Fault-tolerant control method for multiple estimation of robots under input constraints

Abstract

The application discloses a kind of input limited under robot multiple estimation fault-tolerant control method, consisting of the following steps: step S1: in cartesian space, the dynamics equation of the teleoperation system dynamics state that input limited and actuator failure exist simultaneously is established, step S2: the uncertain term caused by actuator failure part in dynamics equation is estimated using radial basis neural network, step S3: the comprehensive uncertain term caused by model parameter, external disturbance and contact force in dynamics equation is estimated using nonlinear disturbance observer, step S4: the control method of teleoperation system that input limited and actuator failure exist simultaneously is designed according to the uncertain term caused by actuator failure and the comprehensive uncertain term caused by model parameter, external disturbance and contact force;The application can improve the applicability of teleoperation robot in extreme complex environment, expand the practical application range of teleoperation robot.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of robot control, and particularly relates to a fault-tolerant control method for robot multiple estimation under input limitation. BACKGROUND

[0002] As the most challenging problem in the field of teleoperation, time delay seriously affects the stability of the teleoperation system and makes the control performance of the system decline. Unknown external disturbance and uncertainty of the robot model also aggravate the degradation of the system performance. The remote robot is often exposed to unknown complex environments, which is prone to induce actuator failure problems. In practical applications, the input of the actuator is limited, and the actuator failure and unknown external disturbance greatly increase the possibility of input limitation of the actuator. If the actuator failure and input limitation problems cannot be properly solved, it will inevitably bring disastrous consequences to the teleoperation system. When the above problems are considered at the same time, the difficulty of controller design is increased. SUMMARY

[0003] The application aims to provide a fault-tolerant control method for robot multiple estimation under input limitation, so as to solve the problem of poor robustness of the teleoperation system under the condition of simultaneous existence of input limitation and actuator failure.

[0004] The application adopts the following technical scheme: a fault-tolerant control method for robot multiple estimation under input limitation, which is composed of the following steps:

[0005] Step S1: under the Cartesian space, a dynamic equation of a teleoperation system with simultaneous existence of input limitation and actuator failure is established,

[0006] Step S2: an actuator failure part caused by the dynamic equation is estimated by using a radial basis neural network,

[0007] Step S3: a comprehensive uncertain term caused by the model parameters, external disturbance and contact force in the dynamic equation is estimated by using a nonlinear disturbance observer,

[0008] Step S4: a control method of the teleoperation system with simultaneous existence of input limitation and actuator failure is designed according to the uncertain term caused by the actuator failure and the comprehensive uncertain term caused by the model parameters, external disturbance and contact force.

[0009] Further, the dynamic equation in step S1 is:

[0010]

[0011] In the formula, u m represents an actual control input, f m represents a controller to be designed, Δu m =um -f m , I∈R n×n The identity matrix, For ι m If the estimated value is , then the estimation bias is . M m The nominal value of the inertia matrix has a positive constant λ. max and λ min , such that λ max I≤M m ≤λ max I, κ m The effective factor matrix representing the actuator, C m For the nominal values ​​of the centrifugal force and Coriolis force matrices, g m D represents the nominal value of the gravity term matrix; m This is the combined uncertainty term caused by model parameter uncertainty, external disturbances, and contact force.

[0012] Furthermore, when establishing the dynamic equations in step S1, the auxiliary system used when the input is constrained is as follows:

[0013]

[0014] In the formula, G1 and G2 are both positive definite symmetric matrices and are both parameters to be designed. Δu is an intermediate variable for the auxiliary system. m =u m -f m .

[0015] Furthermore, when establishing the dynamic equations in step S1, the auxiliary system used to consider actuator failure is as follows:

[0016]

[0017] In the formula, G3 and G4 are both positive definite symmetric matrices and are both parameters to be designed. As an intermediate variable for the auxiliary system, For ι m The estimated value of H m Let be a positive definite symmetric matrix, and let be the parameter to be designed. H represents m The inverse matrix, For H m (κ m -1)f m The estimate,

[0018] in,

[0019]

[0020] wherein α m is a virtual control variable to be designed, is a reference trajectory of the master robot, e m1 and e m2 are error variables.

[0021] Further, the control method f m in step S4 is:

[0022]

[0023] wherein then is:

[0024]

[0025] wherein ∈ mi is a very small positive number, K m2 is a controller parameter to be designed, is the output of the first-order filter, i.e. α m is calculated using a first-order filter.

[0026] Further, the formula for estimating D m by the nonlinear disturbance observer is:

[0027]

[0028] wherein the estimation bias of the nonlinear disturbance observer is then

[0029] The update law of is designed as:

[0030]

[0031] wherein Λ m and are parameters to be designed;

[0032] wherein

[0033] The update law is designed as:

[0034]

[0035] wherein c mi and χ 1i are parameters to be designed.

[0036] The beneficial effects of the present application are: the present application comprehensively considers the robot model parameter uncertainty, unknown external disturbance and unmeasurable interaction force, that is, the influence of the interaction force between the operator and the master robot and the interaction force between the slave robot and the environment on the teleoperation system; the above various uncertainties are mixed together and cannot be estimated separately, the present application can effectively eliminate the negative influence of the above total uncertainty on the system control performance, and the processing method is more suitable for practical application and has engineering significance; the present application adopts double auxiliary systems to process the input limitation and actuator fault problems respectively; the neural network is used to approximate the unknown fault-tolerant control item part; the present application does not need force sensors, and the model of the system does not need to be accurately known, so that the robustness of the teleoperation system under unknown disturbance, input limitation and actuator fault conditions can be improved, and the stable and safe interaction between the teleoperation robot and the environment is ensured; the control method in the present application can improve the applicability of the teleoperation robot in the extreme complex environment, and expand the practical application range of the teleoperation robot. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The teleoperation system control framework of the present application is shown in the figure;

[0038] Figure 2 The tracking effect of the master robot x-y-z axis in embodiment 1 of the present application is shown in the figure;

[0039] Figure 3 The control input of the master robot considering input limitation and actuator fault in embodiment 1 of the present application is shown in the figure. DETAILED DESCRIPTION

[0040] The present application will be described in detail below in combination with specific embodiments.

[0041] It should be noted that the structures, proportions, sizes and the like shown in the drawings of the present application are only used to cooperate with the content disclosed in the specification, so that those skilled in the art can understand and read, and are not used to limit the limiting conditions of the implementation of the present application, so they do not have technical significance. Any modification of structure, change of proportion relationship or adjustment of size, which does not affect the effect and purpose that can be achieved by the present application, should still fall within the scope of the technical content disclosed by the present application.

[0042] The present application discloses a fault-tolerant control method for robot multiple estimation under input limitation, as shown in the figure, which consists of the following steps: Figure 1 The steps are as follows:

[0043] Step S1: in the Cartesian space, the dynamic equation of the teleoperation system with input limitation and actuator fault is established,

[0044] Step S2: Estimate the uncertainty term caused by actuator failure part in the dynamic equation by using radial basis neural network,

[0045] Step S3: Estimate the comprehensive uncertainty term caused by model parameters, external disturbance and contact force in the dynamic equation by using nonlinear disturbance observer,

[0046] Step S4: Design the control method of teleoperation system with input constraint and actuator failure according to the uncertainty term caused by actuator failure and the comprehensive uncertainty term caused by model parameters, external disturbance and contact force.

[0047] Step S1: Establish the dynamic equation of teleoperation system with input constraint and actuator failure in Cartesian space.

[0048] The teleoperation system is a distributed system composed of a pair of n-degree-of-freedom manipulators. The dynamics of master and slave in Cartesian space are as follows:

[0049]

[0050]

[0051] where j e {m, s} is the identification of master and slave robots, q j ∈R n×1 are the joint acceleration, velocity and position of the robot, respectively. x j ∈R n×1 are the acceleration, velocity and position in Cartesian space, respectively. is the inertia matrix, is the centrifugal and Coriolis force matrix, is the gravity term matrix, f j represents the control input, d j represents the total sum of external disturbance uncertainty, f h represents the force applied by the operator, f e represents the contact force between the slave robot and the environment. Considering the uncertainty in robot dynamics, the relationship between the nominal value and the uncertainty is where represents the nominal value, ΔM j , ΔC j , Δg j represent the uncertain part of the dynamic model. Then, equations (1) and (2) can be rewritten as:

[0052]

[0053]

[0054] In formula (3), (4),

[0055] When the input constraint and actuator fault exist simultaneously, there are

[0056] ν j = κ j sat(f j ) (5)

[0057] In formula (5), f j = [f j1 ,…,f ji ] T , j∈{m,s} is the control input to be designed; κ j = diag(κ j1 ,…,κ ji ), κ ji (i = 1,…,n) is a positive definite diagonal matrix, and satisfies 0 < κ ji ≤ 1. u j = [u j1 ,…,u ji ] T , sat(f j ) = [sat(f j1 ),…,sat(f ji )] T , the form of the saturation function is as follows:

[0058]

[0059] In formula (6), represents the known maximum value of the input signal.

[0060] It is assumed that the deviation between the actual control input u ji and the control input to be designed f ji is bounded, that is, there exists a positive number such that Δu ji = u ji -f ji , (i = 1,…,n), then

[0061] The reference trajectory of the master robot can be generated by the desired impedance model:

[0062]

[0063] In formula (7), respectively represent the estimated values of D m , D s , which will be given by a nonlinear disturbance observer later, T b(t) represents the time delay from the end to the master.

[0064] The reference trajectory for the slave robot is: The reference trajectory for the main robot. T serves as the reference trajectory for the end-user robot. f (t) represents the time delay from the master end to the slave end.

[0065] To facilitate the subsequent controller design, the following variables are defined: Taking the design of the master controller as an example, the slave controller is similar, as will be given later. Then the dynamics (3) can be rewritten as:

[0066]

[0067] further,

[0068]

[0069] In equation (9), u m f represents the actual control input. m This represents the controller to be designed, Δu m =u m -f m , I∈R n×n The identity matrix, For ι m If the estimated value is , then the estimation bias is . M m The nominal value of the inertia matrix has a positive constant λ. max and λ min , such that λ max I≤M m ≤λ max I, κ m The effective factor matrix representing the actuator, i.e., the degree of failure of the actuator, C m For the nominal values ​​of the centrifugal force and Coriolis force matrices, g m D represents the nominal value of the gravity term matrix; m This is the combined uncertainty term caused by model parameter uncertainty, external disturbances, and contact force.

[0070] Step S2: Estimate the uncertainty term caused by actuator failure in the dynamic equation using a radial basis function neural network, i.e., use a radial basis function neural network. For the uncertainty term H in the dynamic equation m (κ m -I)f m Make an estimate; among which This indicates the function used to estimate the uncertain part H. m (κ m-1)f m a neural network weight vector, S(f m ) denotes a radial basis neural function vector; f m is the controller to be designed, H m is a positive definite symmetric matrix, and is a parameter to be designed, κ m represents an effective factor matrix of the actuator, i.e., the degree of failure of the actuator; and I is a unit matrix of the same dimension.

[0071] In order to handle the input constraint problem, an auxiliary system is adopted:

[0072]

[0073] In equation (10), G1 and G2 are both positive definite symmetric matrices, and are both parameters to be designed, is an intermediate variable of the auxiliary system, Δu m = u m - f m .

[0074] In order to handle the actuator failure problem, another auxiliary system is introduced:

[0075]

[0076] In equation (11), G3 and G4 are both positive definite symmetric matrices, and are both parameters to be designed, is an intermediate variable of the auxiliary system, is an estimate of ι m . H m is a positive definite symmetric matrix, denotes the inverse matrix of H m (H m is a parameter to be designed). is an estimate of H m (κ m -1)f m . Since the fault-tolerant control variable κ m is unknown, a neural network is used to estimate H m (κ m -1)f m , i.e.

[0077]

[0078] According to the two auxiliary systems (10) and (11), error variables e m1 and e m2 are defined:

[0079]

[0080] In equation (13), α ma virtual control variable to be designed, a reference trajectory of the master robot.

[0081] a virtual control variable a m is designed as:

[0082]

[0083] In order to eliminate the influence of differential explosion, a first-order filter is adopted:

[0084]

[0085] where h m is a positive definite diagonal matrix (to be designed parameter). In the subsequent design process of the controller, a is used instead of a m . Then the virtual control error variable is: The derivative of the error variable is:

[0086]

[0087] Here, the variable is bounded.

[0088] Step S3: using a nonlinear disturbance observer to estimate the model parameters, external disturbances and the comprehensive uncertain items caused by contact force in the dynamic equation, that is, the model parameters, external disturbances and the comprehensive uncertain items D m .

[0089] Since the end of the robot does not have a force sensor, and the uncertain part of the robot dynamics, external disturbances and contact forces are mixed together and cannot be measured, the nonlinear disturbance observer is used to estimate the above total uncertainty. This method is more in line with the real scene, and therefore has more practical significance.

[0090] The nonlinear disturbance observer estimates D m , and its form is as follows:

[0091]

[0092] The estimation error of the nonlinear disturbance observer is Then

[0093] In formula (18), the update law of is designed as:

[0094]

[0095] In formula (18), Λ m and is a designed parameter.

[0096] Step S4: a control method of teleoperation system with input constraint and actuator failure is designed according to uncertain terms caused by actuator failure and model parameters, external disturbance and comprehensive uncertain terms caused by contact force, so that the main robot controller is designed when input constraint and actuator failure are considered simultaneously:

[0097]

[0098] In formula (19), Then is designed as:

[0099]

[0100] In formula (20), ∈ mi is a very small positive number (a designed parameter), in order to prevent the denominator from being 0, K m2 is a designed controller parameter, is the output of the first-order filter, that is, α m is calculated by using a first-order filter.

[0101] In formula (20) Then The update law is designed as:

[0102]

[0103] In formula (21), c mi and χ 1i are designed parameters.

[0104] Regarding the stability of the controller, the Lyapunov function is selected:

[0105]

[0106] The two auxiliary systems, the controller, the adaptive update law and the nonlinear disturbance observer are adopted in the application, so that all signals of the closed-loop system are bounded, and the stability of the system can be guaranteed, and the controller f s of the slave robot is similar to the main controller f m , and will not be repeated here.

[0107] The nonlinear disturbance observer is designed in the application to eliminate the influence of total uncertainty in the teleoperation system, avoids the problem that the robot model uncertainty, unknown external disturbance and interaction force are mixed together and cannot be measured, is more in line with the real scene, and has more practical significance; a double auxiliary system is adopted: an anti-saturation auxiliary system is used to process the input limited problem; an adaptive technology and a fault-tolerant auxiliary system are combined to process the actuator failure problem, the application can improve the robustness of the teleoperation system under uncertain disturbance, input limitation and actuator failure, and ensure the stable and safe interaction between the teleoperation robot and the environment.

[0108] Embodiment 1

[0109] Taking the master robot as an example, the initial conditions of the method for simulation of the application are as follows: the initial position x m =[0,0,0] T , the initial velocity The simulation sampling step is taken as 0.001; the reference trajectory of the master robot is set as: The input limited boundary is set as [0.04, 0.18, 0.05] T The actuator works normally during 0-8 seconds and 15-20 seconds, the actuator fails during 8-15 seconds, and the fault coefficient is set as κ m =diag(0.8,0.8,0.8),.

[0110] The simulation is carried out under the above simulation conditions, and the simulation results are shown in Figures 2-3 . Figure 2 is the tracking effect of the master robot on the x-y-z axes under the consideration of input limitation and actuator failure; wherein, Figure 2 It is shown that the master robot can realize accurate tracking of the reference trajectory under the action of the controller, and the controller can still achieve good tracking effect even if the actuator fails during 8-15 seconds; Figure 3 is the control input of the master robot under the consideration of input limitation and actuator failure; wherein, f xj represents the designed controller, u xj represents the control input under the consideration of input saturation. Figure Three It is shown that in the early stage of the controller, in order to realize tracking of the expected trajectory, the control input of the robot does not violate the input boundary limit condition, avoids the negative influence of input limitation, and achieves good tracking effect.

[0111] The above only describes the preferred embodiments of the application, and is not used to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A fault-tolerant control method for multiple estimation of a robot under input constraints, characterized in that, It consists of the following steps: Step S1: In Cartesian space, establish dynamic equations for the dynamic state of a teleoperation system that simultaneously suffers from input constraints and actuator failure. Step S2: Estimate the uncertainty term caused by actuator failure in the dynamic equation using a radial basis function neural network. Step S3: Use a nonlinear disturbance observer to estimate the combined uncertainty terms in the dynamic equations caused by model parameters, external disturbances, and contact forces. Step S4: Design a control method for a teleoperation system that simultaneously suffers from input constraints and actuator failure, based on the uncertainties caused by actuator failure and the combined uncertainties caused by model parameters, external disturbances, and contact forces. Control method f in step S4 m for: ； In the formula, ,but for: ； In the formula, For a very small positive number representing the parameter to be designed, For the parameters of the controller to be designed, The output of the first-order filter, i.e. Calculated using a first-order filter; in, This is the combined uncertainty term caused by model parameter uncertainties, external disturbances, and contact forces; For the nominal values ​​of the centrifugal force and Coriolis force matrices, ; The initial velocity of the main robot; This represents the nominal value of the gravity term matrix; for The estimated value, , The identity matrix, The effective factor matrix representing the actuator, For error variables; The nominal value of the inertia matrix has positive constants. and , making ; Let be a positive definite symmetric matrix, and let be the parameter to be designed. Let be a positive definite symmetric matrix, and let be the parameter to be designed. As an intermediate variable for the auxiliary system, As an intermediate variable for the auxiliary system, and This is the error variable.

2. The fault-tolerant control method for multiple estimation of a robot under input constraints according to claim 1, characterized in that, The dynamic equation in step S1 is: ； In the formula, Indicates the actual control input. This represents the controller to be designed. , .

3. The fault-tolerant control method for multiple estimation of a robot under input constraints according to claim 2, characterized in that, When establishing the dynamic equations in step S1, the auxiliary system used when considering input constraints is as follows: ， In the formula, Let be a positive definite symmetric matrix, and let be the parameter to be designed. .

4. The fault-tolerant control method for multiple estimation of a robot under input constraints according to claim 3, characterized in that, When establishing the dynamic equations in step S1, the auxiliary system used to consider actuator failure is as follows: ； In the formula, Let be a positive definite symmetric matrix, and let be the parameter to be designed. Let be a positive definite symmetric matrix, and let be the parameter to be designed. express The inverse matrix, for The estimate, in, ， In the formula, This is the reference trajectory for the main robot.

5. The fault-tolerant control method for multiple estimation of a robot under input constraints according to claim 4, characterized in that, The nonlinear perturbation observer The formula for estimation is: ， In the formula, the estimation bias of the nonlinear disturbance observer is: ,but , The update law is designed as follows: ； In the formula, and These are the parameters to be designed; in, , The update law is designed as follows: ； In the formula, and These are the parameters to be designed.

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