טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBen-Itzhak Shay
SubjectArm Reaching Movements - Using Pontryagin's Minimum
Principle to Obtain Minimum Acceleration
Trajectories
DepartmentDepartment of Electrical Engineering
Supervisors Dr. Karniel Amir
Professor Emeritus Gideon Inbar (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

Rapid arm reaching movements are elementary movements that serve as an excellent test bed for any theory about trajectory formation.  A minimum acceleration criterion (MAC) has been examined in the past and the solution obtained, based on Euler-Poisson equation, failed to predict that the hand would begin and end the movement at rest (i.e. with zero acceleration).  Therefore this criterion was rejected in favor of the minimum jerk criterion (MJC) which was proved to be successful in describing many features of human movements.  This work follows an alternative approach, and solves this problem using Pontryagin's minimum principle.  This is done by using the minimum principle to obtain minimum acceleration trajectories and use the jerk as a control signal.  In order to find a solution that does not include non-physiological impulse functions, constraints on the maximum and minimum jerk values are assumed.  The analytical solution provides a piecewise constant jerk signal (bang-bang control) where the magnitude of the jerk and the switching times depend on the magnitude of the maximum and minimum available jerk value.  This result fits the observed trajectories of reaching movements and takes into account both the extrinsic coordinates and the muscle limitations in a single framework.  The minimum acceleration with constraints principle is discussed as a unifying approach to study the neural control of movement.