A method for controlling the performance of a hydraulic cleaning robot at a specified time

Abstract

The application discloses a kind of hydraulic cleaning robot specified time preset performance control method.This method is based on specified time preset performance function, fuses instruction filter, backstepping method and RISE robust compensation idea, designs hydraulic cleaning robot joint trajectory tracking controller.For the problems of model uncertainty and external disturbance existing in joint control process, the virtual control quantity and its derivative are obtained by using the instruction filter, which avoids the differential complexity problem in backstepping design, and the influence of lumped uncertainty is suppressed by RISE robust term.This method can ensure that the joint tracking error is always within the preset performance boundary, and the performance boundary shrinks to the specified range within the specified time, thereby improving the trajectory tracking accuracy and robustness of the system.

Description

Technical Field

[0001] This invention relates to the field of electromechanical servo control technology, specifically to a method for pre-setting the performance of a hydraulic tank cleaning robot at a specified time. Background Technology

[0002] Dry bulk cargo port cleaning is a crucial step in the unloading process. Traditional manual or mechanical cleaning methods suffer from low efficiency, harsh working environments, and high safety risks. Cleaning robots, with their flexible movement, strong environmental adaptability, and ease of unmanned operation, can effectively improve port unloading efficiency and operational safety. When operating in confined, unstructured ship cabin environments, six-degree-of-freedom hydraulic cleaning robots require coordinated movement of multiple joints. Their control performance is easily affected by factors such as load variations, joint friction, hydraulic drive nonlinearity, model parameter uncertainties, and external disturbances. Therefore, the joint control system of the cleaning robot not only needs high trajectory tracking accuracy and robustness but also must meet the requirements of the operation cycle for error convergence time, transient overshoot, and steady-state accuracy.

[0003] Existing robot joint control methods primarily focus on the asymptotic or finite-time stability of the system, making it difficult to directly specify the convergence time and transient range of the tracking error during the controller design phase. Pre-defined performance control methods can constrain the overshoot and steady-state accuracy of the tracking error through performance boundaries, but traditional performance functions typically only guarantee asymptotic convergence, failing to meet the specified time convergence requirements of cleaning operations. Furthermore, backstepping control requires differentiation of virtual control quantities when dealing with high-order nonlinear models of hydraulic systems, easily leading to increased controller complexity and differential computation; model uncertainties and complex disturbances in the system further degrade trajectory tracking performance. Therefore, there is an urgent need for a six-DOF hydraulic cleaning robot joint control method that can pre-define the error convergence time and performance boundaries, reduce the complexity of virtual control quantity differentiation, and effectively compensate for system uncertainties and external disturbances.

[0004] The design challenges of the aforementioned control method lie in the strong coupling between the mechanical dynamics of the six-DOF cleaning robot and the valve-controlled hydraulic system. Load variations, joint friction, pressure and flow nonlinearities, and external disturbances collectively create lumped uncertainties that are difficult to model accurately. Furthermore, the rapid contraction of the specified time error boundary increases the transient response requirements of the controller. Simultaneously, the differentiation of virtual control quantities in the backstepping recursion further increases the implementation complexity of the controller. Therefore, it is necessary to balance the feasibility, continuity, and disturbance rejection capabilities of the controller while meeting the specified time performance constraints. Summary of the Invention

[0005] The purpose of this invention is to provide a time-preset performance control method for a hydraulic tank cleaning robot. This method pre-sets the convergence time, transient overshoot, and steady-state accuracy of joint tracking errors using a time-preset performance function. It also integrates command filtering, backstepping control, and error sign integral robust control concepts. The method utilizes a command filter to obtain the filtered value and derivative of the virtual control quantity, avoiding direct analytical differentiation of complex virtual control quantities. Furthermore, it compensates for model uncertainties and external disturbances through a RISE robust term. This method ensures that the joint tracking error remains within the preset performance boundaries and that these boundaries shrink to a set range within a pre-specified time, achieving high-precision robust tracking of the tank cleaning robot's joint trajectory.

[0006] This invention addresses the problem of simultaneous existence of specified time performance constraints, backstepping control differential complexity, and lumped uncertainty of the hydraulic system during joint tracking of a six-DOF hydraulic cleaning robot. It proposes a control method that collaboratively designs a specified time preset performance function, a second-order instruction filter, and RISE robust compensation, so that error performance constraints, virtual control quantity smoothing, and uncertainty compensation are achieved under the same control framework.

[0007] The technical solution to achieve the objective of this invention is: a method for pre-setting the performance of a hydraulic tank cleaning robot at a specified time, comprising the following steps:

[0008] Step 1: Establish the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, then proceed to Step 2.

[0009] Step 2: Based on the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, construct the joint tracking controller of the cleaning robot with a preset performance function at a specified time, and proceed to Step 3.

[0010] Step 3: Use Lyapunov stability theory to prove the stability of the designed controller, and obtain the result that the joint tracking error meets the preset performance requirements and is asymptotically stable within a specified time.

[0011] Compared with the prior art, the significant advantages of this invention are: (1) Using a performance function preset at a specified time to constrain the joint tracking error, the error convergence time, maximum overshoot and steady-state accuracy can be preset in the controller design stage, so that the tracking error enters the set range within a specified time; (2) Introducing an instruction filter to obtain the filtered value and derivative of the virtual control quantity, avoiding direct analytical differentiation of complex virtual control quantity, reducing the computational complexity of the backstep controller, and making the virtual control instruction smoother; (3) Using RISE robust terms to compensate for the lumped uncertainty term formed by model uncertainty, load change and external disturbance, improving the accuracy and robustness of the joint trajectory tracking of the six-degree-of-freedom hydraulic cleaning robot. Attached Figure Description

[0012] Figure 1 This is a schematic diagram illustrating the principle of the hydraulic tank cleaning robot's time-preset performance control method according to the present invention.

[0013] Figure 2 This is a simplified diagram of the six-degree-of-freedom hydraulic cleaning robot of the present invention.

[0014] Figures 3-8 The graph shows the trajectory tracking process curves of the six joints under the action of the time-preset performance controller designed in this invention, as well as a comparison curve of the tracking error with that of a traditional PID controller. Detailed Implementation

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] Combination Figure 1 and Figure 2 The hydraulic tank cleaning robot's time-preset performance control method of the present invention includes the following steps:

[0017] Step 1: Establish the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot.

[0018] Step 1-1: The hydraulic tank cleaning robot is used for cleaning bulk materials inside the ship's hold. Each joint is driven by a hydraulic actuator. The controller changes the valve opening and hydraulic oil flow by adjusting the input signal of the proportional valve, so that a pressure difference is formed between the two chambers of the hydraulic cylinder, which pushes the piston rod to move and drives the robot joints to move through the mechanical transmission mechanism. Based on the dynamic characteristics of the robot's mechanical system and the pressure and flow characteristics of the proportional valve and hydraulic cylinder, the mechanical system dynamic model and hydraulic drive system model of the six-degree-of-freedom hydraulic tank cleaning robot are established respectively.

[0019] The mechanical system dynamics model of the cleanup robot constructed according to the Lagrange method is as follows:

[0020] (1),

[0021] in, These represent joint angle, angular velocity, and angular acceleration, respectively. Inertia matrix Coriolis force and centrifugal force matrix Gravity term Lumped disturbance vector of mechanical system The lumped disturbance vector of a mechanical system includes unmodeled dynamics of mechanical dynamics and external disturbances, as well as joint driving torques. , Represents a six-dimensional real vector space. This represents the matrix space consisting of all 6×6 real matrices.

[0022] Define the displacement vector of the hydraulic actuator T represents transpose. The relationship between the hydraulic cylinder piston displacement and the robot joint angular displacement is expressed as:

[0023] (2),

[0024] Differentiating it, we obtain the relationship between the hydraulic cylinder piston speed and the joint angular velocity as follows:

[0025] (3),

[0026] In the formula, the displacement mapping function between the hydraulic actuator space and the joint space is... Actuator Motion Jacobian Matrix For any variable , express The first derivative.

[0027] Establish a pressure dynamic model of the hydraulic actuator of a six-degree-of-freedom hydraulic cleaning robot:

[0028] (4),

[0029] In the formula, This indicates the six joint numbers. This indicates the oil pressure in the rodless chamber of the hydraulic cylinder. This indicates the oil pressure in the rod chamber of the hydraulic cylinder. Indicates the effective elastic modulus of the oil. This indicates the effective area of ​​the rodless chamber piston in a hydraulic cylinder. This indicates the effective area of ​​the piston in the rod chamber of a hydraulic cylinder, and the control volume of the rodless chamber. , This represents the initial volume of the rodless cavity and the control volume of the rod-type cavity. , This represents the initial volume of the rod cavity. This indicates the piston displacement of the hydraulic cylinder. This represents the leakage coefficient within the hydraulic cylinder. , Indicates the flow rate of the two chambers. express Unmodeled interference, express Unmodeled interference; Indicates time.

[0030] and The following relationships exist between the proportional valve spool control input signal and the following:

[0031] (5),

[0032] in, This represents the gain coefficient of the proportional valve. Indicates the oil supply pressure. Indicates the return oil pressure. , The pressure difference variable is the pressure difference between the corresponding valve ports of the two chambers. This represents the control input signal for the proportional valve spool, i.e., the control law.

[0033] Therefore, the torques of each joint of the cleaning robot are... Written as:

[0034] (6),

[0035] in, It represents the transmission Jacobian coefficient of the piston displacement of the i-th hydraulic cylinder relative to the corresponding joint angular displacement;

[0036] This leads to the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot.

[0037] Steps 1-2: To facilitate the subsequent design and analysis of the controller, define the set of state variables. State variables State variables State variables The system can then be written in the following state-space form:

[0038] (7),

[0039] in:

[0040] (8),

[0041] in:

[0042] (9),

[0043] In the formula, the inertia matrix Coriolis force and centrifugal force matrix Gravity term Lumped disturbance vector of mechanical system The lumped disturbance vector of a mechanical system includes unmodeled dynamics of mechanical dynamics and external disturbances; the lumped disturbance vector of a hydraulic system... The lumped disturbance vector of a hydraulic system includes pressure dynamic model errors and unknown disturbances; , and These respectively represent the valve-controlled input gain term, the joint motion flow coupling term, and the hydraulic leakage pressure loss term. Indicates the control input vector; These represent the unmodeled disturbance vectors in the pressure dynamics of the rodless and rod-type chambers, respectively. These represent the pressure vectors of the rodless chamber and the rod chamber of the six hydraulic cylinders, respectively. , These represent diagonal matrices formed by the square roots of the pressure differences at the valve ports of the rodless and rod chambers of each hydraulic cylinder, respectively. These represent diagonal matrices formed by the effective areas of the rodless chamber pistons and the rod chamber pistons of each hydraulic cylinder, respectively. These represent diagonal matrices formed by the rodless chamber control volume and the rod chamber control volume of each hydraulic cylinder, respectively. This represents a diagonal matrix composed of the flow gain coefficients of each proportional valve. This represents a diagonal matrix composed of the leakage coefficients of each hydraulic cylinder. This represents the transmission Jacobian matrix between the hydraulic actuator space and the robot joint space. This represents the diagonal matrix construction operator, which arranges the elements within the parentheses sequentially along the main diagonal of the matrix and sets the non-diagonal elements to zero.

[0044] The purpose of establishing the above state-space model is to uniformly describe the dynamics of the robot's mechanical system, the pressure dynamics of the hydraulic actuator, and the input relationship of the proportional valve, so as to provide a model basis for the subsequent step-by-step design of virtual control quantities and actual control inputs using the backstepping method. At the same time, it is convenient to distinguish and handle the lumped disturbances of the mechanical system and the lumped disturbances of the hydraulic system.

[0045] To facilitate controller design, the following assumptions are made:

[0046] Assumption 1: The system expects to track position commands. It is third-order continuously differentiable, and the system expects the position command, velocity command, and acceleration command to be bounded.

[0047] Assumption 2: Lumped disturbance of mechanical system Lumped disturbances in hydraulic systems It is sufficiently smooth, and its first and second derivatives exist and are bounded, that is:

[0048] (10)

[0049] In the formula, They represent and The i-th component, All are unknown positive constants; for any variable , express The second derivative, express The infinite norm of .

[0050] Assumption 3: The natural angular frequency of the second-order command filter Damping ratio satisfy Furthermore, the filter's initial state is bounded; the virtual control quantity is second-order continuously differentiable and its first and second derivatives are bounded.

[0051] Proceed to step 2.

[0052] In step 2, based on the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, a joint tracking controller for the cleaning robot with a preset performance function at a specified time is constructed. The specific steps are as follows:

[0053] Step 2-1: To facilitate controller design, design a preset performance function for a specified time and transform the tracking error to obtain the transformed error. The details are as follows:

[0054] Let the desired joint trajectory be The joint position tracking error is defined as... To constrain tracking error, a preset performance function is introduced at a specified time. :

[0055] (11),

[0056] In the formula, Indicates the initial allowable error boundary. Represents the steady-state boundary after a specified time, and satisfies ; The pre-set convergence time.

[0057] By adjusting the design parameters in the performance function, the error boundary can be changed. The internal contraction speed, when At this time, the performance boundary remains within the steady-state range, that is:

[0058] (12)

[0059] In the formula, The lower boundary coefficient represents the difference between the actual and expected angular displacements of the i-th joint. and upper boundary coefficient All are positive adjustable parameters. and These are used to limit the allowable undershoot and overshoot values ​​for the error, respectively, so that the tracking error remains within the preset steady-state error range after a specified time. and Represents the time Time tracking error The permissible steady-state range.

[0060] Introduce a function with strictly increasing properties. And it satisfies:

[0061] (13)

[0062] in, Indicates joint Conversion error.

[0063] Based on the above characteristics, the tracking error can be rewritten as:

[0064] (14)

[0065] Define function The format is:

[0066] (15)

[0067] Define normalization error Substituting into equation (15) and taking the inverse function, we get:

[0068] (16)

[0069] From the above formula, it can be seen that when the conversion error When bounded, normalized error It always remains within the allowed interval and will not touch the preset boundary, thus making equation (12) true. Therefore, as long as It can asymptotically converge to 0, joint tracking error It will also converge to 0 at the same time.

[0070] Combine the transition errors of each joint into a vector. Differentiating it with respect to time, we get:

[0071] (17)

[0072] In the formula:

[0073] (18)

[0074] in, This is the normalized error diagonal matrix. This is the diagonal matrix of lower boundary coefficients. This is the diagonal matrix of the upper boundary coefficients;

[0075] Define the error transformation gain matrix :

[0076] (19)

[0077] As can be seen from equation (19), It is bounded, that is:

[0078] (20)

[0079] This completes the preset performance transformation of joint tracking error at a specified time.

[0080] The aforementioned error transformation maps the tracking error, which was originally limited by the preset performance boundary, into an unconstrained conversion error, thus transforming the constrained tracking problem into a conversion error stabilization problem. When the conversion error remains bounded, the original tracking error will never touch the preset performance boundary, thereby ensuring that the convergence time, transient overshoot, and steady-state range of the error meet the preset requirements.

[0081] Step 2-2: Based on the mechanical system dynamics model and hydraulic drive system model of the cleaning robot and the conversion error... Design a performance tracking controller with a specified time preset, as follows:

[0082] Differentiating equation (17) with respect to time and substituting equation (7) into it, we get:

[0083] (twenty one),

[0084] Define the following error variable vector:

[0085] (twenty two),

[0086] In the formula:

[0087] (twenty three),

[0088] in, These are all auxiliary error signals introduced during the backstepping design process. All of these are positive definite gain matrices to be designed. This is a virtual control variable.

[0089] Define error transformation related terms and known model nonlinear terms :

[0090] (twenty four),

[0091] (25),

[0092] Based on equations (7), (21), and (22), the error system can be reorganized into the following form:

[0093] (26)

[0094] To address the unknown disturbances and nonlinear uncertainties in the compensation formula, a RISE robust compensation term is introduced, and the virtual control quantity is constructed as follows:

[0095] (27)

[0096] In the formula:

[0097] (28)

[0098] in, For model compensation terms, For linear robust terms, For RISE feedback items, , It is a positive definite gain matrix; A positive gain vector; This represents a symbolic function defined by its components. It is the integral variable.

[0099] Design a second-order instruction filter for the virtual control input:

[0100] (29)

[0101] In the formula This represents the damping ratio of a second-order command filter. This represents the natural angular frequency of the second-order command filter. The virtual control quantity of joint i The filter outputs, and all filter outputs together form the filter virtual control vector. .

[0102] Using a second-order instruction filter to smooth the virtual control quantity and its derivative can avoid repeated analytical differentiation of complex virtual control quantities during the backstepping process, reduce the differential operation of the controller, and reduce the impact of rapid changes in virtual control instructions on the actual control input.

[0103] Then equation (22) is changed to:

[0104] (30)

[0105] Substituting into equation (26), we get:

[0106] (31),

[0107] Differentiating the above equation with respect to time, we get:

[0108] (32),

[0109] Define state-related nonlinear terms respectively sum of uncertain terms for:

[0110] (33),

[0111] According to the Mean Value Theorem:

[0112] (34),

[0113] In the formula, the error signal vector Boundary function Let represent a positive, globally invertible, non-decreasing function. This represents the Euclidean norm.

[0114] Based on assumptions 2 and 3 and equation (20). It satisfies the following properties:

[0115] (35),

[0116] In the formula, express The i-th component, All are unknown positive constants;

[0117] Substituting equations (7) and (30) into equation (22), we get:

[0118] (36)

[0119] Design the control law according to equation (36). for:

[0120] (37)

[0121] In the formula:

[0122] (38),

[0123] in, This represents the model-based compensation term. Represents the linear robust term, This represents the feedback control term in RISE. This represents a positive definite gain diagonal matrix. This represents a positive gain vector.

[0124] By introducing RISE robust terms into both virtual and actual control inputs, continuous compensation is provided for lumped uncertainties caused by mechanical dynamics modeling errors, hydraulic drive nonlinearity, load changes, and external disturbances. This reduces the impact of uncertainties on joint tracking errors and improves the tracking accuracy and robustness of the joint control system of the six-DOF hydraulic cleaning robot.

[0125] Combined formula (37). Differentiating with respect to time yields:

[0126] (39)

[0127] Proceed to step 3.

[0128] Step 3: Apply Lyapunov stability theory to prove the stability of the designed controller, and obtain the result that the joint tracking error meets the preset performance requirements and is asymptotically stable within a specified time, as follows:

[0129] Before proving stability, the following lemma is given to facilitate subsequent analysis:

[0130] Lemma 1: Consider a nonlinear time-varying system ,in Regarding time The system state vector can be written as .function For the state vector and time The nonlinear vector function, the above system has a solution within the considered domain. Wherein, Let be the dimension of the system state vector. Represents an n-dimensional real vector space. Represents the set of nonnegative real numbers. Domain ,in A positive constant. Define a continuously differentiable function that satisfies the following conditions: That is, for satisfy:

[0131] (40)

[0132] in, All are continuous positive definite functions. It is a uniformly continuous positive semi-definite function. If it satisfies equation (40) and the initial value of the system state vector is... ,but:

[0133] (41),

[0134] Among them, the set is defined. for:

[0135] (42),

[0136] In the formula It is a positive constant.

[0137] Based on assumption 2 and equation (35), the gain vector is selected:

[0138] (43),

[0139] Its elements satisfy:

[0140] (44),

[0141] Constructing auxiliary functions:

[0142] (45)

[0143] in:

[0144] (46)

[0145] In the formula All are auxiliary functions. They represent The initial value.

[0146] Based on the above conditions, the function can be obtained. and The constant will be positive.

[0147] Define Lyapunov functions as follows:

[0148] (47)

[0149] In the formula, the system state vector is defined. Error signal vector Additional information:

[0150] (48)

[0151] in:

[0152] (49)

[0153] Analysis of equation (47) shows that:

[0154] (50),

[0155] In the formula:

[0156] (51),

[0157] (52),

[0158] In the formula All are continuous positive definite functions. Let Lyapunov's function be the equivalent lower bound constant. This is an equivalent upper bound constant for the Lyapunov function; This is a lower bound constant for the minimum eigenvalue of the inertia matrix. This is a constant that is the upper bound of the largest eigenvalue of the inertia matrix. It is a six-dimensional identity matrix.

[0159] Differentiating equation (47) with respect to time and substituting it into equations (22), (32), (39), and (45), we obtain:

[0160] (53),

[0161] (54),

[0162] Define the closed-loop gain matrix for:

[0163] (55),

[0164] By adjusting the gain matrix The value of the matrix makes If the matrix is ​​positive definite, then equation (54) can be rewritten as:

[0165] (56),

[0166] This is a state-dependent nonlinear term.

[0167] According to equation (34) and by using Young's inequality to shrink the cross terms, we get:

[0168] (57),

[0169] In the formula and It is the smallest eigenvalue of the corresponding matrix.

[0170] By selecting an appropriate controller gain, the following inequality holds, where the intermediate variable h is a positive number:

[0171] (58),

[0172] In the formula for The inverse function, therefore:

[0173] (59),

[0174] It is a positive semi-definite function, and its domain is:

[0175] (60)

[0176] The Lyapunov function is obtained from equation (59). Regarding the monotony of time not increasing. And because... Non-negative, therefore exist The upper limit is always present; at the same time, it is possible to obtain In the time interval The integral is finite. The error signal is obtained according to equation (47). Both are bounded; this is derived from hypothesis 1. It is also bounded; as can be seen from equations (22), (32), and (39). The derivative with respect to time is also bounded, that is... The set is uniformly continuous within its domain D, and is defined according to Lemma 1. :

[0177] (61),

[0178] Based on the above analysis, we can conclude that:

[0179] (62),

[0180] Depend on From the definition and error transformation relationship, we can see that the system tracking error It is always constrained by a preset performance function at a specified time. This performance function is at the preset time. Contracting to the steady-state boundary, therefore when At that time, the tracking error is limited to a preset steady-state error range. Inside.

[0181] From the error signal vector As can be seen from the definition, when At that time, the error signal The tracking error will asymptotically converge to 0. It can enter the preset steady-state error range within a specified time, that is, satisfy equation (12), and also satisfy:

[0182] (63),

[0183] Therefore, we can conclude that by appropriately selecting the gain matrix... and gain vector This can guarantee the matrix Within the robot's permissible working area, the joint tracking error remains consistently positive definite, always within the preset performance boundaries, and within a pre-specified time. It enters the set steady-state error range and eventually converges asymptotically to 0.

[0184] Example

[0185] The time-preset performance control method designed in this invention is denoted as PTPPF, and a traditional PID control method is selected for comparison.

[0186] In the method of this invention, the control gain matrix is ​​always taken as a positive definite diagonal matrix, and the specific parameters are set as follows:

[0187] k1=diag{1.5,20,8,16,10,6},k2=diag{20,10,5,30,20,8},k3=diag{20,15,20,30,35,15},k r1 =diag{45,250,200,100,60,20},k r2 =diag{8,5,10,5,8,10},k s =diag{8,50,25,20,8,5},β1=[1.5,10,2,1,3,1.5] T , β2=[0.3,0.1,0.1,0.1,0.3,0.2] T .

[0188] The preset performance parameters are: μ0=[0.6,0.4,0.3,0.6,0.6,0.5], μ ∞ =[0.1,0.05,0.05,0.12,0.15,0.1] = = diag{1,1.2,1,1.5,1,1}, T0=[12,20,10,20,12,8].

[0189] PID parameters are set as follows: proportional gain matrix K P = diag{10,90,80,100,5,10}, Integral gain matrix K I =diag{1,25,15,15,5,0.5}, differential gain matrix K D = diag{0,0,0,0,0,0}.

[0190] The desired instructions for the given system are:

[0191] (64),

[0192] The trajectory tracking and error comparison results of the six joints under both PTPPF and PID control methods are as follows: Figures 3-8 As shown in the figure. The top of each figure shows the actual joint trajectory and the expected trajectory under the PTPPF controller designed in this paper, where the solid line represents the actual joint output and the dashed line represents the expected trajectory; the bottom shows the tracking error of the two control methods, where the solid line represents the tracking error under the PTPPF controller, the dotted line represents the tracking error under the PID controller, and the dashed line represents the upper and lower boundaries given by the preset performance function.

[0193] As shown by the trajectory curves of each joint, the PTPPF controller can achieve good trajectory tracking under different amplitudes and frequencies of the desired trajectory. Due to the inconsistency between the initial state of the system and the initial value of the desired trajectory, some joints exhibit certain tracking deviations in the initial stage of simulation. Among them, the errors of joints 5 and 6 show relatively obvious short-term decaying oscillations, but the error amplitude can be reduced rapidly. After a brief initial adjustment, the actual trajectories of each joint can closely match the desired trajectory and maintain good consistency in subsequent motion, indicating that the designed controller has good tracking capability for different joint motion trajectories.

[0194] As can be seen from the error curves below, the tracking errors of the six joints under the PTPPF controller remained within the preset performance boundaries throughout the simulation. The performance boundaries of each joint gradually contracted according to the preset specified time, reaching the steady-state boundary after the corresponding specified time; at the same time, the PTPPF tracking errors all entered the corresponding steady-state error range and remained near zero. This indicates that the constructed preset performance function for the specified time can effectively constrain the transient evolution process, convergence time, and steady-state range of the tracking error.

[0195] In contrast, while the PID controller can achieve basic trajectory tracking, its tracking error still exhibits periodic fluctuations related to changes in the desired trajectory during the steady-state phase. Furthermore, the error amplitude at most joints is significantly larger than that of the PTPPF controller, with particularly pronounced differences at joints 3, 5, and 6. The PTPPF controller, however, can quickly suppress the error to near zero after the initial transient state, while ensuring that the error never exceeds the preset performance boundary, demonstrating better transient constraint capability, steady-state tracking accuracy, and robust tracking performance. In summary, the proposed control method demonstrates superior overall control performance compared to the traditional PID controller in the multi-joint trajectory tracking task of a six-DOF cleaning robot.

Claims

1. A method for pre-setting the performance of a hydraulic tank cleaning robot at a specified time, characterized in that, Includes the following steps: Step 1: Establish the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, then proceed to Step 2; Step 2: Based on the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, construct the joint tracking controller of the cleaning robot with a preset performance function at a specified time, and proceed to Step 3; Step 3: The stability of the joint tracking controller of the above-mentioned cleaning robot is proved by applying Lyapunov stability theory. The results show that the joint tracking error meets the preset performance requirements and is asymptotically stable within a specified time.

2. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 1, characterized in that, In step 1, the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot are established, as follows: Step 1-1: The hydraulic tank cleaning robot is used for cleaning bulk materials inside the ship's hold. Each joint is driven by a hydraulic actuator. The controller changes the valve opening and hydraulic oil flow by adjusting the input signal of the proportional valve, so that a pressure difference is formed between the two chambers of the hydraulic cylinder, which pushes the piston rod to move and drives the robot joints to move through the mechanical transmission mechanism. Based on the dynamic characteristics of the robot's mechanical system and the pressure and flow characteristics of the proportional valve and hydraulic cylinder, the mechanical system dynamic model and hydraulic drive system model of the six-degree-of-freedom hydraulic tank cleaning robot are established respectively. Steps 1-2: To facilitate controller design, define state variables and convert the established mechanical system dynamics model and hydraulic drive system model into state-space equations.

3. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 2, characterized in that, In step 1-1, based on the dynamic characteristics of the mechanical structure, hydraulic cylinder, and proportional valve of the six-degree-of-freedom cleaning robot, the mechanical system dynamic model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot are obtained, as follows: The mechanical system dynamics model of the cleanup robot constructed according to the Lagrange method is as follows: （1）， in, These represent joint angle, angular velocity, and angular acceleration, respectively. Inertia matrix Coriolis force and centrifugal force matrix Gravity term Lumped disturbance vector of mechanical system The lumped disturbance vector of a mechanical system includes unmodeled dynamics of mechanical dynamics and external disturbances, as well as joint driving torques. , Represents a six-dimensional real vector space. This represents the matrix space consisting of all 6×6 real matrices; Define the displacement vector of the hydraulic actuator T represents transpose. The relationship between the hydraulic cylinder piston displacement and the robot joint angular displacement is expressed as: （2）， Differentiating equation (2), we obtain the relationship between the piston speed of the hydraulic cylinder and the angular velocity of the joint as follows: （3）， In the formula, the displacement mapping function between the hydraulic actuator space and the joint space is... Actuator Motion Jacobian Matrix For any variable , express The first derivative; Establish a pressure dynamic model of the hydraulic actuator of a six-degree-of-freedom hydraulic cleaning robot: （4）， In the formula, This indicates the six joint numbers. This indicates the oil pressure in the rodless chamber of the hydraulic cylinder. This indicates the oil pressure in the rod chamber of the hydraulic cylinder. Indicates the effective elastic modulus of the oil. This indicates the effective area of ​​the rodless chamber piston in a hydraulic cylinder. This indicates the effective area of ​​the piston in the rod chamber of a hydraulic cylinder, and the control volume of the rodless chamber. , This represents the initial volume of the rodless cavity and the control volume of the rod-type cavity. , This represents the initial volume of the rod cavity. This indicates the piston displacement of the hydraulic cylinder. This represents the leakage coefficient within the hydraulic cylinder. , Indicates the flow rate of the two chambers. express Unmodeled interference, express Unmodeled interference; Indicates time; and The following relationships exist between the proportional valve spool control input signal and the following: （5）， in, This represents the gain coefficient of the proportional valve. Indicates the oil supply pressure. Indicates the return oil pressure. , The pressure difference variable is the pressure difference between the corresponding valve ports of the two chambers. This represents the control input signal for the proportional valve spool, i.e., the control law; Therefore, the torques of each joint of the cleaning robot are... Written as: （6）， in, It represents the transmission Jacobian coefficient of the piston displacement of the i-th hydraulic cylinder relative to the corresponding joint angular displacement; This leads to the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot.

4. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 3, characterized in that, Steps 1-2: To facilitate controller design, define state variables and convert the established mechanical system dynamics model and hydraulic drive system model into state-space equations, as follows: To facilitate subsequent controller design and analysis, a set of state variables is defined. State variables State variables State variables ; The system can then be written in the following state-space form: （7）， in: （8）， in: （9）， In the formula, the inertia matrix Coriolis force and centrifugal force matrix Gravity term Lumped disturbance vector of mechanical system The lumped disturbance vector of a mechanical system includes unmodeled dynamics of mechanical dynamics and external disturbances; the lumped disturbance vector of a hydraulic system... The lumped disturbance vector of a hydraulic system includes pressure dynamic model errors and unknown disturbances; , and These respectively represent the valve-controlled input gain term, the joint motion flow coupling term, and the hydraulic leakage pressure loss term. Indicates the control input vector; These represent the unmodeled disturbance vectors in the pressure dynamics of the rodless and rod-type chambers, respectively. These represent the pressure vectors of the rodless chamber and the rod chamber of the six hydraulic cylinders, respectively. , These represent diagonal matrices formed by the square roots of the pressure differences at the valve ports of the rodless and rod chambers of each hydraulic cylinder, respectively. These represent diagonal matrices formed by the effective areas of the rodless chamber pistons and the rod chamber pistons of each hydraulic cylinder, respectively. These represent diagonal matrices formed by the rodless chamber control volume and the rod chamber control volume of each hydraulic cylinder, respectively. This represents a diagonal matrix composed of the flow gain coefficients of each proportional valve. This represents a diagonal matrix composed of the leakage coefficients of each hydraulic cylinder. This represents the transmission Jacobian matrix between the hydraulic actuator space and the robot joint space. This represents the diagonal matrix construction operator, which arranges the elements within the parentheses sequentially along the main diagonal of the matrix and sets the non-diagonal elements to zero.

5. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 4, characterized in that, In step 1, for the convenience of controller design, the following assumptions are made: Assumption 1: The system expects to track position commands. It is third-order continuously differentiable, and the system expects bounded position, velocity, and acceleration commands. Assumption 2: Lumped disturbance of mechanical system Lumped disturbances in hydraulic systems It is sufficiently smooth, and its first and second derivatives exist and are bounded, that is: （10）， In the formula, They represent and The i-th component, All are unknown positive constants; for any variable , express The second derivative, express The infinite norm; Assumption 3: The natural angular frequency of the second-order command filter Damping ratio satisfy Furthermore, the filter's initial state is bounded; the virtual control quantity is second-order continuously differentiable and its first and second derivatives are bounded. Proceed to step 2.

6. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 5, characterized in that, In step 2, based on the mechanical system dynamics model and hydraulic drive system model of the six-degree-of-freedom hydraulic cleaning robot, a joint tracking controller for the cleaning robot with a preset performance function at a specified time is constructed, as follows: Step 2-1: To facilitate controller design, design a preset performance function for a specified time and transform the tracking error to obtain the transformed error. ; Step 2-2: Based on the mechanical system dynamics model and hydraulic drive system model of the cleaning robot and the conversion error... Design a performance tracking controller with a specified time preset.

7. The hydraulic tank cleaning robot time-preset performance control method according to claim 6, characterized in that, Step 2-1: Design a preset performance function for a specified time and transform the tracking error to obtain the transformed error. The details are as follows: Let the desired joint trajectory be Define joint position tracking error To constrain tracking error, a preset performance function is introduced at a specified time. : （11）， In the formula, Indicates the initial allowable error boundary. Represents the steady-state boundary after a specified time, and satisfies ; The pre-set convergence time; By adjusting the design parameters in the performance function, the error boundary can be changed. The internal contraction speed, when At this time, the performance boundary remains within the steady-state range, that is: （12）， In the formula, The lower boundary coefficient represents the difference between the expected angular displacement and the actual angular displacement of the i-th joint. and upper boundary coefficient All are positive adjustable parameters. and These are used to limit the allowable undershoot and overshoot values ​​for the error, respectively, so that the tracking error remains within the preset steady-state error range after a specified time. and Represents the time Time tracking error The permissible steady-state range; Introduce a function with strictly increasing properties. And it satisfies: （13）， in, Indicates joint Conversion error; Based on the above characteristics, the tracking error of each joint is... Rewritten as: （14）， Define function The format is: （15）， Define normalization error Substituting into equation (15) and taking the inverse function, we get: （16）， From the above formula, it can be seen that when the conversion error When bounded, normalized error It always remains within the allowed interval and will not touch the preset boundary, making equation (12) valid; therefore, as long as Able to converge asymptotically to 0, joint tracking error It will also converge to 0 at the same time; Combine the transition errors of each joint into a vector. Differentiating it with respect to time, we get: （17）， In the formula: （18）， in, This is the normalized error diagonal matrix. This is the diagonal matrix of lower boundary coefficients. This is the diagonal matrix of the upper boundary coefficients; Define the error transformation gain matrix : （19）， As can be seen from equation (19), It is bounded, that is: （20）， This completes the preset performance transformation of joint tracking error at a specified time.

8. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 7, characterized in that, In step 2-2, based on the mechanical system dynamics model and hydraulic drive system model of the cleaning robot and the conversion error... Design a performance tracking controller with a specified time preset, as follows: Differentiating equation (17) with respect to time and substituting equation (7) into it, we get: （21）， Define the following error variable vector: （22）， In the formula: （23）， in, These are all auxiliary error signals introduced during the backstepping design process. All of these are positive definite gain matrices to be designed. This is a virtual control variable; Define error transformation related terms and known model nonlinear terms : （24）， （25）， Based on equations (7), (21), and (22), the error system can be reorganized into the following form: （26）， To address the unknown disturbances and nonlinear uncertainties in the compensation formula, a RISE robust compensation term is introduced, and the virtual control quantity is constructed as follows: （27）， In the formula: （28）， in, For model compensation terms, For linear robust terms, For RISE feedback items, , It is a positive definite gain matrix; A positive gain vector; This represents a symbolic function defined by its components; For integration variables; Design a second-order instruction filter for the virtual control input: （29）， In the formula This represents the damping ratio of a second-order command filter. This represents the natural angular frequency of the second-order command filter. The virtual control quantity of joint i The filter outputs, and all filter outputs together form the filter virtual control vector. ; Then equation (22) is changed to: （30）， Substituting into equation (26), we get: （31）， Differentiating the above equation with respect to time, we get: （32）， Define state-related nonlinear terms respectively sum of uncertain terms for: （33）， According to the Mean Value Theorem: （34）， In the formula, the error signal vector Boundary function Let represent a positive, globally invertible, non-decreasing function. Denotes the Euclidean norm; Based on assumptions 2 and 3 and equation (20). It satisfies the following properties: （35）， In the formula, express The i-th component, All are unknown positive constants; Substituting equations (7) and (30) into equation (22), we get: （36）， Design the control law according to equation (36). for: （37）， In the formula: （38）， in, This represents the model-based compensation term. Represents the linear robust term, This represents the feedback control term in RISE. This represents a positive gain diagonal matrix. Represents a positive gain vector; Combined formula (37). Differentiating with respect to time yields: （39）， Proceed to step 3.

9. The hydraulic tank cleaning robot's performance control method for preset performance at a specified time according to claim 8, characterized in that, The stability of the designed controller was proven using Lyapunov stability theory, yielding results showing that the joint tracking error meets the preset performance requirements and is asymptotically stable within a specified time. The details are as follows: Based on assumption 2 and equation (35), select the gain vector. : （43）， Its elements satisfy: （44）， Constructing auxiliary functions: （45）， in: （46）， In the formula All are auxiliary functions. They represent The initial value; Based on the above conditions, the function can be obtained. and The constant will be positive definite; Define Lyapunov functions as follows: （47）， In the formula, the system state vector is defined. Error signal vector Additional information: （48）， in: （49）， The stability of the designed controller was proven using Lyapunov stability theory, and the results showed that the joint tracking error met the preset performance requirements and was asymptotically stable within a specified time.

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