Simple models in trajectory planning of human-like reaching movements

The paper deals with modeling of human-like reaching movements. Several models are under study. First, we consider a model of reaching movement that corresponds to the minimization of control effort. It is shown that this model is represented by the well-known Beta function. The representation can be used for the construction of fractional order models and also for modeling of asymmetric velocity profiles. The natural boundary conditions, defined in this part of the paper, can also be used in modeling asymmetric velocity profiles. Finally, we consider the minimum time formulation of the optimization problem and (for the n-th order integrator) find its analytical solution in the general form.