3.1 DCLSPTLS detection range

Zeng et al. (Reference Zeng, Wang, Wei, Cheng, Zheng, Feng and Shan2021) found that the 1,064 nm laser reflectivities of the deck, the Yangtze River surface and the sea surface are 0 · 27, $1 \cdot 08 \times {10^{ - 4}}$ and $2 \cdot 84 \times {10^{ - 5}}$, respectively. Although the laser wavelength used in this paper is 905 nm, it belongs to the near-IR band within the 1,064 nm wavelength. Therefore, it can be considered that the laser reflectivity at the 905 nm wavelength is approximately equal to that at the 1,064 nm wavelength. The laser reflectivities are the theoretical basis of the reliable identification of the ship and the sea surface and the design of the DCLSPTLS.

The laser detection distance of the small view field R can be expressed as:

(1)\begin{equation}R = {\tau _u}\sqrt {{P_t}\frac{{{A_r}}}{{\pi {P_{r{\rm min}}}}} \cdot {\tau _r} \cdot {\tau _t}\rho }\end{equation}

where ${P_t}$ is the transmitting power, $\rho$ is the laser reflectivity, ${A_r}$ is the effective receiving aperture, ${\tau _r}$ is the transmittance of the receiving optical system, ${\tau _t}$ is the transmittance of the transmitting optical system, and ${\tau _u}$ is the transmittance of the one-way transmission path. The parameters are: ${P_t} = 50\,W$, ${A_r} = \pi \times {({15 \times {{10}^{ - 3}}} )^2}{m^2}$, ${\tau _t} = 0 \cdot 8$, ${\tau _r} = 0 \cdot 8$. In the case of 25 km visibility, ${\tau _u} = exp ({ - 3 \times {{10}^{ - 4}} \cdot R} )$. ${P_{r\min }}$ is the minimum detectable power and can be expressed as:

(2)\begin{equation}{P_{r\min }} = \textrm{NEP} \cdot \sqrt {\Delta B} \cdot \textrm{SNR}\end{equation}

where NEP is the equivalent noise power, SNR is the signal-to-noise ratio, and $\Delta B$ is the receiving bandwidth. It can be seen from Table 2 that $\textrm{NEP} = 0 \cdot 027\,\textrm{pW}/\sqrt {\textrm{Hz}}$ and $\Delta B = 50\,\textrm{MHz}$. If SNR = 7 dB then, according to Equation (2), ${P_{r\min }} = 9 \cdot 54 \times {10^{ - 10}}W$.

For the deck, $\rho = 0 \cdot 27$. The detection distance of the single-pulse laser is 1,045 m, according to Equation (1). For the sea surface, $\rho = 2 \cdot 84 \times {10^{ - 5}}$. The detection distance of the single-pulse laser is 14 · 6 m according to Equation (1).

When the detection distance of the single-pulse laser does not meet the requirement, the multi-pulse laser echoes accumulation method is used to increase the detection distance. Suppose that the signal $\zeta (t )$ output from the amplifier circuit is:

(3)\begin{equation}\zeta (t )= s(t )+ n(t )\end{equation}

where $s(t )$ is the target echo signal and $n(t )$ is the noise signal. Accumulating multiple pulse signals can be expressed as:

(4)\begin{equation}\zeta (t )= \sum\limits_{i = 1}^N {[{{s_i}(t )+ {n_i}(t )} ]}\end{equation}

In Equation (4), N is the number of echo pulses. After multiple superpositions, the target echo signal is enhanced and the noise is suppressed due to correlation, so that the target echo signal is highlighted from the noise and the SNR is improved. Theoretical analysis shows that the power SNR of multiple pulses can be increased by $\sqrt N$ times that of the SNR of the single pulse ratio after N pulses are superimposed and correlated (Zhong and Li, Reference Zhong and Li2006).

In order to increase the detection distance from the DCLSPTLS to the ship's deck to 2,000 m, the laser echo power is ${P_r} = 1 \cdot 46 \times {10^{ - 10}}W$ according to Equation (1). In order to achieve the ${P_{r\min }}$ of the design above, there is:

(5)\begin{equation}N = {\left( {\frac{{{P_{r\min }}}}{{{P_r}}}} \right)^2}\end{equation}

The minimum number of accumulated pulses N is 43, according to Equation (5). Table 3 is compiled for ease of use. The DCLSPTLS accumulates according to the number of laser pulses in Table 3, and it can output laser echoes with a 7 dB power SNR.

Table 3. Corresponding table of detection range and number of laser echo pulses required to accumulate

3.2 DCLSPTLS workflow

Figure 4 is a schematic diagram of the rotorcraft using the DCLSPTLS which is installed in the rotorcraft to search, position, track and land on a ship. The whole process is elaborated as follows:

1. (a) Searching and positioning process. Since the laser reflectivity of the ship's deck in the near-IR band is four orders of magnitude higher than that of the sea surface, the peak of the ship's laser echo is 100 times the peak of the sea surface laser echo. By setting the appropriate threshold for the peak of the laser echo, the DCLSPTLS can reliably distinguish the ship from the sea surface, and obtain the distance and angle of the ship relative to the rotorcraft. At the same time, the multi-pulse laser echoes accumulation method is adopted to increase the detection distance of the DCLSPTLS. The specific approach is as follows. Since the DCLSPTLS can sample N laser echoes when the lateral channel laser beam rotates one circle, the k adjacent laser echoes in each circle are added and the sliding window method is adopted. Since the k adjacent ship/sea surface laser echoes are highly correlated and the noise correlation is low, the calculation will greatly improve the SNR of ship/sea surface echoes. The failed peak value of the original laser echo will be effective again using the multi-pulse laser echoes accumulation method, thereby obtaining the distance and angle of the ship relative to the rotorcraft. Of course, the price is a reduction in the angular resolution of the ship.

It should be noted that the ship must be within the range of the farthest horizontal detection distance of the DCLSPTLS. Under this condition, the rotorcraft descends from its maximum flight height, meanwhile the lateral channel laser beam of the DCLSPTLS is used to detect the ship. When the lateral channel of the DCLSPTLS obtains the distance information and angle information of the ship for the first time, it records them and the rotorcraft will hover in the air for a period of time. After the hovering time, the rotorcraft rises quickly. If the lateral channel of the DCLSPTLS obtains the information of the ship during the rising time, it means that the ship is just moving away from the rotorcraft. If there is ship information during the hovering period and there is no information during the rising time, it means that the ship is stationary. The rest of the conditions indicate that the ship is travelling in a direction approaching the rotorcraft. The rotorcraft then descends rapidly for a period of time and records the ship information until the lateral channel of the DCLSPTLS is not able to obtain the ship information.

Figure 4. Rotorcraft searching, positioning, tracking and landing on a ship using DCLSPTLS

Figure 5 shows two kinds of scanning trajectories of the lateral channel laser beam of the DCLSPTLS on a ship. Figure 5(a) is the trajectory of the general ‘scan arc length’ and Figure 5(b) is the trajectory of the longest ‘scan arc length’. ‘Scan arc length’ refers specifically to the arc length in a circle obtained by irradiating on a ship with the lateral laser beam, and the general ‘scan arc length’ refers specifically to the arc length in the middle of all ‘scan arc lengths’.

Figure 5. Two kinds of ship scanning trajectories: (a) scanning trajectory of general ‘scanning arc length’, (b) scanning trajectory of the longest ‘scanning arc length’

It can be seen from Figure 5(a) that the midpoint of the scan trajectory of the general ‘scan arc length’ and the midpoint of the scan trajectory of the previous arc length form a vector $\vec{q}$ and its direction is exactly the same as or opposite to the ship's course. The midpoint of the scan trajectory of the general ‘scan arc length’ and the coordinate points of the ship then obtained for the first time form a vector $\vec{p}$, and the angle between the above two vectors is calculated. If the ship is travelling away from the rotorcraft and the angle between $\vec{p}$ and $\vec{q}$ is an acute angle, then the ship's course is consistent with the direction of the vector $\vec{q}$. If the ship is travelling away from the rotorcraft and the angle between $\vec{p}$ and $\vec{q}$ is an obtuse angle, then the ship's course is opposite to the direction of the vector $\vec{q}$. If the ship is travelling towards the rotorcraft and the angle between $\vec{p}$ and $\vec{q}$ is an acute angle, then the ship's course is opposite to the direction of the vector $\vec{q}$. If the ship is travelling towards the rotorcraft and the angle between $\vec{p}$ and $\vec{q}$ is an obtuse angle, then the ship's course is consistent with the direction of the vector $\vec{q}$. This method of estimating the ship's course is called the ‘midpoint connection method’.

It can be seen from Figure 5(b) that if the ship's course is vertical to the moving direction of the scanning trajectory, then the ‘midpoint connection method’ will be invalid. Therefore, when the ‘scan arc length’ is close to the length of the ship, the rotorcraft flies at the maximum horizontal flight speed to the midpoint of the ‘scan arc’. If the vertical channel laser beam of the DCLSPTLS irradiates on the ship during the horizontal flight, it means that the rotorcraft is near the ship and happens to complete the searching and tracking tasks. If the vertical channel laser beam of the DCLSPTLS irradiates on the sea surface after the horizontal flight, the rotorcraft will restart the searching mission and the ship's course is the same as or opposite to the moving direction of the scanning trajectory.

1. (a) Tracking process. When the rotorcraft detects and acquires information on the distance, angle and speed of the ship at a long distance, the tracking scheme for predicting the ship's trajectory is applied to tracking the ship. The ship's course has been obtained through the searching process. Assuming that the ship's course is unchanged, the typical speed of the ship, the range of the rotorcraft speed and the range of the oblique flight angle of the rotorcraft are considered to estimate a tracking trajectory which is utilised by the rotorcraft to track the ship. Section 4.2 describes how to estimate the tracking trajectory.

When the rotorcraft tracks the ship, the vertical channel laser beam of the DCLSPTLS is used to determine whether there is a deck in the vertical direction of the rotorcraft. When the rotorcraft is far away from the ship, one laser irradiation of the vertical channel laser beam of the DCLSPTLS alone is insufficient to obtain the distance information. Similarly, the multi-pulse laser echoes accumulation method is utilised by the vertical channel of the DCLSPTLS to increase its detection distance.

1. (a) Landing process. In the process of continuous tracking of the ship by the rotorcraft, if the vertical channel laser beam of the DCLSPTLS has been irradiated on the ship, it means that the rotorcraft is nearly above the ship. At that moment, the rotorcraft will use its own camera to observe the apron on the deck and fly to the vicinity of the apron. After that, each time the lateral channel laser beam of the DCLSPTLS rotates one circle, it will accumulate information on the distance and angle of the deck.

The lateral channel of the DCLSPTLS will accumulate a certain amount of information on the deck distance and angle every time it rotates, and the rotorcraft flight control module will calculate the deck attitude information in real time and adjust the rotorcraft attitude. The rotorcraft then descends a certain distance. At the same time, the vertical channel of the DCLSPTLS continuously acquires the height information of the rotorcraft in order to determine whether the rotorcraft can land on the ship. The above process is repeated until the rotorcraft lands smoothly on the ship's deck.

3.3 DCLSPTLS searching and positioning model

The DCLSPTLS searching and positioning model is established to determine the distance, angle and course of the ship relative to the rotorcraft. When the rotorcraft is locked on the target ship, the ship is tracked by the rotorcraft in a relatively optimised way.

As shown in Figure 6, the geodetic coordinate system OXYZ is established with the projection point of the rotorcraft on the sea surface as the coordinate origin O, where the positive direction of the Y-axis is perpendicular to the sea surface and upward, the positive direction of the Z-axis is horizontal to the sea surface and southward, and the positive direction of the X-axis is determined by the right-hand rule. In the XZ plane, the angle from the positive X-axis to the positive Z-axis along the clockwise direction is positive. The XOZ plane is equivalent to the sea surface. The ship whose length, width and height are ${L_s}$, ${W_s}$ and ${H_s}$ respectively are simplified into a cube. At the beginning, the coordinates of the centre point of the deck are $({{x_s},{H_s},{z_s}} )$ and the angle between the deck length direction and the positive direction of the X-axis is ${\theta _s}$. The coordinates of the four endpoints of the deck ${A_1}$, ${A_2}$, ${A_3}$ and ${A_4}$ are as follows:

(6)\begin{equation}\left\{ {\begin{array}{@{}l} {{x_m} = {x_s} + 0\unicode{x2009}\unicode{x00B7}\unicode{x2009}5\sqrt {L_s^2 + W_s^2} \cos ({{\theta_s} + {\alpha_m}} )}\\ {{y_m} = {H_s}}\\ {{z_m} = {z_s} + 0\unicode{x2009}\unicode{x00B7}\unicode{x2009}5\sqrt {L_s^2 + W_s^2} \sin ({{\theta_s} + {\alpha_m}} )} \end{array}} \right.\end{equation}

where $m = 1,2,3,4$, ${\alpha _1} = \arctan ({{W_s}/{L_s}} )$, ${\alpha _2} = \pi - {\alpha _1}$, ${\alpha _3} = \pi + {\alpha _1}$, ${\alpha _4} = 2\pi - {\alpha _1}$. The ship travels along the deck length direction and the sway of the deck during the searching process are not considered. The angle between the driving speed ${V_s}$ and the Y-axis is zero, and the angle between the ${V_s}$ and the X-axis is ${\theta _s}$. At the beginning, the angle between the direction of the rotorcraft nose and the positive direction of the X-axis is ${\theta _0}$, and the direction of the rotorcraft nose is the same as the deck width direction. The DCLSPTLS is placed in the rotorcraft and rotates clockwise. The initial direction of the DCLSPTLS lateral channel laser beam is consistent with the direction of the rotorcraft nose. The angle between the DCLSPTLS lateral channel laser beam and the vertical channel laser beam is ${\theta _D}$. The rotorcraft is within the height range in which the DCLSPTLS lateral channel can detect the ship. The initial coordinates of the rotorcraft at the beginning are $({0,{y_r},0} )$. The rotorcraft falling speed ${V_r}$ is vertically downwards along the Y-axis and the DCLSPTLS rotates clockwise at speed n. The lateral channel laser emission frequency is ${f_{\textrm{side}}}$, and the farthest detection distance of the ship by lateral channel laser is ${L_{s\max }}$. The simulation time step is $\Delta t = 1/{f_{\textrm{side}}}$.

Figure 6. DCLSPTLS searching and positioning model diagram: (a) three-dimensional stereogram, (b) top view

The coordinates of the DCLSPTLS lateral channel laser beam irradiation point on the sea surface are:

(7)\begin{equation}\left\{ {\begin{array}{@{}l} {x = r\cos ({2\pi nt + {\theta_0}} )}\\ {y = 0}\\ {z = r\sin ({2\pi nt + {\theta_0}} )} \end{array}} \right.\end{equation}

where r is the scan radius, t is the rotation time and ${\theta _0}$ is the initial angle of the DCLSPTLS. The DCLSPTLS searching model is established as follows.

1. 1 When $t = a\Delta t({a = 0,1,2, \ldots ,{j_1}} )$, then $r = ({{y_r} - {V_r}a\Delta t} )\tan {\theta _D}$. By putting them into Equation (7), Equation (7) can be represented by Equation (8) as follows:

   (8)\begin{equation}\left\{ {\begin{array}{@{}l} {x = ({{y_r} - {V_r}a\Delta t} )\tan {\theta_D}\cos ({2\pi na\Delta t + {\theta_0}} )}\\ {y = 0}\\ {z = ({{y_r} - {V_r}a\Delta t} )\tan {\theta_D}\sin ({2\pi na\Delta t + {\theta_0}} )} \end{array}} \right.\end{equation}

By connecting the coordinates represented by Equation (8) to the coordinates $({0,{y_r} - {V_r}a\Delta t,0} )$ of the rotorcraft at this time, the direction vector of the lateral channel laser beam can be obtained. Then the linear equations of the lateral channel laser beam are:

(9)\begin{equation}\left\{ {\begin{array}{@{}l} {x = ({{y_r} - {V_r}a\Delta t} )\tan {\theta_D}\cos ({2\pi na\Delta t + {\theta_0}} )u}\\ {y = ({{y_r} - {V_r}a\Delta t} )({1 - u} )}\\ {z = ({{y_r} - {V_r}a\Delta t} )\tan {\theta_D}\sin ({2\pi na\Delta t + {\theta_0}} )u} \end{array}} \right.\end{equation}

where u is the parameter of the linear equations. Combine the coordinates represented in Equation (9) with the plane equation $y = {H_s}$ on which the ship's deck is located. The coordinates of the DCLSPTLS lateral channel laser beam irradiation point on the deck are:

(10)\begin{equation}\left\{ {\begin{array}{@{}l} {x = ({{y_r} - {V_r}a\Delta t - {H_s}} )\tan {\theta_D}\cos ({2\pi na\Delta t + {\theta_0}} )}\\ {y = {H_s}}\\ {z = ({{y_r} - {V_r}a\Delta t - {H_s}} )\tan {\theta_D}\sin ({2\pi na\Delta t + {\theta_0}} )} \end{array}} \right.\end{equation}

According to Equation (10), the coordinates of the four deck endpoints, ${A_1}$, ${A_2}$, ${A_3}$ and ${A_4}$, are:

(11)\begin{equation}\left\{ {\begin{array}{@{}l} {{x_m} = {x_s} + {V_s}a\Delta t\cos {\theta_s} + 0\unicode{x2009}\unicode{x00B7}\unicode{x2009}5\sqrt {L_s^2 + W_s^2} \cos ({{\theta_s} + {\alpha_m}} )}\\ {{y_m} = {H_s}}\\ {{z_m} = {z_s} + {V_s}a\Delta t\sin {\theta_s} + 0\unicode{x2009}\unicode{x00B7}\unicode{x2009}5\sqrt {L_s^2 + W_s^2} \sin ({{\theta_s} + {\alpha_m}} )} \end{array}} \right.\end{equation}

where $m = 1,2,3,4$; ${\alpha _1} = \arctan ({{W_s}/{L_s}} )$; ${\alpha _2} = \pi - {\alpha _1}$; ${\alpha _3} = \pi + {\alpha _1}$; ${\alpha _4} = 2\pi - {\alpha _1}$. At this time, the area enclosed by the deck can be expressed by the inequations introduced by Equation (12):

(12)\begin{equation}\left\{ {\begin{array}{@{}l} {[({z - {z_1}} )- ({x - {x_1}} )\tan {\theta_s}][({z - {z_3}} )- ({x - {x_3}} )\tan {\theta_s}] \le 0}\\ {[({z - {z_1}} )+ ({x - {x_1}} )\cot {\theta_s}][({z - {z_3}} )+ ({x - {x_3}} )\cot {\theta_s}] \le 0}\\ {y = {H_s}} \end{array}} \right.\end{equation}

The linear distance ${L_c}$ between the irradiation point of the lateral channel laser beam on the deck and the point at which the rotorcraft is located can be expressed by the following equation:

(13)\begin{align} L_c^2 & = {[{({{y_r} - {V_r}a\Delta t - {H_s}} )\tan {\theta_D}\cos ({2\pi na\Delta t + {\theta_0}} )} ]^2} + {[{{y_r} - {V_r}a\Delta t - {H_s}} ]^2}\nonumber\\ & \quad+ {[{({{y_r} - {V_r}a\Delta t - {H_s}} )\tan {\theta_D}\sin ({2\pi na\Delta t + {\theta_0}} )} ]^2}\end{align}

If the coordinates of the DCLSPTLS lateral channel laser beam irradiation point on the deck represented by Equation (10) is on the deck area represented by Equation (12) and ${L_c} \le {L_{s\max }}$, then it means the lateral channel laser beam is illuminated on the deck. Otherwise, it means the lateral channel laser beam is illuminated on the surface of the sea.

According to step (a), the target on which the DCLSPTLS lateral channel laser beam is irradiated, the coordinates of the irradiation point, and the orientation of the irradiation point relative to the rotorcraft can be determined or calculated.

1. 1 The midpoint connection method is used to estimate the speed direction of the ship. Suppose the coordinates of the scan points of the general ‘scan arc length’ are $({{{x^{\prime}}_{sk}},{H_s},{{z^{\prime}}_{sk}}} )({k = 1,2, \ldots ,{k_2}} )$, the coordinates of the scan points of the scan arc length previous to the general ‘scan arc length’ are $({{x_{sk}},{H_s},{z_{sk}}} )({k = 1,2, \ldots ,{k_1}} )$, and the ship coordinates first obtained by the DCLSPTLS lateral channel are $({{x_p},{H_s},{z_p}} )$. Then the vector $\vec{p}$ formed by connecting the ship's coordinates first obtained with the mean coordinates of the general ‘scan arc length’ is:

   (14)\begin{equation}\left\{ {\begin{array}{@{}l} {{p_1} = {x_p} - \sum\limits_{k = 1}^{{k_2}} {{{x^{\prime}}_{sk}}} /{k_2}}\\ {{p_2} = 0}\\ {{p_3} = {z_p} - \sum\limits_{k = 1}^{{k_2}} {{{z^{\prime}}_{sk}}} /{k_2}} \end{array}} \right.\end{equation}

The vector $\vec{q}$ formed by connecting the mean coordinates of the general ‘scan arc length’ with the mean coordinates of the previous scan arc length is:

(15)\begin{equation}\left\{ {\begin{array}{@{}l} {{q_1} = \sum\limits_{k = 1}^{{k_2}} {{{x^{\prime}}_{sk}}} /{k_2} - \sum\limits_{k = 1}^{{k_1}} {{x_{sk}}} /{k_1}}\\ {{q_2} = 0}\\ {{q_3} = \sum\limits_{k = 1}^{{k_2}} {{{z^{\prime}}_{sk}}} /{k_2} - \sum\limits_{k = 1}^{{k_1}} {{z_{sk}}} /{k_1}} \end{array}} \right.\end{equation}

Then, the angle $\delta$ between the vector $\vec{p}$ and the vector $\vec{q}$ is:

(16)\begin{equation}\delta = \arccos \left( {\frac{{\vec{p} \cdot \vec{q}}}{{|{\vec{p}} ||{\vec{q}} |}}} \right)\end{equation}

The driving direction flag of the ship is set as FlagAway. If the rotorcraft can obtain the information of the ship during the rising time, then FlagAway = 1 indicates that the ship is driving away from the rotorcraft. Otherwise, FlagAway = 0 indicates that the ship is driving toward the rotorcraft. When the general ‘scanning arc length’ is significantly different from the length of the ship (it means $\sqrt {{{({{{x^{\prime}}_{s{k_2}}} - {{x^{\prime}}_{s1}}} )}^2} + {{({{{z^{\prime}}_{s{k_2}}} - {{z^{\prime}}_{s1}}} )}^2}} < 0 \cdot 9 \times {L_s}$), the driving direction ${\hat{\theta }_s}$ of the ship can be estimated by the following equation:

(17)\begin{equation} {\hat{\theta }_s} = \left\{ {\begin{array}{@{}l} {\arctan \dfrac{{\dfrac{{\sum\nolimits_{k = 1}^{{k_2}} {{{z^{\prime}}_{sk}}} }}{{{k_2}}} - \dfrac{{\sum\nolimits_{k = 1}^{{k_1}} {{z_{sk}}} }}{{{k_1}}}}}{{\dfrac{{\sum\nolimits_{k = 1}^{{k_2}} {{{x^{\prime}}_{sk}}} }}{{{k_2}}} - \dfrac{{\sum\nolimits_{k = 1}^{{k_1}} {{x_{sk}}} }}{{{k_1}}}}},\begin{array}{*{20}{c}} {({\delta < {{90}^ \circ },\textrm{FlagAway} = 1} )}\\ {or({\delta > {{90}^ \circ },\textrm{FlagAway} = 0} )} \end{array}}\\ {\arctan \frac{{\frac{{\sum\nolimits_{k = 1}^{{k_2}} {{{z^{\prime}}_{sk}}} }}{{{k_2}}} - \frac{{\sum\nolimits_{k = 1}^{{k_1}} {{z_{sk}}} }}{{{k_1}}}}}{{\frac{{\sum\nolimits_{k = 1}^{{k_2}} {{{x^{\prime}}_{sk}}} }}{{{k_2}}} - \frac{{\sum\nolimits_{k = 1}^{{k_1}} {{x_{sk}}} }}{{{k_1}}}}} + \pi ,\begin{array}{*{20}{c}} {({\delta < {{90}^ \circ },\textrm{FlagAway} = 0} )}\\ {or({\delta > {{90}^ \circ },\textrm{FlagAway} = 1} )} \end{array}} \end{array}} \right.\end{equation}

when the general ‘scanning arc length’ is close to the length of the ship (it means $\sqrt {{{({{{x^{\prime}}_{s{k_2}}} - {{x^{\prime}}_{s1}}} )}^2} + {{({{{z^{\prime}}_{s{k_2}}} - {{z^{\prime}}_{s1}}} )}^2}} \ge 0 \cdot 9 \times {L_s}$), the rotorcraft restarts the searching task after flying to the midpoint of the general ‘scan arc length’ at the maximum flying speed.

The orientation of the midpoint of the last scanning arc length on the deck relative to the rotorcraft ${\theta _{r0}}$ is then considered as the initial orientation for the rotorcraft to track the ship.

3.4 DCLSPTLS tracking model

At the searching stage, the orientation ${\theta _{r0}}$, the distance ${L_c}\sin {\theta _D}$ of the ship relative to the rotorcraft and the ship driving direction ${\hat{\theta }_s}$ have been obtained. These parameters are combined with the typical speed ${\hat{V}_s}$ of the ship, and a better tracking trajectory can be designed to track the ship.

As shown in Figure 7, the coordinate system established by the searching model is still used for the tracking model. The initial coordinates of the rotorcraft are $({0,{Y_r},0} )$. The rotorcraft tracking speed is ${V_{rt}}$. The angle between the direction of ${V_{rt}}$ and the positive direction of the Y-axis is ${\varphi _r}$. The azimuth angle of ${V_{rt}}$ is ${\theta _r}$. The angle between the direction of the ship speed ${V_s}$ and the positive direction of the Y-axis is $\pi /2$. The azimuth angle of ${V_{st}}$ is ${\theta _s}$. When the rotorcraft starts to track the target, it needs to rotate the nose in the XZ plane. Thus, the nose is towards ${\theta _r}$. At the same time, the nose needs to be rotated in the Y-axis direction so that the nose is towards ${\varphi _r}$. The total tracking time is T.

Figure 7. DCLSPTLS tracking model diagram: (a) lateral view, (b) top view

The following equation can be derived according to the triangular geometric relations in the XY plane shown in Figure 7(a).

(18)\begin{equation}T = \frac{{{L_c}\sin {\theta _D}\cos {\theta _{r0}}}}{{{V_r}\sin {\varphi _r}\cos {\theta _r} - {{\hat{V}}_s}\cos {{\hat{\theta }}_s}}}\end{equation}

Similarly, the following equation can also be obtained according to the cosine theorem in the XZ plane shown in Figure 7(b).

(19)\begin{equation}\cos ({{\theta_{r0}} - {\theta_r}} )= \frac{{{{({{V_r}T\sin {\varphi_r}} )}^2} + {{({{L_c}\sin {\theta_D}} )}^2} - {{({{{\hat{V}}_s}T} )}^2}}}{{2{V_r}T\sin {\varphi _r} \cdot {L_c}\sin {\theta _D}}}\end{equation}

During the tracking time, the maximum flight speed of the rotorcraft ${V_r}$ and the maximum inclination ${\varphi _r}$ are set to 20 m/s and 0 · 53π rad respectively. The typical speed of the ship ${\hat{V}_s}$ is 7 m/s. The above parameters are substituted into Equations (18) and (19). The total tracking time T and the direction of the rotorcraft tracking speed ${\theta _r}$ can then be calculated.

3.5 DCLSPTLS landing model

When the rotorcraft has finished tracking the ship, it can be guided to the vicinity of the apron by using its camera. Even if the ship is moving, the image information obtained by the camera can be used to keep the rotorcraft above the ship apron. Therefore, it can be considered that the rotorcraft and the ship deck are relatively stationary in the horizontal direction.

As shown in Figure 8, the rotorcraft coordinate system OXYZ is established with the centre point of the rotorcraft as the coordinate origin O, where the positive direction of the X-axis is along the rotorcraft nose and outward, the positive direction of the Y-axis is perpendicular to the symmetry plane of the fuselage and points to the right side of the fuselage, and the positive direction of the Z-axis is determined by the right-hand rule. In the XY plane, the angle from the positive X-axis to the positive Y-axis along the clockwise direction is positive. The length and width of the deck at the apron area respectively are ${L_d}$ and ${W_d}$, and the apron is at the centre of the deck. The direction of the DCLSPTLS lateral channel beam in the XY plane is consistent with the positive direction of the X-axis. The angle between the DCLSPTLS lateral channel beam and the vertical channel beam is ${\theta _D}$, the lateral channel rotates clockwise at the speed n, and the lateral channel laser emission frequency is ${f_{\textrm{side}}}$. The simulation time step is $\Delta t = 1/{f_{\textrm{side}}}$.

Figure 8. DCLSPTLS landing model diagram

When the DCLSPTLS lateral channel laser beam rotates once and illuminates the deck at the apron, the circle scanned by the laser beam is exactly tangent to the deck width. At this time, the height of the rotorcraft ${H_{r0}}$ is as follows:

(20)\begin{equation}{H_{r0}} = \frac{{{W_d}}}{{2\tan {\theta _D}}}\end{equation}

When the distance obtained by the DCLSPTLS vertical channel is not larger than ${H_{r0}}$, the DCLSPTLS lateral channel starts to rotate and detect. Assuming that the distances obtained by one rotation of the DCLSPTLS lateral channel laser beam are ${l_{sc}}({c = 0,1, \ldots ,1/({n\Delta t} )} )$, the coordinates of the laser irradiation point of the DCLSPTLS lateral channel including the change of the apron deck attitude, that is, the coordinates of the apron deck, are:

(21)\begin{equation}\left\{ {\begin{array}{@{}l} {x = {l_{sc}}\sin {\theta_D}\cos ({2\pi nc\Delta t} )}\\ {y = {l_{sc}}\sin {\theta_D}\sin ({2\pi nc\Delta t} )}\\ {z = {l_{sc}}\cos {\theta_D}} \end{array}} \right.\end{equation}

Assuming that the normal vector of the plane where the apron is located is $\mu = ({{K_1},{K_2},{K_3}} )$, the plane where the apron is located can be expressed as follows:

(22)\begin{equation}{K_1}x + {K_2}y + {K_3}z = 1\end{equation}

Considering that the attitude of the deck changes slowly, the deck coordinates represented by Equation (21) are fitted by the least squares method. The sum of the squared residuals is as follows:

(23)\begin{equation}\varepsilon = \sum\limits_{i = 1}^{1/({n\Delta t} )} {{{({1 - {k_1}{x_i} - {k_2}{y_i} - {k_3}{z_i}} )}^2}}\end{equation}

In order to find the minimum value of Equation (23), all deck coordinates involved in the calculation are expressed in a matrix as shown below.

(24)\begin{equation}A = \left[ {\begin{array}{*{20}{c}} {{x_1}}& {{y_1}}& {{z_1}}\\ {{x_2}}& {{y_2}}& {{z_2}}\\ \vdots & \vdots & \vdots \\ {{x_{1/({n\Delta t} )}}}& {{y_{1/({n\Delta t} )}}}& {{z_{1/({n\Delta t} )}}} \end{array}} \right]\end{equation}

By combining Equations (23) and (24), the equation can be obtained as follows:

(25)\begin{equation}\mu = {({{A^T}A} )^{ - 1}}{A^T}b\end{equation}

where $b = {\left[ {\begin{array}{*{20}{c}} 1& 1& \ldots & 1 \end{array}} \right]^T}$.

The angle at which the deck rotates around the Y-axis is the pitch angle $\theta$, and the angle at which the deck rotates around the X-axis is the roll angle $\phi$. Then there is:

(26)\begin{equation}\left\{ {\begin{array}{c@{}} {\theta = \arcsin ({{K_1}} )}\\ {\phi = \arctan \left( {\dfrac{{{K_2}}}{{{K_3}}}} \right)} \end{array}} \right.\end{equation}

The rotorcraft adjusts its attitude in the opposite direction according to Equation (26) and descends to a certain height. The descending height value is approximately equal to the distance difference obtained by the DCLSPTLS vertical channel laser beam.

4.1 DCLSPTLS searching and positioning model simulation

The relevant parameters are set as follows: ‘the ship’ refers to the Chinese scientific research ship Xuelong. The ship size is 167 m × 22 · 6 m × 13 · 5 m. The coordinates of the deck centre are (500, 13 · 5, 500) and the speed of the ship ${V_s}$ is 1 · 5m/s. The angle ${\theta _s}$ between the speed and the positive direction of the X-axis is 330°, and the angle ${\theta _D}$ between the DCLSPTLS lateral channel laser beam and the vertical channel laser beam is 25°. The detection distances ${L_{s\max }}$ from each channel laser beam to the ship and to the sea surface are 2,000 m and 37 m respectively, and the initial coordinates of the rotorcraft are (0, 1812, 0). The climbing or landing speed ${V_r}$ of the rotorcraft is 5 m/s, and the rotational speed n of DCLSPTLS is 2r/s, the pulse repetition frequency ${f_{side}}$ of the lateral channel laser is 10 kHz, and the simulation time step $\Delta t$ is 100 μs.

Figure 9 shows the simulation result of the DCLSPTLS searching and positioning model, and Figure 9(a) and 9(b) are the stereogram and the local graph, respectively. The red line is the laser beam irradiated by the DCLSPTLS and the red points are the scanning trajectory of the DCLSPTLS lateral laser beam on the ship, the black rectangle is the ship when the search is stopped, and the blue points are the flight path of the rotorcraft. It can be seen from Figure 9 that the DCLSPTLS searching and positioning model is effective and the ship can be scanned as expected. Some of the red points in Figure 9(b) are outside the ship, which is caused by the movement of the ship. The red points in Figure 9(b) form several straight lines, and the azimuths of the DCLSPTLS lateral laser beam represented by the points on each straight line are the same and the phase difference of two adjacent points on each straight line is 2π. Since the scan diameter is too large and the proportion of the arc is too small, the black dotted line indicates the scanning trend of the DCLSPTLS lateral laser beam.

Figure 9. Simulation result of DCLSPTLS searching and positioning model: (a) stereogram of simulation result, (b) local graph of simulation result

Figure 9 shows that the DCLSPTLS can accurately obtain the distance and azimuth of the ship relative to the rotorcraft. The laser beam is simplified into a line shape in the model and the rotational speed of the rotational component of the DCLSPTLS is assumed to be constant. The theoretical accuracy of the distance and azimuth of the ship relative to the rotorcraft is very high. The accuracy is determined by the ranging accuracy and the rotation accuracy of the DCLSPTLS lateral laser beam.

In order to test the accuracy of the ship speed direction ${\theta _s}$ measured by the midpoint connection method, a simulation is performed with ${\theta _s}$ set with an order of 1° step in [0°, 359°] and the remaining parameters are unchanged. The simulation results are shown in Figure 10. The measured ship speed direction is 0° when the value of ${\theta _s}$ is in the range of [133°, 152°] and [298°, 317°] in Figure 10, because the relative positions of the ship and the rotorcraft are the same as the situation in Figure 5(b) and the scanning arc length of the DCLSPTLS lateral laser beam is close to the ship's length. The measured speed direction is represented by zero because it cannot be calculated. It can be seen from Figure 10 that the error of the measured speed direction is small and is no more than 15°, and the influence of the error can be significantly reduced to estimate the tracking trajectory by considering the error and the shape size.

Figure 10. Simulation velocity direction curve

It should be noted that the simulation parameters of the searching and positioning model are set based on the real parameters of the ship and the DCLSPTLS. Since the angle between the two channels of the DCLSPTLS and the climbing/landing speed of the rotorcraft cannot exceed 25° and 5 m/s respectively, the speed of the ship can be no more than 2 m/s. Otherwise, the rotorcraft will not be able to search the target when the rotorcraft climbs, and it will cause the DCLSPTLS searching and positioning model to fail. In order to make the DCLSPTLS application range wider, the angle between the two channels of DCLSPTLS can be increased. But at the same time, the feasibility of manufacturing the DCLSPTLS and the reduction of detection distance caused by a large incident angle of laser detection should be balanced.

4.2 DCLSPTLS tracking model simulation

The relevant parameters at the end of the simulation of the DCLSPTLS searching and positioning model are used as simulation inputs for the DCLSPTLS tracking model. The relevant parameters are set as follows: The coordinates of the centre of the Xuelong's deck are (587 · 1, 13 · 5, 449 · 7), and the azimuth angle ${\theta _{r0}}$ of the ship relative to the rotorcraft estimated by DCLSPTLS is 43 · 3°. The ship speed ${V_s}$ is 1 · 5m/s, and the angle ${\theta _s}$ between the ship's course and the positive direction of the X-axis is 330°. The angle ${\hat{\theta }_s}$ between the ship's course estimated by the DCLSPTLS and the positive direction of the X-axis is 332°. The distance ${L_c}$ between the rotorcraft and the ship measured by the DCLSPTLS lateral channel laser beam is 1,659 · 3m, the angle ${\theta _D}$ between the DCLSPTLS lateral channel laser beam and the vertical channel laser beam is 25°. The detection distances ${L_{s\max }}$ of each channel laser beam to the ship and to the sea surface are 2,000 m and 37 m respectively. The initial coordinates of the rotorcraft are (0, 1517, 0) and the rotorcraft tracking speed ${V_r}$ is 20 m/s. The angle ${\varphi _r}$ between the direction of the tracking speed and the positive direction of the Y-axis is 95°. The typical speed of the ship ${\hat{V}_s}$ is 7 m/s, and the simulation time step $\Delta t$ is 1 s.

When the rotorcraft starts to track, the above simulation parameters are brought into Equations (18) and (19). The total tracking time T = 42 · 36s and the angle ${\theta _r} = {23\unicode{x2009}\unicode{x00B7}\unicode{x2009}9^ \circ }$ between the tracking speed and the positive direction of the X-axis are then calculated respectively. Finally, the rotorcraft tracks the ship at the maximum speed of the rotorcraft ${V_r}$ = 20 m/s, and the maximum inclination ${\varphi _r}$ = 95° and ${\theta _r}$ = 23 · 9°. Figure 11 shows the simulation results of the DCLSPTLS tracking model: Figure 11(a) is the stereogram of the tracking result, Figure 11(b) is the side view of the tracking result, and Figure 11(c) is the top view of the tracking result. The blue points in Figure 11 are the tracking path of the rotorcraft, and the two red lines are the two channels laser beams of the DCLSPTLS. The two black rectangles are the ship: one is the ship at the beginning of the tracking and the other is the ship at the end of the tracking. It can be seen from Figure 11 that, at the end of the tracking, the position of the rotorcraft is not nearly above the ship, but above the front of the ship. They are 67 · 4 m apart in the horizontal plane.

Figure 11. Simulation result of DCLSPTLS tracking model: (a) tracking result stereogram, (b) tracking result side view, (c) tracking result top view

This is due to the fact that the typical driving speed of the ship used in calculating the tracking trajectory, 7 m/s, is far from the actual driving speed of 1 · 5 m/s. Since the estimated ship's course used in calculating the tracking trajectory is 332°, which is quite close to the actual driving speed direction of 330°, the rotorcraft hovers over the place where the ship is about to arrive. Because the DCLSPTLS has the ship's estimated course and the ship's speed does not exceed 7 m/s (the ship is a cooperation target), the rotorcraft can fly in the opposite direction of the ship's estimated course and it is inevitable that it will fly in the vicinity of the ship.

4.3 DCLSPTLS landing model simulation

The relevant parameters are set as follows: the size of the ship apron is 20 m × 20 m and the height of the apron is 21 · 4 m. The coordinates of the apron centre are (0, 0, 21 · 4). The pitch angle $\theta$ of the apron and the roll angle $\varphi$ of the apron are linearly changed from −45° to 45° in 6 s. The angle ${\theta _D}$ between the DCLSPTLS lateral channel laser beam and the vertical channel laser beam is 25°. The DCLSPTLS rotational speed n is 2 r/s, the pulse repetition frequency ${f_{\textrm{side}}}$ of the lateral channel laser is 10 kHz, the simulation time step $\Delta t$ is 100 μs and the total simulation time is 6 s. The rotorcraft hovers at (0, 0, 0), and only the DCLSPTLS performs a rotating motion. The estimated pitch angle $\hat{\theta }$ and the estimated roll angle $\hat{\varphi }$ of the apron are obtained by the simulation to evaluate the accuracy of the DCLSPTLS landing model.

Figure 12 shows the simulation results of the DCLSPTLS landing model, where Figure 12(a) shows the apron positions corresponding to the apron attitudes, Figure 12(b) is the pitch angle comparison of the apron, and Figure 12(c) is the roll angle comparison of the apron. There are seven rectangles in Figure 12(a) indicating the apron positions corresponding to the apron attitudes at intervals of 1 s in a range of 0 s–6 s, and it is only to prove that the pitch angle and roll angle of the apron are variable. The red curves in Figure 12(b) and (c) are the actual pitch angle curve and the actual roll angle, which vary linearly with time from –45° to 45° in the simulation. The blue curves in Figure 12(b) and (c) are obtained by calculating and estimating the pitch angle and the roll angle of the apron for every 50 coordinates of irradiation points on the apron accumulated by the DCLSPTLS. It can be seen from Figure 12 that the maximum error of the estimated pitch angle is –7 · 23° when the actual pitch angle is –44 · 92°, and the maximum error of the estimated roll angle is –2 · 776° when the actual roll angle is 9 · 904°.

Figure 12. Simulation results of DCLSPTLS landing model: (a) apron position corresponding to the apron attitude, (b) pitch angle comparison of the apron, (c) roll angle comparison of the apron

4.4 Test of DCLSPTLS

The test of the DCLSPTLS was designed to verify the performance of the DCLSPTLS such as the ability to identify the ship and the sea surface, and the ranging and angle measurement accuracy. As shown in Figure 13, the test system is a DCLSPTLS prototype, a rotorcraft, a data link, a total station, a model ship (in the lower right corner of Figure 13, which is equivalent to a reduced-scale ship deck), a lake, a type of portable computer and many different types of batteries. The test parameters of DCLSPTLS are shown in Table 5.

Figure 13. Test conditions and equipment

Table 5. Test parameters of DCLSPTLS

The fixed height measurement test of the rotorcraft was designed as follows. The manually remote-controlled rotorcraft flies to hover nearly above the reduced-scale ship. The DCLSPTLS works and records the laser echo information, ranging information of the DCLSPTLS lateral channel and vertical channel, and the angle information by the pulse encoder. During the test, the DCLSPTLS reduced its gain and its rotation speed to 0 · 5 r/s to adapt to the close detection. Figure 14 shows how the rotorcraft carries the DCLSPTLS for the test on a reduced-scale ship.

Figure 14. Experimental picture from DCLSPTLS

Figure 15 shows the results of the fixed height measurement test of the rotorcraft. The curves from top to bottom are as follows: DCLSPTLS lateral channel laser echo (Echo), DCLSPTLS vertical channel laser ranging curve (DisA), DCLSPTLS lateral channel laser ranging curve (DisB) and DCLSPTLS rotation angle measurement curve (Angle). The initial angle of DCLSPTLS is towards the bow along the long axis of the ship, and it rotates clockwise (when viewed from above). Figure 16 shows the relative positions and azimuths of the rotorcraft and the reduced-scale ship measured by the total station.

Figure 15. Experiment results of the fixed height test

Figure 16. Total station results of the fixed height test

It can be seen from Figure 15 and Figure 16 that:

1. (a) When the rotorcraft is tested at the actual measuring position, the DCLSPTLS vertical channel laser beam is vertically incident on the surface of the ship.

2. (b) The laser echo curve in Figure 15 consists of two curves, which means that it has been performed twice during the test, and the time interval is about 6 s. According to the details of the laser echo in Figure 17, when the DCLSPTLS lateral channel laser illuminates the reduced-scale ship at 25° incident angle, a single laser pulse echo is saturated, which means that the reduced-scale ship can be detected at 12 m height without pulse accumulation. The duration of the DCLSPTLS lateral channel laser irradiation on the reduced-scale ship is about 116 ms every rotation in Figure 17, and the corresponding angle difference is about 20 · 88°. The duration calculated by geometric relation in Figure 16 is about 119 ms, and the corresponding angle difference is about 21 · 37°. Considering the drift of the yaw angle of the rotorcraft, the measurement error with a duration 3 ms is acceptable, and the measurement test results are consistent with the theoretical calculation results.

3. (c) It can be seen from the DisA curve in Figure 15 that the height measured by the DCLSPTLS vertical channel laser to the reduced-scale ship is 11 m–13 m. The height measured by the total station is 12 m, and the maximum error is 1 m.

It should be noted that the two-channel laser outputs a ranging value every 64 ms because the laser pulse repetition period is 4 ms and 16 pulse echoes need to be accumulated. Considering the 80 MHz sampling clock, the 1 m maximum error is acceptable. For close-range ranging, the signal output from the comparison circuit in the DCLSPTLS can be used for ranging. By debugging a reasonable threshold, the DCLSPTLS close-range ranging error can be no more than 0 · 5 m.

1. (a) The curve DisB in Figure 15 shows that the lateral channel laser detects the reduced-scale ship with a 2 s period. The rotation period of the stepper motor is set to 2 s. Thus, the actual measurement period is consistent with the theoretical period. The distance to the reduced-scale ship measured by the DCLSPTLS lateral channel laser is 13 m–15 m while the theoretical distance is 13 · 5 m. The maximum distance error is 1 · 5 m which is acceptable. When the DCLSPTLS lateral channel laser irradiates the lake surface, no ranging value is obtained. It is displayed as 0 m in the curve. When the DCLSPTLS lateral channel laser irradiates the ship, the corresponding azimuth is 152 · 3°–170 · 7° by comparing the special points coordinates of the DisB curve and the Angle curve in Figure 15, while the azimuth calculated theoretically in Figure 16 is 159 · 8°. Considering the drift of the yaw angle of the rotorcraft in the measured process, these errors are acceptable.

Figure 17. Laser echo detail of the fixed height test