Online Trajectory Planning Method and System for Mast Crane with Guaranteed State Constraints

Abstract

The present invention relates to the technical field of automatic control of underactuated systems, and provides an online trajectory planning method and system for a mast crane that guarantees state constraints. The method includes constructing a linear kinematic model of the mast crane and performing model transformation to obtain a state space model for trajectory planning; solving the analytical solutions of the matrices involved in the driven state sub-model and the underactuated state sub-model; discretizing through the zero-order hold method to obtain a discrete model, and calculating the parameter matrices of the discrete model through the analytical solutions of the matrix exponential; constructing a prediction model and an error model; converting the state constraints into input constraints, selecting a cost function to construct a quadratic programming; solving the optimal solution of the quadratic programming, and constructing an online trajectory of the mast crane according to the optimal solution. The present invention realizes precise lifting of goods while guaranteeing the state constraints during the operation of the crane, greatly enhancing the safety of the mast crane during the hoisting and transportation process.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control of underactuated systems, and in particular, to an online trajectory planning method and system for a mast crane that guarantees state constraints. Background Art

[0002] A mast crane is a typical underactuated system and an important construction machinery, which is widely used in ports, construction, wind power and other fields. In the research on mast cranes, the combination of trajectory planning and tracking control is a mainstream framework for realizing its automatic operation. Trajectory planning is responsible for planning the motion speeds of each joint, while the controller is responsible for tracking this trajectory. Among them, trajectory planning is the core link to ensure the regular movement of each joint of the mast crane.

[0003] Due to the need to consider complex underactuated characteristics, the trajectory planning of mast cranes is very difficult. Specifically, the movement of the crane will cause the swing of the goods. The trajectories of the joint variables of the crane need to ensure that while each actuated joint reaches its desired position, the swing of the goods is eliminated. To achieve this goal, the online trajectory planning method makes full use of state feedback, especially swing angle feedback, to generate joint trajectories in real time. The introduction of state feedback makes the robustness of the planned online trajectory stronger than that of traditional offline trajectories.

[0004] However, through the analysis of existing online trajectory planning methods, it can be found that they often cannot guarantee state constraints. The guarantee of state constraints is beneficial to enhancing the safety of the entire mast crane system. For example, the constraints on the luffing angle and slewing angle can avoid the collision between the boom and the surrounding buildings of the crane; the constraints on the swing angle can avoid the collision between large-volume goods and the boom; the constraints on the luffing angle, slewing angle and the change speed of the rope length actually limit the feasible region of the planned trajectory. This constraint mechanism can effectively prevent the actuator from saturating and outputting, thus avoiding other state constraint failure problems caused by actuator saturation. Guaranteeing the state constraints in trajectory planning is the basis for realizing the safety-critical control of mast cranes. The neglect of state constraints is an important reason why existing online trajectory methods are not convenient for practical applications and is also an urgent problem to be solved. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the related art. For this purpose, the present invention provides an online trajectory planning method and system for a mast crane that guarantees state constraints, which can realize precise lifting of goods while guaranteeing state constraints during the operation of the crane, and greatly enhance the safety of the mast crane during the hoisting and transportation process.

[0006] The present invention provides an online trajectory planning method for a mast crane that guarantees state constraints, including:

[0007] S1: Construct a linear kinematic model of the mast crane, and through linear transformation, convert the linear kinematic model of the mast crane into a state space model for trajectory planning;

[0008] S2: Divide the state space model into a driven state sub-model and an undriven state sub-model, and solve the analytical solutions of the matrix exponentials involved in the driven state sub-model and the undriven state sub-model;

[0009] S3: Discretize the driven state sub-model and the undriven state sub-model by the zero-order hold method, and calculate the parameter matrices of the discrete model through the analytical solutions of the matrix exponentials to obtain the discrete model;

[0010] S4: Construct a prediction model based on the discrete model, and construct an error model based on the prediction model and the reference trajectory;

[0011] S5: Convert the state constraints into input constraints, select a cost function according to the error model, and construct a quadratic programming based on the input constraints and the cost function;

[0012] S6: Solve the optimal solution of the quadratic programming, and construct an online trajectory of the mast crane according to the optimal solution.

[0013] Furthermore, in step S1,

[0014] The linear kinematic model of the mast crane is:

[0015]

[0016] where, is the rate of change of the state, is the state variable, is the acceleration of the driven joint, is the input matrix, is the system matrix;

[0017] The linear transformation is:

[0018]

[0019] where, is the acceleration of the driven joint, is the input variable, is the linear transformation matrix;

[0020]

[0021] is the distance between the slewing center of the boom and the upper end point of the hoisting rope, is the acceleration due to gravity, is the expected value of the boom luffing angle;

[0022] Apply a linear transformation to the linear kinematic model of the mast crane to obtain a state-space model. The calculation expression of the state-space model is:

[0023]

[0024] where, is the state transition matrix, .

[0025] Furthermore, in step S2,

[0026] the driven state sub-model is:

[0027]

[0028] where, is the driven state change rate, is the first state transition sub-matrix, is the driven state, is the second state transition sub-matrix, is the undriven state, is the input variable, is the first input sub-matrix;

[0029] the undriven state sub-model is:

[0030]

[0031] where, is the undriven state change rate, is the fourth state transition sub-matrix, is the third state transition sub-matrix, is the second input sub-matrix.

[0032] Furthermore, the analytical solution of the matrix exponential includes the analytical solution of the first matrix exponential and the analytical solution of the second matrix exponential,

[0033] The first matrix exponential has the following analytical solution:

[0034]

[0035] where, is the discrete period, is the 3rd order identity matrix, is 's zero matrix;

[0036] The second matrix exponential has the following analytical solution:

[0037]

[0038] Among them, is the second-order identity matrix, is the zero matrix of.

[0039] Furthermore, in step S3, the calculation expression of the discrete model is:

[0040]

[0041] Among them, is the state at time is the state at time is the input variable at time is the parameterized state matrix, is the parameterized system matrix;

[0042]

[0043]

[0044] is the discrete period, is the distance between the slewing center of the boom and the upper end point of the hoisting rope, is the acceleration due to gravity, is the expected value of the boom luffing angle, is the expected value of the hoisting rope length.

[0045] Furthermore, in step S4, the state at time is used to predict the step state, and a prediction model is obtained. The calculation expression of the prediction model is:

[0046]

[0047] Among them, is the predicted state at time is the predicted input matrix, is the predicted system matrix, is at time the step input vector, is the state at time

[0048] The calculation expression of the error model is:

[0049]

[0050] Among them, is the error at the moment, is an intermediate variable, , is the reference trajectory at the moment.

[0051] Furthermore, in step S5, the state constraint is:

[0052]

[0053] Among them, is the lower bound constant vector, is the upper bound constant vector, is the predicted state at the moment,

[0054] According to the prediction model, the state constraint is converted into an input constraint, and the calculation expression is:

[0055]

[0056] Among them, is the state at the moment, is the prediction input matrix, is the prediction system matrix, is at the moment the step input vector.

[0057] Furthermore, the calculation expression of quadratic programming is:

[0058]

[0059] Among them, is to select to make the minimum, is the cost function, is the reference trajectory at the moment, is the constraint symbol, is the first positive definite parameter matrix, is the second positive definite parameter matrix, is the transpose of the matrix;

[0060] Solve the quadratic programming to obtain the optimal solution. The calculation expression of the optimal solution is:

[0061]

[0062] Among them, is the optimal solution at the moment, is Predict the initial optimal input for the first-step prediction, For Predict the optimal input for the first step of the For Predict the optimal input for the step of the

[0063] Furthermore, in step S6, the calculation expression for the online trajectory of the mast crane is:

[0064]

[0065] Wherein, Is The speed of the driving joint at time Is The initial optimal input for the first-step prediction, Is The speed of the driving joint at time Is the discrete period, Is the linear transformation matrix, Is The state at time

[0066] The speed of the driving joint includes the slewing angular velocity of the boom, the luffing angular velocity, and the rope elongation speed.

[0067] An online trajectory planning system for a mast crane that guarantees state constraints, used to execute the above-mentioned online trajectory planning method for a mast crane that guarantees state constraints, including:

[0068] A model construction and conversion module, which is used to construct a linear kinematic model of the mast crane and convert the linear kinematic model of the mast crane into a state space model for trajectory planning through linear transformation;

[0069] A matrix exponential solution module, which is used to divide the state space model into a driven state sub-model and an undriven state sub-model, and solve the analytical solutions of the matrix exponentials involved in the driven state sub-model and the undriven state sub-model;

[0070] A discretization module, which is used to discretize the driven state sub-model and the undriven state sub-model by the zero-order hold method, and calculate the parameter matrix of the discrete model through the analytical solution of the matrix exponential to obtain the discrete model;

[0071] A prediction model and error model construction module, which is used to construct a prediction model based on the discrete model and construct an error model based on the prediction model and the reference trajectory;

[0072] The quadratic programming construction module is used to transform the state constraints into input constraints, select a cost function according to the error model, and construct a quadratic programming based on the input constraints and the cost function.

[0073] The online trajectory construction module is used to solve the optimal solution of the quadratic programming and construct the online trajectory of the derrick crane according to the optimal solution.

[0074] One or more of the above technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0075] The online trajectory planning method of the present invention ensures the preset constraints of all states of the derrick crane, enhances the safety of the crane lifting operation, and all state constraints in the vector of the discrete model can be transformed into constraints on the input.

[0076] In the process of zero-order hold discretization of the transformed model in the present invention, the matrix exponential can directly calculate the parameterized analytical solution; the optimization problem is a simple quadratic programming problem, and the method for solving this optimization is very mature and has low requirements for computing power, so its implementation is simple.

[0077] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0078] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0079] Figure 1 It is a schematic flowchart of an online trajectory planning method for a derrick crane that ensures state constraints provided by the present invention.

[0080] Figure 2 It is a schematic structural diagram of an online trajectory planning system for a derrick crane that ensures state constraints provided by the present invention.

[0081] Figure 3 It is a schematic diagram of a 5-degree-of-freedom derrick crane provided by an embodiment of the present invention.

[0082] Figure 4 It is a simulation result diagram of an online trajectory planning method for a derrick crane that ensures state constraints provided by an embodiment of the present invention.

[0083] Figure 5It is the simulation two result graph of an online trajectory planning method for a mast crane that guarantees state constraints provided by an embodiment of the present invention.

[0084] Figure 6 It is the simulation three result graph of an online trajectory planning method for a mast crane that guarantees state constraints provided by an embodiment of the present invention.

[0085] Reference numerals:

[0086] 101, Model construction and conversion module; 102, Matrix exponential solution module; 103, Discretization module; 104, Prediction model and error model construction module; 105, Quadratic programming construction module; 106, Online trajectory construction module. Detailed implementation manners

[0087] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0088] In the description of the embodiments of the present invention, it should be noted that the terms "first", "second", and "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance. In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without conflict, those skilled in the art can combine the different embodiments or examples described in this specification and the features of the different embodiments or examples.

[0089] The following combines Figures 1 to 6 to describe an online trajectory planning method and system for a mast crane that guarantees state constraints of the present invention.

[0090] As Figure 1 shown, an online trajectory planning method for a mast crane that guarantees state constraints includes:

[0091] S1: Construct the linear kinematic model of the mast crane, and convert the linear kinematic model of the mast crane into a state - space model through linear transformation;

[0092] As Figure 3 shown in the schematic diagram of the 5 - degree - of - freedom mast crane, is the luffing angle of the boom, is the slewing angle of the boom, is the length of the hoisting rope. The swing of the load is excited by the movement of the boom. Then, it is described with reference to the plane formed by the boom and its projection on the ground, that is, the swing angle along the extension direction (normal direction) of this plane is and the swing angle perpendicular to this plane (tangential direction) is . The 5 joint variables of the mast crane are divided into two parts according to whether there is a driving mechanism, that is, there is a driving output , , where is the first joint variable, is the second joint variable, is the third joint variable, is the transpose of the matrix, and there is no driving output , , is the fourth joint variable, is the fifth joint variable. The acceleration of the driving joint is the quantity to be planned, and it is defined as . Based on the Euler - Lagrange equation, establish the kinematic model of the mast crane as follows:

[0093]

[0094] where is the first inertia matrix, is the second inertia matrix, is the first centripetal - Coriolis matrix, is the second centripetal - Coriolis matrix, is the gravity vector, is 's acceleration, is 's velocity, is 's velocity;

[0095] The specific form of the matrix in the formula is:

[0096]

[0097]

[0098]

[0099] Among them, is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the abbreviation of , is the distance between the slewing center of the mast crane and the upper end point of the hoisting rope, is the acceleration due to gravity, is 's speed, is 's speed, is 's speed, is 's speed, is 's speed;

[0100] Rewrite the kinematic model of the mast crane as:

[0101]

[0102] Among them, is the state variable, , and its derivative is expressed as the non - linear mapping , and the calculation expression of the non - linear model is:

[0103]

[0104] Use the first - order Taylor expansion method to linearize the non - linear model, and obtain the linear kinematic model of the mast crane. The linear kinematic model of the mast crane is:

[0105]

[0106] Among them, is 's derivative, is the state variable, is the acceleration of the driven joint, is the input matrix, , is the system matrix, ; is the expected value of the state variable, , is the expected value of the boom luffing angle, is the expected value of the boom slewing angle, is the expected value of the hoisting rope length;

[0107] The state variable , including the boom luffing angle 、the boom slewing angle 、the hoisting rope length 、the boom luffing angular velocity 、the boom slewing angular velocity 、the hoisting rope elongation speed 、the normal swing angle of the load 、the tangential swing angle of the load 、the normal angular velocity of the load 、the tangential angular velocity of the load .

[0108] The acceleration of the driven joint includes the boom luffing angular acceleration 、the boom slewing angular acceleration 、the acceleration of the hoisting rope length change , and the acceleration of the driven joint .

[0109] Let represent the zero matrix of , and represent the

[0110]

[0111] The matrix is:

[0112]

[0113] Among them, is the first constant matrix, .

[0114] According to the linear kinematic model of the mast crane, a linear transformation is constructed, and the linear transformation is:

[0115]

[0116] Among them, is the acceleration of the driven joint, is the state variable, is the input variable, is the linear transformation matrix, and the calculation expression of the linear transformation matrix is:

[0117]

[0118] Apply the linear transformation to the linear kinematic model of the mast crane to obtain the state space model. The calculation expression of the state space model is:

[0119]

[0120] Among them, is the state transition matrix, .

[0121] S2: Divide the state space model into a driven state sub-model and an undriven state sub-model, and solve the analytical solutions of the matrix exponents of the driven state sub-model and the undriven state sub-model;

[0122] Divide into where, is the driven state, , is the undriven state, , construct , is a set of 6-dimensional real vectors, is a set of 4-dimensional real vectors, is a set of 6-dimensional real matrices, is a set of real matrices of dimension, is a set of real matrices of dimension, is a set of real matrices of dimension, is a set of real matrices of dimension, is a set of real matrices of dimension.

[0123] Divide the state transition matrix into:

[0124]

[0125] Among them, is the state transition matrix, is the first state transition sub-matrix, is the second state transition sub-matrix, is the third state transition sub-matrix, is the fourth state transition sub - matrix;

[0126] The input matrix is divided into:

[0127]

[0128] where, is the input matrix, is the first input sub - matrix, is the second input sub - matrix;

[0129] The state - space model can be divided into two sub - models accordingly. The driven - state sub - model is:

[0130]

[0131] where, is the driven - state change rate, is the driven - state, is the undriven - state, is the input variable;

[0132] The undriven - state sub - model is:

[0133]

[0134] where, is the undriven - state change rate.

[0135] Solve the analytical solutions of the matrix exponents of the driven - state sub - model and the undriven - state sub - model. Denote the discrete period as , the analytical solution of the first matrix exponent is:

[0136]

[0137] The analytical solution of the second matrix exponent is:

[0138]

[0139] S3: Discretize the driven - state sub - model and the undriven - state sub - model by the zero - order hold method, and calculate the parameter matrices of the discrete models through the analytical solutions of the matrix exponents to obtain the discrete models;

[0140] Apply the zero - order hold method to discretize the two sub - models. The calculation expression of the driven - state discrete sub - model is:

[0141]

[0142] where, is The driven state at a moment is the driven state at a moment is the non-driven state at a moment is the input at a moment;

[0143] The calculation expression of the non-driven state discrete sub-model is:

[0144]

[0145] where, is the non-driven state at a moment;

[0146] Integrate the driven state discrete sub-model and the non-driven state discrete sub-model to obtain the discrete model. The calculation expression of the discrete model is:

[0147]

[0148] where, is the state at a moment, is the state at a moment, is the input state at a moment, is the state parameter matrix, is the system parameter matrix;

[0149]

[0150] The parameterized form of calculated from the first matrix exponential and the second matrix exponential and is:

[0151]

[0152]

[0153] S4: Construct a prediction model based on the discrete model, and obtain an error model based on the prediction model and the reference trajectory;

[0154] Let represent the -th step prediction of the state at moment. Then the calculation expression for predicting steps from the state at moment is:

[0155]

[0156] Among them, is the predicted state at time is the predicted input matrix, is the predicted system matrix, is the step input vector, is the state at time ;

[0157]

[0158] The initial value of the reference trajectory with the driving state is: is:

[0159]

[0160] The final value of the reference trajectory with the driving state is: is:

[0161]

[0162] The expected values of both the non-driven swing angle and its speed are 0, generating an expected signal:

[0163] , then the reference trajectory of is:

[0164]

[0165] Among them, is the expected signal at time is the expected signal at time is the expected signal at time ;

[0166] The calculation expression of the error model is:

[0167]

[0168] Among them, is the error at time is an intermediate variable, .

[0169] S5: Convert the state constraint into an input constraint, select a cost function according to the error model, and construct a quadratic programming based on the input constraint and the cost function; ​​​​​​​​​​​​

[0170] When imposing state constraints on the system, the state constraints are transformed into input constraints for processing. When considering state constraints, we have:

[0171]

[0172] where is the lower-bound constant vector, is the upper-bound constant vector, is the predicted state at time

[0173] According to the prediction model, the state constraints are converted into input constraints, and the calculation expression is:

[0174]

[0175] where is the state at time is the prediction input matrix, is the prediction system matrix, is the input vector at step

[0176] The selected cost function is:

[0177]

[0178] where is the cost function, is the first positive definite parameter matrix, is the second positive definite parameter matrix;

[0179] Further calculation gives:

[0180]

[0181] Taking as the decision variable, a quadratic programming is constructed, and the calculation expression is:

[0182]

[0183] where Select to make the minimum, is the cost function, is the expected value of the reference trajectory at time for the step prediction, is the constraint function, is the first positive definite parameter matrix,

[0184] S6: Solve the optimal solution of the quadratic programming, and construct the online trajectory of the mast crane according to the optimal solution.

[0185] Solve the quadratic programming within each planning period to obtain the optimal solution:

[0186]

[0187] Among them, is the optimal solution at time is the optimal input at the initial step of the is the optimal input at the first step of the is the optimal input at the step of the

[0188] The input of the mast crane hardware system is generally the speed signal of the driving mechanism. The online trajectory of the mast crane is obtained by using linear transformation and acceleration formula;

[0189] The calculation expression of the linear transformation at time

[0190]

[0191] Among them, is the acceleration signal of the driving joint at time

[0192] The calculation expression of the acceleration at time

[0193]

[0194] Among them, is the acceleration signal of the driving joint at time is the acceleration signal of the driving joint at time is the discrete period,

[0195] Finally, the generation rule of the online trajectory can be deduced as:

[0196]

[0197] Among them, is the speed of the driving joint at time is the optimal input at the initial step of the is the speed of the driving joint at time is a discrete period, is a linear transformation matrix, is the state at time;

[0198] The speed of the driving joints includes the slewing angular velocity of the boom, the luffing angular velocity, and the rope elongation speed.

[0199] As Figure 2 shown, a mast crane online trajectory planning system for ensuring state constraints, which is used to execute the above-mentioned mast crane online trajectory planning method for ensuring state constraints, includes:

[0200] The model construction and conversion module 101 is used to construct the linear kinematic model of the mast crane, and convert the linear kinematic model of the mast crane into a state space model for trajectory planning through linear transformation;

[0201] The matrix exponential solving module 102 is used to divide the state space model into a driven state sub-model and an undriven state sub-model, and solve the analytical solutions of the matrix exponentials involved in the driven state sub-model and the undriven state sub-model;

[0202] The discretization module 103 is used to discretize the driven state sub-model and the undriven state sub-model by the zero-order hold method, and calculate the parameter matrix of the discrete model through the analytical solution of the matrix exponential to obtain the discrete model;

[0203] The prediction model and error model construction module 104 is used to construct a prediction model according to the discrete model, and construct an error model according to the prediction model and the reference trajectory;

[0204] The quadratic programming construction module 105 is used to convert the state constraints into input constraints, select a cost function according to the error model, and construct a quadratic programming according to the input constraints and the cost function;

[0205] The online trajectory construction module 106 is used to solve the optimal solution of the quadratic programming, and construct the online trajectory of the mast crane according to the optimal solution.

[0206] Through the collaborative work of the above modules, the preset constraints of all states of the mast crane are ensured, the safety of the crane hoisting operation is enhanced, and the constraints of all states in the vector of the discrete model can be converted into constraints on the input.

[0207] In the process of zero-order hold discretization of the transformed model in the present invention, the matrix exponential can directly calculate the parameterized analytical solution; the optimization problem is a simple quadratic programming problem, and the method for solving this optimization is very mature and has little demand for computing power, so its implementation is simple.

[0208] Simulate the method of the present invention in the Matlab environment: Set the simulation period ; Select the boom length to be ; Set the initial value of the luffing angle , the expected value of the luffing angle is , the initial value of the slewing angle , the expected value of the slewing angle , the initial value of the rope length , the expected value , the initial value of the swing angle ; Construct the reference trajectory as , where:

[0209]

[0210]

[0211]

[0212] Set the optimization parameters , where is the th sub - matrix of is the th sub - matrix of

[0213]

[0214]

[0215] Select the following state constraints:

[0216]

[0217] That is, constrain the absolute value of the swing angle within , the absolute value of the angular velocity of the swing angle within , the overshoot of the slewing angle and luffing angle of the boom within , the overshoot of the rope length within , and at the same time constrain the speed of the driven joints planned by the algorithm.

[0218] There are the following three groups of simulation settings:

[0219] Simulation 1 is a conventional test, that is, directly run the simulation with the above settings, and the output results are shown in Figures (a) to (j) of Figure 4 .

[0220] Simulation 2 considers the case where the boom length measurement is inaccurate, that is, set the boom length of the system to , while the planning algorithm still uses , to verify the robustness of the proposed algorithm to inaccurate arm lengths; the output results are shown in Figures (a) to (j) in Figure 5 .

[0221] Simulation three considers the case where there is an initial swing angle, that is, set , to test whether the present invention can make the system converge to the expected value when there is an initial swing angle. The output results are shown in Figures (a) to (j) in Figure 6 .

[0222] As Figures 4 to 6 The results show that all states converge to the target values as the algorithm runs and remain within the desired constraints; even in the face of inaccurate arm length measurements and initial swing angles, the present invention still has sufficient robustness to make each converge to the target value while ensuring state constraints.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for online trajectory planning of a mast crane with guaranteed state constraints, characterized in that: include: S1: Construct a linear kinematic model of the mast crane and convert the linear kinematic model of the mast crane into a state space model for trajectory planning through linear transformation; S2: Divide the state space model into a driven state sub-model and an undriven state sub-model, and obtain analytical solutions of the matrix exponents involved in the driven state sub-model and the undriven state sub-model; S3: discretize the driven state sub-model and the undriven state sub-model by the zero-order hold method, and calculate the parameter matrix of the discrete model by the analytical solution of the matrix exponential to obtain the discrete model; S4: construct a prediction model based on the discrete model, and construct an error model based on the prediction model and the reference trajectory; S5: Convert the state constraints into input constraints, select the cost function according to the error model, and construct the quadratic programming based on the input constraints and the cost function; S6: Find the optimal solution of the quadratic programming and construct the online trajectory of the mast crane based on the optimal solution.

2. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S1, The linear kinematic model of the mast crane is: in, is the rate of change of state, is the state variable, is the acceleration of the driven joint, is the input matrix, is the system matrix; The linear transformation is: in, is the acceleration of the driven joint, is the input variable, is the linear transformation matrix; is the distance between the slewing center of the boom and the upper end point of the suspension rope, is the acceleration due to gravity, is the expected value of the boom luffing angle; Apply the linear transformation to the linear kinematic model of the mast crane to obtain the state space model. The calculation expression of the state space model is: in, is the state transfer matrix, .

3. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S2, The driven state sub-model is: in ， is the driving state change rate, is the first state transition submatrix, In the driven state, is the second state transition submatrix, In the no-drive state, is the input variable, is the first input sub-matrix; The undriven state sub-model is: in, is the rate of change of the undriven state, is the fourth state transition submatrix, is the third state transition submatrix, is the second input sub-matrix.

4. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: The analytical solution of the matrix index includes the analytical solution of the first matrix index and the analytical solution of the second matrix index. First Matrix Exponential The analytical solution is: in, is a discrete period, is the third-order identity matrix, for The zero matrix of ; Second matrix index The analytical solution is: in, is the 2nd-order identity matrix, for The zero matrix of .

5. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S3, the calculation expression of the discrete model is: in, for The state of the moment, for The state of the moment, for The input variables at time, is the parameterized state matrix, is the parameterized system matrix; is a discrete period, is the distance between the slewing center of the boom and the upper end point of the suspension rope, is the acceleration due to gravity, is the expected value of the boom luffing angle, is the expected length of the sling.

6. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S4, Status prediction at each moment Step state, obtain the prediction model, the calculation expression of the prediction model is: in, for The predicted state at the moment, is the prediction input matrix, is the prediction system matrix, for time Step input vector, for The state of the moment; The calculation expression of the error model is: in, for The error in time, is the intermediate variable, , for Reference trajectory at time.

7. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S5, the state constraints are: in, is a lower bound constant vector, is an upper bound constant vector, for The predicted state at the moment, According to the prediction model, the state constraints are converted into input constraints, and the calculation expression is: in, for The state of the moment, is the prediction input matrix, is the prediction system matrix, for time Step input vector.

8. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 7, characterized in that: The calculation expression of quadratic programming is: in, For selection make Minimum, is the cost function, for The reference trajectory at all times, is the constraint symbol, is the first positive definite parameter matrix, is the second positive definite parameter matrix, is the transpose of the matrix; Solve the quadratic programming and obtain the optimal solution. The calculation expression of the optimal solution is: in, for The best solution at any time, for Step 1 predicts the initial optimal input, for Step 1 predicts the optimal input for step 1, for Step prediction The optimal input for the step.

9. The method for online trajectory planning of a mast crane with guaranteed state constraints according to claim 1, characterized in that: In step S6, the calculation expression of the online trajectory of the mast crane is: in, for There is always a speed that drives the joints. for Step 1 predicts the initial optimal input, for There is always a speed that drives the joints. is a discrete period, is the linear transformation matrix, for The state of the moment; The speed of the driven joint includes the boom rotation angular velocity, the luffing angular velocity and the rope extension velocity.

10. An online trajectory planning system for a mast crane with guaranteed state constraints, characterized in that: A method for online trajectory planning of a mast crane for executing a state-guaranteed constraint as claimed in any one of claims 1 to 9, comprising: A model building and transformation module, wherein the model building and transformation module is used to build a linear kinematic model of the mast crane, and transform the linear kinematic model of the mast crane into a state space model for trajectory planning through linear transformation; A matrix index solving module, wherein the matrix index solving module is used to divide the state space model into a driven state sub-model and an undriven state sub-model, and solve the analytical solution of the matrix index involved in the driven state sub-model and the undriven state sub-model; A discretization module, wherein the discretization module is used to discretize the driven state sub-model and the undriven state sub-model by a zero-order hold method, and calculate the parameter matrix of the discrete model by an analytical solution of the matrix exponent to obtain the discrete model; A prediction model and error model construction module, wherein the prediction model and error model construction module is used to construct a prediction model according to a discrete model, and to construct an error model according to the prediction model and a reference trajectory; A quadratic programming construction module, wherein the quadratic programming construction module is used to convert state constraints into input constraints, select a cost function according to an error model, and construct a quadratic programming according to the input constraints and the cost function; An online trajectory construction module is used to solve the optimal solution of the quadratic programming and construct the online trajectory of the mast crane according to the optimal solution.

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