Table 2.

Variables in Figure 9.

Variable	Details	Unit
$v_h$	Human linear speed in the absolute axis	m/s
${\omega }_h$	Human angular speed in the absolute axis	rad/s
d	Human-robot distance	m
θ	Robot angle in the human reference	rad
φ	Human angle in the robot reference	rad
$x^L$ and $y^L$	Laser sensor longitudinal and transversal axis	m
$x^H$ and $y^H$	Human longitudinal and transversal axis	m
$x^R$ and $y^R$	Robot longitudinal and transversal axis	m
$x_h^L$ and $y_h^L$	Human position in the laser sensor reference	m
$x_h^R$ and $y_h^R$	Human position in the robot reference	m
$x_R^h$ and $y_R^h$	Robot position in the human reference	m
${\dot{h}}_{ref}$	Speed vector the robot should follow to keep the formation	m/s
α	Robot orientation in the human reference	rad
${\alpha }_{ref}$	Set-point orientation the robot should achieve to keep the formation	rad
$v_r$	Robot linear speed	m/s
${\omega }_r$	Robot angular speed	m/s
β	Human orientation in the robot reference	rad
$v_{h_x}$	Human linear speed in the transversal axis	m/s
$v_{h_y}$	Human linear speed in the longitudinal axis	m/s
k	Sample time	0.1 s (100 ms)
$k-1$	Previous sample time	0.1 s (100 ms)
$k-1|k$	Positions and angles of instant ($k-1$) projected into instant (k)	0.1 s (100 ms)