SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Optimality in Motor Control

ocean avatar
ocean
24 diapositives · 523 Views · Sep 07, 2014

Optimality in Motor Control. By : Shahab Vahdat Seminar of Human Motor Control Spring 2007. Agenda. Optimal Estimation Optimal Control Proposed Model. Optimality. Wolpert, D. M., Ghahramani, Z. & Jordan, M. I. An internal model for sensorimotor integration. Science (1995).

Optimality in Motor Control - slide 1
01 / 24Optimality in Motor Control
1 / 17

Télécharger la présentation

Optimality in Motor Control
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Optimality in Motor Control By : Shahab Vahdat Seminar of Human Motor Control Spring 2007

  2. Agenda • Optimal Estimation • Optimal Control • Proposed Model

  3. Optimality • Wolpert, D. M., Ghahramani, Z. & Jordan, M. I. An internal model for sensorimotor integration. Science (1995). • Van Beers RJ, Baraduc P & Wolpert DM. Role of uncertainty in sensorimotor control. Transactions of the Royal Society (2002) • Emanuel Todorov. Optimality principles in sensorimotorcontrol. NatureNeuroscience (2004) • Emanuel TodorovOptimal Control Theory. Bayesian Brain, Doya, K. (ed), MIT Press (2006)

  4. Kalman Filter State-space model is described with these equations:

  5. Kalman Filter • The prediction step consists of two calculations: State estimate propagation: Error covariance propagation:

  6. Kalman Filter • The updating step consists of three calculations Kalman gain matrix: State estimate update: Error covariance update:

  7. Sources of Noise For controlling a goal-directed arm movement, there are three sources of noise : • (i) noise in the sensory signals that limits perception, • (ii) noise in the motor commands, leading to inaccurate movements • (iii) sensorimotor noise, which origins from inaccuracies in the forward model and causes noisy predicted location of the body during movement. Therefore, the time-varying Kalman gain is used for minimizing the effect of these noises and uncertainty in the overall estimate.

  8. Kalman Filter: Sensorimotor Integration

  9. Sensorimotor Integration • When we move our arm in darkness, we may estimate the position of our hand based on three sources of information: • proprioceptive feedback. • a forward model of how the motor commands have moved our arm. • by combining our prediction from the forward model with actual proprioceptive feedback. • Experimental procedures: • Subject holds a robotic arm in total darkness. The hand is briefly illuminated. An arrow is displayed to left or right, showing which way to move the hand. In some cases, the robot produces a constant force that assists or resists the movement. The subject slowly moves the hand until a tone is sounded. They use the other hand to move a mouse cursor to show where they think their hand is located.

  10. Experiment: Sensorimotor Integration

  11. Optimal Control Bellman equations:

  12. Continuous control: Hamilton-Jacobi-Bellman equations:

  13. Deterministic control: Pontryagin’s maximum principle Hamiltonian:

  14. Linear-quadratic-Gaussian control: Riccati equation:

  15. Optimal control as a theory of biological movement state equations:

  16. Optimal control as a theory of biological movement

  17. Open-Loop versus Close-Loop Optimal Controller • Feed forward optimality models explain some of the classical motor properties (bell shaped profiles, etc) • Harris & Wolpert, 1998- Min. Variance • Flash and Hogan, 1985- Min. Jerk • Task constraints and motor noise combine to determine optimal motor plans • Humans use continuous visual feedback • Noise in the sensory system very accurately predicts how people use feedback • Task constraints may also impact feedback control strategies

  18. Schematic illustration of open- and closed-loop optimization. (a) The optimization phase, which corresponds to planning or learning, starts with a specification of the task goal and the initial state. Both approaches yield a feedback control law, but in the case of open-loop optimization, the feedback portion of the control law is predefined and not adapted to the task.

  19. (b) Either feedback controller can be used online to execute movements, although controller 2 will generally yield better performance. The estimator needs an efference copy of recent motor commands in order to compensate for sensory delays. Note that the estimator and controller are in a loop; thus they can continue to generate time-varying commands even if sensory feedback becomes unavailable. Noise is typically modeled as a property of the sensorimotor periphery, although a significant portion of it may originate in the nervous system.

  20. Proposed Model: Optimal Primitive State Prediction Force fields as primitives for internal models:

  21. Proposed Model: Optimal Primitive State Prediction Estimation and Control Equations:

  22. Proposed Model: Optimal Primitive State Prediction

  23. Proposed Model: Optimal Primitive State Prediction

  24. Primitive modular representation of the cerebellum