Boundary Conditions in Human Movement I: Constraining Constraints

C.M. Harris (UK) and M.R. Harwood (USA)


: Arm movements, eye movements, minimum jerk, Fourier analysis, measurement noise, boundary conditions


Optimal control models (distal models) play an important role in understanding the principles of human motor control and bio-inspired robotic applications. A major goal has been to identify the cost function (performance index) of the motor behaviour, which has led to such influential models as the `minimum jerk', `minimum torque', and `minimum variance' hypotheses (inter alia). Less attention has been paid to the boundary conditions (BCs) needed to obtain theoretical optimal solutions. The choice of BCs strongly affects solutions, particularly when cost functions depend on high-order derivatives, as in human movement. To avoid the problem of arbitrary hypothetical constraints it is essential to justify BCs biologically. We examine analytically the effects of different BCs on minimum square derivative trajectories (minimum acceleration; minimum jerk) as simple tractable illustrations. We also examine the difference between physical and neuro-musculo-skeletal constraints, and conclude that it is not possible to justify kinematic models without appealing to non-kinematic BCs. Ultimately, BCs are an empirical issue that need to be measured independent of any theoretical model.

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