Active disturbance rejection control method for cable-driven continuum robot under actuator saturation constraints

Abstract

An active disturbance rejection control method for a cable-driven continuum robot under actuator saturation constraints, comprising: first, establishing dynamics models of a cable-driven continuum robot, deriving a segmented dynamics model of the cable-driven continuum robot on the basis of a rotational symmetry theory of the cable-driven continuum robot, and on the basis of the dynamics model of any segment in the segmented dynamics model, obtaining the dynamics model of the cable-driven continuum robot considering actuator saturation constraints; then, using a control input quantity and a system output quantity that are subjected to saturation constraints as two input quantities of an extended state observer to design the extended state observer, and obtaining a state feedback control law on the basis of a first output quantity and a second output quantity of the extended state observer and a system reference input signal; and further obtaining a system control law on the basis of the state feedback control law, a third output quantity of the extended state observer, and an actual control input gain. According to the active disturbance rejection control method, the problem of limited driving cable tension in a cable-driven continuum robot system can be transformed into the problem of actuator saturation, and an actuator saturation constraint problem can be taken into account in controller design, so that the output of an actuator can be limited to a safe range to avoid damage to the system caused by excessive output of the actuator; additionally, in the controller design process, the system control input gain is not estimated, but the actual control input gain of the system is used, thereby not only reducing adjustable parameters of the controller, but also further improving the disturbance rejection performance, the tracking performance and the robustness of the system.

Description

An Active Disturbance Rejection Control Method for a Tether-Driven Continuum Robot with Actuator Saturation Constraint Technical Field

[0001] The present invention relates to the field of automatic control technology, and in particular to an auto-disturbance rejection control method of a rope-driven continuum robot under actuator saturation constraint. Background Art

[0002] Traditional rigid-body robots, made of hard materials, offer advantages such as high precision and strong load capacity. However, their limited freedom of movement and flexibility make them difficult to adapt to confined spaces. Unlike rigid-body robots, tether-driven continuum robots, as biomimetic robots, offer superior compliance, flexibility, and safety, making them better able to adapt to unstructured environments. Consequently, they are attracting increasing attention and research.

[0003] However, due to the highly nonlinear, strongly coupled, time-varying and strong elastic effects of the continuum robot itself, it is very difficult to establish an accurate model of it. As a result, when designing the controller, it is necessary to consider various uncertainties that actually exist in the continuum robot system, such as the system's unmodeled dynamics, external interference, and internal parameter disturbances of the system.

[0004] Active Disturbance Rejection Control (ADRC), a controller that does not rely on a precise system model, is highly effective in solving the control problems of nonlinear control systems with uncertainties such as disturbances. Related technologies use nonlinear ADRCs to control continuum robots. However, these technologies suffer from complex controller design, a large number of adjustable parameters, and a failure to consider actuator saturation constraints during controller design, posing potential safety risks.

[0005] Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides an active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint.

[0007] An active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint, comprising:

[0008] Under the constant curvature assumption, a dynamic model of a rope-driven continuum robot is established using the Euler-Lagrange equations. Based on the rotational symmetry theory of the rope-driven continuum robot, the corresponding relationship between the joint space torque of the rope-driven continuum robot and the tension on the driving rope in the driving space within different ranges of rotation angle values ​​is obtained. Furthermore, a segmented dynamic model of the rope-driven continuum robot is obtained. Based on any segment of the segmented dynamic model, a dynamic model of the rope-driven continuum robot that takes into account actuator saturation constraints is obtained.

[0009] The total disturbance term of the system is determined according to the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint. The control input and the system output after saturation constraint are used as two inputs of the extended state observer, and the extended state observer is designed to estimate the system state and the total disturbance, thereby obtaining three outputs of the extended state observer. The first output and the second output of the extended state observer and the system reference input signal are input to the PD controller, and the state feedback control law is output;

[0010] A system control law is obtained according to the state feedback control law, the third output of the extended state observer and the actual control input gain.

[0011] Furthermore, the obtained segmented dynamic model of the rope-driven continuum robot is:

[0012] in, denotes the generalized coordinates of the system, θ and denote the bending angle and rotation angle of the rope-driven continuum robot, M(q)∈R 2×2 is the system inertia matrix, is the Crolio matrix, D(q)∈R 2×1 is the elasticity matrix, τ∈ R2×1 is the model input vector, B1(q), B2(q) and B3(q) are The conversion matrices corresponding to different ranges are shown in Figure 1. F1, F2, and F3 are the tensions on the three driving ropes of the rope-driven continuum robot.

[0013] Furthermore, the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint is:

[0014] Among them, ω d represents the uncertainty of the system's unmodeled dynamics, parameter perturbations, and external disturbances, τ c ∈R 2×1is the control input vector, B(q) represents any one of the transformation matrices B1(q), B2(q) and B3(q), F=B -1 (q)τ c ∈R 2×1 is the tension vector on the driving rope, the saturation function Among them, F max is the maximum value of the tension vector F.

[0015] Furthermore, the extended state observer is designed as follows:

[0016] Wherein, x1 represents the system state, x1=q, z1, z2 and z3 are the three outputs of the extended state observer, wherein z1 and z2 represent the output of the extended state observer for the system state x1 and its first-order derivative, respectively. The observation value, z3 represents the estimated value of the total disturbance of the system by the extended state observer, M -1 (x1) is the actual control input gain of the system, and β1, β2 and β3 are the gains of the extended state observer respectively.

[0017] Furthermore, the first output and the second output of the extended state observer and the system reference input signal are input to the PD controller, and the output state feedback control law includes:

[0018] The state feedback control law u0 is as follows:

[0019] Among them, r1 represents the system reference input signal, k p and k d is the controller gain.

[0020] Furthermore, obtaining the system control law according to the state feedback control law, the third output of the extended state observer, and the actual control input gain includes:

[0021] System control law τ c As follows: τ c =M(x1)(u0-z3)

[0022] Wherein, M(x1) is the inverse of the actual control input gain of the system.

[0023] The beneficial effects of the present invention include: this method transforms the problem of limited drive rope tension in a rope-driven continuum robot system into an actuator saturation problem, and incorporates the actuator saturation constraint into the controller design, thereby limiting the actuator output to a safe range and preventing damage to the system caused by excessive actuator output. Furthermore, the controller design process does not estimate the system control input gain, but instead uses the actual system control input gain. This not only reduces the controller's adjustable parameters but also further improves the system's interference rejection, tracking, and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments:

[0025] FIG1 is a flow chart of an active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint provided by an embodiment of the present application;

[0026] FIG2 is a schematic diagram of a continuum structure of an active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint provided in an embodiment of the present application;

[0027] FIG3 is a control block diagram of an active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint provided in an embodiment of the present application. DETAILED DESCRIPTION

[0028] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0029] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0030] It will also be understood that the term "and / or" used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0031] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0032] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0033] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0034] In order to illustrate the technical solution described in this application, a specific implementation method is provided below.

[0035] As shown in FIG1 , an embodiment of the present application provides an active disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint, comprising the following steps:

[0036] Step S1: Under the constant curvature assumption, a dynamic model of the rope-driven continuum robot is established by using the Euler-Lagrange equation, and according to the rotational symmetry theory of the rope-driven continuum robot, a corresponding relationship between the joint space torque of the rope-driven continuum robot and the tension on the driving rope in the driving space within different ranges of rotation angle values ​​is obtained, thereby obtaining a segmented dynamic model of the rope-driven continuum robot, and based on any segment dynamic model in the segmented dynamic model, a dynamic model of the rope-driven continuum robot considering actuator saturation constraints is obtained;

[0037] Among them, based on the constant curvature assumption, the dynamic model of the rope-driven continuum robot is established through the Euler-Lagrange equation:

[0038] in, denotes the generalized coordinates of the system, θ and denote the bending angle and rotation angle of the rope-driven continuum robot, M(q)∈R 2×2 is the system inertia matrix, is the Crolio matrix, D(q)∈R 2×1 is the elasticity matrix, τ∈R 2×1 is the input vector of the model, i.e. the joint space torque. When M(q)∈R 2×2 is positive definite and reversible.

[0039] As shown in Figure 2, the rope-driven continuum robot has three driving ropes that are symmetrically distributed at 120° in space. Therefore, according to the rotational symmetry theory, when the rotation angle When the rotation and bending motion of the robot can be realized by controlling the driving ropes 1 and 2, the joint space torque τ∈R 2×1 The corresponding relationship between the tension F1 and F2 on the first and second driving ropes in the driving space is:

[0040] When the rotation angle When the rotation and bending motion of the robot can be realized by controlling the driving ropes 2 and 3, the joint space torque τ∈R 2×1 The corresponding relationship between the tension F2 and F3 on the second and third driving ropes in the driving space is:

[0041] When the rotation angle When the robot is rotated and bent by controlling the driving ropes 3 and 1, the joint space torque τ∈R 2×1 The corresponding relationship between the tension F3 and F1 on the third and first driving ropes in the driving space is:

[0042] Among them, B1(q), B2(q) and B3(q) are The corresponding transformation matrices belong to different ranges.

[0043] From this, the segmented dynamic model of the rope-driven continuum robot can be obtained:

[0044] It can be seen that the values ​​of the three transformation matrices B1(q), B2(q), and B3(q) in the corresponding intervals are equal. Therefore, the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint can be obtained based on any segment of the dynamic model in the segmented dynamic model, and the controller design can be carried out on this basis. Among them, the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint is:

[0045] Among them, ω d represents the uncertainty of the system's unmodeled dynamics, parameter perturbations, and external disturbances, τ c ∈R 2×1 is the control input vector, B(q) represents any one of the transformation matrices B1(q), B2(q) and B3(q), F=B -1 (q)τ c ∈R 2×1 is the tension vector on the driving rope, the saturation function Among them, F max is the maximum value of the tension vector F.

[0046] It's important to note that for a rope-driven continuum robot system, the driver output must meet certain constraints due to the limited tensile strength of the drive rope and its ability to withstand only tension but not thrust. In other words, to better control a rope-driven continuum robot, the driver constraints can be translated into a driver saturation problem and factored into the controller design process. This allows the driver output to be controlled within a safe range, preventing adverse system effects caused by excessive driver output.

[0047] Step S2: Determine the total disturbance term of the system based on the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint The control input and system output after saturation constraint are used as the two inputs of the extended state observer. The extended state observer is designed to estimate the system state and total disturbance, and the three outputs of the extended state observer are obtained. The first output and the second output of the extended state observer and the system reference input signal are input into the PD controller to output the state feedback control law.

[0048] Determine the total disturbance term of the system After that, system (3) can be transformed into:

[0049] Let x1=q, x3=f, and assuming Then the system (4) can be transformed into the state equation form:

[0050] Based on system (5), the state observer is designed as follows:

[0051] Wherein, x1 represents the system state, x1=q, z1, z2 and z3 are the three outputs of the extended state observer, wherein z1 and z2 represent the output of the extended state observer for the system state x1 and its first-order derivative, respectively. The observation value, z3 represents the estimated value of the total disturbance of the system by the extended state observer, M -1 (x1) is the actual control input gain of the system, and β1, β2 and β3 are the gains of the extended state observer. When the observer gain is properly tuned, the observer outputs z1, z2 and z3 are closer to the system state x1 and its first-order derivative. The observed value and the estimated value of the total disturbance f. The parameters can be adjusted by bandwidth parameterization method or multi-objective optimization method.

[0052] It should be noted that in order to reduce the adverse effects of driver saturation on the system, as shown in Figure 3, the control inputs τ1 and τ2 with saturation constraints are used as one of the inputs of the extended state observer instead of τ c1 and τ c2 .

[0053] Furthermore, the first output and the second output of the extended state observer and the system reference input signal are input to the PD controller, and the output state feedback control law includes:

[0054] The state feedback control law u0 is as follows:

[0055] Among them, r1 represents the system reference input signal, k p and k d is the controller gain.

[0056] Step S3: Obtaining a system control law according to the state feedback control law, the third output of the extended state observer, and the actual control input gain.

[0057] Specifically, the system control law τ c The design is as follows: τ c =M(x1)(u0-z3)

[0058] Where M(x1) is the inverse of the actual control input gain of the system.

[0059] Therefore, the system control law τ c The purpose of its design is to compensate for the estimation of unknown disturbances, thereby improving the system's tracking and anti-interference capabilities.

[0060] In summary, according to the active disturbance rejection control method for a cable-driven continuum robot under actuator saturation constraints, an embodiment of the present invention first establishes a dynamic model of the cable-driven continuum robot. Based on the rotational symmetry theory of the cable-driven continuum robot, a segmented dynamic model of the cable-driven continuum robot is derived. Based on any segment of the segmented dynamic model, a dynamic model of the cable-driven continuum robot considering actuator saturation constraints is obtained. The saturation-constrained control input and the system output are then used as the two inputs of an extended state observer (ESO). The ESO is designed, and a state feedback control law is derived based on the first and second outputs of the ESO and a system reference input signal. The system control law is further derived based on the state feedback control law, the third output of the ESO, and the actual control input gain. Thus, the active disturbance rejection control method for a cable-driven continuum robot under actuator saturation constraints, according to the embodiment of the present invention, can transform the problem of limited drive cable tension in the cable-driven continuum robot system into the problem of actuator saturation. The actuator saturation constraint is then taken into account in the controller design, thereby limiting the actuator output to a safe range and preventing damage to the system caused by excessive actuator output. In addition, the system control input gain is not estimated during the controller design process, but the actual control input gain of the system is used. This not only reduces the adjustable parameters of the controller, but also further improves the system's anti-interference, tracking and robustness.

[0061] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. An auto-disturbance rejection control method for a rope-driven continuum robot under actuator saturation constraint, characterized in that: include: Under the assumption of constant curvature, a dynamic model of a rope-driven continuum robot is established by means of the Euler-Lagrange equation, and the corresponding relationship between the joint space torque of the rope-driven continuum robot and the tension on the driving rope in the driving space within different ranges of rotation angle is obtained according to the rotational symmetry theory of the rope-driven continuum robot, thereby obtaining a segmented dynamic model of the rope-driven continuum robot, and based on any segment of the segmented dynamic model, a dynamic model of the rope-driven continuum robot considering actuator saturation constraints is obtained; The total disturbance term of the system is determined according to the dynamic model of the rope-driven continuum robot considering the actuator saturation constraint. The control input and the system output after saturation constraint are used as two inputs of the extended state observer, and the extended state observer is designed to estimate the system state and the total disturbance, and three outputs of the extended state observer are obtained. The first output and the second output of the extended state observer and the system reference input signal are input to the PD controller, and the state feedback control law is output; A system control law is obtained according to the state feedback control law, the third output quantity of the extended state observer and the actual control input gain.

2. The active disturbance rejection control method of a rope-driven continuum robot under actuator saturation constraint according to claim 1, characterized in that: The obtained segmented dynamics model of the rope-driven continuum robot is: in, denotes the generalized coordinates of the system, θ and denote the bending angle and rotation angle of the rope-driven continuum robot, respectively, M(q)∈R 2×2 is the system inertia matrix, is the Crolio matrix, D(q)∈R 2×1 is the elasticity matrix, τ∈R 2×1 is the model input vector, B1(q), B2(q) and B3(q) are The corresponding transformation matrices belong to different ranges. F1, F2 and F3 are the tensions on the three driving ropes of the rope-driven continuum robot.

3. The active disturbance rejection control method of a rope-driven continuum robot under actuator saturation constraint according to claim 1, characterized in that: The dynamic model of the rope-driven continuum robot considering the actuator saturation constraint is: Among them, ω d represents the uncertainty of the system's unmodeled dynamics, parameter perturbations, and external disturbances, τ c ∈R 2×1 To control the input , B(q) represents any one of the transformation matrices B1(q), B2(q) and B3(q), F = B -1 (q)τ c ∈R 2×1 is the tension vector on the driving rope, the saturation function Among them, F max is the maximum value of the tension vector F.

4. The method for active disturbance rejection control of a rope-driven continuum robot under actuator saturation constraint according to claim 1, characterized in that: The extended state observer is designed as: Where x1 represents the system state, x1=q, z1, z2 and z3 are the three outputs of the extended state observer, where z1 and z2 represent the output of the extended state observer to the system state x1 and its first-order derivative, respectively. The observed value, z3 represents the estimated value of the total disturbance of the system by the extended state observer, M -1 (x1) is the actual control input gain of the system, and β1, β2 and β3 are the gains of the extended state observer respectively.

5. The active disturbance rejection control method of a rope-driven continuum robot under actuator saturation constraint according to claim 1, characterized in that: The first output quantity and the second output quantity of the extended state observer and the system reference input signal are input to the PD controller, and the output state feedback control law includes: The state feedback control law u0 is as follows: Where r1 represents the system reference input signal, k p and k d is the controller gain.

6. The active disturbance rejection control method of a rope-driven continuum robot under actuator saturation constraint according to claim 1, characterized in that: The system control law is obtained according to the state feedback control law, the third output of the extended state observer and the actual control input gain, including: System control law τ c as follows: t c =M(x1)(u0-z3) Wherein, M(x1) is the inverse of the actual control input gain of the system.

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