediction horizon; D is the movement distance; and R2 is the correlation coe cient.ffiTable of goodness of fit
Linear tradeoff: Goodness of fit
Symmetrical profile: Asymmetry ratio is 1 for all cases, i.e. all velocity profiles are symmetrical.
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Conclusions
Simulation results closely match observations in human movement experiments
Receding horizon control successfully reproduces Logarithmic speed-accuracy tradeoff (Fitts' law) Asymmetrical (left-skewed) velocity profiles
Receding horizon control successfully reproduces Linear speed-accuracy tradeoff Symmetrical velocity profiles
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Conclusions
Results strongly support the BUMP model and its underlying hypotheses about human motor control
The BUMP model provides a unique theoretical bridge between seemingly disparate speed-accuracty tradeoff and velocity profiles
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Summary
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Neuroengineering is about reverse-engineering the brain
One method: Create models and see if they match the real world
The model must be biologically-feasible Then a successful model provides a possible solution If unsuccessful, at least one theory is eliminated Mere line-fitting is of little value
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Spatially constrained movements Goal: minimise error Results:
Logarithmic speed-accuracy tradeoff (Fitts' law) Asymmetrical (left-skewed) velocity profiles
Spatially and temporally constrained movements Goal: minimise error & move on time Results:
Linear speed-accuracy tradeoff Symmetrical velocity profiles
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The BUMP model Intermittent response planning → submovements Suggests two different response planning strategies
Receding horizon control Fixed horizon control
Simulation results Receding horizon control reproduces
Logarithmic tradeoff asymmetrical profiles
Fixed horizon control reproduces Linear tradeoff symmetrical profiles
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The BUMP model provides one possible account of human aimed movements
Biologically-feasible All components are based on existing structures and
knowledge about the CNS Unique, as it explains both important tradeoffs and
corresponding velocity profiles within one theoretical framework
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Q & A
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References Bionic arm schematic. The Washington Post, 14/09/2006, accessed from
http://www.washingtonpost.com/wp-dyn/content/graphic/2006/09/14/GR2006091400095.html?referrer=emaillink, on 7/09/2007.
Claudia Mitchell's bionic arm. CNN Report: Lady with experimental bionic arm, broadcast 14/09/2006, accessed from http://www.youtube.com/watch?v=xbCN9L6ApU4, on 19/09/2007.
Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381–391.
Schmidt, R. A., Zelaznik, H., Hawkins, B., Frank, J. S., & Quinn, J. (1979). Motor-output variability: A theory for the accuracy of rapid motor acts. Psychological Review, 86 (5), 415–451.
Zelaznik, H. N. (1993). Necessary and sufficient conditions for the production of linear speed-accuracy trade-offs in aimed hand movements. In K. M. Newell & D. M. Corcos (Eds.), Variability and motor control (pp. 91–115). Human Kinetics Publishers.
Plamondon, R., & Alimi, A. M. (1997). Speed/accuracy trade-offs in target-directed movements. Behavioral and Brain Sciences, 20, 279–349.
Crossman, E. R. F. W., & Goodeve, P. J. (1963/1983). Feedback control of hand-movement and Fitts’ law. Quarterly Journal of Experimental Psychology, 35A, 251–278. (Reprint of Communication to the Experimental Society (1963))
Flash, T., & Hogan, N. (1985). The coordination of arm movements: An experimentally confirmed mathematical model. Journal of Neuroscience, 5 (7), 1688–1703.
Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E., & Smith, J. E. K. (1988). Optimality in human motor performance: Ideal control of rapid aimed movements. Psychological Review, 95 (3), 340–370.
Uno, Y., Kawato, M., & Suzuki, R. (1989). Formation and control of optimal trajectory in human multijoint arm movement: Minimum torque-change model. Biological Cybernetics, 61, 89–101.
Neilson, P. D., & Neilson, M. D. (2005). An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control. Journal of Neural Engineering, 2 (3), S279–S312.