Vol.:(0123456789) 1 3 Artificial Life and Robotics https://doi.org/10.1007/s10015-019-00560-y ORIGINAL ARTICLE Reproduction of human dynamic stability in cooperation with human controller model Yoshikazu Yamanaka 1  · Shigeki Matsumoto 2  · Katsutoshi Yoshida 1 Received: 22 April 2019 / Accepted: 3 September 2019 © International Society of Artificial Life and Robotics (ISAROB) 2019 Abstract We investigate the cooperative behavior between our previously proposed human controller model (HCM) and a human operator. In our previous study, we constructed our HCM by which the behavior of human’s individual balancing control can be accurately reproduced. In this study, we examine how accurately our HCM reproduce the dynamic stability of human behavior in a cooperative balancing task performed by a pair of our HCM and a human operator. To this end, the largest Lyapunov exponents (LLEs) of their balancing errors are estimated. Then, the ratios of LLE of our HCM to that of the human operator are calculated. These ratios are compared with those obtained by a conventional controller, indicating that the dynamic stabilities of the human operators are more accurately reproduced by our HCM than the conventional controller. Keywords Cooperative task · Dynamic stability analysis · Human controller model · Lyapunov exponent 1 Introduction Cooperative behavior between a human operator and an artifcial controlled device appears in many applications for such as care of elderly individuals [15, 17, 23], assis‑ tive walking [8, 14, 21] and cooperative handling [1, 20]. In such cooperative behavior, the controllers are sometimes required to reproduce human behavior to perform tasks just like human beings [9–11]. In our previous study, we focused on human’s fuctuated behavior [2–5, 7, 19, 22] and constructed the controller called human controller model (HCM). This reproduced the probability density function (PDF) of human’s balance control motion more than 95% accuracy [13]. However, the cooperation between our HCM and a human operator remains an open issue. In this study, we investigate the cooperative behavior between our HCM and a human operator when they stabi‑ lize an unstable virtual object. In particular, we estimate the largest Lyapunov exponents (LLEs) of the measured time series of their balancing errors. Then, the ratios of LLE of our HCM to that of the human operator are calculated. The obtained ratios are compared with those obtained by a conventional controller proposed by Cabrera et al. [5]. The result indicates that the dynamic stabilities of the human operators were more accurately reproduced by our HCM than the conventional controller. The rest of the paper is organized as follows. In Sects. 2 and 3, we present the cooperative experiment. In Sect. 4, we measure the balancing errors. In Sect. 5, we estimate the LLE values of the measured errors, showing that the LLE values of the human operators were accurately reproduced by our HCM. In Sect. 6, we conclude our study. 2 Experiment on cooperative balancing task 2.1 Experimental system Figure 1 shows the photograph of a human operator and our experimental device, which consists of a numerical This work was presented in part at the 24th International Symposium on Artifcial Life and Robotics, Beppu, Oita, January 23–25, 2019. * Yoshikazu Yamanaka yyamanaka@cc.utsunomiya‑u.ac.jp Katsutoshi Yoshida yoshidak@cc.utsunomiya‑u.ac.jp 1 Utsunomiya University, Yoto 7‑1‑2, Utsunomiya, Tochigi 321‑8585, Japan 2 Intelligent Vision & Image Systems Inc, OGI‑BLDG, Hongo 3‑6‑6, Bunkyo‑ku, Tokyo 113‑0033, Japan