Table 1.

Initial conditions and control parameters used for the computational synthesisation of quiet upright stance with the hierarchical distributed PID-control laws

	Conceptional control	$\mathit{\tau }$-Controller			${\theta }_{\lambda }$-Controller			$\theta$-Controller			Initial conditions
Joint
Lu AA	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Lu FE	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Ce AA	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Ce FE	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Sh AA (l/r)	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Sh FE (l/r)	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Eb FE (l/r)	–	–	–	–	0.01	0.01	0.001	0.1	0.1	0.01	0
Hp AA (l/r)	–	–	–	–	0.01	0.0	0.002	0.05	0.0	0.01	0
Hp FE (l/r)	172	2.0	30	0.0	1.5	1.0	0.1	1.5	1.0	0.1	0
Kn FE (l/r)	467	0.75	15	0.0	0.25	1.0	0.0035	0.25	1.0	0.0035	5
An FE (l/r)	784	3.0	50	0.0	0.5	1.0	0.0035	0.5	1.0	0.0035	$-5$

The conceptional joint-torque controllers are only active for the lower limb DoFs. For the conceptional plan of desired joint torques the additional position-based parameter $g_{\text{Hp,l/r}}=-400\text{N}$ is used [see (43)] with the set-point for the COM of $x_{\text{COM,0}}=2.86\text{cm}$ anterior to the mean ankle joint position. For the structural control law, for each of the k MTUs, the control parameters $p_{\lambda ,k}=1.0/l_{\text{opt},k}^{\mathrm{CE}}$ and $d_{\lambda ,k}=0$ are chosen. As an additional initial condition, the pelvis body is positioned at $X_P(t=0)={[000.9954]}^T$, such that the feet are placed at the ground contacts. The initial activations of the MTUs are in steady state with $a_k=0.1$ for each of the $k=1\dots 36$ MTUs, corresponding to the co-contraction that is parameterised by ${\zeta }_k^u={\zeta }^u=0.1$ and ${\zeta }_j^{\theta }={\zeta }^{\theta }=0.0$