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      Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance

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          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.

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          Most cited references18

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          Feedforward ankle strategy of balance during quiet stance in adults.

          1. We studied quiet stance investigating strategies for maintaining balance. Normal subjects stood with natural stance and with feet together, with eyes open or closed. Kinematic, kinetic and EMG data were evaluated and cross-correlated. 2. Cross-correlation analysis revealed a high, positive, zero-phased correlation between anteroposterior motions of the centre of gravity (COG) and centre of pressure (COP), head and COG, and between linear motions of the shoulder and knee in both sagittal and frontal planes. There was a moderate, negative, zero-phased correlation between the anteroposterior motion of COP and ankle angular motion. 3. Narrow stance width increased ankle angular motion, hip angular motion, mediolateral sway of the COG, and the correlation between linear motions of the shoulder and knee in the frontal plane. Correlations between COG and COP and linear motions of the shoulder and knee in the sagittal plane were decreased. The correlation between the hip angular sway in the sagittal and frontal planes was dependent on interaction between support and vision. 4. Low, significant positive correlations with time lags of the maximum of cross-correlation of 250-300 ms were found between the EMG activity of the lateral gastrocnemius muscle and anteroposterior motions of the COG and COP during normal stance. Narrow stance width decreased both correlations whereas absence of vision increased the correlation with COP. 5. Ankle mechanisms dominate during normal stance especially in the sagittal plane. Narrow stance width decreased the role of the ankle and increased the role of hip mechanisms in the sagittal plane, while in the frontal plane both increased. 6. The modulation pattern of the lateral gastrocnemius muscle suggests a central program of control of the ankle joint stiffness working to predict the loading pattern.
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            Can muscle stiffness alone stabilize upright standing?

            A stiffness control model for the stabilization of sway has been proposed recently. This paper discusses two inadequacies of the model: modeling and empiric consistency. First, we show that the in-phase relation between the trajectories of the center of pressure and the center of mass is determined by physics, not by control patterns. Second, we show that physiological values of stiffness of the ankle muscles are insufficient to stabilize the body "inverted pendulum." The evidence of active mechanisms of sway stabilization is reviewed, pointing out the potentially crucial role of foot skin and muscle receptors.
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              Forward models in visuomotor control.

              In recent years, an increasing number of research projects investigated whether the central nervous system employs internal models in motor control. While inverse models in the control loop can be identified more readily in both motor behavior and the firing of single neurons, providing direct evidence for the existence of forward models is more complicated. In this paper, we will discuss such an identification of forward models in the context of the visuomotor control of an unstable dynamic system, the balancing of a pole on a finger. Pole balancing imposes stringent constraints on the biological controller, as it needs to cope with the large delays of visual information processing while keeping the pole at an unstable equilibrium. We hypothesize various model-based and non-model-based control schemes of how visuomotor control can be accomplished in this task, including Smith Predictors, predictors with Kalman filters, tapped-delay line control, and delay-uncompensated control. Behavioral experiments with human participants allow exclusion of most of the hypothesized control schemes. In the end, our data support the existence of a forward model in the sensory preprocessing loop of control. As an important part of our research, we will provide a discussion of when and how forward models can be identified and also the possible pitfalls in the search for forward models in control.
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                Author and article information

                Contributors
                Journal
                Front Comput Neurosci
                Front Comput Neurosci
                Front. Comput. Neurosci.
                Frontiers in Computational Neuroscience
                Frontiers Media S.A.
                1662-5188
                05 April 2019
                2019
                : 13
                : 16
                Affiliations
                [1] 1Robotics, Brain and Cognitive Sciences Department, Center for Human Technologies, Italian Institute of Technology , Genoa, Italy
                [2] 2Mechanical Science and Bioengineering Department, Graduate School of Engineering Science, Osaka University , Toyonaka, Japan
                Author notes

                Edited by: Jun Izawa, University of Tsukuba, Japan

                Reviewed by: Tetsuro Funato, University of Electro-Communications, Japan; Shunta Togo, University of Electro-Communications, Japan

                *Correspondence: Pietro Morasso pietro.morasso@ 123456iit.it
                Article
                10.3389/fncom.2019.00016
                6461063
                0f413df9-e6a2-46de-a769-8f3d4a355e23
                Copyright © 2019 Morasso, Nomura, Suzuki and Zenzeri.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 08 January 2019
                : 11 March 2019
                Page count
                Figures: 7, Tables: 1, Equations: 24, References: 31, Pages: 15, Words: 11083
                Categories
                Neuroscience
                Original Research

                Neurosciences
                cart inverted pendulum,saddle-like instability,intermittent feedback control,phase reset,internal model simulation

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