【文献阅读】Automatic berthing for an underactuated unmanned surface vehicle: A real-time motion planning approach

（1）文章工作

This paper presents Extended Dynamic Window Approach (EDWA) for the automatic berthing of an underactuated unmanned surface vehicle (USV).

Different from the conventional works based on Control Theory, present approach focuses on the field of planning to complete the process of the automatic berthing.

The approach takes all the dynamic constraints of the USV into account, and obtains the whole predicted trajectories of both constant force and deceleration phases.

By performing the collision detection, the predicted trajectories with obstacles are discarded and remaining trajectories are evaluated by an objective function to select the optimal trajectory for the USV.

The case studies are conducted in order to verify the feasibility and performance of the presented approach.

The results show that the approach can realize the automatic berthing under the influence of wind loads and obstacles.

本文提出一种扩展动态窗口法，从规划角度完成自动靠泊。本方法将USV所有的动力学约束进行考虑，获取恒力与减速阶段的预测轨迹，并舍弃发生碰撞的轨迹。本方法可实现风载荷与障碍物环境中的自动靠泊。

（2）概述中可引用的文献

Automatic navigation in complicated environment is one of the necessary capabilities for USVs.

As a sophisticated task, it is vital to ensure that the ship sails from the fairway area to the designated berthage with a proper speed and meets the heading requirements when a ship enters a port (Im and Nguyen, 2018; Piao et al., 2019; Shuai et al., 2020).

在复杂环境中自动导航是usv的必要功能之一。作为一项复杂的任务，确保船舶以 适当的速度 从球道区域航行到指定的护堤层，并 满足航向要求 是至关重要的。

According to statistics, more than 70% of berthing accidents are related to the wrong manipulation by the pilots in the harbor (Ahmed and Hasegawa, 2013). In order to reduce such accidents, it is of great practical significance to develop the automatic berthing.

据统计，70%以上的靠泊事故与船员在港口的错误操纵有关。为了减少这类事故，发展自动靠泊具有重要的现实意义。

In view of automating the ships berthing process, many researchers have proposed various control methods such as neural network, optimal control theory and evolution strategy, to improve the accuracy or real-time performance on berthing control.

针对船舶自动靠泊过程，许多研究人员提出了神经网络、最优控制理论和进化策略等各种控制方法，以提高靠泊控制的精度或实时性能。

Different from the previously mentioned literatures which focused on the control strategy of local berthing points, Sawada et al. (2020) applied a path-following algorithm to the automatic berthing for an underactuated ship. This algorithm possesses strongly real-time performance with the control accuracy.

与之前提到关注局部靠泊点控制策略的文献不同，Sawada等人（2020）将路径跟踪算法应用于欠驱动船舶的自动靠泊算法。该算法具有较强的实时性和控制精度。

Liao et al. (2019) gave a layered method dividing the automatic berthing into two parts: the planning and control modes. Firstly, the trajectory planning is completed with the aid of an improved artificial potential field method. Then an improved adaptive fuzzy PID controller is designed with precise control of position and heading angle to track the planned trajectory.

廖等人（2019）给出了一种分层的方法，将自动靠泊分为规划和控制模式两部分。首先，利用改进的人工势场方法完成了轨迹规划。然后设计了一种改进的自适应模糊PID控制器，通过精确控制位置和航向角来跟踪规划的轨迹。

Automatic berthing requires the small range of autonomous control and fine operation for USVs. To berth safely, it is necessary to carry out motion planning application to automatic berthing.

自动靠泊需要小范围的自动控制和精细的操作。为了安全停泊，必须对自动靠泊进行运动规划。

Since all the dynamic constraints are considered, a proper motion planning strategy can provide the guidance to the USVs and perform the automatic berthing.

由于考虑了所有的动力学约束，一个适当的运动规划策略可以为usv提供指导，并执行自动靠泊。

Moreover, a hybrid algorithm that effectively combines global and local path planning can also deal with the motion planning problem. The approach can be divided into two steps (Wang and Xu, 2020; Chen et al., 2019). Firstly, an unblocked initial path from the start point to the end point can be acquired by means of traditional global path planning algorithm, such as A* (Shi et al., 2019), Theta* (Kim et al., 2014) and FMM (Wang et al., 2019). Then, the dynamic window approach (DWA) (Fox et al., 1997) is used in the local path planning to produce the final trajectory which contains kinematics and dynamics constraints of USVs. Different from using control method to track the initial global path directly, the hybrid path planning algorithm has good real-time performance and strongly dynamic obstacle avoidance capability.

此外，一种有效结合全局和局部路径规划的混合算法也可以解决运动规划问题。该方法可分为两步。首先，通过传统的全局路径规划算法，如A、Theta和FMM，可以获得从起点到终点的畅通初始路径。然后，在局部路径规划中使用动态窗口方法，生成包含usv运动学和动力学约束的最终轨迹。与使用控制方法直接跟踪初始全局路径不同，该混合路径规划算法具有良好的实时性性能和较强的动态避障能力。

For a fully actuated system, motion planning is unnecessary because the ship can trace many trajectories by adjusting and optimizing the control parameters. However, not all motion states can be satisfied for an underactuated system where the degree of control is less than the degree of freedom. Considering that most ships are underactuated equipped with limited propellers and rudders, present paper focuses on underactuated USVs, using real-time motion planning approach to perform automatic berthing. For an underactuated system, one of the important tasks of motion planning is to figure out which states the USVs can reach. DWA (Fox et al., 1997; Brock and Khatib, 1999) is a local path planning algorithm that has been widely used in the field of robotics, such as mobile robot (Kashyap et al., 2020; Chang et al., 2020), Unmanned Ground Vehicle (Molinos et al., 2019), Unmanned Aerial Vehicle (Vista et al., 2014) and USVs (Wang et al., 2018; Xia et al., 2020). DWA can establish a pre-selected velocity window based on the current velocity and acceleration, and then get the optimal velocity (including velocity and direction) at the next moment through the optimization of objective function.

对于一个完全驱动的系统，运动规划是不必要的，因为船可以通过调整和优化控制参数来跟踪许多轨迹。然而，对于一个控制度小于自由度的欠驱动系统，并不是所有的运动状态都能得到满足。考虑到大多数船舶驱动不足，配备了有限的螺旋桨和方向舵，本文重点关注驱动不足的usv，使用实时运动规划方法进行自动靠泊。对于一个驱动不足的系统，运动规划的重要任务之一是找出usv可以达到哪些状态。DWA是一种局部路径规划算法，广泛应用于机器人领域，如移动机器人、无人地面车辆、无人机和美国无人机。DWA可以根据当前的速度和加速度建立一个预先选择的速度窗口，然后通过目标函数的优化得到下一时刻的最佳速度（包括速度和方向）。

（3）EDWA介绍

This approach establishes a pre-selected force window rather than velocity window in DWA, to get the predicted trajectories containing both the constant force and deceleration phase that the vessel can reach by adopting the dynamic model of the USV. Then a novel objective function is presented to evaluate these trajectories and the optimal solution will be selected as the trace object. The simulation results show that the trajectory obtained by EDWA is relatively smooth, suitable for the USV operation, and what is more, effectively avoids the dynamic obstacles.

该方法在DWA中建立了一个预先选择的力窗口而不是速度窗口，通过USV的动力学模型，得到船舶可以达到的恒力和减速阶段的预测轨迹。然后给出了一个新的目标函数来评价这些轨迹，并选择最优解作为跟踪对象。仿真结果表明，EDWA得到的运动轨迹相对平滑，适合于USV操作，更有效地避免了动态障碍。

In order to simplify the model, the coupling relationship between rudder and propeller is ignored in the hydrodynamic model. Only the surge force and yaw moment are used as the control inputs, because they can directly affect the motions and easy to handle the nonlinearity of ship dynamics.

为了简化模型，在水动力模型中忽略了方向舵和螺旋桨之间的耦合关系。只有冲击力和偏航力矩作为控制输入，因为它们可以直接影响运动，并且容易处理船舶动力学的非线性。

The environmental loads acting on the ships, such as wave and current, is relatively small in harbor compared with open water. The validity of our approach is the focus of the paper. Therefore, in present model, the influence of wind loads on ships is considered first. The wave and current effects will be included and discussed in future works.

与开放水域相比，作用于船舶上的环境负荷，如波浪和水流，在港口内相对较小。该方法的有效性是本文研究的重点。因此，在本模型中，首先考虑了风荷载对船舶的影响。波浪和电流的影响将在未来的工作中包括和讨论。

The objective of the motion planning is to find a practicable trajectory that can be traced by the control system of USVs.

运动规划的目标是找到一个切实可行的轨迹，可以由usv的控制系统跟踪。

If the traditional path planning method is used, especially in sophisticated tasks like automatic berthing, the obtained path may have inflection points of large curvatures, resulting in a phenomenon of ‘‘planning-failure’’.

如果采用传统的路径规划方法，特别是在自动靠泊等复杂任务中，所获得的路径可能会有大曲率的拐点，导致“规划失败”现象。

To have the small range of autonomous control, it is necessary to carry out motion planning for automatic berthing.

为了实现小范围的自动控制，需要进行自动靠泊的运动规划。

EDWA takes the dynamic constraints of the USV into account, obtaining the whole force space which contains all the reachable surge forces and yaw moments within unit sampling time. Then the set of feasible force pairs (, ) are discretized from the force space according to a given interval. For every feasible force pair, the trajectory can be predicted by using kinematics model of the USV. Finally, the objective function is used to evaluate each force pair, and the optimal force pair will be selected as the reference input for the USV controller.

EDWA考虑了USV的动态约束，得到了在单位采样时间内包含所有可达的冲击力和偏航力矩的整个力空间。然后根据给定的区间将力空间离散可行力对（、）。对于每一个可行的力对，都可以利用USV的运动学模型来预测运动轨迹。最后，利用目标函数对每个力对进行评估，并选择最优力对作为USV控制器的参考输入。

The predicted trajectories are divided into two stages, one is the constant force phase, in which the vessel travels forward by inputting each force pair (, ) of the search space within the predicted time . In this phase, the force pairs remain unchanged.

预测的轨迹分为两个阶段，一个是恒力相位，在这个阶段中，通过在预测的时间内输入搜索空间的每个力对（，），船舶向前移动。在这一阶段，力对保持不变。

The other is the deceleration phase. In this phase, the surge force decreases to zero, the USV slows down gradually under the action of inertia. At the same time, the controller adjusts the yaw moment to make the USV’s heading reach the desired direction.

另一个是减速阶段。在这一阶段，冲击力减小到零，USV在惯性作用下逐渐减慢。同时，控制器调整偏航力矩，使USV的航向到达所需的方向。

During the following voyage, the USV maintains the desired heading until it stops, and thus, the predicted trajectories of the USV during the whole deceleration phase can be obtained.

在航行过程中，USV保持目标艏向直至停船，至此可以得到USV在整个减速阶段的预测轨迹。

At the end of the predicted trajectory in the constant force phase, the heading of USV is often inconsistent with the expected heading .

Therefore, it is necessary to set a controller in the deceleration phase to adjust the ship’s heading. PID (proportional–integral–derivative) controller, a widely used control method (Han, 2009), will be applied for determining the yaw moment of the USV by the deviation of the current heading and the expected heading as well as the yaw velocity.

在恒力阶段的预测轨迹结束时，USV的航向常常与预期的航向不一致。因此，有必要在减速阶段设置控制器，调整船首向。PID(比例-积分-导数)控制器是一种应用广泛的控制方法(Han, 2009)，将通过当前航向和预期航向的偏差以及偏航速度来确定USV的偏航力矩。

The objective of the motion planning is that, the USV can avoid obstacles and arrive desired berthage at safe speed in the process of the automatic berthing. As a result, a smooth and safe trajectory that can successfully complete the automatic berthing is acquired.

该运动规划的目标是在自动靠泊过程中，使USV能够以安全的速度避开障碍物，到达预定的靠泊位置。从而获得了能够顺利完成自动靠泊的平稳、安全的轨迹。

Pilot point is a fixed point artificially selected according to the shape, size and location of the quay, it may be the point of entry or exit of the port or USV private lanes.

引航点是根据码头的形状、大小和位置人工选择的定点，它可以是港口的出入口点，也可以是USV专用车道。

The disadvantage of the EDWA is that it is easy to fall into the local extremum and cause the planning failure. To avoid this drawback, local and global planning methods are normally used in combination. The global approach gives a feasible route, then the local approach performs dynamic obstacle avoidance based on this route, and develops a reasonable trajectory. To simplify, the pilot point is taken as a transitional point between the starting and target point in present study so as to avoid falling into the local extremum in the motion planning.

EDWA的缺点是容易陷入局部极值，导致规划失败。为了避免这一缺点，通常结合使用局部和全局规划方法。全局算法给出了一条可行的路径，局部算法基于该路径进行动态避障，并得到了合理的避障轨迹。为了简化问题，本研究将导频点作为起始点与目标点之间的过渡点，以避免在运动规划中陷入局部极值。

Here, the USV firstly takes the pilot point as the target point. When the distance between the terminal position (, ) and pilot point is less than a certain range , the target point is switched from the pilot point to the goal point. The switch can also be achieved when (, ) and goal point are visible.

此处USV首先以先导点为目标点。当终端位置(，)与导点的距离小于一定距离时，将目标点从导点切换到目标点。或者当(，)和目标点可见时也可以实现切换。

As the velocity of the USV increases, the weight of the to obstacle should be increased. So USV can sail with greater safe distance to avoid collisions.

随着USV速度的增加，到障碍物的权重也应该增加。因此，USV可以以更大的安全距离航行，以避免碰撞。

To ensure the safety of the USV, each blocked cell is expanded by meters, which is a configurable value based on the requirement of the user. For this purpose, the method (Niu et al., 2018) is used to expand the obstacle areas, Fig. 4 shows the comparison of Dalian Port before and after expanding.

为了保证USV的安全，每一个被阻塞的cell都是扩展为(0.1)米，这是一个可配置的值，基于用户需求。为此，方法(Niu et al.， 2018)来扩展障碍区域，图4为大连港扩建前后。

CyberShip II (Skjetne et al., 2004) is used in present paper by ignoring the redundant propulsion and steering device. Its mass is 23.8 kg, length is 1.255 m, and breadth is 0.29 m. Considering its size, the grid map obtained after scaling Dalian Port by 100:1 is applied to the simulation for automatic berthing.

本文采用了CyberShip II (Skjetne et al.， 2004)，忽略了冗余的推进和转向装置。其质量为23.8公斤，长1.255米，宽0.29米。考虑到大连港的规模，将大连港按100:1比例变换后得到的网格图应用于自动靠泊的仿真。