Shipborne Stabilization Grasping Low-Altitude Drones Method for UAV-Assisted Landing Dock Stations

Highlights

What are the main findings?

• Present the manipulator arm designed for charging shipborne drones that utilize low-altitude visual servo grasp-docking.
• Present a global Jacobian matrix which covers not only the six degree-of-freedom (DOF) of the manipulator arm, but also the nonholonomic shipborne base.

What is the implication of the main finding?

• Provide a long-endurance way to drones charging and recover on water surface.
• Provide a flow field disturbance stabilization for drones landing on water surface.

Abstract

Shipborne UAV-assisted dock is an important way to recover unmanned systems for remote water surface low-altitude detection. The lack of resisting deck disturbances capability for UAV autonomous landing in dynamic dock stations has led to the inability of traditional hovering recovery methods for single UAV guidance and flight attitude control systems to meet the growing demand for landing assistance. In this work, we present a shipborne manipulator arm designed to grasp drones that use low-altitude visual servo technology for landing on the water surface. The shipborne manipulator arm is fabricated as a key component of a seaplane drone dock comprising a ship-type embedded drone storage, a packaged helistop for power transfer and UAV recovery, and a multi-degree-of-freedom arm integrated with multi-source information sensors for the treatment of air-to-water-related airplane crashes. Dynamic model tests have demonstrated that the end-effector of the shipborne manipulator arm stabilizes and performs optimally for water surface disturbances. A down-to-top grasp docking paradigm for a UAV-assisted perching on a shipborne helistop that enables the charging components of the station system to be equipped automatically to ensure that the drone performs its mission in the best condition is also presented. The surface grasp experiments have verified the efficacy of this grasp paradigm when compared to the traditional autonomous landing method.

1. Introduction

The offshore meteorological and hydrodynamic environment is characterized by more intense sea and air flows, accelerating eddy processes, and a sudden increase in uncertain factors. Whether the various monitoring units in the atmospheric unmanned system can be quickly connected and coordinated will be the key to gaining forecasting advantages [1]. The UAV (Unmanned Aerial Vehicle) and ship coordination have become the main way to observe offshore hydrometeorological environments, and the implementation of aerial forecasting requires reliable long-cycle information for early monitoring. Drone flight limits of shore-based and airborne radar detections can no longer meet the long-cycle needs of aerial early monitoring, which will cause serious constraints to the effectiveness of offshore remote accurate forecasting.

Some ambitious works [2,3,4,5] have investigated the bio-inspired perching and resting way by adding multidegree-of-freedom perching gears at the button of the UAV. This is a difficult scheme to obtain dual-docking stabilization, and the cost of modifying the UAV and the impact on the UAV’s flight-control performance is too great to be suitable for technological diffusion. Meanwhile, some other extensive works [6,7] focus on improvising the single UAV autonomous landing technology by enhancing guidance and flight attitude control systems. Their main requirement is robustness, meaning the ability to land in the presence of various disturbances. Visual-based trajectory planning is the basic method for landing on a moving platform. Such methods are described in [8,9,10]. More advanced controllers, such as deep learning algorithms, are used in [11]. These are good solutions when UAVs have to be operated above water, but it can be challenging to design a robust docking station that can be used in severe wave conditions. They are best suited for small water surfaces with calm water conditions. The lack of resistance to deck disturbances capability for UAV autonomous landing in dynamic dock stations has led to the inability of traditional hovering recovery methods for single UAV guidance and flight attitude control systems to meet the growing demand for landing assistance.

This problem is addressed and is being partially solved by using shipborne dock stations, which provide an aircraft to land safely, charge (or change) the batteries, and take off, as well as being safely stored [12,13,14]. The shipborne dock comprises a ship-type embedded drone storage and a packaged helistop for power transfer and UAV recovery. Based on this, the shipborne drones round robin on duty and periodically return to land on the UAV station to charge power. With the unique advantage of an all-time, all-weather, and mobile replenishment carrier, this method can obtain large-depth and wide-range hydrographic situation and target information without the restriction of offshore sea and air, which is regarded as a potential scheme to enhance the endurance capability of the UAV, and it has gradually become an important force for ship-to-UAV landing [15,16].

This approach refers to the use of shipborne UAV dock stations modified by water surface vessels or floating UAV docks placed at the fixed supply points in the aerial waterway to provide UAVs with functional services such as power supply, status monitoring, storage data processing, and equipment management, etc., so as to realize semi-automated management of the UAV batteries and indirectly enhance the endurance of UAVs. UAV dock stations represent a critical technology for improving the operational efficiency of UAV recovery systems. In land-based scenarios, drone stations utilizing hovering recovery methods have demonstrated significant effectiveness. With the expansion of UAV applications from terrestrial to marine environments, recovery and docking technologies must meet increasingly stringent requirements to adapt to complex and dynamic maritime conditions [17]. The shipborne UAV dock station operates by allowing the mounted UAV to land on the helistop after completing its round robin aerial monitoring, where it can then charge or replace its battery. After the current hydro-meteorological monitoring is completed, the UAV will follow the shipborne UAV dock station to the next working area until all offshore hydro-meteorological monitoring operations are completed.

Currently, the traditional UAV autonomous perching technology struggles to meet the zero-force docking requirements [18,19,20] when shipborne UAV dock stations contact drones, due to limitations from the compact deck space and water/airflow disturbances. Some great works [21,22] have investigated the bio-inspired perching and resting way by adding multi-degree-of-freedom perching gears at the bottom of the UAV. This is a difficult scheme to obtain dual-docking stabilization, and the cost of modifying the UAV and the impact on the UAV’s flight-control performance are too great to be suitable for technological diffusion. Based on these, in this work, we try to install a multi-degree-of-freedom manipulator arm on the ship, and the shipborne manipulator arm is a useful scheme to combine mobile docking stations with vessels operating on the water surface and multirotor UAVs. This kind of system can increase the safety and range of multirotor drones during missions when flying over large water surfaces [23,24], as shown in Figure 1. Due to the strong force coupling of the dual-docking between the manipulator and the UAV, minor deviations can lead to the UAV crashing and the ship being damaged. It is an enormous challenge on dual-docking force control of shipborne manipulators for UAV docking.

From the perspective of UAV-manipulator collaborative operations, soft landing performance critically depends on the coordination accuracy between UAV autonomous landing trajectory planning and the manipulator’s flexible grasping control [25,26]. To achieve millimeter-level safe landing under complex maritime conditions, a coupled dynamic model integrating UAV aerodynamics and manipulator impedance characteristics is essential [27]. Traditional methods often decouple UAV landing control and manipulator grasping into independent processes: first aligning the UAV through attitude adjustments for coarse positioning, then activating the manipulator grasping protocol. Such sequential control strategies neglect the dynamic coupling among ship motion, airflow disturbances, and manipulator compliance, leading to excessive landing impact forces (larger than 15N) or increased grasping instability risks [28].

The main contributions of the present work are as follows:

(1) Aiming at the uncertainty of gentle wave, current, or gentle wind disturbance problems faced by UAVs when landing on a water surface, we present the first manipulator arm designed for charging shipborne drones that utilize low-altitude visual servo grasp-docking to land their UAV on the water surface.

(2) We present a global Jacobian matrix, which covers not only the six degrees of freedom (DOF) of the manipulator arm but also the nonholonomic shipborne base, derived using the kinematic differential equation. Then it is substituted into a convergence control law to obtain the visual servo control rule that covers the whole dock station.

(3) To decouple the coordinated dock movement between UAVs and the ship, we present a down-to-top grasp docking paradigm for UAV-assisted perching on a shipborne helistop, which is based on the UAV’s hovering control during standby. This paradigm enables the automatic equipping of the charging components of the station system, ensuring that the UAV can perform its mission under optimal conditions.

This paper is organized as follows: Section 2 introduces a global Jacobian matrix of the shipborne manipulator arm and its global mathematical model. In Section 3, a down-to-top grasp docking paradigm is proposed to stabilize UAV-assisted landing by the end-effector of the shipborne manipulator arm. Experimental results and discussions are also given in this section. Conclusions are drawn in Section 4.

2. Global Jacobian Matrix and Global Dynamic Model

In this section, a global Jacobian matrix, which covers not only the six-DOF of the manipulator arm but also the nonholonomic ship base, is established. Then the complete dynamics model of the ship-to-arm for UAV-assisted perching is formulated.

2.1. Global Jacobian Matrix and Kinematics of the Shipborne Grasping Arm

The modified Denavit-Hartenberg parameters are needed to establish its configuration of the shipborne manipulator serial arm, as shown in the Figure 2. They are the angle ${\alpha }_{i-1}$ between two adjacent joint axes, the translation length from the origin of one joint axis coordinate system to the origin of the next joint axis coordinate system $a_{i-1}$, the angle of rotation of the next rod relative to this rod ${\theta }_i$, and the translation length of the coordinate origin of the next axis relative to this axis along z the direction $d_i$.

In terms of the serial manipulator arm, the transformation from one axis to the next can be written as follows:

$${}_{i\hspace{1em} }{}^{i-1}T=\left[\begin{array}{cc}{}_{i\hspace{1em} }{}^{i-1}R& {}_{i\hspace{1em} }{}^{i-1}t\\ 0& 1\end{array}\right]=\left[\begin{array}{cccc}c{\theta }_i& -s{\theta }_i& 0& {\alpha }_{i-1}\\ s{\theta }_{i}c{\alpha }_{i-1}& c{\theta }_{i}c{\alpha }_{i-1}& -s{\alpha }_{i-1}& -s{\alpha }_{i-1}{d}_i\\ s{\theta }_{i}s{\alpha }_{i-1}& c{\theta }_{i}s{\alpha }_{i-1}& c{\alpha }_{i-1}& c{\alpha }_{i-1}{d}_i\\ 0& 0& 0& 1\end{array}\right]$$

(1)

For the shipborne 6-degrees-of-freedom serial robotic arm, the transformation of the coordinate system of its $i_{t}h$ link relative to the base coordinate system can be written as follows:

$${}_{i }{}^{0}T={}_1{}^{0}T{}_2{}^{1}T\cdots {}_{i\hspace{1em} }{}^{i-1}T=\left[\begin{array}{cc}{}_{i }{}^{0}R& {}_{i }{}^{0}t\\ 0& 1\end{array}\right]$$

(2)

If any point i on the coordinate system is expressed as $x={\left[\begin{array}{cc}p& 1\end{array}\right]}^{\mathrm{T}}$, where $p={\left[\begin{array}{ccc}x& y& z\end{array}\right]}^{\mathrm{T}}$, then its position in the base coordinate system of the robot can be written as follows:

$$\left[\begin{array}{c}x\\ 1\end{array}\right]={}_{i }{}^{0}T\left[\begin{array}{c}p\\ 1\end{array}\right]=\left[\begin{array}{cc}{}_{i }{}^{0}R& {}_{i }{}^{0}t\\ 0& 1\end{array}\right]\left[\begin{array}{c}p\\ 1\end{array}\right]$$

(3)

where we can obtain

$$x={}_{i }{}^{0}R·p+{}_{i }{}^{0}t$$

(4)

By taking the differential of the joint angle from 0 to i, the Jacobian matrix of the translation part can be written as follows:

$$J_{ati}=\left[{\displaystyle \frac{\partial x}{\partial {\theta }_1}}{\displaystyle \frac{\partial x}{\partial {\theta }_2}}\cdots {\displaystyle \frac{\partial x}{\partial {\theta }_i}}0\cdots 0\right]$$

(5)

where the Jacobian matrix of the rotation part is the differential of the Euler angle to each joint angle. The angular velocity satisfies the vector superposition principle, so i, the angular velocity of the axis, can be written as the sum of the angular velocities of each joint. The magnitude of the angular velocity of each joint is the derivative of the joint angle with respect to time, and the direction is ${}_{i }{}^{0}R$, the third column of the matrix ${}_{i }{}^0{r}_z$. Therefore, the Jacobian matrix of the rotation part can be written as follows:

$$J_{ari}=\left[{}_1{}^0{r}_z{}_2{}^0{r}_z\cdots {}_{i }{}^0{r}_{z}0\cdots 0\right]$$

(6)

Based on the Equations (5) and (6), the Jacobian matrix can be written as follows:

$$J_{ai}=\left[\begin{array}{c}{J}_{ati}\\ J_{ari}\end{array}\right]$$

(7)

where the end of the shipborne manipulator arm, its Jacobian matrix can be written as

$$J_0=\left[\begin{array}{ccccccc}\hfill {\displaystyle \frac{\partial x}{\partial {\theta }_1}}& {\displaystyle \frac{\partial x}{\partial {\theta }_2}}\hfill & \cdots & {\displaystyle \frac{\partial x}{\partial {\theta }_i}}& {\displaystyle \frac{\partial x}{\partial {\theta }_{i+1}}}& \cdots & {\displaystyle \frac{\partial x}{\partial {\theta }_n}}\\ \hfill {}_1{}^0{r}_z& {}_2{}^0{r}_z\hfill & \cdots & {}_{i }{}^0{r}_z& {}_{i+1}{}^{0\hspace{1em}}{r}_z& \cdots & {}_n{}^0{r}_z\end{array}\right]$$

(8)

Next, consider the derivation of the Jacobian matrix after adding the ship as the chassis. The ship usually has six degrees of freedom in water: surge, sway, heave, roll, pitch, and yaw. The robot is mounted on the ship, so the movement of the ship will directly affect the position and attitude of the end effector of the robot. The Jacobian matrix needs to map the robot joint velocity and the ship motion velocity to the end effector velocity, so the overall Jacobian matrix should include these six shipborne motion variables plus the joint variables of the robot itself to form a larger matrix. The Jacobian matrix of a traditional fixed-base robot $J_{arm}$ is a $6\times n$ matrix, where n is the number of joints. When the base can move, such as a mobile robot, the overall Jacobian matrix will be $6\times \left(6+n\right)$, where the first six columns correspond to the six degrees of freedom of the base, and the last n columns correspond to the joints of the robot. With the ship as its base, the six degrees of freedom need to be treated as additional “virtual joints”.

Based on the Equations (5) and (6), overall Jacobian matrix can be written as follows:

$$J_{total}=\left[J_{ship}|J_{arm}\right]$$

(9)

where $J_{ship}$ is the effect of the ship motion on the end effector velocity and $J_{arm}$ is the original Jacobian matrix of the robotic arm.

After that, we will start the derivation of the $J_{ship}$ part. As shown in Figure 3, the six degrees of freedom of the ship in the shipborne manipulator system and the way of translation and rotation and the specific coordinate axes established are shown. The world coordinate system is $(X^W,Y^W,Z^W)$ defined as a standard right-handed system with the position of a certain place on the water surface as the origin $O_W$ and $Z_W$ as the axis vertically upward. $(X^B,Y^B,Z^B)$ is the ship coordinate system, whose origin is defined at the center of mass of the ship, with $X^B$ being the axis that points to the new direction of the ship, $Y^B$ being the axis that points to the left side of the ship, and $Z^B$ being the axis that is vertically upward. $Z_W$ is also the axis vertically upward. $(X^O,Y^O,Z^O)$ is the manipulator base coordinate system, with the center position of the manipulator base fixed on the ship as the origin, $O_{M_0}$, which is obtained by translating $(X^n,Y^n,Z^n)$, the ship coordinate system, for subsequent calculations. $\left\{B\right\}$ is the end-effector coordinate system, with the center point of the tool at the end of the manipulator as the origin $O_E$.

Assume that the change from the world coordinate system to the ship coordinate system is ${}_{B }{}^{W}T$, the transformation from the ship coordinate system to the manipulator base coordinate system is ${}_M{}^{B }T$, and the transformation from the manipulator base to the end is ${}_{E }{}^{M}T$; then the position and posture of the end in the world coordinate system are as follows:

$${}_{E }{}^{W}T={}_{B }{}^{W}T·{}_M{}^{B }T·{}_{E }{}^{M}T\left(q\right)$$

(10)

where

$$\begin{array}{ccc}{}_{B }{}^{W}T=\left[\begin{array}{cc}{}_{B }{}^{W}R& {}_{B }{}^{W}P\\ 0& 1\end{array}\right]& {}_M{}^{B }T=\left[\begin{array}{cc}{}_M{}^{B }R& {}_M{}^{B }P\\ 0& 1\end{array}\right]& {}_{E }{}^{M}T\left(q\right)=\left[\begin{array}{cc}{}_{E }{}^{M}R\left(q\right)& {}_{E }{}^{M}P\left(q\right)\\ 0& 1\end{array}\right]\end{array}$$

${}_{E }{}^{M}T\left(q\right)$ represents ${}_{E }{}^{M}T$, the joint variables that depend on the robot q, and is used q as a parameter to represent its dynamics; ${}_{B }{}^{W}T$ represents the homogeneous transformation from the ship coordinate system to the world coordinate system; ${}_M{}^{B }T$ represents the transformation from the robot base to the ship coordinate system; ${}_{E }{}^{M}T\left(q\right)$ represents the kinematic transformation from the robot base to the end.

First, derive the end position and linear velocity. The translation part of the end is written as follows:

$${}_{E }{}^{W}P={}_{B }{}^{W}R\left({}_M{}^{B }R{}_{E }{}^{M}P\left(\mathrm{q}\right)+{}_M{}^{B }P\right)+{}_{B }{}^{W}P$$

(11)

By taking the derivative of time in Equation (11), we can obtain the linear velocity relationship using the chain rule and the velocity superposition principle, written as follows:

$${}_{E }{}^W\dot{P}={}_{B }{}^W\dot{R}\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)+{}_{B }{}^{W}R{}_M{}^{B }R{}_{E }{}^M\dot{P}+{}_{B }{}^W\dot{P}$$

(12)

where ${}_{B }{}^W\dot{R}\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)$ is the rotation contribution of the ship, ${}_{B }{}^{W}R{}_M{}^{B }R{}_{E }{}^M\dot{P}$ is the contribution of the robot arm joint, and ${}_{B }{}^W\dot{P}$ is the translation contribution of the ship.

From the angular velocity of the ship ${\omega }_{ship}$, we can obtain the following:

$${}_{B }{}^W\dot{R}\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)={\left[{\omega }_{ship}\right]}_{\times }·\left({}_{B }{}^{W}R\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)\right)$$

(13)

In the joint contribution of the robot ${}_{E }{}^M\dot{P}=J_{arm\_linear}\dot{q}$, where $J_{arm\_linear}$ is the linear velocity Jacobian matrix of the robot, it is converted to the world coordinate system:

$${}_{B }{}^{W}R{}_M{}^{B }R{J}_{arm\_linear}\dot{q}$$

(14)

where the final relationship can be written as follows:

$${}_{E }{}^W\dot{P}={\left[{\omega }_{ship}\right]}_{\times }·\left({}_{B }{}^{W}R\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)\right)+{}_{B }{}^{W}R{}_M{}^{B }R{J}_{arm\_linear}\dot{q}+{}_{B }{}^W\dot{P}$$

(15)

Then derive the terminal posture and angular velocity. The terminal rotation matrix is calculated as follows:

$${}_{E }{}^{W}R={}_{B }{}^{W}R{}_M{}^{B }R{}_{E }{}^{M}R\left(q\right)$$

(16)

Using the relationship between the rotation matrix derivative and the angular velocity $\dot{R}=\left[\omega \right]\times R$, the following is obtained:

$${}_{E }{}^W\dot{R}={\left[{\omega }_{end}\right]}_{\times }·{}_{E }{}^{W}R$$

(17)

Based on Equation, we can derive it step by step, written as follows:

$${}_{E }{}^W\dot{R}={}_{B }{}^W\dot{R}{}_M{}^{B }R{}_{E }{}^{M}R+{}_{B }{}^{W}R{}_M{}^{B }R{}_{E }{}^M\dot{R}$$

(18)

where

$$\begin{array}{c}{}_{B }{}^W\dot{R}={\left[{\omega }_{ship}\right]}_{\times }·{}_{B }{}^{W}R\\ {}_{E }{}^M\dot{R}={\left[{\omega }_{arm}\right]}_{\times }·{}_{E }{}^{M}R\end{array}$$

${}_{B }{}^W\dot{R}{}_M{}^{B }R{}_{E }{}^{M}R$ is the angular velocity contribution of the ship, and is the angular velocity contribution of the manipulator joint. ${}_{B }{}^W\dot{R}$ and ${}_{E }{}^M\dot{R}$ and then convert the angular velocity contribution of the manipulator joint to the world coordinate system, and finally obtain the equation:

$${}_{E }{}^W\dot{R}={\left[{\omega }_{ship}\right]}_{\times }·{}_{B }{}^{W}R{}_M{}^{B }R{}_{E }{}^{M}R+{}_{B }{}^{W}R{}_M{}^{B }R{\left[{\omega }_{arm}\right]}_{\times }·{}_{E }{}^{M}R$$

(19)

Combining the two parts, the total angular velocity at the end can be written as follows:

$$\begin{array}{cc}\hfill {\omega }_{end}& ={\omega }_{ship}+{}_{B }{}^{W}R{}_M{}^{B }R{\omega }_{arm}\hfill \\ \hfill \left[\begin{array}{c}{v}_{end}\\ {\omega }_{end}\end{array}\right]& =J_{total}·\left[\begin{array}{c}{v}_{ship}\\ {\omega }_{ship}\\ \dot{q}\end{array}\right]\hfill \end{array}$$

(20)

where the linear and angular velocities as $v_{ship}$ linear combinations of generalized velocities, ship velocity, ${\omega }_{ship}$ and joint velocities $\dot{q}$. The global Jacobian matrix $J_{total}$ can be written as follows:

$$J_{total}=\left[\begin{array}{ccc}{I}_3& -S\left({}_{B }{}^{W}R\left({}_M{}^{B }R{}_{E }{}^{M}P+{}_M{}^{B }P\right)\right)& {}_{B }{}^{W}R{}_M{}^{B }R{J}_{arm\_linear}\\ 0_3& I_3& {}_{B }{}^{W}R{}_M{}^{B }R{J}_{arm\_angular}\end{array}\right]$$

(21)

Based on the global Jacobian matrix $J_{total}$, i.e., the Kinematics of shipborne manipulator and the disturbance motion model of the ship, the objective of this work is to control the end-effector’s position and track zero force of the shipborne manipulator for compliantly realizing the UAV perching in dual-docking space.

2.2. Global Dynamics of the Shipborne Grasping Arm

The global coordinate frame of the shipborne manipulator is shown in Figure 4. $\left\{O_G,X_G,Y_G,Z_G\right\}$ denotes inertial coordinate system, and $\left\{O_0,X_0,Y_0,Z_0\right\}$ denotes ship coordinate system with the origin being the center of mass of the ship. Furthermore, $\left\{O_1,X_1,Y_1,Z_1\right\}$, $\left\{O_2,X_2,Y_2,Z_2\right\}$ and $\left\{O_3,X_3,Y_3,Z_3\right\}$ denote the centroids of shoulder, elbow and wrist joints of the manipulator as the center of the circle, respectively. Employing the Newton–Euler iteration law and the rigid body Denavit–Hartenberg transformation law, the dynamic model of the shipborne manipulator can be written as follows [29]:

$$\left\{\begin{array}{ccc}\hfill \mathbf{M}\left(\mathbf{q}\right)\ddot{\mathbf{q}}+\mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\dot{\mathbf{q}}+\mathbf{G}\left(\mathbf{q}\right)+\mathbf{M}·\dot{\upsilon }+\mathbf{C}·\upsilon & =& \mathbf{U}+{\mathit{U}}_{\mathit{\delta }\mathit{m}}\hfill \\ \hfill {\mathbf{J}}_{\mathbf{s}}\left(\eta \right)\upsilon +{\mathbf{J}}_{\mathbf{m}}\left(\eta \right)\dot{\mathbf{q}}& =& \mathbf{X}\hfill \end{array}\right.$$

(22)

where $\mathbf{X}={[x_m,y_m,z_m]}^{\mathrm{T}}$ denotes the workspace position of the manipulator’s end-effector in the inertial coordinate system; $\upsilon ={[u,v,r]}^{\mathrm{T}}$ denotes velocity vector of the surge, sway and yaw velocities within the ship-fixed frame; $\dot{\mathbf{q}}={[{\dot{q}}_1,{\dot{q}}_2,{\dot{q}}_3]}^{\mathrm{T}}$ denotes angular velocities of the shoulder, elbow and wrist joints; ${\mathbf{J}}_{\mathbf{s}}\left(\eta \right),{\mathbf{J}}_{\mathbf{m}}\left(\eta \right)\in {\mathbf{R}}^{\mathbf{3}\times \mathbf{3}}$ denote the Jacobian matrix of the ship and the manipulator in their respective coordinate system; $\eta ={[{\eta }_s,{\eta }_{\theta }]}^{\mathrm{T}}$ denotes the state vector; ${\eta }_s={[x,y,\phi ]}^{\mathrm{T}}$ denotes the ship position in the inertial coordinate system; ${\eta }_{\theta }={\dot{\theta }}^{\mathrm{T}}$; $\mathbf{M}\left(\mathbf{q}\right),\mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\in {\mathbf{R}}^{\mathbf{3}\times \mathbf{3}}$ denote the manipulator inertial mass and Coriolis force matrix; $\mathbf{G}\left(\mathbf{q}\right)\in {\mathbf{R}}^{\mathbf{3}\times \mathbf{3}}$ denotes gravitational moment; $\mathbf{U}={[{\tau }_1,{\tau }_2,{\tau }_3]}^{\mathrm{T}}$ denotes the joint driving torques; ${\mathit{U}}_{\delta \mathit{m}}$ denotes the disturbances generated by joint friction; $(\mathbf{M}·\dot{\upsilon }+\mathbf{C}·\upsilon )$ denote the inertial and centripetal forces acting on the end-effector due to the ship movements.

In Figure 4, analyze the mechanical coupling correlation of composite flow fields such as gentle wave, current, and wind. Identify the main disturbance source characteristics of the correlation of composite flow fields. Determine the motion model boundaries and switching conditions with multiple disturbance sources. In the inertial coordinate system, based on dynamic main cause interference sources, The dynamic main coupling force is defined in the forward, roll, and yaw plane motions, and the ship motion model can be written as follows:

$$\left\{\begin{array}{ccc}\hfill {\mathbf{M}}_{\mathbf{s}}\dot{\upsilon }+{\mathbf{C}}_{\mathbf{s}}\left(\upsilon \right)\upsilon +{\mathbf{D}}_{\mathbf{s}}\left(\upsilon \right)\upsilon +{\mathbf{M}}_{\mathbf{ms}}\ddot{\mathbf{q}}+{\mathbf{C}}_{\mathbf{ms}}\dot{\mathbf{q}}& =& {\mathit{\tau }}_{\mathit{s}}+{\mathit{\tau }}_{\mathit{\delta }\mathit{s}}\hfill \\ \hfill {\dot{\eta }}_s& =& R\left(\phi \right)\upsilon \hfill \end{array}\right.$$

(23)

where $R\left(\phi \right)$ denotes the rotation matrix; $\phi \in [0,2\pi ]$ denotes the yaw angle; ${\mathbf{M}}_{\mathbf{s}}$, ${\mathbf{C}}_{\mathbf{s}}\left(\upsilon \right)$ and ${\mathbf{D}}_{\mathbf{s}}\left(\upsilon \right)$$\in {\mathbf{R}}^{\mathbf{3}\times \mathbf{3}}$ denote nominal part of the inertia matrix, the Coriolis centripetal force matrix, and the damping matrix of the ship model, respectively; The term $({\mathbf{M}}_{\mathbf{ms}}\ddot{\mathbf{q}}+{\mathbf{C}}_{\mathbf{ms}}\dot{\mathbf{q}})$ denotes the inertial and centripetal force acting on the ship due to the movement of the manipulator; ${\mathit{\tau }}_{\mathit{s}}$ denotes the ship control torque; ${\mathit{\tau }}_{\mathit{\delta }\mathit{s}}$ denotes external main coupling disturbances.

The dynamics model of the shipborne manipulator arm was visualized and simulated in ROS2 using RViz, as shown in the Figure 5. The models include the ship’s hilspot, the 6-DoF manipulator’s joints, and the end-effector. The coordinate frames of the ship and manipulator are defined in RViz, aligning with the dynamic model described in Figure 4.

3. Proposed Grasp Docking Paradigm and Experimental Results

This section describes the autonomous grasp docking paradigm that exploits the image-based visual servoing (IBVS). There are aerodynamic interactions in the handover movement between UAVs and the ship, such as the gentle waves around the ship coming from downward airflow, which is caused by the UAVs hovering in a low-altitude environment. This interaction could move the ship, and collision with the hovering UAV can cause safety problems. To decouple the coordinated dock movement between UAVs and the ship, we present a down-to-top grasp docking paradigm for UAV-assisted perching on a shipborne helistop, which is based on the UAV’s hovering control during standby. That is, before grasp docking, the initial trajectory of the multirotor drone is relatively stationary, for it is hovering at a low altitude above the ship and within the workspace of the end-effector.

In the down-to-top grasp docking paradigm, the payload of the shipborne manipulator could limit heavier UAVs to landing on the water surface. Consider factors like the UAV’s type, weight, and available gripping areas when using this grasp docking paradigm.

The entire system for autonomous drone landing at the dock is illustrated in Figure 6. The ship is assumed to oscillate with six-DOF motions (roll, pitch, yaw, surge, sway, and heave) generated by gentle waves and also move forward. The landing helistop is positioned at the front of the ship, and the GPS is installed on it. The multiple markers are placed on the landing helistop and are used as the features for IBVS, as shown in Figure 7. The mission of the UAV is to maintain four hover positions on the ship’s deck, as monitored by its on-board camera. The mission of the shipborne manipulator is to approach the UAV and grasp the docking mechanism using both GPS and the ship’s on-board camera.

The flowchart of the down-to-top grasping paradigm is shown in Figure 7. First, an image is captured by the camera, and the feature points of the AR tags on the landing helistop are extracted. To estimate the ship’s velocity, the sensor fusion module uses the relative pose of the ship with respect to the camera frame and the GPS position and velocity in the global frame. For the IBVS term, virtual image plane transformation and square compensation are conducted. Using the modified feature positions and the estimated horizontal velocity of the ship, the down-to-top grasping control input in the form of the velocity command is calculated.

After this, The end-effector of the manipulator with the grasped Fasen drone changes posture orientation and, through planning for obstacle avoidance during the trajectory, places the drone into the landing helistop. This change in orientation facilitates the placement of the drone into the dock station, because once the manipulator grasps the drone from the button without changing its orientation when placing the drone, the manipulator arm itself becomes an obstacle in the drone’s trajectory planning.

To verify the correctness of the proposed grasp docking paradigm, a relatively still body of water was created indoors to serve as the experimental environment. On the water surface, the grasping dock experiments platforms, consisting of the low-altitude multirotor drone and the modular shipborne manipulator arm, are shown in Figure 8. The initial experiment conditions for the surface grasping dock scenarios are the gentle waves around the ship coming from downward airflow, which is caused by the drone hovering in a low-altitude environment. The shipborne manipulator platform is a multi-access semi-autonomous system on the water surface with six-DOF motions (roll, pitch, yaw, surge, sway, and heave) generated by gentle waves. The input six-DOF motion conditions can be written as follows:

$$P\left(t\right)=\left[x\left(t\right),y\left(t\right),z\left(t\right),\theta roll\left(t\right),\theta pitch\left(t\right),{\theta }_{yaw}\left(t\right)\right]$$

(24)

where

$$\begin{array}{cc}\hfill x\left(t\right)& =0.25\times sin\left(0.3\pi t\right)\hfill \\ \hfill y\left(t\right)& =0.2\times cos\left(0.3\pi t\right)\hfill \\ \hfill z\left(t\right)& =0.15\times sin\left(0.04\pi t+\pi /4\right)\hfill \\ \hfill {\theta }_{roll}\left(t\right)& =0.2\times sin\left(0.4\pi t+\pi /2\right)\hfill \\ \hfill {\theta }_{pitch}\left(t\right)& =0.15\times cos\left(0.3\pi t+\pi /3\right)\hfill \\ \hfill {\theta }_{yaw}\left(t\right)& =0.2\times sin\left(0.2\pi t+\pi /6\right)\hfill \end{array}$$

Additionally, before grasp docking, the initial trajectory of the multirotor drone is relatively stationary, for it is hovering at a low altitude above the ship and within the workspace of the end-effector. Note that this experimental environment does not focus on the grasping dock in extreme conditions, such as those created by a typhoon or storm, which involve strong waves, currents, and winds; in such cases, a more solid ship, a watertight manipulator, and a heavier drone platform are required. This could be linked to a system-level challenge that seeks to address natural forces by identifying and delineating disturbance boundaries, as well as developing suitable plans to prevent ships and aircraft from operating in typhoon or storm conditions.

The physical parameters of the shipborne grasping platform are listed in

Table 1. The parameters of the modular shipborne multi-access semi-autonomous platform.

Notations	Values	Units
Degrees of freedom	6	$\mathrm{Actuator}$
Grasp workspace	$0.35\times 0.35\times 0.35$	${\mathrm{m}}^3$
End-effector payload	$1.5$	$\mathrm{kg}$
UAV (DJI mini) weight	$0.5$	$\mathrm{kg}$
Camera depth range	1.0	$\mathrm{m}$
Camera stand height	0.3	$\mathrm{m}$
Radar ranging error	0.02	$\mathrm{m}$
Ship size	$1.0\times 0.4\times 0.3$	${\mathrm{m}}^3$

. The on-board camera of the platform provides image-based visual servoing but also classifies drones within the low-altitude field for whether the manipulator arm could grasp the drone in the early stages of the experiment. This classification is obtained through data-driven methods, as shown in Figure 9.

When the ship undergoes periodic disturbances with a confidence interval of [0, 1], the base coordinate system of the shipborne robotic arm will experience periodic changes in position and orientation, as shown in Figure 10. To address this disturbance, this paper analyzes the changes in the position and orientation of the shipborne robotic arm’s end-effector coordinate system using transformations of the global Jacobian matrix. In terms of attitude control, the end-effector coordinate system maintains its stability, with attitude control within 2 cm. This provides the necessary conditions for reliable grasping by the UAVs. In the force control domain, without force sensors, the shipborne manipulator, using on-broad visual servoing system, makes contact with the drone after an initial movement of 1 s, and the gripper successfully docks the drone. The position changes of the drone under similar force conditions are collected, as shown in Figure 11. Before the t = 1 s moment, the hovering drone and the end-effector of the shipborne manipulator do not touch, so there is zero force in the interaction. At the t = 1 s moment, the force exerted by the shipborne manipulator on the drone instantly reaches a maximum of 5.8 N and then stabilizes at 5 N. The shipborne manipulator supports the entire weight of the drone during this process, which slowly stops working and loses its lift force. Furthermore, according to Newton’s third law, the force exerted by the end-effector of the shipborne manipulator can be analyzed in the same way.

To demonstrate the statistical robustness of the proposed IBVS grasp docking paradigm, we compared it with the IBVS method and the UAV autonomous landing method on the same platform and experiment disturbances. Two landing methods compared for their statistical robustness are listed in

Table 2. Two landing methods compared for their statistical robustness.

Method	IBVS	UAV Autoland
$X_{dir}$ Confidence interval	$[-0.16,0.16]$	$[-0.16,0.16]$	$\mathrm{m}$
$Y_{dir}$ Confidence interval	$[-0.16,0.17]$	$[-0.16,0.17]$	$\mathrm{m}$
$Z_{dir}$ Confidence interval	$[-0.08,0.02]$	$[-0.08,0.02]$	$\mathrm{m}$
Docking time	42	53	$\mathrm{s}$
Repeated trials	8	8	$\mathrm{time}$
Docking success rate	87.5	75	%
Peak contact force	$5.8$	$6.5$	$\mathrm{N}$

. Keeping the same disturbances confidence intervals in the experimental environment, we take repeated trials separately for the proposed IBVS grasp docking paradigm and the drone autonomous landing method eight times. For the IBVS methods, they take less docking time and have a better docking success rate. The reason is that the traditional autonomous drone landing method mainly depends on the friction and bouncing forces between the drone and the deck, which are easily lost due to the ship’s gentle disturbances. The comparative results demonstrate the excellent performance of the proposed method in terms of static robustness.

4. Conclusions

This study proposed a down-to-top autonomous strategy for landing on a ship’s deck using feed-forward stabilized control. The shipborne manipulator arm is fabricated as a key component of a seaplane drone dock comprising a ship-type embedded drone storage, a packaged helistop for power transfer and UAV recovery, and a multi-degree-of-freedom arm integrated with multi-source information sensors for the treatment of air-to-water-related airplane crashes. To accomplish the entire landing procedure autonomously, a landing scheme in the form of the state machine structure, including the approach, three IBVS levels according to the relative altitude between the ship and the UAV, and hold states, was designed. The proposed autonomous landing algorithm was verified via various experiments. The experimental efficacy of this grasp paradigm when compared with the traditional autonomous landing method has been verified by statistical robustness.