CN117647979A - MPC self-adaptive path tracking control method based on improved cuckoo algorithm - Google Patents
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Abstract
The invention discloses an MPC self-adaptive path tracking control method based on an improved cuckoo algorithm, which constructs a vehicle system state equation according to a vehicle dynamics model; constructing an objective function to solve the state equation of the vehicle system, introducing external disturbance vectors measured and not measured by the vehicle system into the state equation of the vehicle system to design an adaptive MPC path tracking controller, and updating the state equation of the vehicle system according to the change of the parameters of the vehicle system; introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function; constructing a constraint condition to constrain the steering angle and the steering angle increment of the front wheels; improving a cuckoo algorithm; and carrying out global search learning by adopting an improved cuckoo algorithm to solve the vehicle state under the optimal weight under the dynamic parameters. The method solves the parameter uncertainty caused by communication or system response delay, and improves the algorithm control precision; the problem that the local optimum state is easily trapped is solved.
Description
Technical Field
The invention relates to the technical field of automatic driving, in particular to an MPC self-adaptive path tracking control method and system based on an improved cuckoo algorithm.
Background
In recent years, with the increasing attention of people on automatic driving and traffic safety, research on high-level automatic driving technology is gradually deepened by related enterprises at home and abroad and school of science, and the automatic driving technology is rapidly developed, but due to various reasons, a high-level automatic driving distance still has a certain distance to land. The reliable algorithm is a premise and a foundation for realizing high-level automatic driving of the vehicle, the path tracking control is used as the last ring in an automatic driving vehicle system, the improvement of tracking precision and stability in the driving process is of great significance to the improvement of the technical level of an automatic driving vehicle by researching the vehicle tracking algorithm, and the path tracking control is used as a key technology of automatic driving and gradually becomes a hot point of research of domestic and foreign students.
Current research provides a rich research algorithm and strategy. Researches provide rich path tracking control strategies, but with the change of environment and the state of the vehicle, a control algorithm with good performance faces the problem of reduced tracking precision under some severe conditions, for example, when the vehicle runs at a medium-high speed, the vehicle deviates from a preset running path due to inertia, so that the tracking precision cannot meet the requirement. This situation greatly limits the technological progress of automatic driving automobiles. Mainly because control methods with fixed parameters cannot adapt to the time-varying nature of the driving environment. Secondly, the self-adaptive path tracking control dynamically self-adaptively selects the front wheel turning angle, the transverse displacement error and the weighting coefficient between the centroid slip angles, the transverse deviation is adapted in the road curvature change process, the error reduction, the system establishment time and the overshoot are main challenges of intelligent vehicle steering angle control, and the main challenges of the current optimization controller are to optimize on the local optimization problem.
Disclosure of Invention
Aiming at the defects in the prior art, the MPC self-adaptive path tracking control method and system based on the improved cuckoo algorithm provided by the invention solve the parameter uncertainty caused by communication or system response delay, and enhance global and local searching capability by improving the cuckoo algorithm with dynamic compensation control quantity and discovery probability, thereby solving the problem that the system is easy to fall into a local optimal state.
In a first aspect, the present invention provides an MPC adaptive path tracking control method based on an improved cuckoo algorithm, including:
constructing a vehicle system state equation according to the vehicle dynamics model;
constructing an objective function of a path tracking algorithm based on MPC (MPC), solving an optimal solution for a vehicle system state equation, wherein a first term of the objective function is used for expressing and solving the deviation between the output transverse displacement of the vehicle system and the reference transverse displacement, the deviation between the centroid slip angle and the reference slip angle, a second term of the objective function is used for restraining the control increment, and a third term of the objective function is a relaxation factor;
introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design an adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters;
introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function;
constructing a constraint condition to constrain the steering angle and the steering angle increment of the front wheels;
adding a dynamic compensation control quantity and a dynamic discovery probability to the cuckoo algorithm to obtain an improved cuckoo algorithm;
and (3) performing global search learning by adopting an improved cuckoo algorithm, and determining the vehicle state of the MPC under the optimal weight of the lateral displacement, the slip angle and the increment of the steering angle of the front wheels.
In a second aspect, the present invention provides an MPC adaptive path tracking control system based on an improved cuckoo algorithm, comprising: a first building module, a second building module, an MPC controller module, a system cost function building module, a constraint module, an algorithm improvement module and a weight determination module,
the first construction module is used for constructing a vehicle system state equation according to a vehicle dynamics model;
the second construction module is used for constructing an objective function of a path tracking algorithm based on MPC to solve an optimal solution for a vehicle system state equation, a first term of the objective function is used for expressing and solving deviation between the output transverse displacement of the vehicle system and a reference transverse displacement deviation and deviation between a centroid slip angle and a reference slip angle, a second term of the objective function is used for restraining a control increment, and a third term of the objective function is a relaxation factor;
the MPC controller module is used for introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design a self-adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters;
the system cost function construction module is used for introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function;
the constraint module is used for constructing constraint conditions to constrain the steering angle and the steering angle increment of the front wheels;
the algorithm improvement module is used for adding a cuckoo algorithm with improved dynamic compensation control quantity and dynamic discovery probability into the cuckoo algorithm;
the weight determining module is used for carrying out global search learning by adopting an improved cuckoo algorithm and determining the vehicle state of the MPC under the optimal weight of the transverse displacement, the slip angle and the front wheel steering angle increment.
The invention has the beneficial effects that:
the MPC self-adaptive path tracking control method based on the improved cuckoo algorithm provided by the embodiment of the invention comprises the steps of firstly, designing a self-adaptive MPC path tracking controller by introducing external interference vectors measured and not measured by a system, updating parameters according to the change of the system, and solving parameter uncertainty caused by communication or system response delay;
secondly, simultaneously constructing a multi-objective cost function comprising a front wheel corner, a transverse displacement error and a centroid slip angle, and improving algorithm control precision;
finally, the MPC is self-adaptively solved with the optimal vehicle state under the dynamic parameter weight based on the improved cuckoo algorithm, global and local searching capacity is enhanced based on the dynamic compensation control quantity and the improved cuckoo algorithm of the discovery probability, and the implicit mapping relation between the input and output data is extracted by optimizing the connection weight and the threshold value so as to adapt to the complex road environment, and the problem that the MPC is easy to fall into the local optimal state is solved.
The invention provides an MPC self-adaptive path tracking control system based on an improved cuckoo algorithm, which has the same beneficial effects as an MPC self-adaptive path tracking control method based on the improved cuckoo algorithm based on the same inventive concept.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. Like elements or portions are generally identified by like reference numerals throughout the several figures. In the drawings, elements or portions thereof are not necessarily drawn to scale.
FIG. 1 is a flow chart of an MPC adaptive path tracking control method based on an improved cuckoo algorithm according to a first embodiment of the present invention;
FIG. 2 shows a schematic diagram of a four-degree-of-freedom vehicle model in a first embodiment of the invention;
FIG. 3 is a block diagram of an MPC adaptive path tracking control system based on an improved cuckoo algorithm according to another embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the terms "comprises" and "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
As used in this specification and the appended claims, the term "if" may be interpreted as "when..once" or "in response to a determination" or "in response to detection" depending on the context. Similarly, the phrase "if a determination" or "if a [ described condition or event ] is detected" may be interpreted in the context of meaning "upon determination" or "in response to determination" or "upon detection of a [ described condition or event ]" or "in response to detection of a [ described condition or event ]".
It is noted that unless otherwise indicated, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.
Referring to fig. 1, a flowchart of an MPC (model predictive control) adaptive path tracking control method based on an improved cuckoo algorithm according to a first embodiment of the invention is shown, which includes the following steps:
constructing a vehicle system state equation according to the vehicle dynamics model;
constructing an objective function of a path tracking algorithm based on MPC (MPC), solving an optimal solution for a vehicle system state equation, wherein a first term of the objective function is used for expressing and solving the deviation between the output transverse displacement of the vehicle system and the reference transverse displacement, the deviation between the centroid slip angle and the reference slip angle, a second term of the objective function is used for restraining the control increment, and a third term of the objective function is a relaxation factor;
introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design an adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters;
introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function;
constructing a constraint condition to constrain the steering angle and the steering angle increment of the front wheels;
adding a dynamic compensation control quantity and a dynamic discovery probability to the cuckoo algorithm to obtain an improved cuckoo algorithm;
and (3) performing global search learning by adopting an improved cuckoo algorithm, and determining the vehicle state of the MPC under the optimal weight of the lateral displacement, the slip angle and the increment of the steering angle of the front wheels.
First, a vehicle dynamics model is built, which is a key to building an active steering control model. To balance the complexity and computational load of the model, we constructed a four degree of freedom vehicle model and reduced the steering system to a linear relationship between steering wheel and front wheel angle. Fig. 2 shows a schematic diagram of a four-degree-of-freedom vehicle model. To improve the effectiveness of the model, we propose the following assumptions:
(1) Neglecting vertical movement of the intelligent vehicle when driving on a flat road;
(2) Neglecting load transfer of the vehicle;
(3) The transverse and longitudinal aerodynamic properties are ignored.
The model has four degrees of freedom including longitudinal speed, lateral speed, yaw rate and yaw rate. The dynamics analysis was performed on the vehicle, and the dynamics equations of the vehicle along the x-axis, y-axis and z-axis are as follows:
wherein: m is the quality of the preparation of the vehicle,and->Longitudinal acceleration and lateral acceleration, respectively, of the vehicle, I z Is the product of inertia of the sprung mass about the z-axis, I xz Representing the product of inertia of the sprung mass about the x, y axes, F xi And F yi Force in the x-axis direction and force in the y-axis direction, respectively, applied to the vehicle, ψ is the centroid yaw angle, +.>For yaw angle>Is yaw acceleration.
The center of mass is converted from coordinates in the vehicle coordinate system to coordinates in the geodetic coordinate system, and the relationship between the longitudinal and lateral forces of the tire on the x and y axes of the front wheel can be deduced as follows:
F xwi ＝(F xw1 +F xw2 )cosδ-(F yw1 +F yw2 )sinδ
F ywi ＝(F xw1 +F xw2 )sinδ+(F yw1 +F yw2 )cosδ
wherein: delta is the steering angle of the front wheel, F xw1 ，F xw2 ，F yw 1,F yw 2 are forces applied to the front wheel in the x-axis and y-axis directions, respectively. The vehicle nonlinear dynamics model can be built as:
wherein: d is the track of the vehicle, l f ,l r F is the distance between the front and rear axes and the center of mass xw3 ，F xw4 ，F yw3 ,F yw4 The forces applied to the front wheel in the x-axis and y-axis directions, M Zi Moment about z-axis, m s G is gravity acceleration, h s For the vertical distance from the sprung mass centre to the roll centre, K βf ,K βr For front and rear axle roll stiffness, C βf ,C βr And beta is the centroid side deflection angle. On the basis of the kinematic model, an active steering control model for avoiding rear-end collision is constructed.
And the real-time requirement of the model predictive control algorithm on the vehicle is considered, and the vehicle state is approximately linearized, so that the purpose of reducing the calculated amount of the model is achieved. The vehicle state equation is constructed as follows:
x(k+1)＝Ax(k)+Bμ(k)
y(k+1)＝Cx(k+1)
wherein: the vehicle state vector is x= [ v x ,v y ,ψ,β] T ， μ Represents a control input amount, μ=δ represents a front wheel steering angle as a control input amount, y is a control output amount lateral displacement, k is a time step,B＝[b 1 b 2 0 0]，C＝[0 0 1 0]。
then, in order to secure the function of vehicle running stability, the vehicle path tracking control means that the controller controls the vehicle to run along the target locus given the target locus. The MPC algorithm has the ability to handle multiple constraint models, and thus a great deal of research has been directed to using the MPC algorithm for path tracking control of vehicles. The model prediction controller is based on an error model, solves an optimal control sequence through an objective function, can realize real-time rolling optimization, controls a vehicle to track a target track to run, and performs feedback correction.
The controller includes two types of control strategies, known as feed forward and feedback. The feed forward option may reduce interference rejection and path tracking may be achieved through feedback. The MPC comprises two units for prediction and control, respectively, a prediction time domain and a control time domain, the prediction time domain predicting the next output point, the control time domain calculating the correct control movement based on the predicted output point, and selecting the best predictive control operation to ensure the next decrease of the cost function.
(1) Objective function and constraint construction
The path tracking control requires higher precision of the actual running path and the reference path of the vehicle, so that an objective function of a path tracking algorithm based on MPC needs to be designed to solve the optimal solution of the state equation of the vehicle system, so that the accuracy and stability of the vehicle when following the path are ensured, and the optimal solution is required to be obtained when the vehicle follows the path. According to the requirement of the transverse movement of the vehicle, the tracking deviation is ensured to be smaller in the driving process, and meanwhile, the stability of the vehicle is ensured, so that an objective function is designed:
wherein: j (y (k), μ (k), β (k)) represents an optimization objective of the MPC path tracking controller, predicting the time domain N p And control time domain N c Is two important parameters, wherein the duration of the predicted time domain is the product of the predicted time domain length and the sampling period. Q, M and R are respectively weight coefficients of the vehicle transverse displacement output quantity, the mass center side deflection angle and the front wheel steering angle control quantity, can avoid the excessive control increment generated by a vehicle actuator while the tracking system outputs, ensures the smoothness and stability of the control process,for the system to refer to the transverse displacement, the front wheel rotation angle and the reference yaw angle, the first term of the objective function represents the deviation between the output transverse displacement, the centroid slip angle and the reference displacement and slip angle of the solving system, so as to represent the tracking performance of the vehicle under the algorithm control, and the second term is used for carrying out about the control incrementBundles to characterize the stability of the vehicle. The third term introduces a relaxation factor ρ in the objective function, ε being the relaxation factor weight in order to prevent the objective function from having no solution.
In practical systems, however, vehicle dynamics are affected by a variety of factors, including road conditions, vehicle communication or system response delays, etc., resulting in parameter uncertainty. The introduction of disturbances in the vehicle state equation may more realistically represent the actual vehicle state in the presence of external disturbance factors. By incorporating vehicle state disturbances, the adaptive MPC controller is designed to accommodate changes in system dynamics, actively respond to disturbances, better handle uncertainties, and ensure safety and stability of the control strategy even in the presence of external disturbance factors.
Thus, by introducing system measured and unmeasured external disturbance vectors, the system state equation may be further constructed to update the vehicle state according to changes in system parameters:
in the method, in the process of the invention,external disturbances measured for the system, +.>Is an external disturbance that is not measured by the system,is a state gain matrix. In MPC, the controller state is estimated by a kalman filter, and the estimation operation is determined based on system parameters at the time of initialization. In addition to updating the model, the adaptive MPC updates the gain matrix at each transition.
(2) Cost function construction
A cost function is constructed to measure control system performance. The cost function includes an evaluation of the system state and control inputs at each time step or prediction step to measure the performance of the system. The cost function typically includes input parameter costs and output costs and is used in the MPC to optimize control inputs to solve for the optimal control strategy under system constraints.
The total cost consists of three main parts, the first part being the cost y of the lateral displacement error ref (k) The larger the transverse error is in the tracking process, the higher the cost is; the second part is the cost of the slip angle error ψ ref (k) The larger the slip angle error is in the tracking process, the higher the cost is; the third part represents the cost Γ of the steering angle of the front wheel ref (k) The larger the steering angle increment of the front wheels in the tracking process, the higher the cost. Firstly, constructing a function:
E(k)＝QΥ ref (k)+MΨ ref (k)+RΓ ref (k)
cost y of controlling the lateral displacement error of the parameter ref (k) Cost of slip angle error ψ ref (k) Cost Γ of front wheel steering angle ref (k) Introducing a cost function, defining the cost function as:
J＝[ΔU-E] T Q[ΔU-E]+ΔU T RΔU+ε T ρε
further finishing cost functions are available:
(2) Model constraint construction
To ensure the control amount is executable, it is also necessary to restrict the control amount. Establishing constraints in model predictive control can reduce the degradation of control system performance, embody the idea of optimal control, but if the conditions are too strict, even if the number of linear independent constraints exceeds the number of decision variables, then the solver will have difficulty executing optimal solutions. On the other hand, if the conditions are too relaxed, the probability of the algorithm getting a solution that violates the physical laws to the extent of performance degradation will increase greatly, failing to achieve the effect of the constraint. In view of the performance capabilities and system robustness of the actuators, the front wheel steering angle and steering angle increment are mainly constrained herein. The constraint is constructed as follows:
μ min ≤μ k+i ≤μ max
|Δμ k+i |≤Δμ max
μ max ,μ min to control the upper and lower limits of the input front wheel steering angle,
(3) MPC weight coefficient determination based on improved cuckoo algorithm
The weight in the cost function of the conventional design is set to be constant, but in actual driving, the emphasis on the different parts of the cost should be different due to the different vehicle motion states and road environments. The three weights of the transverse displacement, the front wheel rotation angle and the slip angle in the cost function have relative significance, and the single weights in the research analysis cost function are respectively set as variables, and the other two weights are used as constants so as to analyze the influence of the weights on the path tracking effect. When the path is subjected to tracking control by adjusting the weight, two indexes of tracking accuracy and tracking stability are mainly focused, and the two indexes are coupled, and the improvement of the tracking accuracy can lead to the reduction of the tracking stability, and vice versa. Further analysis, as more attention is paid to vehicle follow-up, the lateral displacement weight should be increased to improve vehicle follow-up, and as more consideration is given to driving stability, the front wheel turning angle and the centroid slip angle should be increased to improve stability, so that it is necessary to adaptively adjust the weight according to the specific requirements of the tracking index while driving.
According to the analysis, the invention designs the self-adaptive adjustment weight coefficient to adapt to the current running state of the vehicle. However, since the analytical relationship between input and output is difficult to quantitatively describe, the present invention proposes to determine MPC control parameters based on an improved cuckoo algorithm: and (3) transversely displacing, increasing the vehicle state under the optimal weight of the side deflection angle and the front wheel steering angle. The cuckoo algorithm principle is to utilize Levy flight to walk randomly and Biased to walk randomly and iterate the optimal bird nest.
The cuckoo algorithm is introduced into the dynamic parameter weight coefficient of the self-adaptive MPCVehicle state search, first the problem can be described as: consider the vehicle system state as a searchable bird's nest position vector x= [ X ] 1 ,...x n ] T Each vehicle system state in the population corresponds to a bird nest fitness value, the fitness value is used for representing the advantages and disadvantages of the bird nest position, namely the vehicle state under the weight coefficient of each current parameter, and the cuckoo algorithm searches the vehicle state of the optimal weight coefficient in the following mode:
wherein: l (lambda) obeys the Levy distribution, h is the compensation control quantity, and the compensation size can be adjusted. The Levy flight comprises random linear movements which are randomly oriented and have no characteristic scale, the steps with short time duration are alternately performed, and after the state update, the bird nest position at the next moment is generated according to a position update mode of preference random walk, namely the vehicle state:
X i (t+1)＝X i (t)+rand*[X k (t)-X j (t)]
wherein: rand E [0,1] n ,X k (t),X j (t) is the random bird's nest location in the population at time t. After the location update, [0,1 ] is used]The value p in the interval is compared with the discovery probability p 'of other bird groups, and if p is more than p', X is changed i (t+1), otherwise, the same is true.
Improvement of cuckoo algorithm: the compensation control quantity h is an important parameter in the algorithm, and when the value of the compensation control quantity h is larger, the global weight searching capacity of each parameter is stronger, the convergence speed is faster, but the refinement capacity of the algorithm is poor; when the value is smaller, the local parameter weight searching capability is enhanced, the convergence speed is slow, and the local optimum condition is easily trapped. Therefore, in order to realize the effective balance between global and local search, the invention increases the ratio of a global optimal adaptation value and an individual optimal adaptation value to adjust the balance between the convergence speed and refinement capacity of the algorithm:
f gbest for global optimum adaptation value, f p Is a locally optimal adaptation value, a, b are constants, f when the local is near optimal gbest /f p The optimization precision of the algorithm is improved; when the local part is far from the optimal, f gbest /f p The global search speed of the algorithm is increased.
The adjusted position of the cuckoo is updated as follows:
furthermore, in the classical cuckoo algorithm, the probability p that a bird nest is found by other bird groups is typically a fixed value. In practice, however, the probability of influence p by various uncertainty factors is not constant. Just as the index weights of the vehicles in the vehicle system are not independent of each other and are coupled, the tracking stability is reduced due to the improvement of the tracking precision, and vice versa, so that the dynamic inertia weight concept is introduced, and the value of p is dynamically balanced:
newp＝pω＝p(Q+R+M)
wherein: newp is dynamic discovery probability, satisfying newp E [0.2,0.5]，ω max ,ω min For the maximum and minimum values of weights, c, e is a constant representing the case of controlling the weight shift, and frnd () represents a random number having asymmetry. The introduction of dynamic inertial weights can dynamically adjust the discovery probability.
The method comprises the steps of carrying out global search learning by adopting a cuckoo algorithm, solving the optimal vehicle state under the dynamic parameter weight, providing an improved cuckoo algorithm based on the dynamic compensation control quantity and the discovery probability to enhance global and local search capability, carrying out optimization on the connection weight and the threshold value to extract the implicit mapping relation between input and output data so as to adapt to a complex road environment, solving the problem that the connection weight is easy to fall into the local optimal state, and ensuring the dynamic adaptability of the control of the self-adaptive MPC path tracking controller.
The MPC self-adaptive path tracking control method based on the improved cuckoo algorithm provided by the embodiment of the invention comprises the steps of firstly, designing a self-adaptive MPC path tracking controller by introducing external interference vectors measured and not measured by a system, updating parameters according to the change of the system, and solving parameter uncertainty caused by communication or system response delay; secondly, simultaneously constructing a multi-objective cost function comprising a front wheel corner, a transverse displacement error and a centroid slip angle, and improving algorithm control precision; finally, the MPC is self-adaptively solved with the optimal vehicle state under the dynamic parameter weight based on the improved cuckoo algorithm, global and local searching capacity is enhanced based on the dynamic compensation control quantity and the improved cuckoo algorithm of the discovery probability, and the implicit mapping relation between the input and output data is extracted by optimizing the connection weight and the threshold value so as to adapt to the complex road environment, and the problem that the MPC is easy to fall into the local optimal state is solved.
In the first embodiment, an MPC adaptive path tracking control method based on an improved cuckoo algorithm is provided, and correspondingly, the application also provides an MPC adaptive path tracking control system based on the improved cuckoo algorithm. Referring to fig. 3, a block diagram of an MPC adaptive path tracking control system based on an improved cuckoo algorithm according to a second embodiment of the invention is shown. Since the apparatus embodiments are substantially similar to the method embodiments, the description is relatively simple, and reference is made to the description of the method embodiments for relevant points. The device embodiments described below are merely illustrative.
Referring now to FIG. 3, a block diagram illustrating an MPC adaptive path tracking control system based on an improved cuckoo algorithm according to another embodiment of the present invention is shown, the system comprising: the system comprises a first construction module, a second construction module, an MPC controller module, a system cost function construction module, a constraint module, an algorithm improvement module and a weight determination module, wherein the first construction module is used for constructing a vehicle system state equation according to a vehicle dynamics model; the second construction module is used for constructing an objective function of a path tracking algorithm based on MPC to solve an optimal solution for a vehicle system state equation, a first term of the objective function is used for expressing and solving deviation between the output transverse displacement of the vehicle system and a reference transverse displacement deviation and deviation between a centroid slip angle and a reference slip angle, a second term of the objective function is used for restraining a control increment, and a third term of the objective function is a relaxation factor; the MPC controller module is used for introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design a self-adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters; the system cost function construction module is used for introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function; the constraint module is used for constructing constraint conditions to constrain the steering angle and the steering angle increment of the front wheels; the algorithm improvement module is used for adding a dynamic compensation control quantity and a cuckoo algorithm with improved dynamic discovery probability into the cuckoo algorithm; the weight determining module is used for carrying out global search learning by adopting an improved cuckoo algorithm and determining the vehicle state of the MPC under the optimal weight of the transverse displacement, the slip angle and the front wheel steering angle increment. For a specific implementation method of each functional module, reference may be made to the method of the first embodiment.
In the above, an embodiment of an MPC adaptive path tracking control system based on an improved cuckoo algorithm is described for the second embodiment of the present invention.
The MPC self-adaptive path tracking control system based on the improved cuckoo algorithm and the MPC self-adaptive path tracking control method based on the improved cuckoo algorithm provided by the invention have the same beneficial effects due to the same inventive concept, and are not repeated here.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (8)
1. An MPC self-adaptive path tracking control method based on an improved cuckoo algorithm is characterized by comprising the following steps:
constructing a vehicle system state equation according to the vehicle dynamics model;
constructing an objective function of a path tracking algorithm based on MPC (MPC), solving an optimal solution for a vehicle system state equation, wherein a first term of the objective function is used for expressing and solving the deviation between the output transverse displacement of the vehicle system and the reference transverse displacement, the deviation between the centroid slip angle and the reference slip angle, a second term of the objective function is used for restraining the control increment, and a third term of the objective function is a relaxation factor;
introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design an adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters;
introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function;
constructing a constraint condition to constrain the steering angle and the steering angle increment of the front wheels;
adding a dynamic compensation control quantity and a dynamic discovery probability to the cuckoo algorithm to obtain an improved cuckoo algorithm;
and (3) performing global search learning by adopting an improved cuckoo algorithm, and determining the vehicle state of the MPC under the optimal weight of the lateral displacement, the slip angle and the increment of the steering angle of the front wheels.
2. The method of claim 1, wherein constructing a vehicle system state equation from a vehicle dynamics model specifically comprises:
a vehicle dynamics model is constructed, the model has four degrees of freedom, including longitudinal speed, transverse speed, yaw rate and yaw rate, the dynamics analysis is carried out on the vehicle, and the dynamics equations of the vehicle along the x axis, the y axis and the z axis are as follows:
wherein: m is the quality of the preparation of the vehicle,and->Longitudinal acceleration and lateral acceleration, respectively, of the vehicle, I z Is the product of inertia of the sprung mass about the z-axis, I xz Representing the product of inertia of the sprung mass about the x, y axes, F xi And F yi The force in the x-axis direction and the force in the y-axis direction, respectively, to which the vehicle is subjected, +.>For centroid yaw rate +.>For yaw angle>Is yaw acceleration;
the mass center is converted from the coordinates under the coordinate system of the vehicle to the coordinates under the ground coordinate system, and the relation between the longitudinal force and the lateral force of the tire on the x axis and the y axis of the front wheel is expressed as follows:
F xwi ＝(F xw1 +F xw2 )cosδ-(F yw1 +F yw2 )sinδ
F ywi ＝(F xw1 +F xw2 )sinδ+(F yw1 +F yw2 )cosδ
wherein: delta is the steering angle of the front wheel, F xw1 ，F xw2 ，F yw1 ,F yw2 The front wheels are respectively in the x axis and the y axisDirection-dependent forces, the vehicle nonlinear dynamics model can be built as:
wherein: d is the track of the vehicle, l f 、l r F is the distance between the front and rear axes and the center of mass xw3 、F xw4 、F yw3 、F yw4 The forces applied to the front wheel in the x-axis and y-axis directions, M Zi Moment about z-axis, m s G is gravity acceleration, h s For the vertical distance from the sprung mass centre to the roll centre, K βf 、K βr For front and rear axle roll stiffness, C βf 、C βr The front and rear axle side-rolling damping is adopted, and beta is the centroid side-deflection angle;
the vehicle system state equation is constructed as follows:
x(k+1)＝Ax(k)+Bμ(k)
y(k+1)＝Cx(k+1)
wherein: the vehicle state vector is x= [ v x ,v y ,ψ,β] T μ represents the control input, y represents the control output lateral displacement, k represents the time step,B＝[b 1 b 2 0 0]，C＝[0 0 1 0]。
3. the method of claim 2, wherein the objective function is
Wherein J represents an optimization objective of the MPC path tracking controller, N p To predict the time domain parameters, N c To control the time domain parameters, Q, M and R are weights of the vehicle lateral displacement output quantity, the centroid slip angle control quantity and the front wheel steering angle control quantity respectivelyThe coefficient of the,the system reference lateral displacement, the reference front wheel rotation angle and the reference yaw angle are respectively, the rho relaxation factor is represented by epsilon, and the epsilon is the relaxation factor weight.
4. A method according to claim 3, wherein the vehicle system state equation is updated according to the change of the system parameters, and the external disturbance vector measured and not measured by the vehicle system is introduced into the vehicle system state equation, and the obtained vehicle system state equation is:
wherein,external disturbances measured for the system, +.>For external disturbances that are not measured by the system,are all state gain matrices.
5. The method of claim 4, wherein the step of introducing the cost of the control parameter lateral displacement error, the cost of the slip angle error, and the cost of the front wheel steering angle into the cost function to obtain the system cost function comprises:
the construction function:
E(k)＝QΥ ref (k)+MΨ ref (k)+RΓ ref (k)
wherein y is ref (k) For the cost of the lateral displacement error, ψ ref (k) At the cost of the slip angle error Γ ref (k) Cost for the front wheel steering angle;
defining a cost function as:
J＝[ΔU-E] T Q[ΔU-E]+ΔU T RΔU+ε T ρε
converting the cost function to obtain
6. The method of claim 5, wherein the constraints are:
μ min ≤μ k+i ≤μ max
|Δμ k+i |≤Δμ max
wherein mu max Sum mu min The upper limit and the lower limit of the steering angle of the front wheel of the control input quantity are respectively.
7. The method of claim 6, wherein the specific method of adding the dynamic compensation control amount and the dynamic discovery probability to the cuckoo algorithm to improve the cuckoo algorithm comprises:
regarding the vehicle system state as a searchable bird's nest position vector x= [ X ] 1 ,...x n ] T Each vehicle system state in the population corresponds to a bird nest fitness value, and the cuckoo algorithm searches the vehicle state of the optimal weight coefficient through the following formula:
wherein: l (lambda) obeys Levy distribution, h is compensation control quantity, the compensation control quantity adopts a ratio of a global optimal adaptation value to an individual optimal adaptation value to adjust convergence speed and refinement capability of a cuckoo algorithm, and a calculation formula of the compensation control quantity is as follows:
wherein f gbest For global optimum adaptation value, f p For the local optimal adaptation value, a and b are constants, and the compensation control quantity is substituted into a cuckoo algorithm to obtain an adjusted cuckoo position updating formula:
adding a dynamic inertia weight into the adjusted cuckoo position updating formula, wherein the probability of the cuckoo found by the bird group is a dynamic probability p:
newp＝pω＝p(Q+R+M)
wherein: newp is dynamic discovery probability, satisfying newp E [0.2,0.5]，ω max ,ω min For the maximum and minimum values of the weights, c, e each represent a constant that controls the case of weight offset, frnd () represents a random number having asymmetry.
8. An MPC adaptive path tracking control system based on an improved cuckoo algorithm, comprising: a first building module, a second building module, an MPC controller module, a system cost function building module, a constraint module, an algorithm improvement module and a weight determination module,
the first construction module is used for constructing a vehicle system state equation according to a vehicle dynamics model;
the second construction module is used for constructing an objective function of a path tracking algorithm based on MPC to solve an optimal solution for a vehicle system state equation, a first term of the objective function is used for expressing and solving deviation between the output transverse displacement of the vehicle system and a reference transverse displacement deviation and deviation between a centroid slip angle and a reference slip angle, a second term of the objective function is used for restraining a control increment, and a third term of the objective function is a relaxation factor;
the MPC controller module is used for introducing vehicle system measurement and unmeasured external interference vectors into a vehicle system state equation to design a self-adaptive MPC path tracking controller, and updating the vehicle system state equation according to the change of vehicle system parameters;
the system cost function construction module is used for introducing the cost of the transverse displacement error, the cost of the slip angle error and the cost of the front wheel steering angle into a cost function to obtain a system cost function;
the constraint module is used for constructing constraint conditions to constrain the steering angle and the steering angle increment of the front wheels;
the algorithm improvement module is used for adding a cuckoo algorithm with improved dynamic compensation control quantity and dynamic discovery probability into the cuckoo algorithm;
the weight determining module is used for carrying out global search learning by adopting an improved cuckoo algorithm and determining the vehicle state of the MPC under the optimal weight of the transverse displacement, the slip angle and the front wheel steering angle increment.
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