TABLE 4.

Observation table for end-to-end training for path following. All states and errors are normalized by the empirical or true maximum value.

Observation		Max
Relative surge + speed	$u_{ro}=\frac{u_r}{u_{\max }}\in \left[-\mathrm{1,1}\right]$	2
Relative sway speed	$v_{ro}=\frac{v_r}{v_{\max }}\in \left[-\mathrm{1,1}\right]$	0.3
Relative heave speed	$w_{ro}=\frac{w_r}{w_{\max }}\in \left[-\mathrm{1,1}\right]$	0.3
Roll	${\varphi }_o=\frac{\varphi }{{\varphi }_{\max }}\in \left[-\mathrm{1,1}\right]$	π
Pitch	${\theta }_o=\frac{\theta }{{\theta }_{max}}\in [-\mathrm{1,1}]$	π
Yaw	${\psi }_o=\frac{\psi }{{\psi }_{\max }}\in \left[-\mathrm{1,1}\right]$	π
Roll rate	$p_o=\frac{p}{p_{\max }}\in \left[-\mathrm{1,1}\right]$	1.2
Pitch rate	$q_o=\frac{q}{q_{\max }}\in \left[-\mathrm{1,1}\right]$	0.4
Yaw rate	$r_o=\frac{r}{r_{\max }}\in \left[-\mathrm{1,1}\right]$	0.4
Course error	${\tilde{\chi }}_o=\frac{{\chi }_d-\chi }{{\chi }_{\max }}\in \left[-\mathrm{1,1}\right]$	π
Elevation error	${\tilde{\upsilon }}_o=\frac{{\upsilon }_d-\upsilon }{{\upsilon }_{\max }}\in \left[-\mathrm{1,1}\right]$	π
Ocean current velocity, surge	$u_{c,o}=\frac{u_c}{V_{c,\max }}\in \left[-\mathrm{1,1}\right]$	1
Ocean current velocity, sway	$v_{c,o}=\frac{v_c}{V_{c,\max }}\in \left[-\mathrm{1,1}\right]$	1
Ocean current velocity, surge	$w_{c,o}=\frac{w_c}{V_{c,\max }}\in \left[-\mathrm{1,1}\right]$	1