Motor StructuresMotor StructuresPyramidal tract: cortico-spinal, crossoverExtra-pyramidal tracts: originating invarious brainstem nuclei (red nucleus, sup.coll., reticular formation etc.)Subcortical structures:- cerebellum- basal gangliaMotorStructuresMotorStructuressubcortical motor structuresMotorStructuresMotor areas of the cerebral cortexMotor StructuresSummary of microstimulation studies of the human cerebralcortex (O. Foerster, 1928)Motor StructuresOrganization of motor cortical areas:- somatotopy (e.g. M1)- contralateral control (decussation ofpyramidal tract)- hierarchical organizationMotor ControlMotor Control: A ComputationalChallengeGiven a trajectory, it is a computationally VERYchallenging task to compute a set of jointmovements or muscle contractions that willproduce this trajectory (inverse problem).Kinetic Equation for Computing Finger Motionin One Direction (Pull) in a 7 DOF Arm (160) V_PULL_N1 = DOT(V_PULL_N>, N1>) V_PULL_N1 = SIN(Q2)*(LA2*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)-LA1*(COS(Q3)* U2-SIN(Q3)*COS(Q2)*U1)) + SIN(Q2)*(LB2*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)* COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))+LB1*(SIN(Q4)*(SIN (Q3)*U2+COS(Q2)*COS(Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))) + (SIN(ALPHA)*COS(BETA)*SIN(Q2)-COS(Q2)*(COS(Q3)*(SIN(BETA)*COS(Q4)+ COS(ALPHA)*COS(BETA)*SIN(Q4))-SIN(Q3)*(SIN(BETA)*SIN(Q4)-COS(ALPHA)* COS(BETA)*COS(Q4))))*(LC1*((COS(ALPHA)*COS(Q5)+SIN(ALPHA)*SIN(BETA)* SIN(Q5))*(U3+U4+SIN(Q2)*U1)+COS(BETA)*SIN(Q5)*(COS(Q4)*(SIN(Q3)*U2+COS (Q2)*COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))+(SIN(ALPHA)* COS(Q5)-SIN(BETA)*COS(ALPHA)*SIN(Q5))*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS (Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1)))-LC3*(COS(BETA)*COS( Q5)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN( Q3)*COS(Q2)*U1))-(COS(ALPHA)*SIN(Q5)-SIN(ALPHA)*SIN(BETA)*COS(Q5))*( U3+U4+SIN(Q2)*U1)-(SIN(ALPHA)*SIN(Q5)+SIN(BETA)*COS(ALPHA)*COS(Q5))*( SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)* COS(Q2)*U1)))) + (SIN(Q2)*(COS(ALPHA)*(SIN(Q7)*COS(Q5)*SIN(ALPHA-Q6)+ SIN(Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)*SIN(Q7)*COS(ALPHA-Q6)))+SIN(ALPHA )*(COS(BETA)*(SIN(BETA)*COS(Q7)-COS(BETA)*SIN(Q7)*COS(ALPHA-Q6))+SIN( BETA)*(SIN(Q5)*SIN(Q7)*SIN(ALPHA-Q6)-COS(Q5)*(COS(BETA)*COS(Q7)+SIN( BETA)*SIN(Q7)*COS(ALPHA-Q6)))))+COS(Q2)*(SIN(Q3)*(SIN(Q4)*(SIN(BETA)*( SIN(BETA)*COS(Q7)-COS(BETA)*SIN(Q7)*COS(ALPHA-Q6))-COS(BETA)*(SIN(Q5)* SIN(Q7)*SIN(ALPHA-Q6)-COS(Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)*SIN(Q7)*COS (ALPHA-Q6))))+COS(Q4)*(SIN(ALPHA)*(SIN(Q7)*COS(Q5)*SIN(ALPHA-Q6)+SIN( Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)*SIN(Q7)*COS(ALPHA-Q6)))-COS(ALPHA)*( COS(BETA)*(SIN(BETA)*COS(Q7)-COS(BETA)*SIN(Q7)*COS(ALPHA-Q6))+SIN(BETA )*(SIN(Q5)*SIN(Q7)*SIN(ALPHA-Q6)-COS(Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)* SIN(Q7)*COS(ALPHA-Q6))))))-COS(Q3)*(COS(Q4)*(SIN(BETA)*(SIN(BETA)*COS( Q7)-COS(BETA)*SIN(Q7)*COS(ALPHA-Q6))-COS(BETA)*(SIN(Q5)*SIN(Q7)*SIN( ALPHA-Q6)-COS(Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)*SIN(Q7)*COS(ALPHA-Q6))) )-SIN(Q4)*(SIN(ALPHA)*(SIN(Q7)*COS(Q5)*SIN(ALPHA-Q6)+SIN(Q5)*(COS(BETA )*COS(Q7)+SIN(BETA)*SIN(Q7)*COS(ALPHA-Q6)))-COS(ALPHA)*(COS(BETA)*(SIN (BETA)*COS(Q7)-COS(BETA)*SIN(Q7)*COS(ALPHA-Q6))+SIN(BETA)*(SIN(Q5)*SIN (Q7)*SIN(ALPHA-Q6)-COS(Q5)*(COS(BETA)*COS(Q7)+SIN(BETA)*SIN(Q7)*COS( ALPHA-Q6))))))))*(PULL2*(U7+COS(BETA)*SIN(ALPHA-Q6)*(U5+SIN(ALPHA)*COS (BETA)*(U3+U4+SIN(Q2)*U1)-SIN(BETA)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS( Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))-COS(ALPHA)*COS(BETA)* (SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)* COS(Q2)*U1)))+COS(ALPHA-Q6)*((COS(ALPHA)*COS(Q5)+SIN(ALPHA)*SIN(BETA)* SIN(Q5))*(U3+U4+SIN(Q2)*U1)+COS(BETA)*SIN(Q5)*(COS(Q4)*(SIN(Q3)*U2+COS (Q2)*COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))+(SIN(ALPHA)* COS(Q5)-SIN(BETA)*COS(ALPHA)*SIN(Q5))*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS (Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1)))+SIN(BETA)*SIN(ALPHA -Q6)*(U6+COS(BETA)*COS(Q5)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)+ SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))-(COS(ALPHA)*SIN(Q5)-SIN(ALPHA )*SIN(BETA)*COS(Q5))*(U3+U4+SIN(Q2)*U1)-(SIN(ALPHA)*SIN(Q5)+SIN(BETA)* COS(ALPHA)*COS(Q5))*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)-COS(Q4)*( COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))))-PULL3*((SIN(BETA)*SIN(Q7)+COS(BETA)* COS(Q7)*COS(ALPHA-Q6))*(U5+SIN(ALPHA)*COS(BETA)*(U3+U4+SIN(Q2)*U1)-SIN (BETA)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2- SIN(Q3)*COS(Q2)*U1))-COS(ALPHA)*COS(BETA)*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2) *COS(Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1)))-COS(Q7)*SIN(AL PHA-Q6)*((COS(ALPHA)*COS(Q5)+SIN(ALPHA)*SIN(BETA)*SIN(Q5))*(U3+U4+SIN( Q2)*U1)+COS(BETA)*SIN(Q5)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)+SIN (Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))+(SIN(ALPHA)*COS(Q5)-SIN(BETA)* COS(ALPHA)*SIN(Q5))*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)-COS(Q4)*( COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1)))-(COS(BETA)*SIN(Q7)-SIN(BETA)*COS(Q7)* COS(ALPHA-Q6))*(U6+COS(BETA)*COS(Q5)*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)*COS( Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))-(COS(ALPHA)*SIN(Q5)- SIN(ALPHA)*SIN(BETA)*COS(Q5))*(U3+U4+SIN(Q2)*U1)-(SIN(ALPHA)*SIN(Q5)+ SIN(BETA)*COS(ALPHA)*COS(Q5))*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1) -COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))))) - SIN(Q3)*COS(Q2)*(LA1*( U3+SIN(Q2)*U1)-LA3*(SIN(Q3)*U2+COS(Q2)*COS(Q3)*U1)) - COS(Q2)*COS(Q3)* (LA2*(U3+SIN(Q2)*U1)-LA3*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1)) - COS(Q2)* SIN(Q3+Q4)*(LB1*(U3+U4+SIN(Q2)*U1)-LB3*(COS(Q4)*(SIN(Q3)*U2+COS(Q2)* COS(Q3)*U1)+SIN(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))) - COS(Q2)*COS( Q3+Q4)*(LB2*(U3+U4+SIN(Q2)*U1)+LB3*(SIN(Q4)*(SIN(Q3)*U2+COS(Q2)*COS( Q3)*U1)-COS(Q4)*(COS(Q3)*U2-SIN(Q3)*COS(Q2)*U1))) - (SIN(Q2)*(COS(ALP HA)*SIN(Q5)-SIN(ALPHA)*SIN(BETA)*COS(Q5))+COS(Q2)*(SIN(Q3)*(COS(BETA)* SIN(Q4)*COS(Q5)+COS(Q4)*(SIN(ALPHA)*SIN(Q5)+SIN(BETA)*COS(ALPHA)*COS( Q5)))-COS(Q3)*(COS(BETA)*COS(Q4)*COS(Q5)-SIN(Q4)*(SIN(ALPHA)*SIN(Q5)+
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