Stability Conditions of Feedforward Control for a Musculoskeletal System with Muscles Whose Lengths Depend on Multiple Joint Angles

Abstract

In this study, we consider a musculoskeletal system in which muscle tension is employed to control a linkage structure consisting of mechanical elements that correspond to a skeletal structure. Because muscles can only transmit force in the tensile direction, more muscles than joint degrees of freedom are needed to achieve control. The musculoskeletal potential method uses the potential field generated by the internal forces between muscles arising from this redundancy. In this method, constant muscle tension balanced at the desired posture is used as the step input to carry out feed forward control, in which sensory feedback and complex real-time computations are not required. However, the potential field generated by the muscle internal forces is highly dependent on muscular arrangement, some of which may fail to converge to the desired posture. For a musculoskeletal system with a specific structure consisting of two joints and six muscles, a previous study identified the conditions of the muscular arrangement required to achieve convergence to the desired posture. A further study analyzed the conditions of convergence for a more general multi-articular multimuscular system with several joints and muscles, although the joints were limited to a single degree of freedom and muscles to mono- and bi-articular ones, whose lengths were dependent on at most two adjacent joints. In this study, we consider cases consisting of joints with multiple degrees of freedom and muscles whose lengths depend on the angles of three or more joints. We mathematically analyze the conditions of convergence in the musculoskeletal potential method and verify the findings by simulation.