1. Motor learning through the combination of primitives. Mussa-Ivaldi & Bizzi Phil.Trans. R. Soc. Lond. B 355:1755-1769.

2. Forward problems a(t) = 1/m F(t) = G 2 (F(t)) v(t) = G 1 (v(t 0 ), a(t)) x(t) = G 0 (x(t 0 ), v(t)) q(t) = G(q(t 0 ),  (t)) a v x F time

3. Inverse problems F(t) = G 2 -1 (a(t)) G -1 (q(t)) =  (t) a v x F time

4. A simple problem D is the torque  of the previous slide

5.  Kinematics  The study of motion when only position and velocity are considered.  Forward Kinematics  Position is specified by setting value for each DOF  Hard to achieve world space constraints  Movement flow (relatively) easy to control  Inverse Kinematics  Specify world space constraints that one or more parts of the skeleton must achieve  Solve for joint angles to achieve these  Good for meeting world space constraints, but movement flow can be a problem  Most skeletons are highly redundant, so problem is underconstrained Forward and Inverse Kinematics

6. Solutions based on feed-back Should be Is feedback real world

7. Solutions based on feedforward a v x F time Not the real world, but solving the inverse problem

8. Memory based computations Use the real world in previous behaviour, i.e. learn and remember

9. 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.

10. The cerebellum If 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.

11. Equilibrium-point hypothesis Polat & Bizzi, 1979

12. Isometric force fields Bizzi et al. 1991

13. Fiber tracts of the spinal cord

14. Evidence for internal models Forward 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

15. Cortical primitives  (t) = G -1 (q(t)) =  c i  i (q(t)) Spinal cord solving the inverse problem Brain Linear interaction

16. Potential modules

17. Simulating a composite movement