CN116382260B - Surface ship berthing track planning method based on safe navigation channel - Google Patents
Surface ship berthing track planning method based on safe navigation channel Download PDFInfo
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Abstract
A unmanned ship berthing track planning method based on a safety channel. Firstly, preliminarily constructing an optimal control problem according to the motion characteristics of the unmanned ship according to berthing requirements; secondly, according to the actual shape of the ship, a plurality of characteristic circles are used for representing the ship body to realize the conversion of obstacle avoidance constraint; thirdly, obtaining a grid map according to the actual map and combining the radius of the characteristic circle; fourth, a coarse path is obtained on the grid map by utilizing a manually guided mixed A-x algorithm; fifthly, resampling the rough path according to the time optimal principle; sixthly, constructing a safe navigation channel according to the resampling result and the obtained grid map; seventh, a final optimal control problem is established and solved. According to the invention, the efficient generation of the coarse path is ensured by the mixed A algorithm, the coarse path is resampled, the concept of a safe navigation channel is constructed by sampling points, sampling parameters are used as an initial solution to construct an optimal control problem, the problem solving difficulty is simplified, and the solving efficiency and the reliable generation of the water surface ship track are ensured.
Description
Technical Field
The invention belongs to the field of equipment intelligent guarantee, and relates to a water surface ship berthing track planning method based on a safe navigation channel.
Background
Ports often have very complex environments, which typically encounter narrow waterways, and more turnouts than open waters, and the prior art [ unmanned ship path planning method of patent application number CN201911064032.7 ] generally encounters the following difficulties in planning the track of a surface ship in the face of a port environment:
(1) An accurate representation of the shape of the vessel is required compared to open waters to prevent leaving less feasible area leading to failure of the path search.
(2) Due to the complex shape of a port, it is often difficult to divide the port into a plurality of obstacles that are easy to collision detect. Meanwhile, an efficient description mode of obstacle avoidance constraint is needed to improve planning efficiency.
(3) According to the demand of berthing task, the boats and ships need berth in the position of being close to the bank, so need to guarantee that the boats and ships not only reach the bank, need to guarantee simultaneously that the boats and ships speed falls to 0 to prevent subsequent collision's emergence.
In order to solve the problems, an accurate and efficient optimal control problem description method and a solving framework are required to be provided, so that a track for safely completing a berthing task of a water supply surface ship can be planned efficiently.
Disclosure of Invention
In order to solve the technical problems, the invention provides a berthing track planning method of a water surface ship in a port environment based on a safe sailing channel. In the present invention, a multi-stage planning strategy is employed. First, using the hybrid a algorithm provides a coarse path that satisfies simple kinematic constraints, ensuring that a high quality homolunic trajectory can be found through the path in the navigable space. Secondly, resampling is carried out on the rough path, and a safe navigation channel is generated according to sampling points to realize an efficient representation method of obstacle avoidance constraint, so that the fact that specific environmental barriers are not relied on in a column type of an optimal control problem is guaranteed, and overall problem solving efficiency is improved.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a water surface ship berthing track planning method based on a safety channel. Firstly, preliminarily constructing an optimal control problem according to the motion characteristics of a water surface ship according to mooring requirements; secondly, according to the actual shape of the ship, the ship body is represented by a plurality of characteristic circles, so that the conversion of obstacle avoidance constraint is realized; thirdly, obtaining a grid map according to the actual map and combining the radius of the characteristic circle; fourth, a coarse path is obtained on the grid map by using a manually guided mixed A algorithm; fifthly, resampling the rough path according to the maximum speed and the maximum acceleration according to the time optimal principle; sixthly, constructing a safe navigation channel according to the resampling result and the obtained grid map; seventh, based on the safe navigation channel, the motion constraint of the surface vessel is established, and the final optimal control problem is solved. The method comprises the following steps:
step 1: according to berthing requirements, initially constructing optimal control problems of motion characteristics of surface vessels
Step 1-1: describing kinematic equations of water surface vessels
The surface environment at port is usually smooth and the speed of the vessel during berthing is low, so we assume negligible heave, roll and pitch caused by wind and currents, at the same time that the hull inertia, additional mass and hydrodynamic damping matrix are diagonal and the available control variables are propulsion and yaw moment, so we can obtain a model of motion in cartesian coordinates. Let M (x, y) be the surface vessel centroid position, ψ be the vessel orientation angle, u be the vessel longitudinal speed, v be the vessel transverse speed, r be the vessel yaw rate (as shown in FIG. 2), M 1 、m 2 、m 3 Is the inertia after containing the additional mass effect, d 1 、d 2 、d 3 Is the hydrodynamic damping coefficient in the motion process, tau u For propulsion of the vessel, τ r Is the yaw moment of the vessel. The control variable of the system is denoted as c= [ τ ] u ,τ r ] T The state variables are denoted as s= [ x, y, ψ, u, v, r] T The system can be described using the differential equation:
wherein f represents the kinematic equation of the surface vessel systemRepresenting the variable (·) deriving time; />Representing the derivative of the barycenter abscissa of the surface vessel with respect to time; />Representing the derivative of the ordinate of the centroid of the surface vessel with respect to time; />Representing the derivative of the orientation angle of the surface vessel with respect to time; />Representing the derivative of the longitudinal speed of the surface vessel with respect to time; />Representing the derivative of the transverse speed of the surface vessel with respect to time; />Representing the derivative of the yaw rate of the surface vessel over time.
In addition, the following constraint conditions in the movement process of the surface ship are considered:
wherein [(s) min ,(·) max ]Represents the permissible range of the variable (·); u (u) min 、u max Respectively representing the minimum and maximum longitudinal speeds allowed by the surface vessel; v min 、v max Respectively representing the minimum and maximum allowable transverse speeds of the surface vessels; r is (r) min 、r max Representing the minimum and maximum yaw rates allowed by the surface vessel, respectively.
Meanwhile, the actual control quantity constraint and the control quantity impossibility of jumping are considered, so the control quantity and the control variable change rate are constrained as follows:
wherein [(s) ·,min ,(·) ·,max ]Represents a variable (& gt) · Is a permissible range of (2); τ u,min 、τ u,max Representing the minimum and maximum propulsion forces allowed, respectively; τ r,min 、τ r,max Representing the allowed minimum and maximum yaw moments, respectively;representing the minimum and maximum allowable thrust rates of change, respectively; />Representing the minimum and maximum allowed yaw moment change rates, respectively.
Step 1-2: description of task requirements
And describing the state of the surface ship at the starting time of the dispatching task and the terminal expected time through boundary conditions. For the initial time t=0, the configuration of the surface vessel is noted as:
[x(0),y(0),ψ(0),u(0),v(0),r(0)]＝[x 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 ] (5)
wherein x is 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 Is a state variable condition of the initial position.
At the terminal moment t=t (T is also a variable to be optimized), the configuration of the surface vessel is noted as:
[x(T),y(T),sinψ(T),cosψ(T),u(T),v(T),r(T)]＝[x F ,y F ,sin(ψ F ),cos(ψ F ),u F ,v F ,r F ] (6)
wherein x is F ,y F ,ψ F ,u F ,v F ,r F Is a state variable condition of the terminal position.
Step 1-3: description of obstacle avoidance constraints
Mapping the state space S to the configuration space using the function g, we denote the entire configuration space as beta, and the surface vessel as the obstacle region beta if it collides with an obstacle obs The passable area can therefore be denoted as beta free ＝β\β obs The crash restraint may be expressed as follows.
Step 1-4: establishing performance index
The energy consumption and the stationarity are two important factors in the berthing process of the surface ships. The run time can be directly reflected by the terminal moment T, although a box constraint has been imposed in steps 1-3, the smoothness of the trajectory should be improved to ensure sufficient stability and comfort for the passengers, while the energy consumption should be reduced as much as possible considering the economic factors, thus obtaining the performance index of the following hybrid form:
wherein P and Q respectively represent weight matrixes of state quantity and control quantity, J is an objective function of the whole optimal control problem, and w is a weight coefficient.
Step 1-5: establishing optimal control problems
Based on the foregoing description, an optimal control problem OCP is established init The concrete form is as follows:
step 2: according to the actual shape of the ship, the ship body is represented by a plurality of characteristic circles to realize the conversion of obstacle avoidance constraint
In FIG. 3, L is the ship length, and the distance from the center of mass of the ship to the stern is denoted as L r Hull of shipThe width is recorded as W, and the radius of the circle is taken asTwo characteristic circles with radius R are respectively taken at two ends to represent, and the rest part uses +.>A circular cover, wherein->Then co-require->Each characteristic circle represents the surface vessel shape, and each characteristic circle except for both ends represents +.>The hull of the corresponding length is shown in figure 3. The center position of any h characteristic circle can be expressed asAnd->The method can be obtained by the following formula:
wherein l h The position from the center of mass of the water surface ship to the center of the h equivalent circle is represented as follows:
through the previous description, the part of all the obstacles in the whole map, which is not overlapped with each circle, can be regarded as obstacle avoidance success, if each characteristic circle is condensed to the circle center position, the corresponding expansion R size of the obstacles is ensured, and the situation that the circle center position is not on the obstacles in the map after expansion can be regarded as collision avoidance is only required.
Step 3: obtaining a grid map according to the actual map and combining the feature circle radius
Based on the expansion mode described in step 2, the resolution D is adopted res A grid map Λ of the deck is established. For any grid, if it overlaps with the inflated obstacle, it is considered to be one obstacle grid; otherwise, it is considered a free grid. The boundaries of the grid map in the X direction and the Y direction are respectively [0, X max ]And [0, Y ] max ]. Let "grid (i, j)" represent a two-dimensional region as follows: { (X, Y) | (i-1) D res ＜X≤iD res ,(j-1)D res ＜Y≤jD res }. In fig. 4, a collision determination method in a grid map is shown.
Step 4: coarse path acquisition on grid map using a manually guided hybrid a-algorithm
A mixed A algorithm is used, the kinematic constraint of the surface ship is combined, a rough path is planned for the mass center M (x, y) of the surface ship, in the planning process of an actual port environment, a rough path is ensured to be generated efficiently because a plurality of narrow branches need to be passed, manual addition of guide points is selected to guide the generation of the path, and the guide points are zeta= { B 0 ,…,B i ,…,B N }, wherein B is 0 And B is connected with N For two-dimensional position information in initial and terminal configuration conditions, B i For the artificially added guide points i=1, 2, …, (N-1). Will be from B 0 Beginning with B i Is the starting point B i+1 The path information obtained by using the mixed A-algorithm for the end point is recorded asObtaining the last piece of path information +.>After the path search is finished, the whole coarse path information +.>The path resulting from this method is in fact a series of waypoints. Suppose Path A From N A A plurality of waypoints, wherein the kth waypoint is a node k (k＝1,2,…,N A )，
Furthermore, the mixed a algorithm realizes smooth generation of a coarse path in a complex environment by adding a guide point in the middle.
Step 5: resampling the rough path according to maximum speed and maximum acceleration according to time optimal principle
Step 5-1: time-consuming transfer estimation T tst
Defining the length of the path as the sum of the distances between any adjacent waypoints, denoted as L path Can be expressed asWherein k represents the interval [1, N ] A ]N is any positive integer A Representing the number of nodes of the path searched by the manual guided hybrid a-algorithm, ++>Respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm>And respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm. Assuming that the acceleration motion in the sampling process is always moved by using the maximum or minimum acceleration in the path by adopting the time optimal motion mode, the acceleration in the sampling process can be expressed as: />Wherein m is 1 Representing the inertia of the vessel including the additional mass effect. The speed is 0 at the two end waypoints of the path. Introducing distance thresholdThen complete along Path A Time-consuming T of the dispatch tst It can be estimated that:
step 5-2: resampling at discrete points
Without loss of generality, consider the time period to be discretized into N in the actual solving process sam A plurality of equal-length time intervals, there is (N) sam +1) discrete points, so that the time interval between every two adjacent discrete points is Δt=t tst /N sam . Variable T tst In effect providing an initial guess for T in the problem, then the kth discrete point corresponds approximately to time T k = (k+1) Δt. At T m At the moment, the state information of the surface vessel is recorded as (x) k ,y k ,ψ k ,u k ,v k ). Next, based on the constraint of the equation of motion and the sum and the formula combination formula, the yaw rate r of the surface vessel k Thrust τ u,k Yaw moment τ r,k It is possible to obtain:
to this end, an initial guess is provided for the actual optimization problem by the resampling process. In particular, the time of dispatch may be T tst Initialization is performed, and at all discrete points, the state variables and control variables can be represented by eight-tuple (x k ,y k ,ψ k ,u k ,v k ,r k ,τ u,k ,τ r,k ) Initialization is performed. The resampled Path is denoted Path sam 。
Step 6: constructing a safe navigation channel according to the resampling result and the obtained grid map
According to Path sam And the sum of the formulas can obtain the circle center O corresponding to any j j Can be calculated and recorded as Traj j . The generation process of the safety dispatching corridor corresponding to each circle center is similar, and O is adopted below j For example, a framework method of a secure transportation corridor is described. Let it be assumed that at the kth discrete point (k=0, 1, …, N sam )，O j The corresponding position is recorded asRecord O j,k The corresponding safe navigation channel is marked as SSC j,k 。
First, SSC is performed j,k Initialized to point O j,k By itself, it can be seen as a rectangle with zero width and zero length. Define the search direction set Δ= [ up, left, down, right ]]. The exploration is continuously performed in each direction in delta with a fixed step deltas. Defining a safe navigation channel obtained by expansion in the previous iteration process asWe will cycle through four directions in delta to continuously update the data of the secure channel. If the following 2 conditions are satisfied at the same time: 1) The safety channel does not overlap any obstacle grid in the grid map Λ; 2) The length of the expansion in the direction lambda does not exceed a predetermined upper expansion distance limit L max The method comprises the steps of carrying out a first treatment on the surface of the The extension is valid and the safe navigation channel information is updated. When at least one of the conditions 1) or 2) is not satisfied, the direction λ is deleted from Δ. The expansion process as above is continued until the set of search directions becomes an empty set.
Repeating the above process (N) sam +1) times, can be applied to O j Each O of (2) j,k (k＝0,1,…,N sam ) Constructing corresponding safe dispatching corridor SSC j,k Wherein N is sam Representing the number of sampling nodes in the resampling of the coarse path. If O j,k Keep in SSC j,k In, then can ensure O j,k No collision with any obstacle on deck occurs. Therefore, the following collision constraint conversion can be realized on the circle center of any jth equivalent circle at any kth sampling position
Step 7: based on the safe navigation channel, the motion constraint of the surface ship is established, the final optimal control problem is established, and the solution is implemented
Substituting the converted constraint in equation (17) for the optimal control problem OCP init The obstacle avoidance conditions constitute the following optimal control problem OCP FIN
Solving the optimal control problem OCP FIN Obtaining the parking track Traj FIN 。
The beneficial effects of the invention are as follows:
the invention realizes the conversion of complex and difficult-to-divide obstacle avoidance constraint by introducing the concept of the safe navigation channel, and finally solves the optimal control problem OCP FIN In the method, the expression form of the obstacle avoidance constraint is not dependent on the actual map any more, and only the number (N sam +1) the offshore safety channels with fixed side length are related, the problem solving difficulty is greatly simplified, and the efficient and reliable generation of the berthing track of the water surface naval vessel is ensured. By using a manually guided hybrid a-algorithm, a coarse trajectory can be obtained quickly in the port environment, ensuring that a safe navigation channel is generated after subsequent resampling and serving as an initial solution for the optimal control problem. The ship shape can be represented as accurately as possible by a method of representing the ship by using a plurality of characteristic circles, so that smooth generation of the berthing track in a narrow channel is ensured.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a view of a water surface vessel motion model in accordance with the present invention.
FIG. 3 is a schematic representation of the water surface vessel dimensions and multi-circle representation of the present invention.
Fig. 4 (a) is a schematic diagram of collision determination on a grid map. Fig. 4 (b) is a schematic diagram of collision determination on the expanded grid map.
Fig. 5 is a map of a port in an embodiment of the present invention.
FIG. 6 is a navigation trajectory of a berthing to a target point in an embodiment of the present invention.
Fig. 7 is a graph showing a longitudinal velocity profile during parking to a target point in an embodiment of the present invention.
Fig. 8 is a graph showing a lateral velocity change during parking to a target point in an embodiment of the present invention.
Fig. 9 is a graph showing a yaw rate and speed change during parking to a target point in an embodiment of the present invention.
Fig. 10 is a graph showing a change in propulsive force during parking to a target point in the embodiment of the present invention.
FIG. 11 is a graph showing yaw moment variations during parking to a target point in an embodiment of the present invention.
Detailed Description
The invention is further illustrated below with reference to specific examples.
Considering the problem of planning a certain ship berthing at a certain port, the relevant parameters of the surface ship are shown in table 1, the relevant parameters of the algorithm are shown in table 2, and the port map is shown in fig. 5. Consider the initial boundary condition terminal target point in table 3.
Table 1 surface vessel parameters
TABLE 2
TABLE 3 initial boundary conditions and terminal target points for pilotless ships
| X(m) | Y(m) | Orientation angle (deg) | |
| Initial boundary conditions | 725 | 150 | 133 |
| Terminal target point | 630 | 715 | 0 |
A water surface ship berthing track planning method based on a safety channel comprises the following steps:
step 1: according to berthing requirements, initially constructing optimal control problems of motion characteristics of surface vessels
Step 1-1: describing kinematic equations of water surface vessels
M (x, y) is recorded as the mass center position of the surface ship, psi is recorded as the ship orientation angle, and u is recordedThe longitudinal speed of the ship, v is denoted as the transverse speed of the ship, and r is denoted as the yaw rate of the ship (as shown in fig. 2), all being variables to be optimized. m is m 1 、m 2 、m 3 The inertia after the additional mass effect is taken as m respectively 1 ＝1.2×10 5 kg、m 2 ＝1.729×10 5 kg、m 3 ＝6.36×10 7 kg·m 2 ，d 1 、d 2 、d 3 Is the hydrodynamic damping coefficient in the motion process, and is respectively taken as d 1 ＝2.15×10 4 kg/s、d 2 ＝9.7×10 4 kg/s、d 3 ＝8.02×10 6 kg·m 2 The propulsion of the ship is denoted as tau u The yaw moment of the ship is denoted as tau r . The control variable of the system is denoted as c= [ τ ] u ,τ r ] T The state variables are denoted as s= [ x, y, ψ, u, v, r] T The system can be described using the differential equation:
wherein f represents the kinematic equation of the surface vessel systemRepresenting the variable (·) deriving time; />Representing the derivative of the abscissa of the water surface ship matter with respect to time; />Representing the derivative of the ordinate of the water surface ship matter with respect to time; />Representing the derivative of the orientation angle of the surface vessel with respect to time; />Time alignment for representing longitudinal speed of surface shipA derivative of the first and second signals; />Representing the derivative of the transverse speed of the surface vessel with respect to time; />Representing the derivative of the yaw rate of the surface vessel over time.
In addition, the following constraint conditions in the movement process of the surface ship are considered:
wherein [(s) min ,(·) max ]Represents the permissible range of the variable (·); u (u) min 、u max Respectively representing the minimum and maximum longitudinal speeds allowed by the surface ships and respectively taking u as min = -0.5m/s and u max ＝4.5m/s；v min 、v max Respectively representing the minimum and maximum transverse speeds allowed by the surface ships and respectively taking v as min = -0.2m/s and v max ＝0.2m/s；r min 、r max Respectively represent the maximum yaw angular velocity allowed by the surface ships and are respectively taken as r min = -5deg/s and r max ＝5deg/s。
Meanwhile, the actual control quantity constraint and the control quantity impossibility of jumping are considered, so the control quantity and the control variable change rate are constrained as follows:
wherein [(s) ·,min ,(·) ·,max ]Represents a variable (& gt) · Is a permissible range of (2); τ u,min 、τ u,max Respectively representThe minimum and maximum propulsive forces allowed by the propulsive force are respectively taken as tau u,min ＝-5×10 3 N and τ u,max ＝1.25×10 5 N；τ r,min 、τ r,max Respectively representing the allowable minimum and maximum yaw moments, respectively taken as tau r,min ＝-1×10 9 N.m and τ r,max ＝1×10 9 N·m；Respectively representing the allowable minimum and maximum thrust rates of change, respectively taken asAnd-> Respectively representing the allowable minimum and maximum yaw moment change rates, respectively taken as +.>And->
Step 1-2: description of task requirements
And describing the state of the surface ship at the starting time of the dispatching task and the terminal expected time through boundary conditions. For the initial time t=0, the configuration of the surface vessel is noted as:
[x(0),y(0),ψ(0),u(0),v(0),r(0)]＝[x 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 ] (5)
wherein x is 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 The state variable condition of the initial position is taken as x 0 ＝725m,y 0 ＝150m,ψ 0 ＝133deg,u 0 ＝0m/s,v 0 ＝0m/s,r 0 ＝0m/s.
At the terminal moment t=t (T is also a variable to be optimized), the configuration of the surface vessel is noted as:
[x(T),y(T),sinψ(T),cosψ(T),u(T),v(T),r(T)]＝[x F ,y F ,sin(ψ F ),cos(ψ F ),u F ,v F ,r F ] (6)
wherein x is F ,y F ,ψ F ,u F ,v F ,r F The state variable condition of the terminal position is taken as x F ＝630m,y F ＝715m,ψ F ＝0deg,u F ＝0m/s,v F ＝0m/s,r F ＝0m/s.
Step 1-3: description of obstacle avoidance constraints
Mapping the state space S to the configuration space using the function g, we denote the entire configuration space as beta, and the surface vessel as the obstacle region beta if it collides with an obstacle obs The passable area can therefore be denoted as beta free ＝β\β obs The crash restraint may be expressed as follows.
Step 1-4: establishing performance index
The energy consumption and the stationarity are two important factors in the berthing process of the surface ships. The run time can be directly reflected by the terminal moment T, although a box constraint has been imposed in steps 1-3, the smoothness of the trajectory should be improved to ensure sufficient stability and comfort for the passengers, while the energy consumption should be reduced as much as possible considering the economic factors, thus obtaining the performance index of the following hybrid form:
wherein, P and Q respectively represent weight matrixes of state quantity and control quantity, J is an objective function of the whole optimal control problem, w is a weight coefficient, and P=diag (0,0,0,0,10,10), Q=diag (1 e-6 ) and w=1 are respectively taken
Step 1-5: establishing optimal control problems
Based on the foregoing description, an optimal control problem OCP is established init The concrete form is as follows:
step 2: according to the actual shape of the ship, the ship body is represented by a plurality of characteristic circles to realize the conversion of obstacle avoidance constraint
In FIG. 3, L is the captain, and the center of mass to stern distance of the vessel is denoted as sum L r The hull width is denoted W, in this case l=32m, L respectively r =15m, w=9m, radius of circleThen get->Two characteristic circles with radius R are respectively taken at two ends to represent, and the rest part uses +.>A circular cover, wherein->And each of the characteristic circles except for both ends represents +.>A hull of corresponding length, available +.>Δl=7m.The feature circles represent the surface vessel profile as shown in fig. 3, with m=4 according to the selected parameters. The center position of any h characteristic circle can be expressed as +.> And->The method can be obtained by the following formula:
wherein l h The position from the center of mass of the water surface ship to the center of the h equivalent circle is represented as follows:
can be specifically obtained by 1 ＝12.5m、l 2 ＝4.5m、l 3 ＝-2.5m、l 4 ＝-10.5m
Through the previous description, the part of all the obstacles in the whole map, which is not overlapped with each circle, can be regarded as obstacle avoidance success, if each characteristic circle is condensed to the circle center position, the corresponding expansion R size of the obstacles is ensured, and the situation that the circle center position is not on the obstacles in the map after expansion can be regarded as collision avoidance is only required.
Step 3: obtaining a grid map according to the actual map and combining the feature circle radius
Based on the expansion mode described in step 2, the resolution D is adopted res =2.5m establishes a grid map Λ of the deck. For any grid, if it overlaps with the inflated obstacle, it is considered to be one obstacle grid; otherwise, it is considered a free grid. Record X direction and Y directionUpward, the boundaries of the grid map are [0, X max ]And [0, Y ] max ]Taking X according to the data in the case max ＝1000m、Y max =1000m. Let "grid (i, j)" represent a two-dimensional region as follows: { (X, Y) | (i-1) D res ＜X≤iD res ,(j-1)D res ＜Y≤jD res }. In fig. 4, a collision determination method in a grid map is shown.
Step 4: coarse path acquisition on grid map using a manually guided hybrid a-algorithm
A mixed A algorithm is used, the kinematic constraint of the surface ship is combined, a rough path is planned for the mass center M (x, y) of the surface ship, in the planning process of an actual port environment, a rough path is ensured to be generated efficiently because a plurality of narrow branches need to be passed, manual addition of guide points is selected to guide the generation of the path, and the guide points are zeta= { B 0 ,…,B i ,…,B N }, wherein B is 0 And B is connected with N For two-dimensional position information in initial and terminal configuration conditions, B i For the artificially added guide points i=1, 2, …, (N-1), in the case n=2, b is taken 0 ＝(725，150)，B 1 ＝(400，600)，B 2 = (630, 715). Will be from B 0 Beginning with B i Is the starting point B i+1 The path information obtained by using the mixed A-algorithm for the end point is recorded asAcquiring the last path information until i+1=NAfter the path search is finished, the whole coarse path information +.>The path resulting from this method is in fact a series of waypoints. Suppose Path A From N A The navigation path point is formed, wherein the kth navigation path point is recorded asIn the present caseN in the coarse Path generated in the example A ＝104
Furthermore, the mixed a algorithm realizes smooth generation of a coarse path in a complex environment by adding a guide point in the middle.
Step 5: resampling the rough path according to maximum speed and maximum acceleration according to time optimal principle
Step 5-1: time-consuming transfer estimation T tst
Defining the length of the path as the sum of the distances between any adjacent waypoints, denoted as L path Can be expressed asWherein k represents any integer, N A Representing the number of nodes of the path searched by the manual guided hybrid a-algorithm, ++>Respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm>Respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm, and obtaining the path length of L path =854 m. Assuming that the acceleration motion in the sampling process is always moved by using the maximum or minimum acceleration in the path by adopting the time optimal motion mode, the acceleration in the sampling process can be expressed as: ,/>Wherein m is 1 Representing the inertia of a vessel containing an additional mass effect according to the selected parameters +.>The speed is 0 at the two end waypoints of the path. Introducing distance threshold->Then complete along Path A Time-consuming T of the dispatch tst It can be estimated that:
t obtained in practice by resampling tst ＝199.99s
Step 5-2: resampling at discrete points
Without loss of generality, consider the time period to be discretized into N in the actual solving process sam For a long time interval, in this case N is taken sam And (N) if =100 sam +1) discrete points, so that the time interval between every two adjacent discrete points is Δt=t tst /N sam There is Δt=1.99 s. Variable T tst In effect providing an initial guess for T in the problem, then the kth discrete point corresponds approximately to time T k = (k+1) Δt. At T m At the moment, the state information of the surface vessel is recorded as (x) k ,y k ,ψ k ,u k ,v k ). Next, based on the constraint of the equation of motion and the sum and the formula combination formula, the yaw rate r of the surface vessel k Thrust τ u,k Yaw moment τ r,k It is possible to obtain:
to this end, an initial guess is provided for the actual optimization problem by the resampling process. In particular, the time of dispatch may be T tst Performing initial processAt all discrete points, the state variables and control variables may be represented by eight-tuple (x k ,y k ,ψ k ,u k ,v k ,r k ,τ u,k ,τ r,k ) Initialization is performed. The resampled Path is denoted Path sam 。
Step 6: constructing a safe navigation channel according to the resampling result and the obtained grid map
According to Path sam And the sum of the formulas can obtain the circle center O corresponding to any j j Can be calculated and recorded as Traj j . The generation process of the safety dispatching corridor corresponding to each circle center is similar, and O is adopted below j For example, a framework method of a secure transportation corridor is described. Let it be assumed that at the kth discrete point (k=0, 1, …, N sam )，O j The corresponding position is recorded asRecord O j,k The corresponding safe navigation channel is marked as SSC j,k 。
First, SSC is performed j,k Initialized to point O j,k By itself, it can be seen as a rectangle with zero width and zero length. Define the search direction set Δ= [ up, left, down, right ]]. The search is continuously performed in each of the directions Δ with a fixed step Δs=1m. Defining a safe navigation channel obtained by expansion in the previous iteration process asWe will cycle through four directions in delta to continuously update the data of the secure channel. If the following 2 conditions are satisfied at the same time: 1) The safety channel does not overlap any obstacle grid in the grid map Λ; 2) The length of the expansion in the direction lambda does not exceed a predetermined upper expansion distance limit L max Wherein L is max =100m; the extension is valid and the safe navigation channel information is updated. When at least one of the conditions 1) or 2) is not satisfied, the direction λ is deleted from Δ. The expansion process as above is continued until the set of search directions becomes an empty set.
Repeating the above process (N) sam +1) times, can be applied to O j Each O of (2) j,k (k＝0,1,…,N sam ) Constructing corresponding safe dispatching corridor SSC j,k Wherein N is sam Representing the number of sampling nodes in the resampling of the coarse path. If O j,k Keep in SSC j,k In, then can ensure O j,k No collision with any obstacle on deck occurs. Therefore, the following collision constraint conversion can be realized on the circle center of any jth equivalent circle at any kth sampling position
Step 7: based on the safe navigation channel, the motion constraint of the surface ship is established, the final optimal control problem is established, and the solution is implemented
Substituting the converted constraint in equation (17) for the optimal control problem OCP init The obstacle avoidance conditions constitute the following optimal control problem OCP FIN
And resampling the obtained information (x k ,y k ,ψ k ,u k ,v k ,r k ,τ u,k ,τ r,k ) Solving the optimal control problem OCP as an initial solution FIN Obtaining the parking track Traj FIN As shown in fig. 6.
Fig. 6 shows a navigation path from an initial point to a target point, and fig. 7 to 11 show the variation histories of five variables, namely, the longitudinal speed, the transverse speed, the yaw rate, the propulsive force and the yaw moment of the surface ship under the navigation situation. The method can be seen to be capable of completing the path planning task well.
For the path planning efficiency of the method, a comparison of the efficiency of obtaining the rough path under the boundary condition in the third table by using the manually guided a-algorithm and the traditional mixed a-algorithm is shown in table 4, and a comparison of the planning time of the algorithm and other algorithms for completing the planning task of the boundary condition in table 3 is shown in table 5.
TABLE 4 Table 4
TABLE 5
The examples described above represent only embodiments of the invention and are not to be understood as limiting the scope of the patent of the invention, it being pointed out that several variants and modifications may be made by those skilled in the art without departing from the concept of the invention, which fall within the scope of protection of the invention.
Claims (4)
1. The surface ship berthing track planning method based on the safe sailing channel is characterized by comprising the following steps of:
firstly, preliminarily constructing an optimal control problem according to the motion characteristics of a water surface ship according to mooring requirements;
secondly, according to the actual shape of the ship, the ship body is represented by a plurality of characteristic circles, so that the conversion of obstacle avoidance constraint is realized;
thirdly, obtaining a grid map according to the actual map and combining the radius of the characteristic circle;
fourth, a coarse path is obtained on the grid map by using a manually guided mixed A algorithm;
fifthly, resampling the rough path according to the maximum speed and the maximum acceleration according to the time optimal principle;
sixthly, constructing a safe navigation channel according to the resampling result and the obtained grid map;
seventh, based on the safe navigation channel, the motion constraint of the surface vessel is established, and the final optimal control problem is solved;
the method comprises the following steps:
step 1: according to berthing requirements, initially constructing optimal control problems of motion characteristics of surface vessels
Step 1-1: describing kinematic equations of water surface vessels
Assuming that heave, roll and pitch caused by wind and water currents are negligible, and assuming that the hull inertia, additional mass and hydrodynamic damping matrix are diagonal and available control variables are propulsion and yaw moment, a model of motion in cartesian coordinates can be obtained; m (x, y) is recorded as the centroid position of the surface ship, psi is the ship orientation angle, u is the longitudinal speed of the ship, v is the transverse speed of the ship, r is the yaw rate of the ship, M 1 、m 2 、m 3 Is the inertia after containing the additional mass effect, d 1 、d 2 、d 3 Is the hydrodynamic damping coefficient in the motion process, tau u For propulsion of the vessel, τ r Is the yaw moment of the ship; the control variable of the system is denoted as c= [ τ ] u ,τ r ] T The state variables are denoted as s= [ x, y, ψ, u, v, r] T The system can be described using the differential equation:
wherein f represents the kinematic equation of the surface vessel systemRepresenting the variable (·) deriving time; />Representing the derivative of the barycenter abscissa of the surface vessel with respect to time; />Representing the derivative of the ordinate of the centroid of the surface vessel with respect to time; />Representing the derivative of the orientation angle of the surface vessel with respect to time; />Representing the derivative of the longitudinal speed of the surface vessel with respect to time; />Representing the derivative of the transverse speed of the surface vessel with respect to time; />Representing the derivative of the yaw rate of the surface vessel over time;
in addition, the following constraint conditions in the movement process of the surface ship are considered:
wherein [(s) min ,(·) max ]Represents the permissible range of the variable (·); u (u) min 、u max Respectively representing the minimum and maximum longitudinal speeds allowed by the surface vessel; v min 、v max Respectively representing the minimum and maximum allowable transverse speeds of the surface vessels; r is (r) min 、r max Respectively representing the minimum and maximum yaw rates allowed by the surface vessel;
meanwhile, the actual control quantity constraint and the control quantity impossibility of jumping are considered, so the control quantity and the control variable change rate are constrained as follows:
wherein [(s) ·,min ,(·) ·,max ]Represents a variable (& gt) · Is a permissible range of (2); τ u,min 、τ u,max Representing the minimum and maximum propulsion forces allowed, respectively; τ r,min 、τ r,max Representing the allowed minimum and maximum yaw moments, respectively;representing the minimum and maximum allowable thrust rates of change, respectively; />Representing the minimum and maximum allowed yaw moment rates of change, respectively;
step 1-2: description of task requirements
Describing the state of the water surface ship at the starting moment of the dispatching task and the expected moment of the terminal through boundary conditions; for the initial time t=0, the configuration of the surface vessel is noted as:
[x(0),y(0),ψ(0),u(0),v(0),r(0)]＝[x 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 ] (5)
wherein x is 0 ,y 0 ,ψ 0 ,u 0 ,v 0 ,r 0 A state variable condition for an initial position;
at the terminal moment t=t, where T is also the variable to be optimized, the configuration of the surface vessel is noted as:
[x(T),y(T),sinψ(T),cosψ(T),u(T),v(T),r(T)]＝[x F ,y F ,sin(ψ F ),cos(ψ F ),u F ,v F ,r F ] (6)
wherein x is F ,y F ,ψ F ,u F ,v F ,r F A state variable condition for the terminal position;
step 1-3: description of obstacle avoidance constraints
Mapping the state space S to the configuration space using the function g, and recording the entire configuration space as beta, and recording the surface vessel as the obstacle region beta if it collides with the obstacle obs The passable area can therefore be denoted as beta free ＝β\β obs The crash restraint may be expressed in the following form;
step 1-4: establishing performance index J
The performance index formula for the mixed form is as follows:
wherein P and Q respectively represent weight matrixes of state quantity and control quantity, J is an objective function of the whole optimal control problem, and w is a weight coefficient;
step 1-5: establishing optimal control problems
Based on the foregoing description, an optimal control problem OCP is established init The concrete form is as follows:
step 2: according to the actual shape of the ship, the ship body is represented by a plurality of characteristic circles to realize the conversion of obstacle avoidance constraint
Defining the ship length as L, and recording the distance from the center of mass of the ship to the stern as L r The width of the hull is marked as W, and the radius of the rounding isTwo characteristic circles with radius R are respectively taken at two ends to represent, and the rest part uses +.>A circular cover, whereinThen co-require->Each characteristic circle represents the surface vessel shape, and each characteristic circle except for both ends represents +.>A hull of a corresponding length; the center position of any h characteristic circle can be expressed as +.> And->The method can be obtained by the following formula:
wherein l h The position from the center of mass of the water surface ship to the center of the h equivalent circle is represented as follows:
the part of all the obstacles in the whole map, which is not overlapped with each circle, is regarded as obstacle avoidance success, if each characteristic circle is condensed to the circle center position, the corresponding expansion R size of the obstacles is ensured, and the situation that the circle center position is not on the obstacles in the map after expansion can be regarded as no collision;
step 3: obtaining a grid map according to the actual map and combining the feature circle radius
Based on the expansion mode described in step 2, the resolution D is adopted res Establishing a grid map lambda of a deck; for any grid, if it overlaps with the inflated obstacle, it is considered to be one obstacle grid; otherwise, it is considered a free grid; the boundaries of the grid map in the X direction and the Y direction are respectively [0, X max ]And [0, Y ] max ]The method comprises the steps of carrying out a first treatment on the surface of the Let "grid (i, j)" represent a two-dimensional region as follows: { (X, Y) | (i-1) D res ＜X≤iD res ,(j-1)D res ＜Y≤jD res -a }; in fig. 4, a collision determination method in a grid map is illustrated;
step 4: coarse path acquisition on grid map using manually guided hybrid a-algorithm
A mixed A algorithm is used, the kinematic constraint of the surface ship is combined, a rough path is planned for the mass center M (x, y) of the surface ship, in the planning process of an actual port environment, a rough path is ensured to be generated efficiently because a plurality of narrow branches need to be passed, manual addition of guide points is selected to guide the generation of the path, and the guide points are zeta= { B 0 ,…,B i ,…,B N }, wherein B is 0 And B is connected with N For two-dimensional position information in initial and terminal configuration conditions, B i For artificially added guide points i=1, 2, …, (N-1); will be from B 0 Beginning with B i Is the starting point B i+1 The path information obtained by using the mixed A-algorithm for the end point is recorded asObtaining the last piece of path information +.>After the path search is finished, the whole coarse path information +.>The path obtained by the method is a series of route points in fact; suppose Path A From N A A plurality of waypoints, wherein the kth waypoint is a node k (k＝1,2,…,N A )，
Step 5: resampling the rough path according to maximum speed and maximum acceleration according to time optimal principle
Step 5-1: time-consuming transfer estimation T tst
Defining the length of the path as the sum of the distances between any adjacent waypoints, denoted as L path Can be expressed asWherein k represents the interval [1, N ] A ]N is any positive integer A Representing the number of nodes of the path searched by the manual guided hybrid a-algorithm, ++>Respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm>Respectively representing the barycenter abscissa of the water surface ship between the current node and the last node on the path searched by the manual guidance mixed A-type algorithm;
assuming that the acceleration motion in the sampling process is set to always adopt the maximum or minimum acceleration for motion by adopting a time optimal motion mode in the path, the acceleration in the sampling process is expressed as:wherein m is 1 Representing the vessel inertia including the additional mass effect; the speed is 0 on the two end waypoints of the path; introducing distance threshold->Then complete along Path A Time-consuming T of the dispatch tst It can be estimated that:
step 5-2: resampling at discrete points
Without loss of generality, consider the time period to be discretized into N in the actual solving process sam A plurality of equal-length time intervals, there is (N) sam +1) discrete points, so that the time interval between every two adjacent discrete points is Δt=t tst /N sam The method comprises the steps of carrying out a first treatment on the surface of the Variable T tst In effect providing an initial guess for T in problem (8), then the kth discrete point corresponds approximately to time T k ＝(k+1) Δt; at T m At the moment, the state information of the surface vessel is recorded as (x) k ,y k ,ψ k ,u k ,v k ) The method comprises the steps of carrying out a first treatment on the surface of the Next, based on the constraint of equation of motion (1) in combination with equations (2) and (5) and (6), the yaw rate r of the surface vessel is obtained k Thrust τ u,k Yaw moment τ r,k ；
To this end, an initial guess is provided for the actual optimization problem through the resampling process; in particular, the time of dispatch may be T tst Initialization is performed, and at all discrete points, the state variables and control variables can be represented by eight-tuple (x k ,y k ,ψ k ,u k ,v k ,r k ,τ u,k ,τ r,k ) Initializing; the resampled Path is denoted Path sam ；
Step 6: constructing a safe navigation channel according to the resampling result and the obtained grid map
According to Path sam And formulas (10) and (11), the circle center O corresponding to any jth circle center can be obtained j Can be calculated and recorded as Traj j The method comprises the steps of carrying out a first treatment on the surface of the The generation process of the safety dispatching corridor corresponding to each circle center is similar, and O is adopted below j For example, a construction method of a secure transportation corridor is described; let it be assumed that at the kth discrete point (k=0, 1, …, N sam )，O j The corresponding position is recorded asRecord O j,k The corresponding safe navigation channel is marked as SSC j,k ；
First, SSC is performed j,k Initialized to point O j,k Itself, the search direction set Δ= [ up, left, down, right ]]The method comprises the steps of carrying out a first treatment on the surface of the Continuously exploring in each direction in delta with a fixed step delta s; defining a safe navigation channel obtained by expansion in the previous iteration process asExpanding the circulation along four directions in delta to continuously update the data of the safety channel;
repeating the above stepsThe flow (N) sam +1) times, can be applied to O j Each O of (2) j,k (k＝0,1,…,N sam ) Constructing corresponding safe dispatching corridor SSC j,k Wherein N is sam Representing the number of sampling nodes in the process of resampling the coarse path; if O j,k Keep in SSC j,k In, then can ensure O j,k No collision with any obstacle on deck occurs; therefore, the following collision constraint conversion can be realized on the center of any jth equivalent circle at any kth sampling position:
step 7: based on the safe navigation channel, the motion constraint of the surface ship is established, the final optimal control problem is established, and the solution is implemented
Substituting the converted constraint in equation (17) for the optimal control problem OCP init The obstacle avoidance conditions constitute the following optimal control problem OCP FIN
Solving the optimal control problem OCP FIN Obtaining the parking track Traj FIN 。
2. The method for planning a berthing track of a water surface ship based on a safe navigation channel according to claim 1, wherein in the step 6, when updating the data of the safe navigation channel, if the following 2 conditions are satisfied at the same time: 1) The safety channel does not overlap any obstacle grid in the grid map Λ; 2) The length of the expansion in the direction lambda does not exceed a predetermined upper expansion distance limit L max The method comprises the steps of carrying out a first treatment on the surface of the Then the extended availability and updating of safe navigation channel information; deleting the direction λ from Δ when at least one of condition 1) or condition 2) is not satisfied; the expansion process as above is continued until the set of search directions becomes an empty set.
3. The method for planning a berthing track of a water surface ship based on a safe navigation channel according to claim 1, wherein in the step 4, the mixed a algorithm is used for smoothly generating a rough path in a complex environment by adding a guide point in the middle.
4. The method for planning berthing track of water surface vessels based on safe navigation channel as set forth in claim 1, wherein in said step 5-2, yaw rate r of water surface vessels is as follows k Thrust τ u,k Yaw moment τ r,k The formula is as follows:
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