Implementing Stretch Reflex in Musculoskeletal Robots Driven by Pneumatic Artificial Muscles Using Nonlinear Spring Model*

This paper introduces a method to realize stretch reflexes in musculoskeletal robots without length sensors. A pneumatic artificial muscle (PAM) was modeled as a nonlinear spring with a spring constant dependent on deformation and pressure. The dimension of the spring constant had physical bases in prior research, and its coefficients were derived from static tensile tests that measured force and length under constant pressure. We applied the model to estimate length of four PAMs with different materials and shapes, verifying the general applicability. When incorporated into an arm driven by antagonistic muscles, the model proved effective in monitoring the velocity change of PAM length and triggering a stretch reflex, enhancing the robot’s adaptability to disturbances. The reflex trajectory with a conventional sensor was well replicated with the model, offering a practical alternative to length sensors.