Rope-driven snake-arm adaptive control method and system based on stiffness pre-distribution

Abstract

The present disclosure relates to a stiffness pre-distribution-based adaptive control method and system for a rope-driven snake arm, the method comprising: obtaining a desired end stiffness and an actual end stiffness of the rope-driven snake arm, and establishing a total fitness function according to the stiffness of each joint of the rope-driven snake arm; calculating the rope tension of each joint of the rope-driven snake arm by using the total fitness function in the guidance of an escape gradient, and controlling the stiffness of each joint and the end stiffness by controlling the rope tension; designing an adaptive damping variation rate based on a contact force error to establish an adaptive admittance control model, adjusting the parameters of the adaptive admittance control model by the real-time monitored contact force error; calculating a position correction amount by using a Lyapunov energy function to correct a reference trajectory, converting the corrected reference trajectory into a control instruction, and driving the movement of the rope-driven snake arm. The method of the present disclosure can realize adaptive impedance control of the rope-driven snake arm, adapt to different environments, and improve the operation efficiency.

Description

Technical Field

[0001] The present disclosure relates to the technical field related to robot motion control, and in particular to a rope-driven serpentine arm adaptive control method and system based on stiffness pre-distribution. Background Art

[0002] A rope-driven serpentine arm is a flexible multi-segment robot that uses a power element on a base as its power source and ropes to drive each joint. Rope-driven joints are a common control method in rope-driven serpentine arms, characterized by high degrees of freedom, simple structure, and high power density. Furthermore, the motion control unit of the rope-driven serpentine arm is located at the end base. This allows the robot's joints to be designed with only the rope fixing position in mind, without having to consider the installation location of the power element. This control method significantly reduces the robot's size, enabling it to meet the needs of specialized operations in extreme environments such as aircraft engines and nuclear power plants.

[0003] Several challenges remain in the interactive control of rope-driven serpentine arm control systems: 1) For a single joint, to avoid overconstraint, two of the three ropes control the two degrees of freedom of a joint through position control, while the other rope uses tension control, but there is no clear reference for the magnitude of the tension. 2) Rope-driven serpentine arms are driven by ropes, and the ropes, as flexible structures, run through each joint. Therefore, the stiffness of the rope-driven serpentine arm greatly affects the robot's control accuracy and motion characteristics. 3) Currently, impedance control on rope-driven serpentine arms, after fixing the impedance parameters, can only operate in the same environment. In a constantly changing environment, the rope-driven serpentine arm cannot adapt well to changes in the external environment. Therefore, research on adaptive impedance control methods for rope-driven serpentine arms combined with stiffness pre-distribution is very meaningful. Summary of the Invention

[0004] To address the problem that conventional rope-driven serpentine arm control methods cannot adapt well to changes in the external environment and have low operating efficiency under constantly changing conditions, this disclosure proposes an adaptive control method for rope-driven serpentine arm based on stiffness pre-distribution to solve the above problems.

[0005] According to one aspect of the present disclosure, a rope-driven serpentine arm adaptive control method based on stiffness pre-distribution is provided, comprising:

[0006] S10, obtaining an expected end stiffness and an actual end stiffness of the rope-driven serpentine arm, establishing a planetary fitness function based on the expected end stiffness and the actual end stiffness, establishing a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishing an overall fitness function based on the planetary fitness function values ​​and the characteristic fitness function values;

[0007] S20, guided by the escape gradient, using the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm, and controlling the stiffness of each joint and the end stiffness by controlling the rope tension;

[0008] S30, designing an adaptive damping change rate based on the contact force error, establishing an adaptive admittance control model according to the adaptive damping change rate, and adjusting parameters of the adaptive admittance control model according to the contact force error monitored in real time;

[0009] S40. Calculate the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, correct the reference trajectory according to the obtained position correction value, convert the corrected reference trajectory into a control instruction, and drive the rope-driven serpentine arm to move.

[0010] Preferably, a planetary fitness function is established based on the expected end stiffness and the actual end stiffness, and a characteristic fitness function is established according to the stiffness of each joint of the rope-driven serpentine arm. The planetary fitness function is expressed as:

[0011] f ind (X)=|K xd -K x (X)| 2 ,

[0012] Where K xd is the expected end stiffness, K x (X) is the actual end stiffness;

[0013] The feature fitness function is expressed as:

[0014]

[0015] Where n is the number of joints or arms, X i represents the i-th dimension feature of individual X, K ci (X i ) represents the joint stiffness matrix of the i-th joint of individual X.

[0016] Preferably, a total fitness function is established based on the planet fitness function value and the characteristic fitness function value, which is expressed as:

[0017]

[0018] Preferably, the escape gradient is used as the guide, and the gradient direction update formula is:

[0019]

[0020] Where, represents the coordinates of the “spacecraft” in the solution space in the i-th dimension, λ irepresents the learning rate, Indicates that the fitness function is The gradient in direction, represents the fitness function.

[0021] Preferably, an adaptive damping change rate is designed based on the contact force error, and the adaptive damping change rate is expressed as:

[0022]

[0023] Where b0 is the initial value of the damping coefficient, Δb(t) is the change law of the adaptive damping coefficient, and b p is the force error proportional gain coefficient, b i is the force error integral gain coefficient, b d is the force error differential gain coefficient, is the error change rate, Δf(t) is the contact force error, and ε is a very small positive constant used to avoid When the value approaches 0, the denominator will be zero, which will cause calculation errors.

[0024] Preferably, an adaptive admittance control model is established according to the adaptive damping change rate, and the adaptive admittance control model is expressed as:

[0025]

[0026] Where e(t) is the position error between the actual position and the reference trajectory, k is the one-dimensional expression of the desired stiffness coefficient matrix, and m is the one-dimensional expression of the desired inertia coefficient matrix.

[0027] Preferably, the position correction amount is calculated using the Lyapunov energy function, and the position correction amount is expressed as:

[0028]

[0029] Where ΔX represents the correction amount of the reference trajectory, f Δ (t) represents the time-varying compensation function, e represents the contact force error, p(t) and d(t) represent the time-varying proportional coefficient of the contact force error and the time-varying error change rate coefficient, respectively. M is the mass coefficient matrix, B is the damping coefficient matrix, K is the stiffness coefficient matrix, p0, d0 and f Δ0 is the initial value of the integral, For speed, is the acceleration.

[0030] According to one aspect of the present disclosure, a rope-driven serpentine arm adaptive control system based on stiffness pre-distribution is provided, comprising:

[0031] A total fitness function construction module obtains the expected end stiffness and actual end stiffness of the rope-driven serpentine arm, establishes a planetary fitness function based on the expected end stiffness and actual end stiffness, establishes a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishes a total fitness function based on the planetary fitness function values ​​and the characteristic fitness function values;

[0032] The joint stiffness and terminal stiffness control module is guided by the escape gradient and uses the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm. The stiffness of each joint and terminal stiffness is controlled by controlling the rope tension.

[0033] The parameter adjustment module of the adaptive admittance control model designs an adaptive damping change rate based on the contact force error, establishes an adaptive admittance control model based on the adaptive damping change rate, and adjusts the parameters of the adaptive admittance control model through the contact force error monitored in real time;

[0034] The reference trajectory correction module calculates the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, corrects the reference trajectory according to the obtained position correction value, and converts the corrected reference trajectory into a control instruction to drive the rope-driven serpentine arm to move.

[0035] According to one aspect of the present disclosure, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the above-mentioned rope-driven serpentine arm adaptive control method based on stiffness pre-distribution is implemented.

[0036] Compared with the prior art, the beneficial effects of the present disclosure are:

[0037] 1) This paper adopts and improves the Kepler optimization algorithm. Based on Kepler's three laws of planetary motion, it introduces an escape gradient-guided exploration rule. Based on the structural characteristics and expected stiffness of each joint of the rope-driven serpentine arm and the expected stiffness index of the end, a global comprehensive evaluation index based on the stiffness model is established. This enables the optimization strategy to be reasonably adjusted at different stages according to the search progress, thereby improving the speed of escaping from the local optimal solution and the convergence speed, while also improving the control accuracy.

[0038] 2) The present invention analyzes the dynamic performance of impedance control and adopts a variable damping coefficient to adaptively adjust the impedance controller parameters based on the analysis results. An adaptive damping change rate is established according to the contact force error, the accumulated force error, and the force error step rate. The dynamic performance of the system can be adaptively adjusted to ensure the control accuracy and flexibility of the rope-driven serpentine arm during movement.

[0039] 3) The present invention uses the Lyapunov energy function to calculate the position correction amount, and compensates the position of the reference trajectory through an impedance controller based on the expected reference trajectory. While avoiding the influence of environmental estimation error on the contact force control accuracy, it solves the impact of changes in environmental parameters on the system contact force control accuracy and effectively improves the system's adaptability to the environment.

[0040] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

[0041] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings herein are incorporated into and constitute a part of the specification. These drawings illustrate embodiments consistent with the present disclosure and, together with the specification, are used to explain the technical solutions of the present disclosure.

[0043] Figure 1 The flowchart of the adaptive control method of the rope-driven serpentine arm based on stiffness pre-distribution is shown;

[0044] Figure 2 A flow chart showing a control method for adaptive variable impedance control;

[0045] Figure 3 The schematic diagram of the rope-driven serpentine arm control method based on force / position hybrid control is shown;

[0046] Figure 4 A schematic diagram of the Kepler optimization method based on escape gradient in an example of the present disclosure is shown;

[0047] Figure 5 A flow chart of the Kepler optimization method based on escape gradient in an example of the present disclosure is shown;

[0048] Figure 6 The structural block diagram of the rope-driven serpentine arm adaptive control system based on stiffness pre-distribution in an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0049] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0050] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0051] The term "and / or" herein simply describes an association relationship between associated objects, indicating that three relationships can exist. For example, "A and / or B" can represent the existence of three situations: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" herein refers to any combination of at least two of any one or more of a plurality of items. For example, "at least one of A, B, and C" can represent any one or more elements selected from the set consisting of A, B, and C.

[0052] In addition, numerous specific details are provided in the following detailed description to better illustrate the present disclosure. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.

[0053] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0054] Example 1

[0055] Based on the above ideas, the present disclosure proposes a rope-driven serpentine arm adaptive control method based on stiffness pre-distribution. Figure 1 A flow chart of a rope-driven serpentine arm adaptive control method based on stiffness pre-distribution is shown. The method comprises:

[0056] S10, obtaining an expected end stiffness and an actual end stiffness of the rope-driven serpentine arm, establishing a planetary fitness function based on the expected end stiffness and the actual end stiffness, establishing a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishing an overall fitness function based on the planetary fitness function values ​​and the characteristic fitness function values;

[0057] S20, guided by the escape gradient, using the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm, and controlling the stiffness of each joint and the end stiffness by controlling the rope tension;

[0058] S30, designing an adaptive damping change rate based on the contact force error, establishing an adaptive admittance control model according to the adaptive damping change rate, and adjusting parameters of the adaptive admittance control model according to the contact force error monitored in real time;

[0059] S40. Calculate the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, correct the reference trajectory according to the obtained position correction value, convert the corrected reference trajectory into a control instruction, and drive the rope-driven serpentine arm to move.

[0060] The flow chart of the control method of adaptive variable impedance control provided by the embodiment of the present disclosure is as follows: Figure 2 As shown, the rope-driven serpentine arm robot is controlled by a force controller and a position controller. Adaptive position compensation is performed based on the current contact environment according to forward kinematics. An adaptive damping change rate is designed based on the contact force error. Adaptive admittance control is performed based on the damping coefficient change rate. Furthermore, stiffness pre-distribution is performed based on the adaptive admittance control to achieve the purpose of driving the rope-driven serpentine arm. The rope-driven serpentine arm adaptive control method based on stiffness pre-distribution includes the following steps:

[0061] S10. Obtain the expected end stiffness and the actual end stiffness of the rope-driven serpentine arm, establish a planetary fitness function based on the expected end stiffness and the actual end stiffness, establish a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establish an overall fitness function based on the planetary fitness function value and the characteristic fitness function value.

[0062] In this embodiment, based on the over-constrained control scheme of the rope-driven serpentine arm with three ropes controlling two degrees of freedom, force / position hybrid control is adopted for each rope-driven joint, that is, two of the three ropes are used for position control and the other one is used for force control. Figure 3 This diagram shows a control method for a rope-driven serpentine arm based on force / position hybrid control. It details how overconstrained control of two degrees of freedom (DOF) is achieved using three ropes. First, the system acquires the current position and force of the rope-driven serpentine arm through sensors. The force controller and position controller are then controlled based on statics and the inverse solution of the rope space. Specifically, position control is performed on two ropes, while force control is performed on the third rope, according to a preset control strategy. Furthermore, the force controller and position controller are used to adjust the control parameters of the single-joint model of the rope-driven serpentine arm robot in real time. This method ensures that the rope-driven serpentine arm possesses certain mechanical properties while maintaining a certain position accuracy for the robot arm.

[0063] The Kepler optimization algorithm based on escape gradient is used to pre-distribute the stiffness of the rope-driven serpentine arm, such as Figure 4As shown in the figure, the main contents of this method are as follows: the Kepler optimization algorithm is used as a meta-heuristic optimization algorithm for stiffness pre-allocation. According to Kepler's planetary motion rules, the algorithm is guided to search in the direction of minimizing error, further reducing the possibility of falling into local optimal solutions. By incorporating Kepler's three laws into the optimization process, based on the spacecraft and its orbit, it is expected to effectively find the global optimal solution to the inverse problem of the stiffness model among the planets (candidate solutions), thereby improving the performance and accuracy of the system. Figure 5 This is a flow chart of the Kepler optimization method based on escape gradient. The figure describes in detail the specific steps and process of the optimization algorithm, including initialization, planetary motion simulation, application of the escape gradient rule, and output of the optimization results. The specific steps are as follows:

[0064] Initialization: Randomly generate the position and velocity of the planets. First, establish a planetary group and evaluate the position goodness of each planet according to the fitness function. Then establish the solar system and calculate the Euclidean distance between the sun and each planet. Further, obtain the position and velocity of the planet according to the universal gravitation. Calculate fitness: Based on the current position and velocity of the planet, record the direction of the planet's movement to ensure that the fitness of the planet at the next moment is not inferior to that of the previous moment, and calculate the fitness value of each planet. Exploration condition judgment: Determine whether the planet meets the exploration conditions based on the planet's fitness value and gradient information. If the gradient of the planet's position is greater than a certain threshold (Escape gradient), the planet is considered to meet the exploration conditions. If the conditions are met, the algorithm will enter the next step and launch a "spacecraft" to explore along the gradient direction of the planet; otherwise, the exploration step will be skipped and the position and velocity of the planet will be updated directly. Spacecraft exploration: Launch a spacecraft to explore along the negative gradient direction. Update planet position and velocity: Adjust the position and velocity of the planet according to the exploration results. Optimal solution judgment: Determine whether the optimal solution has been reached. If not, continue to iterate. If the gradient value explored by the spacecraft is less than a certain threshold |δfit k (t)|<δ min If the solution is not optimal (i.e. the gradient approaches zero), the solution is considered to have reached the optimal or local optimal state, and a new planet is established at the spacecraft and incorporated into the solar system, thereby determining the planet with the best fitness among all the planets as the new sun; otherwise, the process returns to the fitness calculation step, continues to iteratively calculate the fitness value of the planet, and conducts the next round of exploration and update until t <t max Output the final solution. This rule effectively improves the global search capability of the algorithm and further reduces the possibility of falling into the local optimal solution.

[0065] The adaptability of each planet in the environment is called planetary fitness, and the fitness of each dimension of the planet in the solution space is called characteristic fitness. The planetary fitness function is established based on the expected end stiffness and the actual end stiffness, and the characteristic fitness function is established based on the stiffness of each joint of the rope-driven serpentine arm. The planetary fitness function is expressed as:

[0066] f ind (X)=|K xd -K x (X)| 2 ,

[0067] Where K xd is the expected end stiffness, K x (X) is the actual end stiffness.

[0068] The method for evaluating the stiffness similarity of the end-arm is to approximately evaluate whether two matrices are similar by comparing their moduli. Although this method is simple, it is very effective in the evaluation process of this embodiment. In the rope-driven serpentine arm, due to the similarity of each joint, the joints of the rope-driven serpentine arm tend to have a more uniform stiffness distribution scheme. The characteristic fitness function is expressed as:

[0069]

[0070] Where n is the number of joints or arms. There are 6 joints in the research object of this embodiment, so n=6, X i represents the i-th dimension feature of individual X, K ci (X i ) represents the joint stiffness matrix of the i-th joint of individual X.

[0071] Taking into account that the planetary fitness value and the characteristic fitness value have relatively obvious effects at the same time, the total fitness function is established based on the planetary fitness function value and the characteristic fitness function value, which is expressed as:

[0072]

[0073] S20. Guided by the escape gradient, the total fitness function is used to calculate the rope tension of each joint of the rope-driven snake arm through a meta-heuristic optimization algorithm, and the stiffness of each joint and the end stiffness are controlled by controlling the rope tension.

[0074] Because the original Kepler optimization method has large orbits and slow speeds for planets farther from the Sun, and because many random numbers are involved in the gravitational and velocity calculations, the direction of the planet's velocity and the direction of the fitness gradient there may differ significantly, significantly reducing optimization efficiency compared to the inner ring. Therefore, based on modern human exploration of outer space, this embodiment establishes an exploration optimization rule guided by the current position gradient of the outer ring planets, analogous to the third cosmic velocity. This can accelerate the Sun's escape from a local optimal solution when it is trapped, reducing optimization runtime.

[0075] In this embodiment, by analogy with the escape velocity (the third cosmic velocity), the escape gradient δ is defined esc As a "spacecraft" in the solution space, the conditional threshold for launching an exploration of the unknown solution space is: when the gradient of the location of the distant planet group in any direction is greater than the escape gradient δ esc When The planet meets the exploration conditions, and a spacecraft is launched to explore along the negative gradient direction of the planet's position in the solution space, guided by the escape gradient. The gradient direction update formula is:

[0076]

[0077] Where, represents the coordinates of the “spacecraft” in the solution space in the i-th dimension, λ i represents the learning rate, Indicates that the fitness function is The gradient in direction, Represents the fitness function. When the spacecraft explores to a gradient value less than a certain value δ min ,Right now When the spacecraft reaches an optimal solution or a local optimal solution, it is considered to be the desired "habitable area" for the parent planet. A new planet is established at this coordinate and incorporated into the solar system, following Kepler's three laws of solution space. This can accelerate the escape of the local optimal solution when the Sun is trapped in it, reducing the algorithm's runtime in complex solution spaces.

[0078] S30. Design an adaptive damping change rate based on the contact force error, establish an adaptive admittance control model according to the adaptive damping change rate, and adjust parameters of the adaptive admittance control model through the contact force error monitored in real time.

[0079] In this embodiment, the dynamic performance of the impedance model is analyzed and adaptive variable impedance parameters are established to adjust the dynamic performance of the system. The contact environment is equivalent to a first-order spring model, and the influence of position tracking error on the system is ignored, that is, X = X c , where the environmental stiffness is K e , then:

[0080] F e =K e (XX e )=K e (X c -X e ),

[0081] The admittance control model can be expressed as:

[0082]

[0083] Where, X r is the reference trajectory of the rope-driven serpentine arm, X c is the target trajectory output by the rope-driven serpentine arm, X is the actual position of the rope-driven serpentine arm, and X e is the environmental position, F e is the contact force between the rope-driven serpentine arm and the environment, F r is the desired contact force, ΔF=F r -F e is the contact force error, M is the mass coefficient matrix, B is the damping coefficient matrix, and K is the stiffness coefficient matrix. Since the position error between the actual position of the robot arm and the reference trajectory can be expressed as:

[0084] E=XX r =X c -X r ,

[0085] Then the admittance control model is expressed as:

[0086]

[0087] Since the environment parameters are unknown and it is impossible to obtain an accurate reference trajectory, we can set X r =X e , and according to the impedance model and the environmental contact model, the transfer function between the position error and the expected contact force is:

[0088]

[0089] The characteristic equation of the admittance control system is expressed as:

[0090] ms 2 +bs+k+k e =0,

[0091] Among them, m, b, k and k e They are M, B, K and K e According to the transfer function of a typical second-order system, the admittance control damping ratio ζ and the undamped natural frequency ω can be obtained. n for:

[0092]

[0093] Since ζ and ω n Directly affects the dynamic performance of the system. Considering that the mass coefficient m is more sensitive to the dynamic performance of the system, the stiffness coefficient k and the environmental stiffness coefficient k e Together, they affect the system's dynamic performance, and the damping coefficient b directly affects the system's damping ratio ζ. Therefore, assuming both the mass coefficient and stiffness coefficient are constants, the system response is dynamically adjusted by designing the adaptive rate of the damping coefficient.

[0094] From the above analysis, we can see that the initial environment position x e Can replace x r , then e=x c -x e , so the admittance control can be expressed as:

[0095]

[0096] Where, Δf(t), e(t) is time-varying, in order to further ensure that Δf ss →0, the damping coefficient is adaptively adjusted to compensate for the time-varying contact force error, thereby adjusting the impedance characteristics of the robot arm.

[0097] Based on the above analysis of the dynamic performance of impedance control, this embodiment uses variable damping to achieve adaptive variable admittance coefficient. An adaptive damping change rate is established based on the contact force error, force error accumulation, and force error rate to achieve adaptive dynamic adjustment of the damping coefficient. The adaptive damping change rate is expressed as:

[0098]

[0099] Where b0 is the initial value of the damping coefficient, Δb(y) is the variation law of the adaptive damping coefficient, and b p is the force error proportional gain coefficient, b i is the force error integral gain coefficient, b d is the force error differential gain coefficient, is the error change rate, Δf(t) is the contact force error, ε=10 -8 The main purpose of introducing this parameter is to adjust the error rate in the actual adaptive adjustment process. There may be a situation where it approaches 0, resulting in The denominator in one term is 0. In order to avoid this situation, the constant ε is introduced.

[0100] Furthermore, an adaptive admittance control model is established according to the adaptive damping change rate. The adaptive admittance control model is expressed as:

[0101]

[0102] Where e(t) is the position error between the actual position and the reference trajectory, k is the one-dimensional expression of the desired stiffness coefficient matrix, and m is the one-dimensional expression of the desired inertia coefficient matrix.

[0103] The adaptive variable admittance method described above dynamically adjusts the damping coefficient via a gain factor. The value of the gain factor determines the system's stable operation. Therefore, it is necessary to analyze the system's stability and identify constraints on the gain factor.

[0104] Performing Laplace transform on the above adaptive admittance control model yields:

[0105]

[0106] where e(s) = x c (s)-x e (s), and substituting the one-dimensional representation of the environmental contact force into it, we can obtain:

[0107]

[0108] The contact force error Δf(s) = f r (s)-f e Substituting (s) into the above formula, the transfer function between the contact force error and the desired force can be obtained as follows:

[0109]

[0110] The stability analysis of the characteristic equation is performed using the Routh stability criterion. In order to ensure the stability of the system, all the elements in the first column of the Routh table are positive, and the value of the gain coefficient should satisfy:

[0111]

[0112] S40. Calculate the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, correct the reference trajectory according to the obtained position correction value, convert the corrected reference trajectory into a control instruction, and drive the rope-driven serpentine arm to move.

[0113] In this embodiment, since a small estimation error of the environmental parameters will greatly affect the contact force control accuracy, this embodiment adopts the Lyapunov energy function to calculate the position correction amount. Based on the expected reference trajectory, the position of the reference trajectory is compensated by the impedance controller to improve the system's adaptability to the environment.

[0114] After the rope-driven serpentine arm comes into contact with the target task point, the contact force error between the robot and the environment is obtained by constructing the robot impedance model and the environment stiffness model:

[0115] ΔF=F r -K e (X r +G(s)ΔF-X e ),

[0116] in,

[0117]

[0118] F e =K e (XX e )=K e (X c -X e ),

[0119] Where G(s) is the robot impedance model, F e Represents the environmental stiffness model.

[0120] When t→∞, s→0, then the steady-state error of the contact force is:

[0121]

[0122] Therefore, when K e (X e -X r )+F r = 0 to meet the system steady-state error ΔF ss =0, so the relationship between the reference trajectory and the environmental variables is:

[0123]

[0124] By the environmental parameter K e and X e The reference trajectory input during the operation of the rope-driven serpentine arm is adjusted based on the estimation of the position control, thereby reducing the interference of the position control on the end contact force control.

[0125] However, since a small estimation error of the environmental parameters will greatly affect the contact force control accuracy, the Lyapunov energy function is used to calculate the position correction, and the reference trajectory correction is designed as follows:

[0126]

[0127] Among them, X r represents the expected reference trajectory, X crepresents the corrected reference trajectory, ΔX represents the correction amount of the reference trajectory, and f Δ (t) represents the time-varying compensation function, e represents the contact force error, p(t) and d(t) represent the time-varying proportional coefficient of the contact force error and the time-varying error change rate coefficient, respectively.

[0128] Substituting the impedance model and simplifying it, the expression for contact force error is:

[0129]

[0130] The state space equation is further established as follows:

[0131]

[0132] make Then the state space equation can be expressed as:

[0133]

[0134] Since the goal of this embodiment is to expect the contact force error to be 0, we have:

[0135]

[0136] Similarly, the state space is expressed as:

[0137]

[0138] Define the error between the expected error and the actual error as E e =E d -E p , then substituting the above two state equations into the state space equation for the error is:

[0139]

[0140] In order to ensure that the error between the actual contact force error and the expected contact force error approaches 0, the Lyapunov second method is used to make the system asymptotically stable. Therefore, a Lyapunov function is constructed and the state space equation of the error is guaranteed to be asymptotically stable.

[0141]

[0142] The position correction is calculated using the Lyapunov energy function, which is expressed as:

[0143]

[0144] Where ΔX represents the correction amount of the reference trajectory, f Δ(t) represents the time-varying compensation function, e represents the contact force error, p(t) and d(t) represent the time-varying proportional coefficient of the contact force error and the time-varying error change rate coefficient, respectively. M is the mass coefficient matrix, B is the damping coefficient matrix, K is the stiffness coefficient matrix, p0, d0 and f Δ0 is the initial value of the integral, where p 12 and p 22 are two constants of a positive definite matrix in the Lyapunov function, For speed, is the acceleration.

[0145] The disclosed embodiment integrates adaptive parameters and reference trajectory corrections as the adaptive impedance control part of the rope-driven serpentine arm, combined with stiffness pre-distribution to enable the robot to flexibly respond to complex external environments and provide a solid guarantee for its stable and efficient operation.

[0146] Example 2

[0147] As another aspect of the embodiment of the present disclosure, a rope-driven serpentine arm adaptive control system 100 based on stiffness pre-distribution is also provided. Figure 6 As shown, including:

[0148] Total fitness function construction module 1, obtains the expected end stiffness and actual end stiffness of the rope-driven serpentine arm, establishes a planetary fitness function based on the expected end stiffness and actual end stiffness, establishes a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishes a total fitness function based on the planetary fitness function values ​​and the characteristic fitness function values;

[0149] Joint stiffness and terminal stiffness control module 2, guided by the escape gradient, uses the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm, and controls the stiffness of each joint and terminal stiffness by controlling the rope tension;

[0150] The parameter adjustment module 3 of the adaptive admittance control model designs an adaptive damping change rate based on the contact force error, establishes an adaptive admittance control model based on the adaptive damping change rate, and adjusts the parameters of the adaptive admittance control model through the contact force error monitored in real time;

[0151] The reference trajectory correction module 4 calculates the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, corrects the reference trajectory according to the obtained position correction value, and converts the corrected reference trajectory into a control instruction to drive the rope-driven serpentine arm to move.

[0152] In the absence of any contradiction, the above modules in the system of the embodiment of the present disclosure can implement any implementation of the above method.

[0153] Based on the description of the above embodiments, it can be seen that the embodiments of the present disclosure can achieve the following technical effects:

[0154] 1) This paper adopts and improves the Kepler optimization algorithm. Based on Kepler's three laws of planetary motion, it introduces an escape gradient-guided exploration rule. Based on the structural characteristics and expected stiffness of each joint of the rope-driven serpentine arm and the expected stiffness index of the end, a global comprehensive evaluation index based on the stiffness model is established. This enables the optimization strategy to be reasonably adjusted at different stages according to the search progress, thereby improving the speed of escaping from the local optimal solution and the convergence speed, while also improving the control accuracy.

[0155] 2) The present invention analyzes the dynamic performance of impedance control and adopts a variable damping coefficient to adaptively adjust the impedance controller parameters based on the analysis results. An adaptive damping change rate is established according to the contact force error, the accumulated force error, and the force error step rate. The dynamic performance of the system can be adaptively adjusted to ensure the control accuracy and flexibility of the rope-driven serpentine arm during movement.

[0156] 3) The present invention uses the Lyapunov energy function to calculate the position correction amount, and compensates the position of the reference trajectory through an impedance controller based on the expected reference trajectory. While avoiding the influence of environmental estimation error on the contact force control accuracy, it solves the impact of changes in environmental parameters on the system contact force control accuracy and effectively improves the system's adaptability to the environment.

[0157] The present disclosure also provides an electronic device comprising: a processor; and a memory for storing instructions executable by the processor; wherein the processor is configured to implement the aforementioned method for adaptive control of a rope-driven serpentine arm based on stiffness pre-distribution. The electronic device can be provided as a terminal, server, or other device.

[0158] The present disclosure also provides a computer-readable storage medium having computer program instructions stored thereon. When executed by a processor, the computer program instructions implement the aforementioned method for adaptive control of a rope-driven serpentine arm based on stiffness pre-distribution. The computer-readable storage medium may be a non-volatile computer-readable storage medium.

[0159] Those skilled in the art will understand that in the above-mentioned rope-driven serpentine arm adaptive control method and system based on stiffness pre-distribution in the specific implementation method, the writing order of each step does not mean a strict execution order and constitutes any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0160] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and the part of the module, program segment or instruction contains one or more executable instructions for realizing the prescribed logical function. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the prescribed function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0161] While various embodiments of the present disclosure have been described above, the above descriptions are illustrative, non-exhaustive, and not intended to be limiting of the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technical improvements to existing technologies, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A rope-driven serpentine arm adaptive control method based on stiffness pre-distribution, characterized in that: The steps include: S10, obtaining an expected end stiffness and an actual end stiffness of the rope-driven serpentine arm, establishing a planetary fitness function based on the expected end stiffness and the actual end stiffness, establishing a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishing an overall fitness function based on the planetary fitness function values ​​and the characteristic fitness function values; S20, guided by the escape gradient, using the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm, and controlling the stiffness of each joint and the end stiffness by controlling the rope tension; S30, designing an adaptive damping change rate based on the contact force error, establishing an adaptive admittance control model according to the adaptive damping change rate, and adjusting parameters of the adaptive admittance control model according to the contact force error monitored in real time; S40. Calculate the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, correct the reference trajectory according to the obtained position correction value, convert the corrected reference trajectory into a control instruction, and drive the rope-driven serpentine arm to move.

2. The method according to claim 1, characterized in that The planetary fitness function is established based on the expected end stiffness and the actual end stiffness, and the characteristic fitness function is established according to the stiffness of each joint of the rope-driven serpentine arm. The planetary fitness function is expressed as: ， Where, is the expected end stiffness, is the actual end stiffness; The feature fitness function is expressed as: ， Where n is the number of joints or arms, Represents an individual The i-th dimension feature, Represents an individual The joint stiffness matrix of the i-th joint.

3. The method according to claim 2, characterized in that The total fitness function is established based on the planet fitness function value and the characteristic fitness function value, which is expressed as: 。 4. The method according to claim 1, wherein Guided by the escape gradient, the gradient direction update formula is: ， Where, represents the coordinates of the "spacecraft" in the solution space in the i-th dimension, represents the learning rate, Indicates that the fitness function is The gradient in direction, represents the fitness function.

5. The method according to claim 1, wherein The adaptive damping change rate is designed based on the contact force error, and the adaptive damping change rate is expressed as: ， Where, is the initial value of the damping coefficient, is the variation law of the adaptive damping coefficient, is the force error proportional gain coefficient, is the force error integral gain coefficient, is the force error differential gain coefficient, is the error change rate, is the contact force error, is a minimal positive constant, used to avoid When the value approaches 0, the denominator will be zero, which will cause calculation errors.

6. The method according to claim 5, characterized in that An adaptive admittance control model is established according to the adaptive damping change rate. The adaptive admittance control model is expressed as: ， Where, is the position error between the actual position and the reference trajectory, k is the one-dimensional expression of the desired stiffness coefficient matrix, and m is the one-dimensional expression of the desired inertia coefficient matrix.

7. The adaptive control system of rope-driven serpentine arm based on stiffness pre-distribution is characterized by: include: A total fitness function construction module obtains the expected end stiffness and actual end stiffness of the rope-driven serpentine arm, establishes a planetary fitness function based on the expected end stiffness and actual end stiffness, establishes a characteristic fitness function according to the stiffness of each joint of the rope-driven serpentine arm, and establishes a total fitness function based on the planetary fitness function values ​​and the characteristic fitness function values; The joint stiffness and terminal stiffness control module is guided by the escape gradient and uses the total fitness function through a meta-heuristic optimization algorithm to calculate the rope tension of each joint of the rope-driven snake arm. The stiffness of each joint and terminal stiffness is controlled by controlling the rope tension. The parameter adjustment module of the adaptive admittance control model designs an adaptive damping change rate based on the contact force error, establishes an adaptive admittance control model based on the adaptive damping change rate, and adjusts the parameters of the adaptive admittance control model through the contact force error monitored in real time; The reference trajectory correction module calculates the position correction value using the Lyapunov energy function according to the parameters of the adaptive admittance control model, corrects the reference trajectory according to the obtained position correction value, and converts the corrected reference trajectory into a control instruction to drive the rope-driven serpentine arm to move.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the rope-driven serpentine arm adaptive control method based on stiffness pre-distribution according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the rope-driven serpentine arm adaptive control method based on stiffness pre-distribution according to any one of claims 1 to 6 is implemented.

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