Abstract
Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations are constructed for both collocated and non-collocated force sensor configurations. The models take into account large time delays in the feedback loop, which may occur, for example, in case of human or remote force control. The corresponding stability charts are compared for the collocated and non-collocated cases. The bifurcations at the stability boundaries are analyzed in the presence of the relevant nonlinearity that is originated in the saturation of the actuation. The stability properties as well as the nonlinear vibrations for the two sensor locations are compared also from the viewpoint of the achievable maximal proportional gains. The bifurcation calculations are done with the method of multiple scales and normal form calculations. The results on global dynamic properties are supported with numerical simulations, and the two force control strategies are discussed from application viewpoint.
Highlights
The tasks of human motion control can be classified in many different ways
Where m and k refer to the inertia and the stiffness of the controlled mechanical system, respectively, which may be the model of certain parts of the human body, while Q refers to the control force of certain muscles, which is actuated as a function of the sensed position q, velocity qand/or acceleration qwith dot referring to time derivatives
This paper investigates the basic models of force control in the presence of human reaction time delays from nonlinear vibrations viewpoint to the Hopf bifurcation analyses in delayed oscillators [25,26,27], predator–prey population models [28,29,30] or delayed networks in transportation, biological and neural systems [31,32,33]
Summary
The tasks of human motion control can be classified in many different ways. One of the simplest categorizations can be represented with the help of the basic single-degree-of-freedom (DoF) mechanical model mq + kq = Q(q, q, q),. This paper investigates the basic models of force control in the presence of human reaction time delays from nonlinear vibrations viewpoint to the Hopf bifurcation analyses in delayed oscillators [25,26,27], predator–prey population models [28,29,30] or delayed networks in transportation, biological and neural systems [31,32,33] These calculations are usually based on the center manifold reduction and normal form theory summarized in [34], which are combined with the infinite dimensional representation of delay differential equations [35].
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