ACTIVE SENSING Lecture 10: High-order motor loops (planning and execution)

K1K1 K2K2 d F P = 0 d F P Desired: d = d D d F 0 0 d=-k 1 F F = k 2 (d-d D ) F = k 2 d 0 controlling the loop’s set-point

K1K1 K2K2 d F P = 0 d F P Desired: d = d D d F 0 0 d=-k 1 F F = k 2 (d-d D ) F = k 2 d 0 dDdD Proportional control d ss controlling the loop’s set-point d ss ≠ d D

d F P 0 controlling the loop’s set-point ways to decrease the error loop gain servo-mechanism

Locomotion control Cowan, N. J. et al. J. Neurosci. 2007;27: Noah’s movie

Copyright ©2007 Society for Neuroscience Cowan, N. J. et al. J. Neurosci. 2007;27: Figure 1. Identifying the whole-animal transfer function for longitudinal tracking behavior in Eigenmannia Figure 1. Identifying the whole- animal transfer function for longitudinal tracking behavior in Eigenmannia. A, The fish (brown) maintains its position within a rectangular tube. This refuge has a clear polycarbonate top and white plastic sides with ceramic-filled windows (gray). B, Schematic view of the video data captured using a camera positioned above the fish. Three values are the position of the fish [x(t), purple lines], the position of the refuge [r(t), green lines], and the relative difference between the fish and the refuge [e(t), dashed blue line]. C, Tracking data from a fish (stimulus amplitude, 0.5 cm). The height of each trace is scaled identically; the width of each trace is scaled to show two stimulus cycles (bottom; green) at three rates of motion (labeled). The amplitude of fish movements, x(t), decreased with increasing stimulus frequency with increasing phase lag. D, Bode amplitude. E, Bode phase plots for stimulus rates from 0.1–1.3 Hz. Error bars indicate the SD (N = 4 fish). The dashed curve indicates the first-order model (rejected), and the gold region indicates 95% confidence intervals for this model. The solid curve indicates the second-order model, and the blue region indicates 95% confidence intervals for this model.

d F P I. nested loops Loops hierarchy

K1K1 K2K2 d F P I. nested loops Loops hierarchy K3K3 d* dDdD d F 0 P d=P-F F = k 2 (d-d D ) F = k 2 d d F P

K1K1 K2K2 d F P I. nested loops Loops hierarchy d F 0 0 d=P-F F = k 2 (d-d D ) K3K3 d dDdD d dDdD 0 0 d D =-k 3 d d=G/(1+G) d D

I. nested loops Loops hierarchy d F 0 0 d=P-F F = k 2 (d-d D ) d dDdD 0 0 d D =-k 3 d d=G/(1+G) d D K1K1 K2K2 F P K3K3 d dDdD K3K3 d dDdD G 1+G

Multiple-level (nested) control loops Control loops can be arranged in multiple levels for each level, controlled variables, loop variables and transfer functions can be defined independently the stability and dynamics of each loop can be analyzed independently

K1K1 K2K2 F P d F P Loops hierarchy d F 0 P d=P-F F = k 2 d+ k 3 d K3K3 II. parallel loops K1K1 dd dDdD

K1K1 K2K2 F P d F P Loops hierarchy d F 0 P d=P-F F = k 2 d+ k 3 d K3K3 II. parallel loops K1K1 dd dDdD

K1K1 K2K2 F P d F P Loops hierarchy K3K3 III. cascade of loops K1K1 dd dDdD

Motor Sensory Sensory-motor loops of the vibrissal system

Motor Sensory Brainstem Loop Facial Nucleus - Zona Incerta extralemniscal lemniscal paralemniscal Cerebellar/Olivary VL Thalamic Nuclei Vibrissae Thalamus Cortex POm Trigeminal Ganglion Primary Motor Cortex Secondary Superior Colliculus + Red Nucleus Reticular Formation Brainstem Reticular Nucleus Pontine Primary Sensory Cortex VPM-dm VPM-vl Trigeminal Nuclei Sensory-motor loops of the vibrissal system

Motor Sensory Brainstem Loop Facial Nucleus - Zona Incerta extralemniscal lemniscal paralemniscal Cerebellar/Olivary VL Thalamic Nuclei Vibrissae Thalamus Cortex POm Trigeminal Ganglion Primary Motor Cortex Secondary Superior Colliculus + Red Nucleus Reticular Formation Brainstem Reticular Nucleus Pontine Primary Sensory Cortex VPM-dm VPM-vl Trigeminal Nuclei Sensory-motor loops of the vibrissal system

Motor Sensory Brainstem Loop Facial Nucleus - Zona Incerta extralemniscal lemniscal paralemniscal Cerebellar/Olivary VL Thalamic Nuclei Vibrissae Thalamus Cortex POm Trigeminal Ganglion Primary Motor Cortex Secondary Superior Colliculus + Red Nucleus Reticular Formation Brainstem Reticular Nucleus Pontine Primary Sensory Cortex VPM-dm VPM-vl Trigeminal Nuclei Sensory-motor loops of the vibrissal system

Motor Sensory Brainstem Loop Facial Nucleus - Zona Incerta extralemniscal lemniscal paralemniscal Cerebellar/Olivary VL Thalamic Nuclei Vibrissae Thalamus Cortex POm Trigeminal Ganglion Primary Motor Cortex Secondary Superior Colliculus + Red Nucleus Reticular Formation Brainstem Reticular Nucleus Pontine Primary Sensory Cortex VPM-dm VPM-vl Trigeminal Nuclei Sensory-motor loops of the vibrissal system PCT Perceptual Control Theory W.T. Powers, 1973 “an organism's behavior is a means of controlling its perceptions.” “a control system does not control what it does; it controls what it senses. ”

Motor Sensory Brainstem Loop Facial Nucleus - Zona Incerta extralemniscal lemniscal paralemniscal Cerebellar/Olivary VL Thalamic Nuclei Vibrissae Thalamus Cortex POm Trigeminal Ganglion Primary Motor Cortex Secondary Superior Colliculus + Red Nucleus Reticular Formation Brainstem Reticular Nucleus Pontine Primary Sensory Cortex VPM-dm VPM-vl Trigeminal Nuclei Sensory-motor loops of the vibrissal system Standard conception Motor Control Theory M Jordan and others “perceptions are means of controlling an organism's behavior ” “a control system does control what it does, using what it senses. ”

so far lecture 10