Immersion and invariance control for an antagonistic joint with nonlinear mechanical stiffness

Tendon controlled robots with nonlinear mechanical tendon stiffness are becoming more and more popular. With the appropriate actuation, the joint position and the stiffness between motor and link side can be prescribed at the same time. In this paper, the modeling of tendon-driven elastic systems with nonlinear couplings is recapitulated. Based on the Immersion and Invariance (I&I) framework a control law is developed that takes trajectories of the desired joint position and the pretension as input. The contribution of this paper are the application of the I&I framework to tendon-controlled systems with variable stiffness which requires to consider the internal degrees of freedom to realize the pretension, respectively the mechanical joint stiffness. But also, and even more importantly, the handling of nonlinear transmission elements between the motor and the joint link is included. The performance and sensitivity is analyzed by simulating an antagonistically driven robot joint.