Motor learning through the combination of primitives.

Mussa-Ivaldi & Bizzi

Phil.Trans. R. Soc. Lond. B 355:1755-1769.

Forward problems

a(t) = 1/m F(t) = G2(F(t))v(t) = G1(v(t0), a(t))x(t) = G0(x(t0), v(t))

q(t) = G(q(t0), (t))

a

v

x

F

time

Inverse problems

F(t) = G2-1(a(t))

G-1(q(t)) = (t)

a

v

x

F

time

A simple problem

D is the torque of the previous slide

Kinematics The study of motion when only position and velocity are considered.

Forward KinematicsPosition is specified by setting value for each DOFHard to achieve world space constraintsMovement flow (relatively) easy to control

Inverse KinematicsSpecify world space constraints that one or more parts of the skeleton must achieveSolve for joint angles to achieve theseGood for meeting world space constraints, but movement flow can be a problemMost skeletons are highly redundant, so problem is underconstrained

Forward and Inverse Kinematics

Solutions based on feed-back

Should be

Is

feedback

real world

Solutions based on feedforward

a

v

x

F

time

Not the real world,but solving the inverse problem

Memory based computations

Use the real world in previous behaviour,i.e. learn and remember

The cerebellum

The cerebellum ("little brain") has convolutions similar to those of cerebral cortex, only the folds are much smaller. Like the cerebrum, the cerebellum has an outer cortex, an inner white matter, and deep nuclei below the white matter.

The cerebellumIf we enlarge a single fold of cerebellum, or a folium, we can begin to see the organization of cell types. The outermost layer of the cortex is called the molecular layer, and is nearly cell-free. Instead it is occupied mostly by axons and dendrites. The layer below that is a monolayer of large cells called Purkinje cells, central players in the circuitry of the cerebellum. Below the Purkinje cells is a dense layer of tiny neurons called granule cells. Finally, in the center of each folium is the white matter, all of the axons traveling into and out of the folia. These cell types are hooked together in stereotypical ways throughout the cerebellum.

Equilibrium-point hypothesis

Polat & Bizzi, 1979

Isometric force fields

Bizzi et al. 1991

Fiber tracts of the spinal cord

Evidence for internal modelsForward model:

• The transformation from a motor command to the consequent behaviour• Predict the expected outcome of a command• Estimate the current state inthe presence of feedback delays

Inverse model:• The transformation of the desired behaviour to the corresponding motor command

Cortical primitives

(t) = G-1(q(t)) = ci i(q(t))

Spinal cord solvingthe inverse problem

Brain

Linear interaction

Potential modules

Simulating a composite movement