Fig. 7.

Simulation results of quiet upright stance with joint-based co-contraction variations (see Sects. 3.4 and 4.3 ). The middle graphs show the default (${\zeta }_j^{\theta }={\zeta }^{\theta }=0.0$), where in the left column a joint-based co-contraction of ${\zeta }_j^{\theta }={\zeta }^{\theta }=-0.05$ in all leg joints ($j\in [{\text{Hp}}_{\text{FE,l/r}},{\text{Hp}}_{\text{AA,l/r}},{\text{Kn}}_{\text{l/r}},{\text{An}}_{\text{l/r}}]$) is used, and ${\zeta }_j^{\theta }={\zeta }^{\theta }=0.2$ in the right column. In both variations, the MTU stimulations are adjusted according to ${\zeta }^{\theta }$ and so are the respective MTU forces. The joint-based co-contraction is hereby based on the null-space of the Jacobian transformations. Due to the approximations of the associated angle–stimulation Jacobian $J^{\mathit{u}\mathit{\theta }}$ (25), the resulting joint trajectories are slightly different