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Computing Movement Geometry

Explore the intricate sensory-motor transformations in movement planning using geometric stage postural paths. Analyze how the brain computes joint angles for hand positioning, engaging in error correction by orienting with sensory feedback. Delve into gradient descent simulations and experiments involving co-articulation. Gain a deeper understanding of movement speed invariance and the strategies employed for accurate arm postures.

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Computing Movement Geometry

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  1. Computing Movement Geometry A step in Sensory-Motor Transformations Elizabeth Torres & David Zipser

  2. Postural Path Geometry Speed ? Sensory Input Kinematics Motor output

  3. Stuff that’s easy in the Geometric Stage • Specifying movement paths. • Dealing with excess degrees of freedom. • Some constraint satisfaction. • Some error correction.

  4. Geometric Stage target position Arm postural Path target orientation arm posture Geometric Stage Input -- OutputReaching to Grasp with a Multi-jointed Arm What goes on in here? Represented as changes in joint angles

  5. Gradient Descent

  6. r = hand to target distance Hand to target distance

  7. Joint Angles

  8. Posture in 7D Joint Angle Space Hand position 3D Space Hand to target distance As function of joint angles

  9. On each time step the change in joint angles is: Hand path Posture path Gradient Descent for Simulating Hand Translation

  10. Example: Reconfiguring Joint Angle Space

  11. Orientation Matching S O H

  12. A constant chosen so that total distance = total rotation Co-articulation parameter Distance function for translation and rotation

  13. Experiments

  14. Fitting G to Experimental Data Worst Best G symmetrical and positive-definite

  15. fast normal slow Speed Invariance of Movement Path TARGET One subject, one movement at each speed

  16. Six subjects, six movements each

  17. Co-articulation

  18. Error Correction

  19. Hand -Target Offset Using chain rule Correcting error with retinal image feedback Retina(s)

  20. Discussion Break

  21. Each of these terms can be computed in different brain areas The gradient of a sum = the sum of the gradients

  22. dq Hidden Units posture target position target orientation

  23. Preferred Directions Rotate across External Space

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