Computer Simulation Study for FES Walking with a Three-Dimensional Entire-Body Nuero-Musculo-Skeletal Model

Goro Obinata*, Kazunori Hase, Mitsuhiro Obara, Norimasa Adachi, Atsushi Nakayama

Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan

Introduction

A three-dimensional musculo-skeletal model of a human body, including the neuronal system, is considered for FES bipedal walking in this paper. The dynamics of the human body is represented by a 14-rigid-link system and 60 muscles. The neuronal system consists of 32 neural oscillators, the sensory feedback system, and the peripheral system to determine the muscle forces. Unknown parameters in the neuronal system were adjusted by minimizing an evaluative index for locomotion, which is a linear combination of the locomotive energy efficiency and the smoothness of the muscle tensions. The model has successfully generated continuous walking patterns and the stability has some robustness against external disturbance forces. It is easy to see that this neuronal system can be implemented with appropriate sensors into FES framework for restoring bipedal walking as the controller. Computational experiments have been carried out to investigate the influence of variation of generated muscle forces and of time delay (introduced in the sensory feedback pass) on the walking stability.

Method

The three-dimensional entire-body neuro-musculo-skeletal model proposed in our previous paper [1] has been employed as a walking simulator in this study. A three-dimensional, 14-rigid-link system represents the dynamics of the entire human body under the gravitational field of earth. These links include the feet, calves, thighs, pelvis, lower lumbar region, upper lumber region, thorax, upper arms, and forearms. The link system is driven by 60 muscles, which are placed to emulate dominant muscles in human body. The link connection and the muscle placement are shown in Fig.1. The shaded thin bars abstractly represent the rigid link system of the entire-body. The bold lines indicate the muscle geometry and the placement. Energy consumption in the muscle is calculated from the generated muscle tension. The control system consists of three subsystems emulating neuronal functions. The first one is a rhythm generator corresponding to the spinal cord level [2]. This is modeled as a nonlinear dynamical network system consisting of 32 second-order neural oscillators. The network system generates the neuronal stimulus for each degree of freedom of the joint by feeding back the sensory signals. The second one is the feedback system, which receives somatic signals such as the angular displacement and angular velocity of the joints and the body segments, and the foot-ground contact information. These signals are sent to the rhythm generator. The third subsystem is a neuronal system corresponding to the peripheral level. This allocates each muscle force to generate the corresponding joint moment determined by the stimulus from the rhythm generator. The allocation is described mathematically by a static optimization procedure [3]. The parameters of the control system are to be adjusted by minimizing a criterion for locomotion, which is a linear combination of the locomotive energy efficiency and the smoothness of the muscle tensions.

Results of computational experiments

A genetic algorithm is used to find the parameters which achieve a local mimimum of the criterion. Several simulation results of walking were obtained to indicate similar motions to human walking. For example, an assumed height of 180 cm and weight of 60 kg for the musculo-skeletal model yielded a walking velocity of 1.4 m/s and a consumption energy rate of 444 W. An external force was applied to the pelvis segment to judge whether the model could walk continuously for the prescribed walking steps without falling down. This examination was repeated, with the external force increased in a stepwise manner, until the model fell down. Most of the obtained models could walk on a flat surface against external forces from four directions up to a magnitude of 50[N] or 100[N].

The effect of time delay was investigated as the control property of obtained controller. It is known that the neuronal system in actual humans has some delay in muscular activation, or in efferent/afferent transmission, and that the delay becomes more than 100 ms in some neurons. On the other hand, it is also known that introducing time-delay in feedback path destabilizes the control system. In the simulations with obtained controllers, setting delay of only 2 ms or 4 ms made the walking pattern unstable.

Finally, the muscle force allocation by the second subsystem of the proposed controller was investigated for evaluating the adaptability of the method to FES implementation. In the situation of FES, the generated forces by FES may vary during several time spans due to several reasons. Therefore, it is important that the control system works well against the variations of generated muscle forces. Fig.2 shows the comparison of simulation results in the cases whether the appropriate generated muscle force was assumed for the rectus femoris or not. The reallocation by using a static optimization procedure indicates a good compensation for the reduced maximum force of the rectus femoris.

References

[1] Hase, K. and Yamazaki, N., Computer Simulation Study of Human Locomotion with a Three-Dimensional Entire-Body Neuro-Musculo-Skeletal Model. I. Acquisition of Normal Walking, JSME Int. J., Ser. C, 2002. 45(4): p.1040-50.

[2] Taga, G., Yamaguchi, Y. and Shimizu, H., Self-Organized Control of Bipedal Locomotion by Neural Oscillators in Unpredictable Environment, Biological Cybernetics, 1991. 65: p.147-59.

[3] Hase, K. and Obinata G., Computer Simulation Study of Human Locomotion with a Three-Dimensional Entire-Body Neuro-Musculo-Skeletal Model. II. Biomechanical Relationship between Walking Stability and Neuro-Musculo-Skeletal System, JSME Int. J., Ser. C, 2002. 45(4): p.1051-7.