Adaptive continuum robot optimal control method and system considering uncertainty

Abstract

The invention discloses a self-adaptive continuum robot optimal control method and system considering uncertainty, and belongs to the field of robots. Constructing a robust problem model of the continuum robot considering uncertainty terms and external disturbance, matching an auxiliary model, constructing a performance index function, and obtaining an auxiliary optimal control model; constructing an HJB estimation equation; constructing an estimation model of an optimal control signal based on an evaluation neural network; constructing an evaluation neural network weight updating model; inputting an HJB estimation equation of an actual continuum robot into the constructed evaluation neural network weight updating model to solve the weight of the evaluation neural network, taking the weight of the evaluation neural network as the input of the evaluation neural network-based optimal control signal estimation model, and solving to obtain the estimation of the optimal control signal; and adaptive continuum robot optimal control considering uncertainty is realized. According to the method, uncertainty and disturbance scenes are considered, the control strategy process is simplified, the weight is updated in a self-adaptive mode, and the optimal control strategy is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of robot technology, and more specifically, relates to an optimal control method and system for a continuum robot taking uncertainty adaptation into account. Background Art

[0002] Continuum robots have great potential in many practical fields with limited space due to their flexibility and benign bending properties. However, continuum robots are designed to perform manipulation tasks in specific complex and narrow scenarios, and the complexity, nonlinearity and strong coupling characteristics of their structure increase the difficulty of control. When considering the complex uncertainties associated with the environment and the robot itself, designing a trajectory tracking controller becomes very challenging. In addition, the unknown external environment may bring uncertain disturbance effects, and it is particularly critical to conduct high-performance robust control research on continuum robots.

[0003] Prior art document 1 (CN109581868B) discloses a decentralized neural optimal control method for a reconfigurable robot based on a judgment identification structure. Its shortcomings are that the proposed method cannot be directly applied to a continuum robot system and cannot guarantee the real-time performance of the control process. It does not consider the external interference of the robot system, resulting in low control process accuracy. It does not provide an efficient update law and iteration method for the judge network, and the control process is complex and difficult to operate.

[0004] Prior art document 2 (CN108789417B) discloses a cost-guaranteed decentralized control method for a reconfigurable manipulator based on adaptive dynamic programming. Its shortcomings are that the proposed method cannot be directly applied to a continuum robot system and cannot guarantee the real-time performance of the control process. It does not consider the external interference of the robot system, resulting in a lack of stability in the control system. It does not provide an efficient update law and iteration method for the judge network, resulting in a complex and difficult control process. It fails to consider the state quantity of the robot system in the performance index function, resulting in poor control performance and low accuracy of the control process.

[0005] Prior art document 3 (CN107544261B) discloses a decentralized learning optimal control method for a reconfigurable robot under uncertain environmental contact. Its shortcomings are that the proposed method cannot be directly applied to a continuum robot system and cannot guarantee the real-time performance of the control process. It does not consider the influence of external interference on the robot system, the influence of internal coupling and unmodeled dynamics of the robot system, and thus the control of the system lacks stability under the influence of external interference, and cannot guarantee the robustness of the control process. It does not provide an efficient update law and iteration method for the judge network, which makes the control process complex and difficult to operate. It fails to consider the state quantity of the robot system in the performance index function, resulting in low accuracy of the control process. Summary of the invention

[0006] In order to solve the deficiencies in the prior art, the present invention provides an optimal control method and system for a continuum robot taking uncertainty adaptation into account. The present invention transforms the robust control of CRs into an equivalent optimal control problem. By designing an auxiliary system and constructing a performance index function, the tracking error and input of the system can be adjusted simultaneously, and better transient performance can be obtained. This problem is indirectly solved by matching the optimal tracking control of the equivalent auxiliary system. By training a single evaluation neural network, the solution of the HJB (Hamilton-Jacobi-Bellman) equation is approximated, and the optimal control strategy is obtained, and the controller design of the original robust tracking control problem is further obtained. The weight update learning of the evaluation neural network is performed online using a novel adaptation method. Finally, the effective model information is integrated into the designed controller to reduce the difficulty of parameter adjustment. The feasibility and effectiveness of the proposed method are illustrated by stability analysis and numerical simulation comparison.

[0007] The present invention adopts the following technical solution.

[0008] A first aspect of the present invention provides an optimal control method for a continuum robot taking uncertainty adaptation into account, comprising:

[0009] Construct a robust problem model of continuum robots taking into account uncertainties and external disturbances;

[0010] Matching the auxiliary model according to the robust problem model, constructing a performance index function, and obtaining an auxiliary optimal control model;

[0011] The HJB estimation equation is constructed based on the auxiliary optimal control model;

[0012] Construct an estimation model of the optimal control signal based on an evaluation neural network;

[0013] According to the constructed HJB estimation equation, a weight update model of the evaluation neural network is constructed;

[0014] The HJB estimation equation of the actual continuum robot is input into the constructed evaluation neural network weight update model to solve the evaluation neural network weight, and then the solved evaluation neural network weight is used as the input of the estimation model of the optimal control signal based on the evaluation neural network to solve the estimation of the optimal control signal, thereby realizing the optimal control of the continuum robot with uncertainty adaptation.

[0015] Preferably, the robust problem model of the continuum robot taking into account uncertainty terms and external disturbances is expressed by the following formula:

[0016]

[0017] In the formula,

[0018] is the trajectory tracking controller, where x1 = q,

[0019] q is the state space parameter of the continuum robot,

[0020] is the first-order derivative of q,

[0021] q d is the reference trajectory,

[0022] u r is the control signal to be solved,

[0023] F(x,t) is the lumped uncertainty term,

[0024] is the first-order derivative of the sliding surface function s, and the sliding surface function s is expressed by the following formula:

[0025]

[0026] In the formula,

[0027] κ is a positive definite diagonal matrix parameter,

[0028] e is the tracking error, e = x1-q d ,

[0029] is the first-order derivative of e,

[0030] for q d The first derivative of .

[0031] Preferably, the lumped uncertainty F(x,t) is expressed as follows:

[0032]

[0033] In the formula,

[0034] x is the total state matrix, x = [x1x2] T ,

[0035] is the known part of the inertia matrix,

[0036] F is the uncertainty term, expressed as follows:

[0037]

[0038] represents the uncertain part in the inertia matrix,

[0039] represents the uncertain part in the Coriolis force matrix,

[0040] represents the uncertain part in the linear impedance matrix,

[0041] represents the uncertain part of the structure-dependent damping matrix,

[0042] is the second-order derivative of q,

[0043] d(t) is the external disturbance model, which is expressed as follows:

[0044]

[0045] In the formula,

[0046] t represents the time series.

[0047] Preferably, the trajectory tracking controller It is expressed as follows:

[0048]

[0049] In the formula,

[0050] represents the known part of the inertia matrix,

[0051] represents the known part of the Coriolis force matrix,

[0052] represents the known part of the linear impedance matrix,

[0053] represents the known part of the structure-dependent damping matrix,

[0054] for q d The second derivative of .

[0055] Preferably, the auxiliary model is matched according to the robust problem model, a performance index function is constructed, and an auxiliary optimal control model is obtained. The auxiliary optimal control model is expressed by the following formula:

[0056]

[0057] In the formula,

[0058] is the optimal control signal,

[0059] R is the parameter matrix,

[0060] Denotes the optimal cost function J * (s,x,u c ) calculates the partial derivative of the sliding surface model s.

[0061] Preferably, the optimal cost function J * (s,x,u c ), expressed as follows:

[0062] J * (s,x,u c )=min J(s,x,u c ) (15)

[0063] J(s,x,u c ) is the performance index function, which is expressed as follows:

[0064]

[0065] In the formula,

[0066] v represents continuous time,

[0067] ψ M (x) represents the robust suppression term,

[0068] U(s,u c ) represents the performance function.

[0069] Preferably, the HJB estimation equation is expressed as follows:

[0070]

[0071] In the formula,

[0072] is the estimate of the optimal HJB equation,

[0073] is an estimate of the optimal cost function,

[0074] ψ M (x) represents the robust suppression term,

[0075] represents the estimate of the optimal utility function,

[0076] is the estimate of the optimal control signal,

[0077] is the trajectory state function.

[0078] Preferably, the estimation model of the optimal control signal based on the evaluation neural network is expressed by the following formula:

[0079]

[0080] In the formula,

[0081] is the estimate of the optimal control signal,

[0082] R is the parameter matrix,

[0083] φ(s) is the activation function for evaluating the neural network,

[0084] is the first-order derivative of φ(s),

[0085] Represents the weight estimates for the evaluation neural network.

[0086] Preferably, Estimation of weights of an evaluation neural network in an estimation model for an optimal control signal by replacing the evaluation neural network Update weights and evaluate the neural network weight update model, which is expressed as the following formula:

[0087]

[0088] in,

[0089] To evaluate the weight estimates of the online update of the neural network,

[0090] η and ζ represent normal coefficients,

[0091] represents the covariance symmetric matrix, expressed as follows:

[0092]

[0093] In the formula,

[0094] is δ HJB Weight estimation for evaluating neural networks The partial guide,

[0095] δ HJB is the residual error between the HJB estimation equation and the optimal HJB equation,

[0096] t represents the time series,

[0097] τ represents continuous time.

[0098] The second aspect of the present invention provides an optimal control system for a continuum robot taking uncertainty self-adaptation into account, which is used to run the optimal control method for a continuum robot taking uncertainty self-adaptation into account, comprising:

[0099] Problem model building module: used to build a robust problem model of a continuum robot taking into account uncertainties and external disturbances;

[0100] Auxiliary optimal control model construction module: used to match the auxiliary model according to the robust problem model of the continuum robot taking into account uncertainty terms and external disturbances, construct a performance index function, and obtain the auxiliary optimal control model;

[0101] HJB estimation equation construction module: used to construct the HJB estimation equation based on the auxiliary optimal control model;

[0102] Estimation model building module: used to build an estimation model of the optimal control signal based on the evaluation neural network;

[0103] Weight update module: used to construct an evaluation neural network weight update model based on the constructed HJB estimation equation;

[0104] Solution module: It is used to input the HJB estimation equation of the actual continuum robot into the constructed evaluation neural network weight update model to solve the evaluation neural network weight, and then use the solved evaluation neural network weight as the input of the estimation model of the optimal control signal based on the evaluation neural network to solve and obtain the estimation of the optimal control signal, thereby realizing the optimal control of the continuum robot taking into account uncertainty adaptation.

[0105] Compared with the prior art, the beneficial effects of the present invention include at least:

[0106] 1. To solve the robust tracking control problem of CRs, this method converts the problem into an optimal control method. Taking the tracking error into account, a trajectory tracking controller is designed, and a robust problem description method for the continuum robot system containing internal uncertainty and external disturbance is proposed. The original robust problem is indirectly solved through equivalent optimal control, and the corresponding proof is given. By considering the internal uncertainty and external disturbance, the stability of the control process is guaranteed; the tracking error, system state and input are comprehensively considered, and the corresponding performance index function is proposed. By designing the performance index function to adjust the tracking error and input of the system, better transient performance is obtained, and the accuracy of the control process is improved. This method fully utilizes the advantages of optimal control, ensures the robustness of the control process, and maintains a simpler controller structure.

[0107] 2. An ADP (Adaptive Dynamic Programming) method for evaluating the neural network structure is introduced to dynamically solve the derived HJB equation online, ensuring the real-time performance of the control algorithm and enabling the control system to adjust the trajectory of CRs in real time. It is worth noting that this method is different from the traditional ADP scheme in that it omits the actuator network part, thereby simplifying the control structure and control strategy process and reducing the complexity of the control process.

[0108] 3. By designing a novel adaptive method to evaluate the learning of the neural network online, the convergence of the estimated value of the neural network weight is guaranteed, and the accuracy of the control process is improved. The prior effective model information is incorporated into the controller design to reduce the difficulty of parameter adjustment, reduce the operational complexity of the control system, improve the operability and control accuracy of the control system, and improve the control performance.

[0109] 4. Stability analysis and numerical simulation comparative experiments verify the effectiveness of the proposed method. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 is a schematic diagram of an optimal control method for a continuum robot taking uncertainty adaptation into account according to an embodiment of the present invention;

[0111] Figure 2 is a schematic diagram of a simulation example provided according to an embodiment of the present invention;

[0112] Figure 3 is a schematic diagram of evaluating the convergence of neural network weights provided according to an embodiment of the present invention;

[0113] Figure 4 It is a schematic diagram of a time series of a cost function provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0114] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are only embodiments of a part of the present invention, not all embodiments. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0115] like Figure 1 As shown, embodiment 1 of the present invention provides an optimal control method for a continuum robot taking uncertainty adaptation into account, comprising the following steps:

[0116] Step 1: Construct a robust problem model of CRs taking into account uncertainties and external disturbances;

[0117] The kinetic model of CRs can be expressed as:

[0118]

[0119] in,

[0120] q=[Δx,Δy,ΔL] T represents the state space parameters of the continuum robot,

[0121] Δx and Δy represent the state parameters of the continuum robot, which are obtained by nonlinear transformation of the measurable driving quantity of the continuum robot (including the radius of the circle formed by the connecting holes of the driving wires, the rotation angle and the bending angle).

[0122] ΔL represents the length change of the continuum robot.

[0123] is the first-order derivative of q,

[0124] is the second-order derivative of q,

[0125] B q (q), D q (q) and K q They represent the inertia matrix, Coriolis force matrix, linear impedance and structure-related damping matrix of the continuum robot respectively, and all of them are diagonal matrices.

[0126] m represents the lumped end mass of the continuum robot, J q Represents the Jacobian matrix of the continuum robot.

[0127] K q =diag{κ Δx,Δy ,κ Δx,Δy ,κ ΔL},D q (q) = diag{σ Δx,Δy ,σ Δx,Δy ,σ ΔL},κ Δx,Δy ,κ Δx,Δy ,k ΔL and σ Δx,Δy ,σ Δx,Δy ,σ ΔL represent the unknown parameters in the linear impedance and structure-related damping matrix of the continuum robot respectively.

[0128] l0 represents the initial length of the continuum robot. In this embodiment, m = 3 kg, l0 = 2 m, k Δx,Δy =2Nm / rad,k ΔL=2N / m,σ Δx,Δy =0.3Nms / rad,σ ΔL =0.3Ns / m, the initial value of the system is: q0 = [0.8, 0.3, 0.01] T , q0 is the initial value of q, for The initial value of .

[0129] A q (q) represents the input mapping matrix,

[0130] u represents the end torque vector, u=[τ x ,τ y ,f z ] T ,

[0131] τ x represents the torque along the x-axis at the end of the continuum robot,

[0132] τ y represents the torque along the y-axis at the end of the continuum robot,

[0133] f z Represents the torque along the z-axis at the end of the continuum robot.

[0134] The robustness problem can be described as follows: when formula (1) contains uncertain terms and external disturbances, such as:

[0135]

[0136] The dynamic model of CRs considering uncertainties and external disturbances is constructed as follows:

[0137]

[0138] Among them, represent the inertia matrix, Coriolis force matrix, linear impedance and structure-related damping matrix of the continuum robot, and they are all diagonal matrices.

[0139] represents the known part of the inertia matrix,

[0140] represents the uncertain part in the inertia matrix,

[0141] represents the known part of the Coriolis force matrix,

[0142] represents the uncertain part in the Coriolis force matrix,

[0143] represents the known part of the linear impedance matrix,

[0144] represents the uncertain part in the linear impedance matrix,

[0145] represents the known part of the structure-dependent damping matrix,

[0146] represents the uncertain part of the structure-dependent damping matrix,

[0147] τ0 represents the control input,

[0148] t represents a time series, such as Figure 4 As shown, Figure 4 The time series of the cost function in the control method of the present invention supplements the effectiveness of the method.

[0149] F represents the uncertainty term, which is expressed as follows:

[0150]

[0151] The uncertainty of the system is set as:

[0152]

[0153] d(t) represents the external disturbance model:

[0154]

[0155] The state space equation is constructed based on the dynamic model of CRs taking into account uncertainties and external disturbances:

[0156]

[0157] in,

[0158]

[0159] Lumped uncertainty:

[0160]

[0161] x is the total state matrix, x = [x1x2] T ,

[0162] is the first-order derivative of x1(t),

[0163] is the first-order derivative of x2(t),

[0164] Construct the sliding surface model based on the state space equation:

[0165] The sliding surface model is constructed as:

[0166]

[0167] in,

[0168]

[0169] κ is a positive definite diagonal matrix parameter.

[0170] e is the tracking error, e = x1-q d ,

[0171] is the first-order derivative of e, also representing the tracking error,

[0172] s represents the sliding surface function,

[0173] s1(Δx) represents the sliding surface function of the continuum robot state parameter Δx,

[0174] s2(Δy) represents the sliding surface function of the continuum robot state parameter Δy,

[0175] s3(ΔL) represents the sliding surface function of the state parameter ΔL of the continuum robot,

[0176] q d represents the reference trajectory,

[0177] Indicates q d The first derivative of .

[0178] The number of neurons N = 5, and the activation function is The parameter matrix in the performance index function is set to: Q = diag{100,100,100}, R = diag{20,20,5}, The parameters of the evaluator network weight update law are η=0.08,ζ=0.02, The sliding surface parameter κ = 0.3. Consider the reference input trajectory q d (t), The reference input is:

[0179]

[0180] The sliding surface model is derived to obtain the robust problem model of the continuum robot taking into account uncertainty terms and external disturbances:

[0181]

[0182] in,

[0183] is the first-order derivative of the sliding surface function s,

[0184] u r represents the control signal to be solved,

[0185] Trajectory tracking controller It is expressed as follows:

[0186]

[0187] In the formula,

[0188] represents the known part of the inertia matrix,

[0189] represents the known part of the Coriolis force matrix,

[0190] represents the known part of the linear impedance matrix,

[0191] represents the known part of the structure-dependent damping matrix,

[0192] κ is a positive definite diagonal matrix parameter,

[0193] is the first-order derivative of e, e = x1-q d , and e both represent tracking errors,

[0194] for q d The first derivative of

[0195] for q d The second derivative of .

[0196] Step 2: Based on the robust problem model of CRs taking into account uncertainty terms and external disturbances constructed in step 1, match the auxiliary model, construct the performance index function, and obtain the auxiliary optimal control model.

[0197] In order to achieve robust control of CRs, an auxiliary system is designed to indirectly solve its robustness problem by solving the optimal control of the auxiliary system. Matching auxiliary model:

[0198]

[0199] in,

[0200] is the first-order derivative of the sliding surface function s,

[0201] u c is the control signal to be solved.

[0202] Construct performance indicator function:

[0203]

[0204] in,

[0205] ψ M (x) = ρF M (x) 2 , ρ is the parameter to be adjusted, and in this embodiment, ρ=3 is set.

[0206] ψ M (x) represents the robust suppression term,

[0207] F M (x) represents the robust suppression function,

[0208] U(s,u c ) represents the efficiency function, which satisfies U(0,0)=0, and U(s,u c )=s T Qs+u c T Ru c ,

[0209] v represents continuous time,

[0210] s represents the sliding surface function,

[0211] in Q and R are both symmetric positive definite matrices to be adjusted.

[0212] The optimal cost function derived from formula (12) can be expressed as:

[0213] J * (s,x,u c )=min J(s,x,u c ) (15)

[0214] Therefore, the auxiliary optimal control model can be obtained in the following way:

[0215]

[0216] In the formula,

[0217] is the optimal control signal, is the optimal u obtained by solving formula 15 c ,Right now

[0218] where J(s,x,u c ) satisfies J * (0) = 0 and is continuously differentiable,

[0219] Denotes the optimal cost function J * (s,x,u c ) Take the partial derivative of s.

[0220] Step 3: Construct the HJB estimation equation based on the auxiliary optimal control model in step 2.

[0221] Furthermore, the HJB equation derived from the system can be obtained:

[0222]

[0223] in, represents J(s,x,u c ), the optimal control signal The optimal HJB equation satisfied It is expressed as the following formula:

[0224]

[0225] in,

[0226] is the optimal HJB equation,

[0227] is the optimal control signal, is the optimal u obtained by solving formula 15 c ,Right now is the optimal cost function,

[0228] ψ M (x) represents the robust suppression term,

[0229] is the optimal performance function,

[0230] is the optimal control signal.

[0231] Estimating equation (18) yields the HJB estimation equation, which can be expressed as:

[0232]

[0233] in, is the estimate of the optimal HJB equation,

[0234] is an estimate of the optimal cost function,

[0235] ψ M (x) represents the robust suppression term,

[0236] represents the estimate of the optimal utility function,

[0237] is the estimate of the optimal control signal,

[0238] is the trajectory state function.

[0239] Step 4: Construct an estimation model of the optimal control signal based on the evaluation neural network.

[0240] Design an evaluation neural network to approximate the optimal cost function, further expressed as the following formula:

[0241]

[0242] in,

[0243] is the ideal weight vector for evaluating a neural network,

[0244] N represents the number of neurons.

[0245] φ(s) is the activation function of the evaluation neural network, Its derivative is

[0246] is the first-order derivative of φ(s).

[0247] for have

[0248] ò(s) is the approximation error of the evaluation neural network.

[0249] Furthermore, equations (20) and (21) can be expressed in an estimated manner, and the estimation model of the optimal control signal based on the evaluation neural network is expressed as follows:

[0250]

[0251]

[0252] in, represents the weight estimate of the evaluation neural network,

[0253] represents the estimate of the optimal control signal, that is, the estimate of the robust optimal control signal when CRs contain uncertainties,

[0254] represents an estimate of the optimal cost function.

[0255] The optimal control signal is estimated By updating the efficiency function and reconstructing the HJB estimation equation, the weights of the evaluator network model are adaptively updated again, and the evaluator network model is input to obtain the updated estimate of the optimal control signal.

[0256] Step 5: Based on the HJB estimation equation constructed in step 3, construct an evaluation neural network weight update model;

[0257] Optimal performance index function J * (s, x) can be approximated by the critic NN. In order to implement the control strategy, it is necessary to solve the derived HJB equation, which will be approximated by the neural network approximation. The optimal control signal is approximated by the solution of the HJB equation through the evaluator network, which is also the solution to the CRs robustness problem. Numerical simulation can be performed based on the parameter design in step 1. At the same time, the method based on the extended state observer and the method based on heuristic dynamic programming are compared. The numerical results show the effectiveness of the proposed method, such as Figure 2 shown.

[0258] The residual error between the HJB estimation equation and the optimal HJB equation can be defined as:

[0259]

[0260] Among them, is equal to zero, equation (18) can be expressed as:

[0261]

[0262] In the formula, δ HJB is the residual error between the HJB estimation equation and the optimal HJB equation.

[0263] Recalling equation (19), we define the Bellman error function ε(δ HJB ):

[0264]

[0265] in,

[0266] t represents the time series,

[0267] τ represents continuous time,

[0268] Taking partial derivative of formula (26), we can get:

[0269]

[0270] in,

[0271] represents the Bellman error function ε(δHJB ) to estimate the weights of the evaluation neural network Find the partial derivative,

[0272] is δ HJB Weight estimation for evaluating neural networks The partial guide,

[0273] Further, evaluate the weight estimation of the neural network It is expressed as follows:

[0274]

[0275] in,

[0276] θ T is the transpose of θ, expressed as follows:

[0277]

[0278] To evaluate the first-order derivative of the activation function φ(s) of the neural network,

[0279] Furthermore, formula (29) can be used to construct the evaluation neural network weight update model by batch least squares method, which can be expressed as:

[0280]

[0281] in,

[0282] To evaluate the weight estimates of the online update of the neural network,

[0283] η and ζ represent normal coefficients,

[0284] represents the covariance symmetric matrix, It can be expressed as the following formula:

[0285]

[0286] The first-order derivative of is expressed as follows:

[0287]

[0288] like Figure 3 As shown, the evaluation of neural network weight convergence proposed by the present invention reflects the effectiveness of the network weight updating strategy of the present invention.

[0289] Step 6, input the HJB estimation equation of the actual continuum robot into the evaluation neural network weight update model constructed in step 4 to solve the evaluation neural network weight, and then use the solved evaluation neural network weight as the input of the estimation model of the optimal control signal based on the evaluation neural network constructed in step 5, and solve to obtain the estimate of the optimal control signal, thereby realizing the optimal control of the continuum robot taking into account uncertainty adaptation.

[0290] Step 6: Input the performance index function, HJB estimation equation, and state parameters of the actual continuum robot into step 5 to obtain the evaluation neural network weights. Input the weights into step 4 to obtain the robust optimal control signal, thus realizing the adaptive robust optimal control of the continuum robot taking into account the system uncertainty. Figure 2 As shown, the simulation example of the method proposed in the present invention is compared with the control method based on ESO and the control method based on DHP, which reflects the advancement and effectiveness of the present invention.

[0291] Compared with the prior art, the beneficial effects of the present invention include at least:

[0292] 1. To solve the robust tracking control problem of CRs, this method converts the problem into an optimal control method. Taking the tracking error into account, a trajectory tracking controller is designed, and a robust problem description method for the continuum robot system containing internal uncertainty and external disturbance is proposed. The original robust problem is indirectly solved through equivalent optimal control, and the corresponding proof is given. By considering the internal uncertainty and external disturbance, the stability of the control process is guaranteed; the tracking error, system state and input are comprehensively considered, and the corresponding performance index function is proposed. By designing the performance index function to adjust the tracking error and input of the system, better transient performance is obtained, and the accuracy of the control process is improved. This method fully utilizes the advantages of optimal control, ensures the robustness of the control process, and maintains a simpler controller structure.

[0293] 2. An ADP (Adaptive Dynamic Programming) method for evaluating the neural network structure is introduced to dynamically solve the derived HJB equation online, ensuring the real-time performance of the control algorithm and enabling the control system to adjust the trajectory of CRs in real time. It is worth noting that this method is different from the traditional ADP scheme in that it omits the actuator network part, thereby simplifying the control structure and control strategy process and reducing the complexity of the control process.

[0294] 3. By designing a novel adaptive method to evaluate the learning of the neural network online, the convergence of the estimated value of the neural network weight is guaranteed, and the accuracy of the control process is improved. The prior effective model information is incorporated into the controller design to reduce the difficulty of parameter adjustment, reduce the operational complexity of the control system, improve the operability and control accuracy of the control system, and improve the control performance.

[0295] 4. Stability analysis and numerical simulation comparative experiments verify the effectiveness of the proposed method.

[0296] Embodiment 2 of the present invention provides an optimal control system for a continuum robot taking uncertainty self-adaptation into account, and runs an optimal control method for a continuum robot taking uncertainty self-adaptation into account as described in embodiment 1, including:

[0297] Problem model building module: used to build a robust problem model of a continuum robot taking into account uncertainties and external disturbances;

[0298] Auxiliary optimal control model construction module: used to match the auxiliary model according to the robust problem model of the continuum robot taking into account uncertainty terms and external disturbances, construct a performance index function, and obtain the auxiliary optimal control model;

[0299] HJB estimation equation construction module: used to construct the HJB estimation equation based on the auxiliary optimal control model;

[0300] Estimation model building module: used to build an estimation model of the optimal control signal based on the evaluation neural network;

[0301] Weight update module: used to construct an evaluation neural network weight update model based on the constructed HJB estimation equation;

[0302] Solution module: It is used to input the HJB estimation equation of the actual continuum robot into the constructed evaluation neural network weight update model to solve the evaluation neural network weight, and then use the solved evaluation neural network weight as the input of the estimation model of the optimal control signal based on the evaluation neural network to solve and obtain the estimation of the optimal control signal, thereby realizing the optimal control of the continuum robot taking into account uncertainty adaptation.

[0303] 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 above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. An optimal control method for a continuum robot taking uncertainty adaptation into account, characterized in that: include: Construct a robust problem model of continuum robots taking into account uncertainties and external disturbances; Matching the auxiliary model according to the robust problem model, constructing a performance index function, and obtaining an auxiliary optimal control model; Constructing a HJB estimation equation according to the auxiliary optimal control model; Construct an estimation model of the optimal control signal based on an evaluation neural network; According to the constructed HJB estimation equation, a weight update model of the evaluation neural network is constructed; The HJB estimation equation of the actual continuum robot is input into the constructed evaluation neural network weight update model to solve the evaluation neural network weight, and then the solved evaluation neural network weight is used as the input of the estimation model of the optimal control signal based on the evaluation neural network to solve the estimation of the optimal control signal, thereby realizing the optimal control of the continuum robot with uncertainty adaptation.

2. The optimal control method for a continuum robot taking uncertainty into account according to claim 1, characterized in that: The robust problem model of the continuum robot taking into account uncertainty terms and external disturbances is expressed as follows: In the formula, is the trajectory tracking controller, where x1 = q, q is the state space parameter of the continuum robot, is the first-order derivative of q, q d is the reference trajectory, u r is the control signal to be solved, F(x,t) is the lumped uncertainty term, is the first-order derivative of the sliding surface function s, and the sliding surface function s is expressed by the following formula: In the formula, κ is a positive definite diagonal matrix parameter, e is the tracking error, e = x1-q d , is the first-order derivative of e, for q d The first derivative of .

3. The optimal control method of a continuum robot taking uncertainty into account according to claim 2, characterized in that: The lumped uncertainty F(x,t) is expressed as follows: In the formula, x is the total state matrix, x = [x1x2] T , is the known part of the inertia matrix, F is the uncertainty term, expressed as follows: represents the uncertain part in the inertia matrix, represents the uncertain part in the Coriolis force matrix, represents the uncertain part in the linear impedance matrix, represents the uncertain part of the structure-dependent damping matrix, is the second-order derivative of q, d(t) is the external disturbance model, which is expressed as follows: In the formula, t represents the time series.

4. The optimal control method for a continuum robot taking uncertainty into account according to claim 2, characterized in that: Trajectory tracking controller It is expressed as the following formula: In the formula, represents the known part of the inertia matrix, represents the known part of the Coriolis force matrix, represents the known part of the linear impedance matrix, represents the known part of the structure-dependent damping matrix, for q d The second derivative of .

5. The optimal control method for a continuum robot taking uncertainty into account according to claim 1, characterized in that: According to the robust problem model matching auxiliary model, the performance index function is constructed to obtain the auxiliary optimal control model, and the auxiliary optimal control model is expressed by the following formula: In the formula, is the optimal control signal, R is the parameter matrix, Denotes the optimal cost function J * (s,x,u c ) calculates the partial derivative of the sliding surface model s.

6. The optimal control method of a continuum robot taking uncertainty into account according to claim 5, characterized in that: Optimal cost function J * (s,x,u c ), expressed as follows: J * (s,x,u c )=min J(s,x,u c ) (15) J(s,x,u c ) is the performance index function, which is expressed as follows: J(s,x,u c )=∫0 ∞ ψ M (x)+U(s,u c )dv (14) In the formula, v represents continuous time, ψ M (x) represents the robust suppression term, U(s,u c ) represents the performance function.

7. The optimal control method of a continuum robot taking uncertainty into account according to claim 1, characterized in that: The HJB estimation equation is expressed as follows: In the formula, is the estimate of the optimal HJB equation, is an estimate of the optimal cost function, ψ M (x) represents the robust suppression term, represents the estimate of the optimal utility function, is the estimate of the optimal control signal, is the trajectory state function.

8. The optimal control method for a continuum robot taking uncertainty into account according to claim 1, characterized in that: The estimation model of the optimal control signal based on the evaluation neural network is expressed as follows: In the formula, is the estimate of the optimal control signal, R is the parameter matrix, φ(s) is the activation function for evaluating the neural network, is the first-order derivative of φ(s), Represents the weight estimates for the evaluation neural network.

9. The optimal control method of a continuum robot taking uncertainty adaptation into account according to claim 1, characterized in that: Estimation of weights of an evaluation neural network in an estimation model for an optimal control signal by replacing the evaluation neural network Update weights and evaluate the neural network weight update model, which is expressed as the following formula: in, To evaluate the weight estimates of the online update of the neural network, η and ζ represent normal coefficients, represents the covariance symmetric matrix, expressed as follows: In the formula, is δ HJB Weight estimation for evaluating neural networks The partial guide, δ HJB is the residual error between the HJB estimation equation and the optimal HJB equation, t represents the time series, τ represents continuous time.

10. An optimal control system for a continuum robot taking uncertainty into account and adapting, characterized in that: include: Problem model building module: used to build a robust problem model of a continuum robot taking into account uncertainties and external disturbances; Auxiliary optimal control model construction module: used to match the auxiliary model according to the robust problem model, build the performance index function, and obtain the auxiliary optimal control model; HJB estimation equation construction module: used to construct the HJB estimation equation based on the auxiliary optimal control model; Estimation model building module: used to build an estimation model of the optimal control signal based on the evaluation neural network; Weight update module: used to construct an evaluation neural network weight update model based on the constructed HJB estimation equation; Solution module: It is used to input the HJB estimation equation of the actual continuum robot into the constructed evaluation neural network weight update model to solve the evaluation neural network weight, and then use the solved evaluation neural network weight as the input of the estimation model of the optimal control signal based on the evaluation neural network to solve and obtain the estimation of the optimal control signal, thereby realizing the optimal control of the continuum robot taking into account uncertainty adaptation.

Images