An underwater electric mechanical arm control method based on model predictive control
By employing model predictive control in an underwater robotic arm, a nonlinear dynamic model was established and the joint driving torque was optimized, solving the problem of precise control of PID controllers in underwater environments and achieving higher control accuracy and disturbance rejection performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2023-05-16
- Publication Date
- 2026-04-21
AI Technical Summary
Existing PID controllers are difficult to achieve precise control in underwater environments, especially when faced with the effects of buoyancy, water resistance, and parameter uncertainties, resulting in low trajectory tracking accuracy of the robotic arm and the presence of overshoot and jitter.
A model predictive control-based approach is adopted to establish a nonlinear dynamic model, taking into account the effects of hydrodynamics. The joint driving torque is optimized through model predictive control, and model mismatch is compensated in real time to achieve real-time control of the robotic arm.
It improves the control accuracy and robustness of the underwater robotic arm, reduces motion control errors in the underwater environment, and demonstrates good anti-disturbance performance and smooth control output.
Smart Images
Figure CN116673945B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a control method for an underwater electric robotic arm, specifically a control method for an underwater electric robotic arm based on model predictive control. Background Technology
[0002] The ocean is rich in resources such as oil and gas, minerals, compounds, and marine life, and the development and utilization of these resources are receiving increasing attention. However, the marine environment is characterized by high pressure, low temperature, and high risk, making it unsuitable for prolonged, continuous human operations. Therefore, underwater robots and robotic arms, capable of replacing manual labor, have become crucial tools for exploring the ocean and developing its resources. Given the complex marine environment, underwater robotic arms require superior motion control methods to improve their performance and meet operational requirements.
[0003] Due to the unique nature of the underwater working environment, robotic arms inherently exhibit model nonlinearity and parameter uncertainties. They are also affected by buoyancy, water resistance, and additional mass forces, resulting in low trajectory tracking accuracy for commonly used PID controllers during underwater operations, making precise control difficult. Furthermore, the actual joint movements of robotic arms are subject to constraints, limiting the control output and the state variables of each joint. Under the influence of transient underwater disturbances, PID controllers struggle to address these constraints, leading to overshoot and chattering phenomena in the robotic arm. Summary of the Invention
[0004] To address the problems in the background technology, it is necessary to utilize model-based nonlinear controllers to improve control performance and obtain relatively smooth control outputs. This invention provides a model predictive control (MMC)-based control method for underwater electric manipulators. This method considers the influence of hydrodynamics during dynamic modeling and employs MMC to reduce motion control errors of the manipulator's end effector while ensuring system closed-loop stability. In the underwater environment, the manipulator is affected by buoyancy, water resistance due to fluid-structure interaction, additional mass forces, and other uncertainties, thus impacting the accurate modeling and control of the manipulator. To address these issues, this invention can reduce motion control errors in the electric manipulator, improving accuracy and operational performance.
[0005] The technical solution adopted in this invention is:
[0006] The underwater electric robotic arm control method of the present invention includes the following steps:
[0007] Step 1: Establish a nonlinear dynamic model of the underwater electric manipulator; based on the nonlinear dynamic model, use model predictive control to establish a predictive model for the underwater electric manipulator.
[0008] The second step is to input the angular displacement and angular velocity of each joint of the underwater electric manipulator into the prediction model in real time. The prediction model outputs the driving torque of each joint of the underwater electric manipulator in real time, thereby controlling the continuous operation of the underwater electric manipulator and realizing the real-time control of the underwater electric manipulator.
[0009] The nonlinear dynamic model of the underwater electric manipulator established in the first step, under hydrodynamic terms and external disturbances, is as follows:
[0010]
[0011]
[0012] Where M() represents the inertia matrix of the underwater electro-manipulator, C() represents the Coriolis force and centripetal force matrices of the underwater electro-manipulator, G1() represents the equivalent gravity matrix of the underwater electro-manipulator; H() represents the added mass acceleration matrix; D() represents the added mass velocity matrix; q, and Let q represent the joint angular displacement, angular velocity, and angular acceleration of the underwater electro-mechanical arm, respectively, where q = [q1 q2 … q n ], q1, q2 … q n These represent the angular displacements of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. These represent the angular velocities of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. τ represents the angular acceleration of the 1st, 2nd...nth joints of the underwater electric robotic arm; n The term τ represents the hydrodynamic term, which includes the buoyancy, added mass force, and water resistance of the underwater electro-manipulator; τ represents the joint control torque of the underwater electro-manipulator, τ = τ d +τ m , τ d and τ m Let represent the water resistance matrix and the added mass force matrix of the underwater robotic arm, respectively; d represents the model uncertainty and underwater external disturbances of the underwater electric robotic arm, ||d||≤d max d max This represents the maximum value of the model uncertainty term and the underwater external disturbance d for the underwater electric robotic arm. The model uncertainty term specifically includes modeling error and model parameter uncertainty, while the underwater external disturbance specifically refers to the interference from the underwater environment, such as ocean currents.
[0013] Considering the effects of water resistance and additional mass forces on the robotic arm underwater, the Morison formula is used to perform hydrodynamic modeling of the robotic arm.
[0014] The equivalent gravity matrix of the underwater electric manipulator, taking into account the buoyancy force experienced by the manipulator during underwater operation, is as follows:
[0015]
[0016] Where, ρ w Let ρ represent the density of water, ρ represent the equivalent density of the underwater electro-mechanical arm, and G() represent the gravity matrix of the underwater electro-mechanical arm.
[0017] The prediction model for the underwater electric robotic arm established in the first step is as follows:
[0018]
[0019]
[0020]
[0021] U k =[u(k∣k) T u(k+1∣k) T … u(k+p-1∣k) T ] T
[0022]
[0023]
[0024]
[0025]
[0026] Where J represents the objective function of the prediction model; U k This represents the control quantity matrix in the prediction time domain at the current time k. Each prediction time domain contains N control cycles, where k represents the discrete state count variable, and u(k|k) represents the state variable x predicted at time k in the prediction time domain at the current time k. k The control variable, u(k+1|k), represents the state variable x at time k+1 in the prediction time domain at the current time k. k+1 The control variable, u(k+p-1|k), represents the state variable x at time k+p-1 in the prediction time domain at the current time k. k+p-1 The control variable; P represents the coefficient of the quadratic term of the objective function; V represents the coefficient of the linear term of the objective function; R and These represent the first preset weight matrix and the matrix it forms; Let L represent the parameters of the first discretized prediction model. The matrix formed; Rk This represents the reference state quantity matrix in the prediction time domain at the current time k, i.e., the reference trajectory; Q and These represent the second preset weight matrix and the matrix formed by the second preset weight matrix F, respectively; K represents the parameters of the first discretized prediction model. Second Discrete Prediction Model Parameters The matrix formed.
[0027] The control matrix U in the time domain at the current k-time is predicted. k The first element in the formula is extracted as the control output of the prediction model, which is to predict the state variable x at time k in the prediction time domain at the current time k. k The control quantity u(k|k) is used as the control output of the predictive model.
[0028] Optimize the corresponding objective function J to obtain the control output within a complete control time domain that minimizes the objective function. Extract the first element and use it as the control output for that control cycle. Using the angular displacement and angular velocity of each joint of the robotic arm as input, the state variable x at the current time k can be obtained. k With real-time updated discretized prediction model parameters Then, the corresponding intermediate variable matrices K and L can be calculated. Based on the preset weight matrices Q, R, and F, the intermediate variable matrix can be obtained. Finally, based on the target state R k and current state x k To obtain the objective function, we need to find the control variable that minimizes the objective function, i.e., to find the control variable with respect to U. k This is a quadratic programming problem with variables as independent variables.
[0029] The objective function conforms to the standard form of quadratic programming, and the optimal control quantity U can be solved using quadratic programming theory. k , take U k The first state is used as the control variable u in the current control cycle. k This completes the solution and outputs the control variable, namely the joint driving torque u. k Repeat the above process, continuously updating the prediction model and a series of intermediate variable matrices based on the input joint angular displacement and angular velocity. The final output, i.e., the u of the joint driving torque, is obtained by calculating the optimal solution of the objective function. k This enables real-time control of the robotic arm.
[0030] The state variable x at the current time k. k Specifically as follows:
[0031]
[0032] Where, q k and These represent the joint angular displacement and angular velocity of the underwater electric manipulator at time k, respectively.
[0033] The aforementioned prediction of the state variable x at time k within the prediction time domain at the current time k. k The control quantity u(k|k) is as follows:
[0034] u(k∣k)=τ-G1(q k )
[0035] Where τ represents the joint control torque of the underwater electro-manipulator; G1() represents the equivalent gravity matrix of the underwater electro-manipulator; q k This represents the joint angular displacement of the underwater electric robotic arm at time k.
[0036] Predict the state variable x at time k within the current time k prediction domain. k The control quantity u(k|k) is used as the driving torque of each joint of the underwater electric manipulator at the current time k.
[0037] The parameters of the first discretization prediction model Second Discrete Prediction Model Parameters Specifically as follows:
[0038]
[0039]
[0040] Where I represents the identity matrix; T represents the sampling period; M′ represents the matrix containing the inertia matrix M() and the additional mass acceleration matrix H() of the underwater electro-manipulator, M′(q)=M(q)+H(q); C′ represents the matrix containing the Coriolis force and centripetal force matrix C() of the underwater electro-manipulator and the additional mass velocity matrix D(). q and These represent the joint angular displacement and angular velocity of the underwater electric robotic arm, respectively.
[0041] The reference state quantity matrix R in the prediction time domain at the current time k is mentioned. k Specifically as follows:
[0042] R k =[r(k+1|k) T r(k+2|k) T … r(k+p|k) T ] T
[0043] Where r(k+1|k) represents the reference state quantity at time (k+1) in the prediction time domain at the current time k, r(k+2|k) represents the reference state quantity at time (k+2) in the prediction time domain at the current time k, and r(k+p|k) represents the reference state quantity at time (k+p) in the prediction time domain at the current time k.
[0044] The beneficial effects of this invention are:
[0045] 1. This invention takes into account the effects of hydrodynamics, focusing on the effects of water resistance, additional mass force and buoyancy to conduct a relatively accurate underwater dynamic model of the robotic arm and use it as a prediction model. The model prediction control method is used to improve the control accuracy of the robotic arm in underwater scenarios.
[0046] 2. Model predictive control can compensate for model mismatch in a timely manner when dealing with time-varying disturbances. Therefore, it exhibits good robustness for nonlinear underwater manipulator systems under actual constraints such as torque, angular velocity and angular acceleration. That is, under underwater transient disturbances, it can obtain relatively smooth control output at the program level and has good anti-disturbance performance. Attached Figure Description
[0047] Figure 1 This is a flowchart illustrating the predictive control principle of an electric robotic arm model that takes into account the effects of hydrodynamics.
[0048] Figure 2 The target trajectory of the joint movement of the underwater electric robotic arm;
[0049] Figure 3 This is a comparison chart of the control effects of the electric robotic arm model predictive controller designed in this invention, which takes into account the effects of hydrodynamics, and the traditional PID controller.
[0050] Figure 4 (a) is the shoulder joint error curve of the PID controller tracking the reference trajectory;
[0051] Figure 4 (b) is a shoulder joint error curve of the MPC controller tracking the reference trajectory predicted by the model of the present invention;
[0052] Figure 4 (c) is the error curve of the boom joint when the PID controller tracks the reference trajectory;
[0053] Figure 4 (d) is the error curve of the boom joint that the MPC controller predicts for tracking the reference trajectory in the model of this invention;
[0054] Figure 4 (e) is the forearm joint error curve of the PID controller tracking the reference trajectory;
[0055] Figure 4 (f) is the forearm joint error curve of the MPC controller tracking the reference trajectory predicted by the model of this invention;
[0056] Figure 5 (a) is the shoulder joint angular velocity curve of the PID controller tracking the reference trajectory;
[0057] Figure 5 (b) is a curve of shoulder joint angular velocity predicted by the model of the present invention for the MPC controller to track the reference trajectory;
[0058] Figure 5 (c) is the angular velocity curve of the boom joint when the PID controller tracks the reference trajectory;
[0059] Figure 5 (d) is the curve of the boom joint angular velocity predicted by the model of the present invention for the MPC controller tracking the reference trajectory.
[0060] Figure 5 (e) is the forearm joint angular velocity curve of the PID controller tracking the reference trajectory;
[0061] Figure 5 (f) is the forearm joint angular velocity curve of the MPC controller tracking the reference trajectory predicted by the model of this invention. Detailed Implementation
[0062] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0063] like Figure 1 As shown, the underwater electric robotic arm control method based on model predictive control of the present invention includes the following steps:
[0064] Step 1: Establish a nonlinear dynamic model of the underwater electric manipulator; based on the nonlinear dynamic model, use model predictive control to establish a predictive model for the underwater electric manipulator.
[0065] The nonlinear dynamic model of the underwater electric manipulator established in the first step under hydrodynamic terms and external disturbances is as follows:
[0066]
[0067]
[0068] Where M() represents the inertia matrix of the underwater electro-manipulator, C() represents the Coriolis force and centripetal force matrices of the underwater electro-manipulator, G1() represents the equivalent gravity matrix of the underwater electro-manipulator; H() represents the added mass acceleration matrix; D() represents the added mass velocity matrix; q, and Let q represent the joint angular displacement, angular velocity, and angular acceleration of the underwater electro-mechanical arm, respectively, where q = [q1 q2 … q n ], q1, q2 … q n These represent the angular displacements of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. These represent the angular velocities of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. τ represents the angular acceleration of the 1st, 2nd...nth joints of the underwater electric robotic arm; n The term τ represents the hydrodynamic term, which includes the buoyancy, added mass force, and water resistance of the underwater electro-manipulator; τ represents the joint control torque of the underwater electro-manipulator, τ = τ d +τ m , τ d and τ m Let represent the water resistance matrix and the added mass force matrix of the underwater robotic arm, respectively; d represents the model uncertainty and underwater external disturbances of the underwater electric robotic arm, ||d||≤d max d max This represents the maximum value of the model uncertainty term and the underwater external disturbance d for the underwater electric robotic arm. The model uncertainty term specifically includes modeling error and model parameter uncertainty, while the underwater external disturbance specifically refers to the interference from the underwater environment, such as ocean currents.
[0069] Considering the effects of water resistance and additional mass forces on the robotic arm underwater, the Morison formula is used to perform hydrodynamic modeling of the robotic arm.
[0070] The equivalent gravity matrix of the underwater electric robotic arm, considering the buoyancy force acting on the arm during underwater operation, is as follows:
[0071]
[0072] Where, ρ w Let ρ represent the density of water, ρ represent the equivalent density of the underwater electro-mechanical arm, and G() represent the gravity matrix of the underwater electro-mechanical arm.
[0073] The prediction model for the underwater electric robotic arm established in the first step is as follows:
[0074]
[0075]
[0076]
[0077] U k =[u(k∣k) T u(k+1∣k) T … u(k+p-1∣k)T ] T
[0078]
[0079]
[0080]
[0081]
[0082] Where J represents the objective function of the prediction model; U k This represents the control quantity matrix in the prediction time domain at the current time k. Each prediction time domain contains N control cycles, where k represents the discrete state count variable, and u(k|k) represents the state variable x predicted at time k in the prediction time domain at the current time k. k The control variable, u(k+1|k), represents the state variable x at time k+1 in the prediction time domain at the current time k. k+1 The control variable, u(k+p-1|k), represents the state variable x at time k+p-1 in the prediction time domain at the current time k. k+p-1 The control variable; P represents the coefficient of the quadratic term of the objective function; V represents the coefficient of the linear term of the objective function; R and These represent the first preset weight matrix and the matrix it forms; Let L represent the parameters of the first discretized prediction model. The matrix formed; R k This represents the reference state quantity matrix in the prediction time domain at the current time k, i.e., the reference trajectory; Q and These represent the second preset weight matrix and the matrix formed by the second preset weight matrix F, respectively; K represents the parameters of the first discretized prediction model. Second Discrete Prediction Model Parameters The matrix formed.
[0083] The control matrix U in the time domain at the current k-time is predicted. k The first element in the formula is extracted as the control output of the prediction model, which is to predict the state variable x at time k in the prediction time domain at the current time k. k The control quantity u(k|k) is used as the control output of the predictive model.
[0084] Optimize the corresponding objective function J to obtain the control output within a complete control time domain that minimizes the objective function. Extract the first element and use it as the control output for that control cycle. Using the angular displacement and angular velocity of each joint of the robotic arm as input, the state variable x at the current time k can be obtained. k With real-time updated discretized prediction model parameters Then, the corresponding intermediate variable matrices K and L can be calculated. Based on the preset weight matrices Q, R, and F, the intermediate variable matrix can be obtained. Finally, based on the target state R k and current state x k To obtain the objective function, we need to find the control variable that minimizes the objective function, i.e., to find the control variable with respect to U. k This is a quadratic programming problem with variables as independent variables.
[0085] The objective function conforms to the standard form of quadratic programming, and the optimal control quantity U can be solved using quadratic programming theory. k , take U k The first state is used as the control variable u in the current control cycle. k This completes the solution and outputs the control variable, namely the joint driving torque u. k Repeat the above process, continuously updating the prediction model and a series of intermediate variable matrices based on the input joint angular displacement and angular velocity. The final output, i.e., the u of the joint driving torque, is obtained by calculating the optimal solution of the objective function. k This enables real-time control of the robotic arm.
[0086] In the model prediction process, let X be the system state within the next N control cycles, i.e., in the prediction time domain. k :
[0087] X k =[x(k+1|k) T x(k+2∣k) T … x(k+N∣k) T ] T
[0088] Here, (k+1|k) represents the prediction of the system state at time k+1 at the current time k, and so on.
[0089] The system state for N control cycles is predicted sequentially using the discretized state equations as follows:
[0090]
[0091]
[0092]
[0093] Following this logic, we get:
[0094]
[0095] The matrix can be integrated as follows:
[0096] X k =Lxk +KU k
[0097] x k =x(k)
[0098] The state variable x at time k k Specifically as follows:
[0099]
[0100] Where, q k and Let x represent the joint angular displacement and angular velocity of the underwater electric manipulator at time k, respectively. The state variable x at time k is predicted within the prediction time domain at time k. k The control quantity u(k|k) is as follows:
[0101] u(k∣k)=τ-G1(q k )
[0102] Where τ represents the joint control torque of the underwater electro-manipulator; G1() represents the equivalent gravity matrix of the underwater electro-manipulator; q k This represents the joint angular displacement of the underwater electric robotic arm at time k.
[0103] Predict the state variable x at time k within the current time k prediction domain. k The control quantity u(k|k) is used as the driving torque of each joint of the underwater electric manipulator at the current time k.
[0104] First Discretization Prediction Model Parameters Second Discrete Prediction Model Parameters Specifically as follows:
[0105]
[0106]
[0107] Where I represents the identity matrix; T represents the sampling period; M′ represents the matrix containing the inertia matrix M() and the additional mass acceleration matrix H() of the underwater electro-manipulator, M′(q)=M(q)+H(q); C′ represents the matrix containing the Coriolis force and centripetal force matrix C() of the underwater electro-manipulator and the additional mass velocity matrix D(). q and These represent the joint angular displacement and angular velocity of the underwater electric robotic arm, respectively.
[0108] The reference state quantity matrix R in the time domain is predicted at the current time k. k Specifically as follows:
[0109] Rk =[r(k+1|k) T r(k+2|k) T … r(k+p|k) T ] T
[0110] Where r(k+1|k) represents the reference state quantity at time (k+1) in the prediction time domain at the current time k, r(k+2|k) represents the reference state quantity at time (k+2) in the prediction time domain at the current time k, and r(k+p|k) represents the reference state quantity at time (k+p) in the prediction time domain at the current time k.
[0111] The second step is to input the angular displacement and angular velocity of each joint of the underwater electric manipulator into the prediction model in real time. The prediction model outputs the driving torque of each joint of the underwater electric manipulator in real time, thereby controlling the continuous operation of the underwater electric manipulator and realizing the real-time control of the underwater electric manipulator.
[0112] like Figure 1 The diagram shown is a basic control flow chart for model predictive control. The input reference trajectory R is... k and predicted state X k Then, the planning error E is obtained by subtraction. k The objective function J is defined, simplified to a quadratic programming form, and solved using quadratic programming to obtain the control output u. k And input the data into the robotic arm for control.
[0113] The objective function J is defined as follows:
[0114]
[0115] Taking a three-joint robotic arm as an example, this invention establishes a dynamic model considering the influence of hydrodynamics, and conducts simulation experiments on MATLAB / Simulink using the model predictive control method described above. The model predictive MPC controller of this invention is compared with a PID controller to verify the control effect of the control method of this invention.
[0116] Regarding controller parameter settings, the PID parameter is set to: K p =diag[1000;1200;1000],K i =diag[150; 150; 100], K d=[100; 100; 50]; The model predictive control parameters are set as follows: N = 30, Q = 1000 × diag[0.1, 0.1, 0.1, 10, 10, 10], F = 10000 × diag[0.1, 0.1, 0.1, 10, 10, 10], R = 0.001 × diag[1, 1, 1]; The parameters of the underwater multi-joint electric manipulator are shown in Table 1.
[0117] Table 1
[0118] Simulation parameters Parameter value Simulation parameters Parameter value <![CDATA[m1]]> 9.6kg <![CDATA[m2]]> 6.4kg <![CDATA[l1]]> 0.424m <![CDATA[l2]]> 0.268m g <![CDATA[9.8m / s 2 ]]> t 0.001s D 0.084m <![CDATA[C d ]]> 1 <![CDATA[C m ]]> 2 <![CDATA[P noise ]]> <![CDATA[1×10 -8 ]]>
[0119] Where m1 and m2 represent the weights of the first and second sections of the underwater multi-joint electro-hydraulic arm, respectively; l1 and l2 represent the lengths of the first and second sections of the underwater multi-joint electro-hydraulic arm, respectively; C d and C m P represents the water resistance coefficient and the added mass coefficient, respectively; noise Indicates noise power.
[0120] like Figure 2 The figure shows the planned trajectory curve of the target joint of the robotic arm. Figure 3 The graph shows the tracking performance of the PID controller and MPC controller for the robotic arm. The solid line represents the tracking performance of the MPC controller, and the dashed line represents the tracking performance of the PID controller. It can be observed that in the dynamic phase, the MPC tracking performance is significantly better than the PID controller. In the steady-state phase, due to the gravity of the upper and lower joints of the robotic arm, the PID controller exhibits significant overshoot, while the MPC controller, based on model planning and optimization control, shows no significant overshoot.
[0121] like Figure 4 of (a), Figure 4 (b) Figure 4 (c) Figure 4 (d) Figure 4 (e) and Figure 4 As shown in (f), the angle error of each joint of the robotic arm is given by a noise power of 1×10⁻⁶. -8 At that time, the dynamic error of the three joint angles in MPC control was less than 5×10. -3 rad, steady-state error less than 1×10 -3 The rad can be calculated from the robot arm's own parameters. The dynamic tracking error is less than 3mm and the steady-state error is less than 1mm, both of which are better than the PID controller.
[0122] like Figure 5 of (a), Figure 5 (b) Figure 5 (c) Figure 5 (d) Figure 5 (e) and Figure 5As shown in (f), the angular velocity curves of each joint of the robotic arm are displayed, and the noise power is observed to be 1×10. -8 In practice, the speed curve controlled by a PID controller exhibits abrupt speed changes and large overall speed fluctuations, which is unacceptable in real-world control. In contrast, the MPC controller relies on constrained quadratic programming to solve for the control torque, resulting in a relatively smooth control output while maintaining good control performance.
[0123] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.
Claims
1. A control method for an underwater electric robotic arm based on model predictive control, characterized in that: The method includes the following steps: Step 1: Establish a nonlinear dynamic model of the underwater electric manipulator; based on the nonlinear dynamic model, use model predictive control to establish a predictive model for the underwater electric manipulator. The second step is to input the angular displacement and angular velocity of each joint of the underwater electric manipulator into the prediction model in real time. The prediction model outputs the driving torque of each joint of the underwater electric manipulator in real time, thereby controlling the continuous operation of the underwater electric manipulator and realizing the real-time control of the underwater electric manipulator. The nonlinear dynamic model of the underwater electric manipulator established in the first step, under hydrodynamic terms and external disturbances, is as follows: in, The inertia matrix represents the inertia matrix of the underwater electric robotic arm. The matrix representing the Coriolis force and centripetal force of the underwater electric robotic arm. Represents the equivalent gravity matrix of the underwater electric robotic arm; Represents the added mass acceleration matrix; Represents the additional mass velocity matrix; , and These represent the joint angular displacement, angular velocity, and angular acceleration of the underwater electric robotic arm, respectively. , , , These represent the angular displacements of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. These represent the angular velocities of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. These represent the angular accelerations of the 1st, 2nd...nth joints of the underwater electric robotic arm, respectively. This represents the hydrodynamic terms, which include the buoyancy, added mass force, and water resistance of the underwater electric robotic arm. This represents the joint control torque of the underwater electric robotic arm. , and These represent the water resistance matrix and the additional mass force matrix of the underwater robotic arm, respectively. This represents the model uncertainty and underwater external disturbances of the underwater electric robotic arm. , This represents the model uncertainty and underwater external disturbances of the underwater electric robotic arm. The maximum value.
2. The underwater electric robotic arm control method based on model predictive control according to claim 1, characterized in that: The equivalent gravity matrix of the underwater electric manipulator is as follows: in, This indicates the density of water. This represents the equivalent density of the underwater electric robotic arm. This represents the gravity matrix of the underwater electric robotic arm.
3. The underwater electric robotic arm control method based on model predictive control according to claim 1, characterized in that: The prediction model for the underwater electric robotic arm established in the first step is as follows: in, This represents the objective function of the prediction model; Indicates the current The control quantity matrix in the prediction time domain is defined at each time point, and each prediction time domain contains... One control cycle, Indicates the current Time-domain prediction State variables at time 1 The control quantity, Indicates the current Time-domain prediction State variables at time 1 The control quantity, Indicates the current Time-domain prediction State variables at time 1 The control quantity; The coefficients corresponding to the quadratic terms of the objective function are represented by these terms. The coefficients corresponding to the linear terms of the objective function; and These represent the first preset weight matrix and the matrix it forms; Represents the parameters of the first discretized prediction model. Represents the parameters of the first discretized prediction model The matrix formed; Indicates the current Predict the reference state quantity matrix in the time domain at any given moment; and They respectively represent the second preset weight matrix and its relationship with the second preset weight matrix. The matrix formed; Represents the parameters of the first discretized prediction model Second Discrete Prediction Model Parameters The matrix formed; Will the current Predict the control matrix in the time domain at any given time. The first element in the model is extracted as the control output of the prediction model, which will be used in the current... Time-domain prediction State variables at time 1 control quantity As the control output of the predictive model.
4. The underwater electric robotic arm control method based on model predictive control according to claim 3, characterized in that: The current State variables at time 1 Specifically as follows: in, and They represent the current The joint angular displacement and angular velocity of the underwater electric robotic arm at any given time.
5. The underwater electric robotic arm control method based on model predictive control according to claim 3, characterized in that: The above is in the current Time-domain prediction State variables at time 1 control quantity Specifically as follows: in, This indicates the joint control torque of the underwater electric robotic arm; Represents the equivalent gravity matrix of the underwater electric robotic arm; Indicates the current The joint angular displacement of the underwater electric robotic arm at any given moment; In the present Time-domain prediction State variables at time 1 control quantity As the present The driving torque of each joint of the underwater electric robotic arm at all times.
6. The underwater electric robotic arm control method based on model predictive control according to claim 3, characterized in that: The parameters of the first discretization prediction model Second Discrete Prediction Model Parameters Specifically as follows: Where I represents the identity matrix; T represents the sampling period; Represents the inertia matrix containing the underwater electric manipulator. and the additional mass acceleration matrix The matrix, ; This represents the matrix of Coriolis force and centripetal force of the underwater electric manipulator. and additional mass velocity matrix The matrix, , and These represent the joint angular displacement and angular velocity of the underwater electric robotic arm, respectively.
7. The underwater electric robotic arm control method based on model predictive control according to claim 3, characterized in that: The current Predict the reference state matrix in the time domain at any given time. Specifically as follows: in, Indicates the current Predicting the first time in the time domain Reference state quantity at time t, Indicates the current Predicting the first time in the time domain Reference state quantity at time 10:00 Indicates the current Predicting the first time in the time domain Reference state quantity at any given time.
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Predictive control method
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