Abstract
Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). The intermittent control paradigm is based on the alternation of on-phases, driven by a proportional/derivative delayed feedback controller, and off-phases, where the feedback is switched off and the motion evolves according to the intrinsic dynamics of the CIP. In its standard formulation, the switching mechanism consists of a simple threshold operator: the feedback control is switched off if the current (delayed) state vector is closer to the stable than to the unstable manifold of the off-phase and is switched on in the opposite case. Although this simple formulation is effective for explaining upright standing as well as CIP balancing, it fails in the most challenging configuration of the CIP. In this work we propose a modification of the standard intermittent control policy that focuses on the explicit selection of switching times and is based on the phase reset of the estimated state vector at each switching time and on the simulation of an approximated internal model of CIP dynamics. We demonstrate, by simulating the modified intermittent control policy, that it can match the limits of human performance, while operating near the edge of instability.
Highlights
The manual stabilization of an inverted pendulum hinged on a cart, allowed to shift in a forward/backward manner, is an example of the many unstable tasks that humans must face in everyday life
The different balancing paradigms mentioned above involve a number of degrees of freedom it is always possible, at least as a first approximation, to focus on a simplified inverted pendulum paradigm (IP) with a single degree of freedom: the ankle joint, in the case of upright standing, or the virtual joint that characterizes the relative motion of the stick on the fingertip in the stick balancing task
As a matter of fact, the simplicity and availability of a stiffness mechanism has been suggested by some researcher (Winter et al, 1998), supporting the hypothesis that ankle stiffness strategy is sufficient for the stabilization of upright standing, without any need of an additional control loop that is complicated by the significant delay of sensory feedback
Summary
The manual stabilization of an inverted pendulum hinged on a cart, allowed to shift in a forward/backward manner (shortly CIP: Cart Inverted Pendulum), is an example of the many unstable tasks that humans must face in everyday life.
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