Mast crane online track planning method and system capable of guaranteeing state constraint

Abstract

The invention relates to the technical field of automatic control of an under-actuated system, and provides a mast crane online trajectory planning method and system capable of guaranteeing state constraint, the method comprises the following steps: constructing a linear kinematics model of a mast crane and carrying out model transformation to obtain a state space model for trajectory planning; solving analytic solutions of matrix indexes related to the sub-model with the driving state and the sub-model without the driving state; discretization is carried out through a zero-order retention method, a discrete model is obtained, and a parameter matrix of the discrete model is calculated through an analytical solution of a matrix index; constructing a prediction model and an error model; converting a state constraint into an input constraint, and selecting a cost function to construct quadratic programming; and solving the optimal solution of the quadratic programming, and constructing the online track of the mast crane according to the optimal solution. According to the mast type crane, the state constraint during operation of the crane is guaranteed while accurate hoisting of cargoes is achieved, and the safety of the mast type crane in the hoisting and transporting process is greatly improved.

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 with guaranteed state constraints. Background Art

[0002] Mast crane is a typical underactuated system and an important engineering machinery, which is widely used in ports, construction, wind power and other fields. In the research on mast crane, the combination of trajectory planning and tracking control is a mainstream framework for realizing its automated operation. Trajectory planning is responsible for planning the movement speed of each joint, while the controller is responsible for tracking the trajectory. Among the two, trajectory planning is the core link to ensure the standardized movement of each joint of the mast crane.

[0003] Trajectory planning for mast cranes is difficult due to the need to consider complex underactuated characteristics. Specifically, the movement of the crane causes the cargo to swing. The trajectory of the crane's joint variables needs to be guaranteed to eliminate cargo swing while all driven joints reach their desired positions. To achieve this goal, online trajectory planning methods make full use of state feedback, especially swing angle feedback, to generate joint trajectories in real time. The introduction of state feedback makes the planned online trajectory planning more robust than 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 conducive to enhancing the safety of the entire mast crane system. For example, constraints on the luffing angle and the slewing angle can avoid the collision between the boom and the buildings around the crane; constraints on the swing angle can avoid the collision between large-volume cargo and the boom; imposing constraints on the luffing angle, the slewing angle and the rope length change speed is essentially to limit the feasible domain of the planned trajectory. This constraint mechanism can effectively prevent the actuator from saturating the output, thereby avoiding other state constraint failures caused by actuator saturation. Ensuring state constraints in trajectory planning is the basis for achieving safety-critical control of mast cranes. Ignoring state constraints is an important reason why existing online trajectory methods are not convenient for practical application, and it is also a problem that needs to be solved urgently. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the related art. To this end, the present invention provides a method and system for online trajectory planning of a mast crane with guaranteed state constraints, which can achieve accurate lifting of goods while ensuring the state constraints during crane operation, greatly enhancing the safety of the mast crane during lifting and transportation.

[0006] The present invention provides a method for online trajectory planning of a mast crane with guaranteed state constraints, comprising: 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.

[0007] Furthermore, 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, .

[0008] Furthermore, 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.

[0009] Further, the analytical solution of the matrix index includes an analytical solution of the first matrix index and an 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 .

[0010] Furthermore, 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.

[0011] Furthermore, in step S4, by 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.

[0012] Furthermore, in step S5, the state constraint is: 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.

[0013] Furthermore, the calculation expression of the 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.

[0014] Furthermore, 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.

[0015] A mast crane online trajectory planning system with guaranteed state constraints, used to execute the above-mentioned mast crane online trajectory planning method with guaranteed state constraints, comprising: A model building and conversion module, wherein the model building and conversion module is used to build 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; 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.

[0016] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: The online trajectory planning method of the present invention ensures the preset constraints of all states of the mast crane, enhances the safety of the crane hoisting operation, and the constraints of all states in the vector of the discrete model can be converted into constraints on the input.

[0017] In the process of zero-order hold discretization of the transformed model in the present invention, the matrix exponent can directly calculate the parameterized analytical solution; the optimization problem is a simple quadratic programming problem, the method for solving the optimization is very mature and has low demand for computing power, so it is easy to implement.

[0018] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] 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 described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 It is a flow chart of an online trajectory planning method for a mast crane with guaranteed state constraints provided by the present invention.

[0021] Figure 2It is a structural schematic diagram of an online trajectory planning system for a mast crane with guaranteed state constraints provided by the present invention.

[0022] Figure 3 It is a schematic diagram of a 5-DOF mast crane provided in an embodiment of the present invention.

[0023] Figure 4 It is a simulation result diagram of an online trajectory planning method for a mast crane with guaranteed state constraints provided by an embodiment of the present invention.

[0024] Figure 5 It is a simulation result diagram of a method for online trajectory planning of a mast crane with guaranteed state constraints provided by an embodiment of the present invention.

[0025] Figure 6 These are three simulation result diagrams of an online trajectory planning method for a mast crane with guaranteed state constraints provided by an embodiment of the present invention.

[0026] Reference numerals: 101. Model building and conversion module; 102. Matrix index solving module; 103. Discretization module; 104. Prediction model and error model building module; 105. Quadratic programming building module; 106. Online trajectory building module. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme in the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection 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.

[0028] In the description of the embodiments of the present invention, it should be noted that the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance. In the description of this specification, the description of reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiments of the present invention. In this specification, the schematic representation of the above terms does 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, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples without contradiction.

[0029] Combine the following Figures 1 to 6 The present invention describes a method and system for online trajectory planning of a mast crane with guaranteed state constraints.

[0030] like Figure 1 As shown, a method for online trajectory planning of a mast crane with guaranteed state constraints comprises: 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 through linear transformation; like Figure 3 In the schematic diagram of the 5-DOF mast crane shown in FIG. is the luffing angle of the boom, is the swing angle of the boom, is the length of the sling rope. The swing of the cargo is stimulated by the movement of the boom. The description is based on the plane formed by the boom and its projection on the ground, that is, the swing angle along the extension direction (normal) of the plane is , the swing angle perpendicular to the plane (tangential) is The five 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 , ,in, is the first joint variable, is the second joint variable, is the third joint variable, Transpose of the matrix, no driver output , , is the fourth joint variable, is the fifth joint variable, and the acceleration of the driven joint is the quantity to be planned, which is defined as , the kinematic model of the mast crane is established based on the Euler-Lagrange equation as follows: in, is the first moment of inertia matrix, is the second moment of inertia matrix, is the first centripetal-Riolis matrix, is the second centripetal-Riolis matrix, is the gravity vector, for The acceleration of for speed, for speed; The specific form of the matrix is: in, for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of for Abbreviation of 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, for speed, for speed, for speed, for speed, for speed; The kinematic model of the mast crane is rewritten as: in, is the state variable, , whose derivative is expressed as a nonlinear mapping , the calculation expression of the nonlinear model is: The nonlinear model is linearized using the first-order Taylor expansion method to obtain the linear kinematic model of the mast crane. The linear kinematic model of the mast crane is: in, for The derivative of 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 rotation angle, is the expected value of the sling length; State variables , including the boom luffing angle of mast cranes , boom swing angle , Rope length 、Boom luffing angular velocity 、Boom rotation angular velocity , the speed of rope extension , the normal swing angle of the cargo , the tangential swing angle of the cargo , the normal angular velocity of the cargo , the tangential angular velocity of the cargo .

[0031] The acceleration of the driven joint includes the angular acceleration of the boom 、Boom rotation angular acceleration , the acceleration of the rope length change , with the acceleration of the driven joint .

[0032] by express The zero matrix of express The matrix is ​​the identity matrix of order, then for: matrix for: in, is the first constant matrix, .

[0033] According to the linear kinematic model of the mast crane, a linear transformation is constructed, which is: in, 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: 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, .

[0034] S2: Divide the state space model into a driven state sub-model and an undriven state sub-model, and obtain the analytical solution of the matrix index of the driven state sub-model and the undriven state sub-model; Will Divide into ,in, In the driven state, , In the no-drive state, ,structure , is a 6-dimensional real vector set, is a 4-dimensional real vector set, for The set of 6-dimensional real matrices, for The set of real matrices of dimension , for The set of real matrices of dimension , for The set of real matrices of dimension , for The set of real matrices of dimension , for dimensional real matrices.

[0035] Divide the state transfer matrix into: in, is the state transfer matrix, is the first state transition submatrix, is the second state transition submatrix, is the third state transition submatrix, is the fourth state transfer submatrix; Divide the input matrix into: in, is the input matrix, is the first input sub-matrix, is the second input sub-matrix; The state space model can be divided into two sub-models. The driven state sub-model is: in, is the driving state change rate, In the driven state, In the no-drive state, is the input variable; The undriven state submodel is: in, is the rate of change of the undriven state.

[0036] Solve the analytical solution of the matrix index of the driven state submodel and the undriven state submodel, and record the discrete period as , the first matrix exponential The analytical solution is: Second Matrix Index The analytical solution is: 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; The two sub-models are discretized by using the zero-order hold method. The calculation expression of the discrete sub-model with driving state is: in, for Always in driving state, for Always in driving state, for No drive status at any time. for Input of time; The calculation expression of the discrete sub-model of the undriven state is: in, for The non-driven state at all times; The discrete model is obtained by integrating the driving state discrete sub-model and the non-driving state discrete sub-model. The calculation expression of the discrete model is: in, for The state of the moment, for The state of the moment, for The input status at the moment, is the state parameter matrix, is the system parameter matrix; By the first matrix index and the second matrix index Calculated and The parameterized form of is: S4: construct a prediction model according to the discrete model, and obtain an error model according to the prediction model and the reference trajectory; by Indicates the status The moment Step prediction, then Status of the moment predict The calculation expression of the step is: in, for The predicted state at the moment, is the prediction input matrix, is the prediction system matrix, for Step input vector, for The state of the moment; Drive status The reference trajectory The initial value of for: Drive status The reference trajectory The final value for: The expected values ​​of the undriven swing angle and its speed are both 0, generating the expected signal: ,but The reference trajectory for: in, for The expected signal of the moment, for The expected signal of the moment, for The expected signal of the moment; The calculation expression of the error model is: in, for The error in time, is the intermediate variable, .

[0037] 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; When applying state constraints to the system, the state constraints are converted into input constraints for processing. When considering state constraints, there 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 Step input vector.

[0038] The selected cost function is: in, is the cost function, is the first positive definite parameter matrix, is the second positive definite parameter matrix; Further calculations yield: by As decision variables, construct quadratic programming, and the calculation expression is: in, Select make Minimum, is the cost function, for Time reference trajectory The expected value of the step-by-step forecast, is the constraint function, is the first positive definite parameter matrix, is the second positive definite parameter matrix.

[0039] S6: Find the optimal solution of the quadratic programming and construct the online trajectory of the mast crane based on the optimal solution.

[0040] Solve the quadratic programming in each planning cycle to obtain the optimal solution: 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.

[0041] The input of the mast crane hardware system is generally the speed signal of the driving mechanism, and the online trajectory of the mast crane is obtained by using linear transformation and acceleration formula; The calculation expression of the linear transformation of time is: in, for There is always an acceleration signal driving the joint. The calculation expression of acceleration at the moment is: in, for +1 moment there is an acceleration signal driving the joint, for There is always an acceleration signal driving the joint. is a discrete period, The generation rule of online trajectories can be finally deduced as follows: 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.

[0042] like Figure 2 As shown, a mast crane online trajectory planning system with guaranteed state constraints is used to execute the above-mentioned mast crane online trajectory planning method with guaranteed state constraints, comprising: The model building and conversion module 101 is used to build 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; The matrix index solving module 102 is used to divide the state space model into a driven state sub-model and an undriven state sub-model to solve the analytical solution of the matrix index involved in the driven state sub-model and the undriven state sub-model; The discretization module 103 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 index to obtain the discrete model; The prediction model and error model construction module 104 is used to construct a prediction model according to the discrete model, and to construct an error model according to the prediction model and the reference trajectory; The quadratic programming construction module 105 is used to convert the state constraints into input constraints, select the cost function according to the error model, and construct the quadratic programming according to the input constraints and the cost function; 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.

[0043] Through the collaborative work of the above modules, the preset constraints of all states of the mast crane are guaranteed, the safety of the crane's lifting operations is enhanced, and the constraints of all states in the vector of the discrete model can be converted into constraints on the input.

[0044] In the process of zero-order hold discretization of the transformed model in the present invention, the matrix exponent can directly calculate the parameterized analytical solution; the optimization problem is a simple quadratic programming problem, the method for solving the optimization is very mature and has low demand for computing power, so it is easy to implement.

[0045] Simulate the method of the present invention in Matlab environment: Set the simulation cycle ; Select the boom length as ; Set the initial value of the variable angle , the expected value of the amplitude angle is , the initial value of the rotation angle , the expected value of the rotation angle , the initial value of the rope length , expected value , the initial value of the swing angle ; Construct the reference trajectory as ,in: Setting optimization parameters ,in, for No. sub-matrices, for No. sub-matrices, Select the following state constraints: The absolute value of the swing angle is constrained to The absolute value of the angular velocity of the swing angle is constrained to The overshoot of the boom rotation angle and luffing angle is constrained within Within, the overshoot of rope length is constrained to , while constraining the velocities of the driven joints planned by the algorithm.

[0046] There are three groups of simulation settings: The first simulation is a regular test, that is, the simulation is directly run with the above settings, and the output results are as follows Figure 4 As shown in Figures (a) to (j) in the figure.

[0047] Simulation 2 considers the case where the arm length measurement is inaccurate, that is, the arm length of the system is set to , while the planning algorithm still uses , to verify the robustness of the proposed algorithm to inaccurate arm length; the output results are as follows Figure 5 As shown in Figures (a) to (j) in the figure.

[0048] Simulation 3 considers the situation where the initial swing angle exists, that is, setting , to test whether the present invention can make the system converge to the expected value when it has an initial swing angle, and the output result is as follows Figure 6 As shown in Figures (a) to (j) in the figure.

[0049] like 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 measurement and initial swing angle, the present invention is still robust enough to ensure that each state converges to the target value while ensuring the state constraints.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions 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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