Geometric conditions of a two-link-and-six muscle structure based on internal force stability

Hiroaki Ochi,Yuki Matsutani,Kenji Tahara,Hitoshi Kino

doi:10.1186/s40648-020-00164-3

Abstract

In a musculoskeletal system, internal tensile forces are generated among the muscles because it is a redundant system. The balancing of the internal tensile forces for a given posture generates a potential field in the system. Therefore, the potential field is utilized for the sensorless feedforward position control and improvement of stability based on the feedback method. However, the stability of the internal tensile forces is strongly influenced by the muscular arrangement. Previous studies showed that a stable condition can be identified through the minimization of the potential at a desired posture, and the sufficient condition has been theoretically established; however, the geometric condition of the muscular arrangement has not been determined. To effectively exploit the characteristics of the internal tensile forces, the geometric condition must be elucidated in the design of a musculoskeletal system. This paper aims to clarify the geometric condition to generate stable internal tensile forces. Based on the conditions generating the potential that is minimum at the desired posture, the paper analyzes that the geometric condition on a musculoskeletal structure with two-link and six-muscle. Additionally, the identified condition is assessed based on simulations. As a result, we revealed the geometric condition of the muscular arrangement to generate stable internal tensile forces. By designing the muscular arrangement to satisfy the condition, the stability of the internal tensile forces is ensured, and consequently, a control method utilizing the characteristics of the internal tensile force is stably implemented.

Highlights

Human can generate a variety of adequate motions to adapt to their environs and specific tasks
This study has analyzed the geometric muscular arrangement condition based on the generation of stable internal tensile forces for a musculoskeletal manipulator with two-link and six-muscle
The geometric muscular arrangement conditions have been derived from the mathematical conditions in which the potential is minimum at the desired posture

Summary

Introduction

Human can generate a variety of adequate motions to adapt to their environs and specific tasks. (13) and (14) based on the second-order approximation, when each coefficient aj , ck , b5 , b6 ( j = 1, 2, 5, 6 , k = 3, 4, 5, 6 ) defined as the approximated muscular length qi∗ is satisfied as follows: Stable conditions of the internal tensile forces when using Taylor expansion coefficient in the neighborhood of the desired posture θd. Analysis of geometric muscular arrangement conditions The stable conditions of internal tensile forces highlighted in the preceding section (20)–(23) described in the reference [14] are merely the conditions of the coefficients for the Taylor-extended muscular length using the joint angle θ. The simple-joint muscular arrangement required to generate stable internal tensile forces at a desired posture must be satisfied with either of the following conditions:

The geometric conditions of the simple-joint muscular arrangement

Conclusion