*4.2. Follower Robot Controller*

The next step is to design the tracking controller for the follower. The proposed position and attitude control laws for the followers have a similar structure to the leader's controllers and are given by

$$\mu\_{\rm fi} = \dot{\mathbf{x}}\_{\rm d}(t - \tau\_{\rm i}) + (1 - \tau\_{\rm i})\mathbf{x}\_{\rm d}(t - \tau\_{\rm i}) + \mathbf{K}\_{\rm f\&i}\mathbf{\mathcal{g}}\_{\rm fi} \tag{24a}$$

$$
\omega\_{\rm fi} = \omega\_{\rm difi} + k\_{\rm ofi} \Theta\_{\rm difi}^{\perp} \mathcal{S} \Theta\_{\rm fi} \tag{24b}
$$

where *Kβ*f*<sup>i</sup>* = *K <sup>β</sup>*f*<sup>i</sup>* > *<sup>O</sup>*, *<sup>k</sup>*of*<sup>i</sup>* > 0 are the control gains and *<sup>β</sup>*f*<sup>i</sup>* ∈ <sup>2</sup> is obtained as the solution of

$$
\dot{\mathcal{B}}\_{\rm fi} = -\mathbf{K}\_{\rm ffi}\boldsymbol{\mathcal{B}}\_{\rm fi} - \mathbf{K}\_{\rm \eta \rm fi}\boldsymbol{\eta}\_{\rm fi} \tag{25}
$$

with *Kη*f*<sup>j</sup>* = *K <sup>η</sup>*f*<sup>j</sup>* <sup>&</sup>gt; *<sup>O</sup>* and *<sup>η</sup>*f*<sup>j</sup>* <sup>=</sup> *x*f*<sup>j</sup>* <sup>+</sup> *<sup>β</sup>*f*<sup>j</sup>*

To avoid complex calculations, the time-derivative of **Θ**d*<sup>i</sup>* can be approximated by a low-pass filter, **<sup>Θ</sup>**˙ <sup>d</sup>*<sup>i</sup>* <sup>=</sup> *<sup>s</sup> λs* + 1 **Θ**d*<sup>i</sup>* with *λ* > 0 is the cutoff frequency. It is important to point out that the attitude control laws (22b) and (24) does not explicitly use the orientation error *θ i*.

.
