Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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