Unmanned ship path planning method based on self-triggering model predictive control

Abstract

The invention relates to the technical field of unmanned ship path planning, in particular to an unmanned ship path planning method based on self-triggering model predictive control, a mathematical model of unmanned ship motion is established, a predictive model is obtained through forward Euler method discretization, and a system dynamic equation containing input, output and state variables is defined. And by introducing an event self-triggering mechanism, system calculation and communication resources are saved. An objective function containing a self-triggering control law and constraint conditions are defined and expressed as an optimization problem with constraints. And by solving the optimization problem, the unmanned surface vehicle performs feedback correction at the event self-triggering moment, and finally, path planning of the unmanned surface vehicle is realized. According to the method provided by the invention, the precision of unmanned ship path planning can be effectively improved, and system calculation and communication resources are saved.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned boat path planning, and in particular to an unmanned boat path planning method based on self-triggering model predictive control. Background Art

[0002] The path planning technology of unmanned boats has shown wide application value in many fields such as seabed mapping, environmental monitoring, hydrological measurement, maritime search and rescue, and port surveillance. The path planning technology of unmanned boats integrates real-time sensor information and environmental data to ensure that unmanned boats can flexibly avoid obstacles in complex and changing dynamic environments, thereby improving the safe and autonomous navigation capabilities of unmanned boats.

[0003] For the path planning problem of unmanned boats, traditional methods mainly include grid-based methods, artificial potential fields, and heuristic search. Among them, the grid method discretizes the workspace for path search, which is easily affected by the density of the grid. The artificial potential field method guides the unmanned boat to avoid obstacles by constructing virtual gravitational and repulsive fields, but it is easy to fall into the local minimum. The heuristic search algorithm has poor adaptability in dynamic environments. Summary of the invention

[0004] In view of this, the purpose of the present invention is to propose an unmanned boat path planning method based on self-triggered model predictive control to solve the problem that traditional methods are easily affected by grid density and trapped in local minima.

[0005] Based on the above purpose, the present invention provides a path planning method for an unmanned boat based on self-triggered model predictive control, comprising the following steps:

[0006] S1. Establish a mathematical model of the unmanned boat movement;

[0007] S2. Based on the mathematical model of the unmanned boat motion, the prediction model is discretized by the forward Euler method to define the system dynamic equations containing input, output and state variables;

[0008] S3. Introduce the event self-triggering mechanism, define the objective function and constraints containing the self-triggering control law, and express it as a constrained optimization problem;

[0009] S4. By solving the optimization problem, the unmanned boat performs feedback correction at the moment of event self-triggering to achieve path planning for the unmanned boat.

[0010] Preferably, based on the mathematical model of the unmanned boat motion, the prediction model obtained by discretization through the forward Euler method includes:

[0011] The forward Euler method is used to discretize the mathematical model, and the first-order Taylor expansion is used to express it as a differential equation that can approximately solve the motion of the unmanned boat.

[0012] Preferably, the system dynamic equation is based on a discretized mathematical model of the unmanned boat motion, including the state variable ξ and control input u of the unmanned boat motion, expressed as ξ(k+1)=Aξ(k)+Bu(k), wherein ξ(k+1) is the state of the next time step, ξ(k) and u(k) are the state and control input of the current time step, respectively, and A and B are weight matrices.

[0013] Preferably, the self-triggering control law is u(t)=μ(t k ), the self-triggering condition is composed of the control signal interval between two consecutive triggering moments and the change rate of the control signal interval. When the control input u(t) changes at a uniform speed or remains unchanged, the change rate remains unchanged, the trigger interval becomes longer. On the contrary, if the control input u(t) changes rapidly, the rate of change As the value increases, the trigger interval will become shorter.

[0014] Preferably, the objective function J containing the self-triggering control law includes the deviation ρ between the current position of the unmanned boat and the reference path k and the obstacle avoidance constraint function ρ obs , taking into account the length of the minimized path, physical constraints and environmental constraints.

[0015] Preferably, the constraints include the lower limits w of the longitudinal speed, lateral speed and bow angular velocity of the unmanned boat. min 、v min 、r min , and the upper limits of the longitudinal speed, lateral speed and bow angular velocity of the unmanned boat w max 、v max 、r max .

[0016] Preferably, the feedback correction includes: in each time step, the optimal control input sequence is obtained by solving, and when the event self-triggering condition is met, the unmanned boat performs prediction, optimization, and feedback.

[0017] Beneficial effects of the present invention:

[0018] (1) High accuracy of path planning: The method proposed in the present invention combines the high efficiency of the self-triggering mechanism and the accuracy of model predictive control. It copes with various uncertain factors in complex sea areas through strict constraints and real-time feedback correction, and achieves high accuracy and low error in path planning.

[0019] (2) Save communication and computing resources: While ensuring the normal operation of the system, the number and frequency of system sampling are reduced, the efficiency of the controller is improved, and computing and communication resources are saved.

[0020] (3) Good reliability: Through real-time monitoring and feedback control, deviations and errors in path planning can be discovered and corrected in a timely manner, ensuring that the unmanned boat can navigate safely and accurately according to the predetermined target. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0022] Figure 1 A schematic diagram of a mathematical model of the motion of an unmanned boat according to an embodiment of the present invention;

[0023] Figure 2 The present invention is a flowchart of the path planning method for an unmanned boat according to an embodiment of the present invention. DETAILED DESCRIPTION

[0024] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0025] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0026] S1. In order to accurately capture the motion characteristics of the unmanned boat, optimize its navigation performance, and improve the accuracy and stability of control, the dynamics and kinematics systems of the unmanned boat were modeled. Figure 1 As shown in the figure, the mathematical model of unmanned boat motion is established as:

[0027]

[0028] in, are the first-order differentials of the longitudinal velocity, lateral velocity and bow angular velocity of the unmanned boat, m v、m w 、m r are the mass inertia in the longitudinal velocity direction, the transverse velocity direction and the bow angular velocity direction, respectively, K w , K |w|w , K v , K |v|v , K r , K |r|r are the hydrodynamic damping coefficients, τ w , τ v , τ r are the thrust or torque in the longitudinal velocity direction, transverse velocity direction and bow angular velocity direction respectively; |w|, |v|, |r| are the absolute values ​​of the longitudinal velocity, transverse velocity and bow angular velocity of the unmanned boat.

[0029] S2. In model predictive control, a prediction model needs to be established. The prediction model can predict the motion state and possible obstacles in the future based on the historical motion information of the unmanned boat (such as position, speed, direction, etc.) and environmental data. The prediction model is based on the mathematical model of the unmanned boat motion. Through the forward Euler method, the time and function derivatives are discretized, and the first-order Taylor expansion is used to approximate the differential equation of the unmanned boat motion. Specifically,

[0030]

[0031] Among them, w k+1 、v k+1 、r k+1 are the longitudinal velocity, lateral velocity and bow angular velocity of the unmanned boat in the next time step, w k 、v k 、r k are the longitudinal velocity, lateral velocity and bow angular velocity of the unmanned boat at the current time step, Δt is the discrete time step, τ wk , τ vk , τ rk They are respectively the thrust or torque in the longitudinal velocity direction, lateral velocity direction and bow angular velocity direction of the unmanned boat at the current time step.

[0032] In order to accurately describe the relationship between the control input and output of the unmanned boat, adapt to the real-time changes of the local environment, and ensure that the model can accurately predict the future state of the unmanned boat, the path planning and control strategy can be optimized to achieve safe and efficient navigation. According to the discretized mathematical model of the unmanned boat motion, the state variable of the unmanned boat is defined as The control input is u=[τ w ,τ v ,τ r ] Τ , the dynamic equation of the system is defined as

[0033] ξ(k+1)=Aξ(k)+Bu(k)

[0034] Among them, ξ(k+1) is the state of the next time step, ξ(k) and u(k) are the state and control input of the current time step respectively, and A and B are weight matrices.

[0035] S3. Aiming at the problem of large computational complexity of traditional model predictive controller, an event self-triggering mechanism is introduced, and the performance index function and constraint conditions containing the self-triggering control law are defined, and it is expressed as a constrained optimization problem.

[0036] Traditional model predictive controllers need to solve a large number of complex optimization problems. By introducing the event self-triggering mechanism, the number and frequency of system sampling can be reduced while ensuring the normal operation of the system, thereby improving the control efficiency of the controller and saving system computing and communication resources. The event self-triggering control law is designed as

[0037]

[0038] Among them, t k is the current triggering moment, t k+1 is the next trigger moment, ε>0, σ>0 are positive design parameters. |u(t)| is the absolute value of the control input, Indicates the control signal interval between two consecutive trigger moments. is the absolute value of the derivative of the self-triggered control law, It means taking parameters σ and The maximum value of σ and is the rate of change of the control signal interval. When the control input u(t) changes at a constant speed or remains unchanged, the rate of change is a constant, the trigger interval will become longer and longer. On the contrary, if the control input u(t) changes rapidly, the rate of change As the value increases, the trigger interval will become shorter.

[0039] Set the objective function of path planning to minimize the length of the path while taking into account physical and environmental constraints. The objective function with the self-triggered control law can be expressed as

[0040]

[0041] Among them, N p is the length of the prediction time domain, R and Q are weight coefficients that control the relative importance of each target, and ρ k is the deviation between the current position of the unmanned boat and the reference path, indicating the shortest path, ρ obs Represents the obstacle avoidance constraint function of the unmanned boat, which is used to avoid obstacles. δ is a positive value close to 0.

[0042] Through the above design, model predictive control can balance multiple objectives and generate an optimal path, so that the unmanned boat can avoid obstacles while shortening the path and reducing energy consumption as much as possible. In order to ensure the smooth and safe navigation of the unmanned boat, the constraints are set as follows:

[0043]

[0044] Among them, w min 、v min 、r min They represent the lower limits of the longitudinal velocity, lateral velocity and bow angular velocity of the unmanned boat, respectively, and w max 、v max 、r max They respectively represent the upper limits of the longitudinal speed, lateral speed and bow angular velocity of the unmanned boat.

[0045] In each time step, the model predictive control determines the optimal control input of the unmanned boat by solving an optimization problem. The optimization problem is usually a constrained quadratic programming problem, the goal is to minimize the cost function of the predicted path while satisfying all constraints. The constrained optimization problem is expressed as

[0046]

[0047] Constraints:

[0048] S4. Feedback correction: In each time step, the optimal control input sequence is obtained by solving the above optimization problem. When the event self-triggering condition is met, the unmanned boat gets the first control input The controller state is updated and enters the next control time step. Prediction, optimization, and feedback are repeated to finally achieve path planning for the unmanned boat.

[0049] Through the above specific implementation methods, the unmanned boat path planning method proposed in the present invention can adapt to complex sea environments.

[0050] Those skilled in the art should understand that the discussion of any of the above embodiments is only exemplary and is not intended to imply that the scope of the present invention is limited to these examples; under the concept of the present invention, the technical features in the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other changes in different aspects of the present invention as described above, which are not provided in detail for the sake of simplicity. Any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A path planning method for an unmanned boat based on self-triggered model predictive control, characterized in that: The following steps are involved: S1. Establish a mathematical model of the unmanned boat movement; S2. Based on the mathematical model of the unmanned boat motion, the prediction model is discretized by the forward Euler method to define the system dynamic equations containing input, output and state variables; S3. Introduce the event self-triggering mechanism, define the objective function and constraints containing the self-triggering control law, and express it as a constrained optimization problem; S4. By solving the optimization problem, the unmanned boat performs feedback correction at the moment of event self-triggering to achieve path planning for the unmanned boat.

2. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1 is characterized in that: The mathematical model based on the motion of the unmanned boat is discretized by the forward Euler method to obtain the prediction model, which includes: The forward Euler method is used to discretize the mathematical model, and the first-order Taylor expansion is used to express it as a differential equation that can approximately solve the motion of the unmanned boat.

3. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1, characterized in that: The system dynamic equation is based on the discretized mathematical model of the unmanned boat motion, including the state variable ξ and control input u of the unmanned boat motion, expressed as ξ(k+1)=Aξ(k)+Bu(k), where ξ(k+1) is the state of the next time step, ξ(k) and u(k) are the state and control input of the current time step, respectively, and A and B are weight matrices.

4. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1, characterized in that: The self-triggering control law is u(t)=μ(t k ), the self-triggering condition is composed of the control signal interval between two consecutive triggering moments and the change rate of the control signal interval. When the control input u(t) changes at a uniform speed or remains unchanged, the change rate remains unchanged, the trigger interval becomes longer. On the contrary, if the control input u(t) changes rapidly, the rate of change As the value increases, the trigger interval will become shorter.

5. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1, characterized in that: The objective function J with the self-triggering control law includes the deviation ρ between the current position of the unmanned boat and the reference path k and the obstacle avoidance constraint function ρ obs , taking into account the length of the minimized path, physical constraints and environmental constraints.

6. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1, characterized in that: The constraints include the lower limit w of the longitudinal speed, lateral speed and bow angular velocity of the unmanned boat. min 、v min 、r min , and the upper limits of the longitudinal speed, lateral speed and bow angular velocity of the unmanned boat w max 、v max 、r max .

7. The unmanned boat path planning method based on self-triggered model predictive control according to claim 1, characterized in that: The feedback correction includes: in each time step, the optimal control input sequence is obtained by solving, and when the event self-triggering condition is met, the unmanned boat performs prediction, optimization and feedback.

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