Under-actuated unmanned ship navigation control system based on smooth airway guidance

Abstract

The invention discloses an underactuated unmanned ship navigation control system based on smooth route guidance, and the system comprises a construction module which is used for constructing an underactuated unmanned ship motion model under uncertain environment disturbance and system uncertainty, and combining an actuator gain damage and input saturation maneuverability limited model, an under-actuated unmanned ship maneuverability limited motion model is obtained; the planning module is used for obtaining a planned driving path of the underactuated unmanned ship based on a fast expansion random tree algorithm of a non-uniform rational B-spline; and the control module is used for observing the lumped error of the maneuverability limited motion model system of the underactuated unmanned ship by adopting a finite time observer, designing a control law through a feedback linearization method and reducing the disturbance of an intermediate variable through a first-order auxiliary filtering system, and realizing the control of the underactuated unmanned ship running according to a planned path.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent navigation control of unmanned boats, and relates to a navigation control system of an under-actuated unmanned boat based on smooth path guidance. Background Art

[0002] Currently, mainstream research typically uses algorithmically generated waypoints, completes path planning through curve fitting, and uses these waypoints for guidance and control to achieve path tracking. Therefore, the proper selection of waypoints is crucial, as it directly impacts the smoothness of path planning and mission suitability, and also determines the guidance and control accuracy and overall system performance.

[0003] Among the path planning algorithms, the Rapidly Exploring Random Tree (RRT) algorithm is often used by researchers to solve the path planning problem of unmanned boats because of its advantages such as not requiring all the information of the environment to be solved, strong robustness, and easy implementation. The RRT algorithm was proposed by Lavalle et al. [1] However, due to its weak real-time performance and difficulty in obtaining the optimal solution, it is not applicable to actual engineering problems. [2] applied the RRT algorithm after sampling optimization to a robotic arm and verified the feasibility of the algorithm running on a six-degree-of-freedom robotic arm; [3] The bounding box tree is built in parallel for hierarchical detection, and the path is fitted using Bezier curves, resulting in a safer and smoother path. [4] Aiming at the collision problem between the RRT algorithm and dynamic obstacles during the path planning process, Yao et al. proposed an improved path planning algorithm combining Informed-RRT* with the artificial potential field method, which achieved global optimal exploration and local obstacle avoidance functions; [5] Aiming at the problem that the RRT algorithm has slow convergence speed in large waters, a global trajectory planning method for underactuated unmanned vessels based on efficient convergence random trees and B-spline interpolation was proposed; Zeng et al. [6] Aiming at the problem of non-smooth path of RRT algorithm, a continuous curvature-based RRT (CC-RRT) path planning algorithm is proposed, which uses Clozoide curve for local smoothing. This method can convert the path generated by RRT algorithm into a continuous curvature path. [7] Aiming at the poor adaptability and robustness of the RRT algorithm in complex environments and sudden obstacles, an optimization strategy combining the RRT algorithm and the APF method is proposed. This strategy not only reduces the path length, but also achieves more efficient and reliable path planning by improving the path search efficiency of the RRT algorithm and combining the goal guidance and obstacle avoidance capabilities of the APF.

[0004] In the field of unmanned boat guidance control, due to the existence of nonholonomic constraints, the system does not meet the Brockett necessary conditions for smooth stabilization control. [8] In the field of unmanned ship guidance and control, the method of deploying waypoints is often used to promote its guidance and autonomous navigation. Lu et al. [9] In order to improve the path tracking control accuracy of the unmanned ship, the particle swarm optimization algorithm is used to optimize the PID controller to track the heading of the unmanned ship, and the adaptive acceptance circle is used to improve the LOS algorithm to track the waypoints to achieve the tracking control of the unmanned ship's driving path; Wang et al.

[10] In order to solve the problem that the unmanned boat will be affected by unknown disturbances during the guidance process, a finite-time disturbance observer was designed; Yuan et al.

[11] In order to solve the environmental noise problem, Sahal et al. transformed the unmanned boat waypoint tracking control problem into a stabilization control problem based on nonholonomic system state estimation through coordinate transformation and UD-UKF.

[12] Aiming at the problem that the system is disturbed when the external environment changes, a stable intelligent controller is designed using fuzzy logic sliding mode control and several variants are studied to obtain a method that can reach the waypoint in a faster time and shorter distance. Tao et al.

[13] Aiming at the collision avoidance problem of USV with irregular static obstacles and ships in coastal waters, a new waypoint guidance and motion control scheme for USV based on nonlinear model predictive control was proposed.

[0005] Through the review and analysis of existing work, the following deficiencies still exist in the route guidance, navigation and tracking control of under-actuated unmanned vehicles:

[0006] (1) Previous path planning studies have failed to solve the redundancy problem in the waypoint generation process, resulting in the generated path being not smooth enough or the order being too high after path parameterization, which increases the difficulty of subsequent control and lacks practicality. In addition, traditional route fitting methods are difficult to pass through all waypoints smoothly and continuously, which makes it impossible for the unmanned boat to accurately pass through the corresponding waypoints even if it can track the corresponding path with high precision.

[0007] (2) During the waypoint guidance process, the existing waypoint-based guidance method can usually only enable the unmanned boat to reach a small neighborhood near the waypoint. When the unmanned boat approaches the target waypoint, strange phenomena will inevitably occur, making it difficult for the current waypoint guidance control method to achieve accurate arrival at the target point.

[0008] (3) Most studies separate path planning and path tracking, which makes it difficult for the planned path to be effectively used for path tracking, and the reference path used for path tracking is too ideal. Although a few studies have attempted to combine path planning with path tracking, they still do not consider the path smoothness and control difficulty sufficiently, making it difficult to meet the needs of practical applications. Summary of the Invention

[0009] In order to solve the above problems, the technical solution adopted by the present invention is: a navigation control system for an underactuated unmanned vessel based on smooth path guidance, comprising the following steps:

[0010] Construction module: used to construct the motion model of the underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties. Combined with the maneuverability-constrained model of the actuator gain damage and input saturation, the maneuverability-constrained motion model of the underactuated unmanned vehicle is obtained.

[0011] Planning module: used to obtain the planned path of the under-actuated unmanned vehicle using a fast-expanding random tree algorithm based on non-uniform rational B-splines;

[0012] Control module: It is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle using a finite-time observer, and to design the control law and the first-order auxiliary filter system through the feedback linearization method to filter out high-frequency interference, so as to realize the control of the under-actuated unmanned vehicle to travel according to the planned path.

[0013] Furthermore, the process of obtaining the planned path of the under-actuated unmanned vehicle using the non-uniform rational B-spline fast expansion random tree algorithm is as follows:

[0014] The fast expanding random tree algorithm is used to obtain the waypoints, and then the weighted screening strategy is used to screen the waypoints of the under-actuated unmanned vehicle.

[0015] Based on the non-uniform rational B-spline curve, the waypoints of the screened under-actuated unmanned vehicle are fitted to obtain the driving planning path of the under-actuated unmanned vehicle that can accurately pass through the waypoints.

[0016] Furthermore, the process of using the rapidly expanding random tree algorithm and then using the weighted screening strategy to screen the waypoints of the under-actuated unmanned vehicle is as follows:

[0017] S1: p start As the starting point for random tree expansion, first find a random sampling point p in the specified area rand ,

[0018] S2: Select the root node p that is closest to the generated sampling point near , the root node p nearConnected to the random sampling point, and continue to intercept a line segment on the line with the specified step length as the starting point, the end point of the line segment is the new child node p generated by the algorithm new ;

[0019] S3: Determine the new child node p new Whether the node collision detection is passed, if the new child node p new If the node obstacle detection fails, the point is discarded and resampled, and the process returns to S2;

[0020] If the new child node p new If the node obstacle is detected, it will be used as the new root node and continue to expand, and the new child node p new Add random trees;

[0021] S4: Determine the new child node p new Whether it passes the node weight test, when the new child node p new If the node weight test fails, S5 is performed to determine whether the new node reaches the target point's range;

[0022] When the new child node P new Through node weight detection, the new child node P new Add waypoint matrix P W , and update the weight detection starting point Ps, then S5 is performed to judge whether the new node reaches the range of the target point;

[0023] S5: When the new node does not reach the target point range, return to S2;

[0024] When the new node reaches the target point, it stops sampling and outputs the waypoint P new .

[0025] Furthermore, the process of fitting the waypoints of the screened under-actuated unmanned vehicle based on the non-uniform rational B-spline curve to obtain the planned path of the under-actuated unmanned vehicle is as follows:

[0026] S6: Calculate node vector;

[0027] S7: Calculate the boundary conditions of the underactuated unmanned vehicle;

[0028] S8: inverse calculation of control vertices;

[0029] S9: Calculate the parameter-containing fitting function;

[0030] S10: Determine whether the fitting curve passes the collision detection;

[0031] When the fitting curve fails the collision test, the tree node closest to the collision point is selected and added to the waypoint matrix P.new , return to S6;

[0032] When the fitting curve passes the collision detection, the planned path of the under-actuated unmanned vehicle is obtained.

[0033] Furthermore, the condition for detecting the node obstacle is as follows: constructing a path segment between the judgment base point and the new next node, and judging whether the distance between the path segment and the obstacle is less than or equal to a specified value Ω.

[0034] Furthermore: the detection process of the node weight is as follows:

[0035] According to the completed tree structure T, from the starting point p start Start weight judgment and set it as the judgment base point p s (x s ,y s ), the tree node is p ti (x ti ,y ti )=P t (i),i=1,2,…,n,P t is the node matrix in the tree structure. Among the environmental obstacles, the circular obstacles satisfy p r (x r ,y r ), r r are the coordinates of the circle center and the obstacle radius respectively, are the vertices of the rectangular obstacle, represents a line segment between two points, Defined as a line segment vector, then for point To line segment The distance is expressed as:

[0036]

[0037] in: is a vector In vector The minimum distance from the connecting line segment to the obstacle is expressed as:

[0038] d obs =min{d r ,d rec} (7)

[0039] Among them, d r =d r-sti -r r , d rec =min{d 12 ,d 23 ,d 34 ,d 41}, d23 ,d 34 ,d 41 Same as d 12 , and d 12 =min{d rec1-sti ,d rec2-sti ,d s-rec12 ,d ti-rec12};

[0040] For line segment p s p ti Perform collision analysis. If a collision occurs, p s =P t (i-1); if no collision occurs, then determine line segment p s p ti The distance between the obstacle and the object, if d obs >Ω, it means the node weight is low and the node is discarded; if d obs ≤Ω, indicating that the node weight is high, then p s =p ti , then the final waypoint is P w ={p s1 ,p s2 ,…,p goal}.

[0041] Furthermore, the non-uniform rational B-spline curve is defined as follows:

[0042]

[0043] in, is a point on the curve, is the control point, w j are the weights associated with the control points, is the j-th k-order B-Spline basis function, m is the last control point number, which is determined by the node vector and satisfies the following conditions:

[0044]

[0045]

[0046] in, is a non-decreasing sequence of nodes, And define If the node vector is obtained using the cumulative chord length method and cubic curve fitting is adopted, we have:

[0047]

[0048] Based on the waypoint tangent conditions and supplemented with the start and end tangent vector conditions, the curve control points are calculated inversely. The calculation formula is as follows:

[0049] Θd=χ (12)

[0050] Among them, Θ is the weighted spline basis function matrix; d is the control point matrix; χ is the weighted reference point matrix, and the tangent vector condition is given as:

[0051]

[0052] The matrix parameters are given as:

[0053]

[0054] Among them, d j For control vertices, g j To fit the tangent condition, a j ,b j ,c j are the non-zero terms in the basis function parameters.

[0055] A navigation control method for an underactuated unmanned vessel based on smooth path guidance comprises the following steps:

[0056] A motion model of an underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties is constructed. Combined with the maneuverability-constrained model of actuator gain impairment and input saturation, a maneuverability-constrained motion model of an underactuated unmanned vehicle is obtained.

[0057] The planned path of the under-actuated unmanned vehicle is obtained by using a fast-expanding random tree algorithm based on non-uniform rational B-splines.

[0058] A finite-time observer is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle. The control law is designed through the feedback linearization method, and the first-order auxiliary filter system is used to filter out high-frequency interference, so that the under-actuated unmanned vehicle can be controlled to move along the planned path.

[0059] The present invention provides an underactuated unmanned vessel navigation control system based on smooth path guidance, which has the following advantages:

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. Based on the RRT path planning algorithm, the practicality of the planned path is fully considered. Through waypoint weight screening, redundant path points are removed, valid waypoints are screened out, and the curve fitting efficiency is improved;

[0062] 2. Using the NURBS inverse calculation method to perform curve fitting on waypoints, the fitted parameterized path can accurately pass through the waypoints, transforming the problem of accurate waypoint tracking into a high-precision path tracking problem, reducing the control difficulty and improving the control accuracy of the corresponding waypoints;

[0063] 3. A fault-tolerant control strategy based on a finite-time observer is proposed to solve the path tracking problem of an underactuated unmanned vehicle in unknown environmental disturbances under conditions of input saturation and actuator gain impairment, increase the robustness of path tracking, and improve the ability to cope with adverse conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0065] Figure 1 This is the NRRT-FTC system framework diagram;

[0066] Figure 2 Schematic diagram of the RRT algorithm;

[0067] Figure 3 Filter schematics for waypoints;

[0068] Figure 4 This is the NURBS inverse fitting effect diagram;

[0069] Figure 5 It is the logic diagram of NRRT algorithm;

[0070] Figure 6 This is a schematic diagram of path tracking;

[0071] Figure 7 This is the NRRT curve fitting effect diagram;

[0072] Figure 8 This is a comparison chart of curve fitting effects;

[0073] Figure 9 The path tracking control effect diagram is shown in Figure 1. (a) is the tracking effect diagram under no-disturbance conditions, and (b) is the tracking effect diagram under disturbance conditions.

[0074] Figure 10 Comparison diagram of speed tracking control effect; (a) is the speed tracking effect under no-disturbance condition, (b) is the speed tracking effect under disturbance condition;

[0075] Figure 11 Comparison diagram of position tracking error; (a) shows the speed tracking effect under no-disturbance conditions, and (b) shows the speed tracking effect under disturbance conditions;

[0076] Figure 12Comparison diagram of motion state errors; (a) is the comparison diagram of sway velocity control error, (b) is the comparison diagram of sway velocity control error; (c) is the comparison diagram of yaw velocity control error, and (d) is the comparison diagram of heading angle control error;

[0077] Figure 13 Comparison diagram of under-actuated control torque output; (a) is the undisturbed sway control output, (b) is the undisturbed sway control output, (c) is the undisturbed yaw control output, and (d) is the yaw control output with disturbance.

[0078] Figure 14 A comparison chart of time-varying parameters. DETAILED DESCRIPTION

[0079] It should be noted that, unless there is any conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0080] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0081] Figure 1 This is the NRRT-FTC system framework diagram;

[0082] A navigation control system for an underactuated unmanned vessel based on smooth path guidance, comprising:

[0083] Construction module: used to construct the motion model of the underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties. Combined with the maneuverability-constrained model of the actuator gain damage and input saturation, the maneuverability-constrained motion model of the underactuated unmanned vehicle is obtained.

[0084] Planning module: used to obtain the planned path of the under-actuated unmanned vehicle using the Non-Uniform Rational B-Spline Based Rapidly Exploring Random Tree (NRRT) algorithm;

[0085] Control module: It is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle using a finite-time observer, and to design the control law and the first-order auxiliary filter system through the feedback linearization method to filter out high-frequency interference, so as to realize the control of the under-actuated unmanned vehicle to travel according to the planned path.

[0086] The process of constructing the motion model of the underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties, combined with the maneuverability-constrained model of actuator gain impairment and input saturation, to obtain the maneuverability-constrained motion model of the underactuated unmanned vehicle is as follows:

[0087] The process of establishing a finite-time convergent system is as follows:

[0088] Lemma 1: For the following nonlinear system:

[0089]

[0090] It converges in finite time. Among them, sig α (*)=sign(*)|*| α , L, λ i (i=0,1,…,n) are all positive numbers.

[0091] The control model of the unmanned boat is established as follows:

[0092] The dynamic equation of the unmanned boat can be expressed as:

[0093]

[0094] Where: variable η = [x, y, ψ] T Represents the position and attitude of the unmanned boat in the earth coordinate system; variable v = [u, v, r] T represents the longitudinal and transverse velocities and yaw angular velocity of the unmanned boat in the appendage coordinate system; the variable τ = [τ u ,0,τ r ] T is the control input; R(ψ) is the transposed matrix, which is expressed as follows:

[0095]

[0096] M is the mass matrix expressed as follows:

[0097]

[0098] System dynamics f(v)=[f u ,f v ,f r ] T , where f u =m 22 vr-d 11u,f v =-m 11 ur-d 22 v, f r =-(m 22 -m 11 )uv-d 33 r, m are inertial masses, d is the hydrodynamic parameter; the system complex unknown term τ δ =[τ δu ,τ δv ,τ δr ] T Contains unknown environmental disturbances and system uncertainties, and satisfies the following general assumptions: Assumption 1: Complex unknown τ δ is differentiable, that is, there exists a bounded constant Γ, Γ < ∞, such that

[0099] Gain loss or gain loss failure often occurs due to wear, current interference, voltage drop or other mechanical reasons. This type of gain loss failure can be described by the following model:

[0100] τ f =(IF)τ (3)

[0101] Where: I = diag (1, 1, 1) is the identity matrix in is the gain-loss coefficient, when When , it means that the actuator has no fault and all power can be output; when When the actuator is completely faulty, there is no power output.

[0102] In addition, due to the practical properties of the actuator's performance, the actuator's output often has a maximum value, so the traditional input saturation model is as follows:

[0103]

[0104] Among them, τ i (i=u,r) are the surge control output and the steering control output respectively.

[0105] Bringing the fault model and saturation model into the unmanned boat mathematical model yields:

[0106]

[0107] Among them, τ of is the actual control output under multiple constraints, and the actuator fault is represented by τ of =τ o -Fτ o , τ o is a saturated input.

[0108] The process of obtaining the planned path of the under-actuated unmanned vehicle using the non-uniform rational B-spline fast expansion random tree algorithm is as follows:

[0109] The fast expanding random tree algorithm is used to obtain waypoints, and a weighted screening strategy is further used;

[0110] Based on the non-uniform rational B-spline curve, the waypoints of the screened under-actuated unmanned vehicle are fitted to obtain the planned path of the under-actuated unmanned vehicle that can accurately pass through the waypoints.

[0111] Figure 2 Schematic diagram of the RRT algorithm;

[0112] As a random sampling method, the RRT algorithm generates multiple child nodes by random sampling in an unknown space, connects the root node with the child nodes, and finally forms a tree structure. When the child node includes the target node or the distance between the child node and the target node is less than the step size set by the algorithm, the child node and the target node will be connected to find the only path from the root node to the target point.

[0113] As shown in Table 1, is the environmental information containing obstacle boundary conditions, It is a collision judgment function, which determines whether the generated edge collides with obstacles in the environment to determine the retention of the corresponding nodes and edges.

[0114] Table 1

[0115]

[0116]

[0117] The RRT algorithm uses p start As the starting point for random tree expansion, first find a random sampling point p in the specified area rand Then select the root node p that is closest to the generated sampling point near , connect it with the random sampling point, and continue to intercept a line segment on the line with the specified step length as the starting point, then the end point of the line segment is the new child node p generated by the algorithm new After the generation, it is necessary to determine whether it collides with an obstacle. If it collides with an obstacle, the point is discarded and resampled; if it does not collide, it is used as a new root node and continues to expand. Repeat the above steps and finally reach the target point p goal , generating a unique path to the target point in the random tree.

[0118] However, the traditional RRT algorithm often generates too many nodes, most of which are redundant in actual navigation, which not only makes the path of the unmanned boat more tortuous, but also often increases the difficulty of control. Therefore, the RRT algorithm can be improved to increase the judgment of the necessity weight of the navigation nodes so as to screen out the truly effective waypoints p w .

[0119] Therefore, the generated nodes must be screened after the random tree generation is completed, such as Figure 3 : Construct a path segment between the judgment base point and the new next node, and determine whether the distance between the path segment and the obstacle is less than or equal to the specified value Ω, which is the condition for node collision detection;

[0120] The process of screening the waypoints of the under-actuated unmanned vehicle using the rapidly expanding random tree algorithm is as follows:

[0121] S1: p start As the starting point for random tree expansion, first find a random sampling point p in the specified area rand ,

[0122] S2: Select the root node p that is closest to the generated sampling point near , the root node p near Connected to the random sampling point, and continue to intercept a line segment on the line with the specified step length as the starting point, the end point of the line segment is the new child node p generated by the algorithm new ;

[0123] S3: Determine the new child node p new Whether the node collision detection is passed, if the new child node p new If the node obstacle detection fails, the point is discarded and resampled, and the process returns to S2;

[0124] If the new child node p new If the node obstacle is detected, it will be used as the new root node and continue to expand, and the new child node p new Add random trees;

[0125] S4: Determine the new child node p new Whether it passes the node weight test, when the new child node p new If the node weight test fails, S5 is performed to determine whether the new node reaches the target point's range;

[0126] When the new child node p new Through node weight detection, the new child node p ne x is added to the waypoint matrix P W, and update the weight detection starting point Ps, then S5 is performed to judge whether the new node reaches the range of the target point;

[0127] S5: When the new node does not reach the target point range, return to S2;

[0128] When the new node reaches the target point, it stops sampling and outputs the waypoint p new .

[0129] Specifically: Based on the completed tree structure T, from the starting point p start Start weight judgment and set it as the judgment base point p s (x s ,y s ), the tree node is p ti (x ti ,y ti )=P t (i),i=1,2,…,n,P t is the node matrix in the tree structure. Among the environmental obstacles, the circular obstacles satisfy p r (x r ,y r ), r r are the coordinates of the circle center and the obstacle radius respectively, are the vertices of the rectangular obstacle, represents a line segment between two points, Defined as a line segment vector, then for point To line segment The distance is expressed as:

[0130]

[0131] in is a vector In vector The minimum distance from the connecting line segment to the obstacle is expressed as:

[0132] d obs =min{d r ,d rec} (7)

[0133] Among them, d r =d r-sti -r r , d rec =min{d 12 ,d 23 ,d 34 ,d 41}, d 23 ,d 34 ,d 41 Same as d 12, and d 12 =min{d rec1-sti ,d rec2-sti ,d s-rec12 ,d ti-rec12}.

[0134] For line segment p s p ti Perform collision analysis. If a collision occurs, p s =P t (i-1); if no collision occurs, then determine line segment p s p ti The distance between the obstacle and the object, if d obs >Ω, it means the node weight is low and the node is discarded; if d obs ≤Ω, indicating that the node weight is high, then p s =p ti The final waypoint is P w ={p s1 ,p s2 ,…,p goal}

[0135] The process of fitting the waypoints of the screened under-actuated unmanned vehicle based on the non-uniform rational B-spline curve to obtain the planned path of the under-actuated unmanned vehicle is as follows:

[0136] S6: Calculate node vector;

[0137] S7: Calculate the boundary conditions of the underactuated unmanned vehicle;

[0138] S8: inverse calculation of control vertices;

[0139] S9: Calculate the parameter-containing fitting function;

[0140] S10: Determine whether the fitting curve passes the collision detection;

[0141] When the fitting curve fails the collision test, the tree node closest to the collision point is selected and added to the waypoint matrix p new , return to S6;

[0142] When the fitting curve passes the collision detection, the planned path of the under-actuated unmanned vehicle is obtained.

[0143] NURBS stands for Non-Uniform Rational B-Spline, and its mathematical definition is as follows:

[0144]

[0145] in, is a point on the curve, is the control point, wj are the weights associated with the control points, is the j-th k-order B-Spline basis function, m is the last control point number, which is determined by the node vector and satisfies the following conditions:

[0146]

[0147]

[0148] in, is a non-decreasing sequence of nodes, And define If the node vector is obtained using the cumulative chord length method and a cubic curve fit (i.e., k = 3), then:

[0149]

[0150] In order to achieve the curve fitting through the waypoint accurately, the curve control point can be inversely calculated based on the waypoint tangent condition and the start and end tangent vector conditions. The calculation formula is as follows:

[0151]

[0152] Among them, Θ is the weighted spline basis function matrix; d is the control point matrix; χ is the weighted reference point matrix, and the tangent vector condition is given as:

[0153]

[0154] And d=[d1,d2,…,d m+1 ] T ,χ=[g1,g2,…,g m+1 ] T ,

[0155] The matrix parameters are given as:

[0156]

[0157] Among them, d j For control vertices, g j To fit the tangent condition, a j ,b j ,c j are the non-zero terms in the basis function parameters.

[0158] The fitting effect is as follows Figure 4 The overall process of NRRT planning algorithm is as follows: Figure 5 As shown:

[0159] The finite-time observer is used to observe the lumped error of the maneuverability-constrained motion model system of the underactuated unmanned vehicle. The control law and the first-order auxiliary filter system are designed through the feedback linearization method to reduce the disturbance of the intermediate variables. The process of controlling the underactuated unmanned vehicle to follow the planned path is as follows:

[0160] The guidance law design process is as follows:

[0161] For fitting path The position of the point on the curve is affected by the time-varying parameter Control, so for a certain task, there is a completion time t final , so that the non-decreasing sequence The range is mapped from [0, 1] to the range [0, final ]. Then for the tracking curve Every moment has a unique point Consider the curve at point The tangent coordinate system at , the angle between its coordinate system and the earth coordinate system can be expressed as:

[0162]

[0163] in And the function atan2(y,x) represents the angle between the point with coordinate value (x,y) and its x-axis.

[0164] The actual position (x, y) of the unmanned boat and the reference position of the expected path The error between them can be expressed as:

[0165]

[0166] Among them, x e ,y e are the longitudinal error and lateral error in the path-tangent reference frame respectively. For the time derivative, we have:

[0167]

[0168] Among them, u vs is the total velocity of the virtual target ship moving along the curve, and the velocity magnitude is given as:

[0169]

[0170] Furthermore, the sideslip angle is defined as follows:

[0171]

[0172] The present invention is based on a line-of-sight guidance method consisting of a heading and a "virtual target" guidance law. The specific heading guidance law is as follows:

[0173]

[0174] Among them, φ p is the path tangent angle, is the expected heading speed of the USV, Δ is the foresight distance.

[0175] The virtual target guidance law is designed as follows:

[0176] u vs =k1x e +U d cos(ψ-φ p +β d )+u e cos(ψ-φ p ) (twenty one)

[0177] Among them, k1>0, u e =uu d .

[0178] Note that in fact, the actual heading angle of the USV can track the desired heading angle ψ with high accuracy. d , that is to say

[0179]

[0180] Theorem 2: For the error tracking system mentioned above, the designed guidance law can make the system error exponentially converge to zero.

[0181] Proof: Applying and to have:

[0182]

[0183] Consider the following Lyapunov function:

[0184]

[0185] The time derivative of the above formula is:

[0186]

[0187] in And v max ≥v≥v min >0.

[0188] The proof is complete.

[0189] Control law design

[0190] Design the following finite-time observer:

[0191]

[0192] in is the observed value of vector v, δ f is the lumped error, λ 1,2 >0,L>0,sig α (*)=sign(*)|*| α Theorem 1: Through the designed finite-time observer (20), the error of the observation value can be converged to zero in a finite time.

[0193] Proof: Define the following observation error:

[0194]

[0195] Find the time derivative of the above formula and substitute it into the formula:

[0196]

[0197] Applying Lemma 1, the observation error e i , (i=1,2) can converge to zero in a finite time, that is, there is a time Τ δ ,0<Τ δ <∞, so that

[0198] Furthermore, for the control input, the control dimensions are considered: Then accordingly: where r d It is a virtual control quantity and is designed as follows:

[0199]

[0200] where ψ e =ψ-ψ d ,r e =rr d .

[0201] Then, considering the fault and input saturation conditions, the control model can be simplified as:

[0202]

[0203] Introducing Satisfaction The first-order auxiliary system of , and the system error is defined as:

[0204]

[0205] The time derivative of the above formula is:

[0206]

[0207] In order to avoid complex calculations, a first-order filtering system is introduced:

[0208]

[0209] Among them df yes The filtered value, where the filtering error can be expressed as;

[0210]

[0211] Its differential form is expressed as:

[0212]

[0213] Then the closed-loop system controller can be designed as:

[0214]

[0215] in

[0216] Theorem 3: The designed control law can make the closed-loop system uniformly eventually bounded and stable, and its system error converges to a small neighborhood around zero.

[0217] prove:

[0218] Consider the following Lyapunov function:

[0219]

[0220] The time derivative is calculated and the application formula is:

[0221]

[0222] Then, the following Lyapunov function is constructed:

[0223]

[0224] The differential form is:

[0225]

[0226] According to Young's inequality, scaling it up will yield:

[0227]

[0228] in,

[0229]

[0230] Since the designed finite time observer can make the error be observed in a finite time, that is, t>Τ δ hour, σ is bounded, and the parameters are selected so that It can be rewritten as:

[0231]

[0232] in

[0233] The proof is complete.

[0234] Figure 6 This is a schematic diagram of path tracking;

[0235] A navigation control method for an underactuated unmanned vessel based on smooth path guidance comprises the following steps:

[0236] A motion model of an underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties is constructed. Combined with the maneuverability-constrained model of actuator gain impairment and input saturation, a maneuverability-constrained motion model of an underactuated unmanned vehicle is obtained.

[0237] The planned path of the under-actuated unmanned vehicle is obtained by using a fast-expanding random tree algorithm based on non-uniform rational B-splines.

[0238] A finite-time observer is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle. The control law is designed through the feedback linearization method, and the first-order auxiliary filter system is used to filter out high-frequency interference, so that the under-actuated unmanned vehicle can be controlled to move along the planned path.

[0239] Example 1:

[0240] First, the parameters of the USV model are given as follows: m11 = 50.05 kg, m22 = 84.36 kg, m33 = 17.21 kg, d11 = 151.57 kg / s, d22 = 132.5 kg / s, d33 = 34.56 kg / s. The environmental obstacle settings are shown in Table 2.

[0241] Table 2

[0242]

[0243]

[0244] The mixing error is given by: The input saturation model parameter is given as τ imax =115,τ imin =-60, the expected speed is given as u d=0.8+0.03sin(0.1t). The waypoint weight judgment standard is given as: Ω=1, and the control point weight is given as: w i =1, i = 0, 1, ..., n. The target points are given as: P1 = (2, 2), P2 = (39, 6), P3 = (22, 40), P4 = (5, 22), and the tangent vector conditions are given as: p0′ = (1, 0), p n ′=(-1,-1). The observer parameters are set to: L=1200, λ1=diag(0.1,0.1), λ2=diag(0.001,0.001). The forward distance Δ=2m, and the controller coefficients are set to: k1=2, k2=0.8, Λ=diag(75,50), Λ1=diag(0.1,0.1), G=diag(1,1),

[0245] In the simulation results: the NRRT-FTC strategy is the control framework proposed in this invention; RRT-N-FTC is a fault-tolerant control strategy that uses NURBS for fitting but does not filter waypoints; NRRT-SMC is a sliding mode control strategy that uses an improved RRT algorithm; and RRT-FTC is a traditional RRT algorithm combined with fault-tolerant control.

[0246] Comparison of paths planned using the NRRT algorithm and traditional path planning: Figure 7 、 Figure 8 Obviously, the NRRT planning algorithm can obtain a smoother and more controllable curve. Compared with the original planning algorithm, it removes redundant points and obtains truly effective waypoints. Figure 8 In the figure, RRT-N is the curve fitted by the traditional RRT method of selecting path points combined with NURBS inverse calculation technology, and RRT is the curve fitted by the traditional RRT method of selecting path points combined with B-spline fitting. The figure does not include the curve of RRT combined with B-spline fitting based on screening waypoints. This is because from the comparison between NURBS inverse curve fitting and traditional B-spline fitting in the previous article, it can be seen that when the path points become sparse, the NURBS inverse curve fitting will strictly pass through the waypoints, while the curve fitted by B-spline is very likely to fit the path in a certain area among the waypoints, which will cause the fitted curve to fail to effectively use the importance weights of the waypoints, resulting in the fitted path passing through obstacles, thereby generating an unusable path.

[0247] Based on the above premise, we can find that when the path points are dense, the curve generated by the RRT-N method is more tortuous than the curve generated by the RRT method because the NURBS inverse fitting needs to pass through each path point accurately; the NRRT method, by screening and then fitting all path points, produces a curve that is much smoother than the curves generated by the RRT and RRT-N methods, and its practicality and controllability will also be higher.

[0248] Figure 9 The path tracking control effect diagram is shown in Figure 1. (a) is the tracking effect diagram under no-disturbance conditions, and (b) is the tracking effect diagram under disturbance conditions.

[0249] exist Figure 9 The reference path, shown as a solid black line, is the fitting curve obtained by planning the paths of the aforementioned multiple target points using the NRRT path planning algorithm, achieving the transformation from waypoint control targets to parameterized curves. Furthermore, the green line represents the model predictive control curve, and the blue line represents the fault-tolerant control curve. Overall, the control effects of both lines effectively track the reference path, demonstrating the effective integration of guidance control and path planning. The parameterized path of path planning can meet the corresponding path tracking requirements. Furthermore, the blue line can more accurately track the reference path under fault-tolerant conditions, thereby achieving precise tracking of waypoints.

[0250] Figure 10 Comparison diagram of speed tracking control effect; (a) is the speed tracking effect under no-disturbance condition, (b) is the speed tracking effect under disturbance condition;

[0251] exist Figure 10 In the figure, it can be seen from the speed tracking curve that the NRRT-FTC control scheme can track the desired speed well regardless of whether there is a disturbance or not. The difference is that when switching between states at 15s and 75s, the speed tracking curve in the case of disturbance has a larger overshoot and takes longer to settle. In the case of system failure, the NRRT-SMC control scheme, without a finite-time observer and a fault-tolerant control scheme, can be clearly seen to be unable to track the desired speed curve. During this period, due to the presence of disturbances, the fluctuation of its curve in the case of disturbances is greater than that in the case of no disturbances. For the RRT-N-FTC control scheme and the RRT-FTC control scheme, it can be seen that their speed tracking effects are very poor. Among them, the RRT-N-FTC control scheme has the worst tracking effect, which is manifested as violent oscillation and fluctuation. Considering the influence of the reference path smoothness on control mentioned above and the higher volatility of the RRT-N fitting curve than the RRT fitting curve, the poor tracking effect here is mainly due to the inappropriate reference path.

[0252] Figure 11 Comparison diagram of position tracking error; (a) shows the speed tracking effect under no-disturbance conditions, and (b) shows the speed tracking effect under disturbance conditions;

[0253] Position error such as Figure 11As shown in the figure, although there are still several large fluctuations in tracking, it is obvious that the control error of the NRRT-FTC control scheme is better than the other three control schemes in terms of both lateral error and longitudinal error accuracy. Its error range fluctuates within 0.5m as a whole. The control errors of the two unscreened control schemes are much larger than the control error of the NRRT-FTC control scheme, and the NRRT-SMC control scheme also produces a large tracking error when the system fails. The control effect of the NRRT-FTC control scheme can also be seen through Figure 12 The contrast of the movement state is reflected.

[0254] Figure 12 Comparison diagram of motion state errors; (a) is the comparison diagram of sway velocity control error, (b) is the comparison diagram of sway velocity control error; (c) is the comparison diagram of yaw velocity control error, and (d) is the comparison diagram of heading angle control error;

[0255] Figure 13 Comparison diagram of under-actuated control torque output; (a) is the undisturbed sway control output, (b) is the undisturbed sway control output, (c) is the undisturbed yaw control output, and (d) is the yaw control output with disturbance.

[0256] also, Figure 13 is the system control input, where the steering torque and forward torque are both limited to [-55,115]. The solid line is the control output, and the dotted line is the control output after first-order filtering. It can be seen that due to the tortuosity of the tracking route, the RRT-N-FTC control scheme and the RRT-FTC control scheme show high control output and high control change rate in the entire control process, which is reflected in the violent jitter of the control torque and the full-state output caused by the failure to meet the corresponding control effect; in the NRRT-FTC control scheme and the NRRT-SMC control scheme, the change rate of the control output will be correspondingly smaller.

[0257] Focusing on the performance of the NRRT-FTC control scheme and the NRRT-SMC control scheme during system failures, it can be seen that when a failure occurs, the NRRT-FTC control scheme will actively increase the control input to compensate for the discounted control input caused by the actuator failure, thereby making its corresponding control accuracy higher. It is also noted that in the presence of disturbances, its filtered control input is closer to the actual control input, which is manifested as: the corresponding line is thinner and the noise is less. The reason is that the disturbance-based observer can provide more observation compensation at this time, so that it can fit the actual control output more accurately.

[0258] Figure 14The comparison of time parameter changes reflects the changes in overall control efficiency. Among them, the NRRT-FTC control scheme has the fastest change rate and completes the task first, reflecting the effectiveness of the NRRT-FTC control system in terms of time efficiency.

[0259] As shown in Table 3, by measuring efficiency by time, the control efficiency increased by 14.58%; the overall operating efficiency of the system increased by 40.5%; in terms of curve fitting, both NRRT-FTC and RRT-N-FTC have smaller fitting errors and control errors than RRT-FTC. The fitting accuracy under comprehensive disturbance conditions increased by 45.53% and 51.09%, respectively, and the control errors increased by 30.40% and 75.28%, respectively. The control effect diagram and the corresponding state diagram and error diagram all demonstrate that the NRRT-FTC, RRT-N-FTC, and RRT-FTC control strategies can achieve adaptive resistance to environmental disturbances and effectively handle actuator failures and input saturation. In addition, NRRT-FTC can achieve lower control errors and faster convergence speeds compared to the latter two. The experimental results verify the effectiveness of the NRRT-FTC control system designed by the present invention.

[0260] Table 3

[0261]

[0262] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

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Claims

1. A navigation control system for an underactuated unmanned vessel based on smooth path guidance, characterized by: The following steps are involved: Construction module: used to construct the motion model of the underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties. Combined with the maneuverability-constrained model of the actuator gain damage and input saturation, the maneuverability-constrained motion model of the underactuated unmanned vehicle is obtained. Planning module: used to obtain the planned path of the under-actuated unmanned vehicle using a fast-expanding random tree algorithm based on non-uniform rational B-splines; Control module: It is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle using a finite-time observer, and to design the control law and the first-order auxiliary filter system through the feedback linearization method to filter out high-frequency interference, so as to realize the control of the under-actuated unmanned vehicle to travel according to the planned path.

2. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 1, characterized in that: The process of obtaining the planned path of the under-actuated unmanned vehicle using the non-uniform rational B-spline fast expansion random tree algorithm is as follows: The fast expanding random tree algorithm is used to obtain the waypoints, and then the weighted screening strategy is used to screen the waypoints of the under-actuated unmanned vehicle. Based on the non-uniform rational B-spline curve, the waypoints of the screened under-actuated unmanned vehicle are fitted to obtain the driving planning path of the under-actuated unmanned vehicle that can accurately pass through the waypoints.

3. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 2, characterized in that: The process of using the rapidly expanding random tree algorithm and then using the weighted screening strategy to screen the waypoints of the under-actuated unmanned vehicle is as follows: S1: p start As the starting point for random tree expansion, first find a random sampling point p in the specified area rand , S2: Select the root node p that is closest to the generated sampling point near , the root node p near Connected to the random sampling point, and continue to intercept a line segment on the line with the specified step length as the starting point, the end point of the line segment is the new child node p generated by the algorithm new ; S3: Determine the new child node p new Whether the node collision detection is passed, if the new child node p new If the node obstacle detection fails, the point is discarded and resampled, and the process returns to S2; If the new child node p new If the node obstacle is detected, it will be used as the new root node and continue to expand, and the new child node p new Add random trees; S4: Determine the new child node P new Whether it passes the node weight test, when the new child node P new If the node weight test fails, S5 is performed to determine whether the new node reaches the target point's range; When the new child node p new Through node weight detection, the new child node p new Add waypoint matrix P W , and update the weight detection starting point Ps, then S5 is performed to judge whether the new node reaches the range of the target point; S5: When the new node does not reach the target point range, return to S2; When the new node reaches the target point, it stops sampling and outputs the waypoint p new .

4. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 2, characterized in that: The process of fitting the waypoints of the screened under-actuated unmanned vehicle based on the non-uniform rational B-spline curve to obtain the planned path of the under-actuated unmanned vehicle is as follows: S6: Calculate node vector; S7: Calculate the boundary conditions of the underactuated unmanned vehicle; S8: inverse calculation of control vertices; S9: Calculate the parameter-containing fitting function; S10: Determine whether the fitting curve passes the collision detection; When the fitting curve fails the collision test, the tree node closest to the collision point is selected and added to the waypoint matrix p new , return to S6; When the fitting curve passes the collision detection, the planned path of the under-actuated unmanned vehicle is obtained.

5. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 2, characterized in that: The conditions for node obstacle detection are: constructing a path segment between a judgment base point and a new next node, and judging whether the distance between the path segment and the obstacle is less than or equal to a specified value Ω.

6. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 2, characterized in that: The detection process of the node weight is as follows: Based on the completed tree structure From the starting point p start Start weight judgment and set it as the judgment base point p s (x s ,y s ), the tree node is p ti (x ti ,y ti )=P t (i),i=1,2,…,n,P t is the node matrix in the tree structure. Among the environmental obstacles, the circular obstacles satisfy p r (x r ,y r ), r r are the coordinates of the circle center and the obstacle radius respectively, are the vertices of the rectangular obstacle, represents a line segment between two points, Defined as a line segment vector, then for point To line segment The distance is expressed as: in: is a vector In vector The minimum distance from the connecting line segment to the obstacle is expressed as: the obs =min{d r ,d rec } (7) where, d r = d r-sti - r r , d rec = min{d 12 , d 23 , d 34 , d 41}, d 23 , d 34 , d 41 is the same as d 12 , and d 12 = min{d rec1-sti , d rec2-sti , d s-rec12 , d ti-rec12}; For line segment p s p ti Perform collision analysis. If a collision occurs, p s =P t (i-1); if no collision occurs, then determine line segment p s p ti The distance between the obstacle and the object, if d obs >Ω, it means the node weight is low and the node is discarded; if d obs ≤Ω, indicating that the node weight is high, then p s =p ti , then the final waypoint is P w ={p s1 ,p s2 ,…,p goal }.

7. The underactuated unmanned vessel navigation control system based on smooth path guidance according to claim 2, characterized in that: The definition of the non-uniform rational B-spline curve is as follows: in, is a point on the curve, is the control point, w j are the weights associated with the control points, is the j-th k-order B-Spline basis function, m is the last control point number, which is determined by the node vector and satisfies the following conditions: in, is a non-decreasing sequence of nodes, And define If the node vector is obtained using the cumulative chord length method and cubic curve fitting is adopted, we have: Based on the waypoint tangent conditions and supplemented with the start and end tangent vector conditions, the curve control points are calculated inversely. The calculation formula is as follows: Θd=χ (12) Among them, Θ is the weighted spline basis function matrix; d is the control point matrix; χ is the weighted reference point matrix, and the tangent vector condition is given as: And d=[d1,d2,…,d m+1 ] T ,χ=[g1,g2,…,g m+1 ] T , The matrix parameters are given as: Among them, d j For control vertices, g j To fit the tangent condition, a j ,b j ,c j are the non-zero terms in the basis function parameters.

8. A navigation control method for an underactuated unmanned vessel based on smooth path guidance, characterized by: The following steps are involved: A motion model of an underactuated unmanned vehicle under uncertain environmental disturbances and system uncertainties is constructed. Combined with the maneuverability-constrained model of actuator gain impairment and input saturation, a maneuverability-constrained motion model of an underactuated unmanned vehicle is obtained. The planned path of the under-actuated unmanned vehicle is obtained by using a fast-expanding random tree algorithm based on non-uniform rational B-splines. A finite-time observer is used to observe the lumped error of the maneuverability-constrained motion model system of the under-actuated unmanned vehicle. The control law is designed through the feedback linearization method, and the first-order auxiliary filter system is used to filter out high-frequency interference, so that the under-actuated unmanned vehicle can be controlled to move along the planned path.

Images