Abstract
This paper focuses on a dynamic sensory-motor control mechanism of reaching movements for a musculo-skeletal redundant arm model. The formulation of a musculo-skeletal redundant arm system, which takes into account non-linear muscle properties obtained by some physiological understandings, is introduced and numerical simulations are perfomed. The non-linear properties of muscle dynamics make it possible to modulate the viscosity of the joints, and the end point of the arm converges to the desired point with a simple task-space feedback when adequate internal forces are chosen, regardless of the redundancy of the joint. Numerical simulations were performed and the effectiveness of our control scheme is discussed through these results. The results suggest that the reaching movements can be achieved using only a simple task-space feedback scheme together with the internal force effect that comes from non-linear properties of skeletal muscles without any complex mathematical computation such as an inverse dynamics or optimal trajectory derivation. In addition, the dynamic damping ellipsoid for evaluating how the internal forces can be determined is introduced. The task-space feedback is extended to the 'virtual spring-damper hypothesis' based on the research by Arimoto et al. 2006 to reduce the muscle output forces and heterogeneity of convergence depending on the initial state and desired position. The research suggests a new direction for studies of brain-motor control mechanism of human movements.
Highlights
The natural movements of a human seem to be smooth, dexterous and sophisticated compared with today’s robots
We introduce non-linear muscle characteristics that correspond to the findings of physiological studies (Hill 1938; Mashima et al 1972) and propose a simple task-space feedback control scheme for the arm model taking into account internal forces
Asymptotic convergence of the closed-loop dynamic system was obtained based on the concept of stability theory on a manifold
Summary
The natural movements of a human seem to be smooth, dexterous and sophisticated compared with today’s robots. These internal forces belong to the null-space of the muscle space with respect to the joint space and thereby they are independent of a principal part of the joint torques in relation to generation of movements of the arm end point towards the target It causes an ill-posed problem of how to determine the internal forces uniquely. The task-space feedback manner is extended to the ‘virtual spring-damper hypothesis’ proposed by Arimoto et al (2005) to reduce the muscle output forces and the heterogeneity of convergence, which depends on the initial state and desired position of the arm These results suggest a direction for studies of the brainmotor control mechanism of human movements. This relation does not mean an optimisation, and it expresses only decomposition of the muscle force space with respect to the joint space into two spaces, one is the image space and the other is the kernel space
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