Flexible continuum robot motion control method based on improved angle and exendinium optimization algorithm

Abstract

The invention discloses a flexible continuum robot motion control method based on an improved Kerr-Ren optimization algorithm. The method comprises a novel flexible continuum robot 3D printing piece structure and a closed-loop model-free control method based on the improved Kerr-Ren optimization algorithm. According to the method, the improved angle exenx optimization algorithm is introduced, the Henon chaotic mapping theory, the linear adaptive weight and the mirror reflection learning model are introduced on the basis of the original algorithm, the diversity of population initialization is increased through improvement, the optimization precision of the algorithm is improved, and the optimization precision of the algorithm is improved. The global search capability and the local search capability of the algorithm in each stage are balanced, the convergence speed is effectively improved, and the algorithm is prevented from falling into local optimum; through combination of the improved angle exid optimization algorithm and the closed-loop model-free control method provided by the invention, path planning and attitude adjustment of the novel flexible continuum robot are realized, and a guarantee is provided for high-precision control of the novel flexible continuum robot.

Description

Technical Field

[0001] The invention relates to a flexible continuum robot motion control method, in particular to a flexible continuum robot motion control method based on an improved horned lizard optimization algorithm, and belongs to the technical field of flexible continuum robot control. Background Art

[0002] Flexible continuum robots (SCRs) have attracted widespread attention in recent years due to their good motion characteristics, environmental adaptability and structural compliance, and have become a research hotspot in the fields of environmental exploration, biomedicine, social services, etc. Different from existing rigid continuum robots, the structural units of SCRs are mostly made of flexible intelligent materials, and the reaction force generated during the execution of tasks is relatively small, which effectively reduces the collision damage during the grasping process. At the same time, the rise of soft robotics technology and 3D / 4D printing technology has brought many possibilities to the design of SCRs. Among them, origami technology stands out due to its good fold-to-expansion ratio, multi-stable characteristics, variable stiffness and other mechanical properties. While optimizing the inherent stiffness of SCRs, it can greatly improve the movement flexibility of SCRs.

[0003] In the prior art, a pneumatic continuum mechanism based on an origami structure is disclosed in publication number CN113580119A, which includes a mounting assembly, an origami assembly, and an air drive assembly. The mounting assembly includes a base plate and a control box; the origami assembly includes a plurality of origami structures, which are supported in parallel between the base plate and the control box, each of which is foldable and foldably connects the base plate and the control box; the air drive assembly includes a plurality of bellows, which are supported in parallel between the base plate and the control box, and each bellows is provided with a joint for air supply and exhaust. This prior art is based on an air drive mode, and a multi-layer prefabricated module with multiple degrees of freedom is complexly controlled, which releases the working space and environment, and solves the problem that a large number of drive units are required and it is difficult to achieve lightweight. The foldable structure is lightweight, compact, scalable and miniaturized, while maintaining its motion performance. However, the related designs combining origami structures and SCRs mostly rely on inherent folds for movement, and are still limited by limited degrees of freedom. Secondly, the research work on modeling and control is mostly focused on dynamic models or static deformation models, so as to design corresponding control methods. At the same time, the nonlinearity and fatigue effects of soft materials can easily lead to uncertain changes in the relevant parameters of the mechanical model, which brings great difficulties to the modeling and control of SCRs.

[0004] In recent years, meta-heuristic algorithms have been widely used in various optimization problems. -Delgado proposed a Horned Lizard Optimization Algorithm in 2024. The algorithm simulates the passive defense behavior and living habits of horned lizards, has strong adaptability, and shows effectiveness in balancing utilization and exploration mechanisms, and can achieve effective search capabilities in optimization problems. However, the algorithm itself is prone to fall into local optimality, and the initialization uncertainty is large. There are still some problems in terms of convergence speed and convergence accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a flexible continuum robot motion control method based on an improved horned lizard optimization algorithm in order to solve at least one of the above technical problems, so as to achieve high-precision motion control of the new flexible continuum robot along the expected trajectory.

[0006] The present invention achieves the above-mentioned purpose through the following technical solutions: a flexible continuum robot motion control method based on an improved horned lizard optimization algorithm, including a new flexible continuum robot 3D printed part structure and a closed-loop model-free control method based on the improved horned lizard optimization algorithm, the new flexible continuum robot 3D printed part structure includes a flexible telescopic unit and a flexible bending unit, the flexible telescopic unit and the flexible bending unit both use Kresling origami with tristable characteristics as structural units, and the flexible bending unit is equipped with a deformable auxiliary airbag;

[0007] The closed-loop model-free control method includes the following steps:

[0008] Step 1: Taking the new flexible continuum robot 3D printed structure as the research object, set the coordinates of the initial target position (X t ,Y t ,Z t ); and obtain the coordinates of the end position of the new flexible continuum robot 3D printed structure through the visual system (X e ,Y e ,Z e );

[0009] Step 2: Based on the horizontal and vertical coordinates X of the initial target position t and Y t Determine the quadrant in which it is located, control the auxiliary airbags of the flexible telescopic unit and the flexible bending unit to realize the position of the end of the 3D printed structure of the new flexible continuum robot (X e ,Y e ,Z e ) to set the initial target position (X t ,Y t ,Z t )sports;

[0010] Step 3: Using a PID controller to compensate and control the pressure in the auxiliary airbags of the flexible telescopic unit and the flexible bending unit;

[0011] Step 4: Introduce the improved horned lizard optimization algorithm to adaptively optimize the closed-loop model-free control system of the new flexible continuum robot 3D printed structure;

[0012] Step 5. According to the improved horned lizard optimization algorithm, the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure are optimized and selected, and the new flexible continuum robot 3D printed structure is made to move along the expected trajectory.

[0013] As a further solution of the present invention: the new flexible continuum robot 3D printed structure is formed by coupling a flexible telescopic unit and a flexible bending unit in series; the flexible telescopic unit and the flexible bending unit are both designed based on a double-layer Kresling origami configuration, and the unfolded state of the flexible telescopic unit is an origami plane pattern of the same chirality, and the unfolded state of the flexible bending unit is an origami plane pattern of the opposite chirality.

[0014] As a further solution of the present invention: the movement achieved by the new flexible continuum robot 3D printed structure is specifically:

[0015] The flexible bending unit controls the telescopic and torsional coupled motion of the new flexible continuum robot 3D printed structure, which is driven by the air pressure in the unit chamber and can achieve a large contraction ratio.

[0016] The flexible bending unit controls the bending movement of the new flexible continuum robot 3D printed structure. The flexible bending unit achieves flexible adjustment of the surface stiffness by changing the expansion / contraction state of the airbag. When the unit chamber is in a negative pressure state, the airbag expands, increasing the surface stiffness of the unit, resulting in a stiffness difference in the flexible bending unit, causing the unit as a whole to bend to the opposite side of the action surface.

[0017] As a further solution of the present invention: in step 3, the pressure compensation formula of the PID controller is:

[0018]

[0019] Among them, e Θ =Θ e -Θ t (Θ=x,y,z) is the end of the new flexible continuum robot 3D printed structure (X e ,Y e ,Z e ) and the target position (X t ,Y t ,Z t ) between the two; K P, K I , K D are the proportional coefficient, integral coefficient and differential coefficient of the PID controller respectively; dt represents the time interval between iteration steps; K P The existence of will compensate for the possible large coordinate error e Θ , bringing a larger pressure compensation P to the main chamber of the new flexible continuum robot 3D printed structure Θ ; At the same time, when the coordinate deviation is small or close to 0, K I and K D This will help eliminate steady-state errors and avoid overshoot, respectively.

[0020] As a further solution of the present invention: the main chamber of the new flexible continuum robot 3D printed structure requires three states of positive pressure, negative pressure and steady pressure; the closed-loop model-free control system of the new flexible continuum robot 3D printed structure realizes the state change of the terminal through a solenoid valve group composed of four two-position two-way valves and one two-position three-way valve, wherein R1 to R4 are two-position two-way valves, and R5 is a two-position three-way valve; R1 and R2 are arranged in parallel, R1 and R3 are connected in series, R2 and R5 are connected in series, and the parallel circuit of R1 and R2 is connected in series with R4;

[0021] The closed-loop model-free control system works as follows:

[0022] When R1 is powered on, R2 is powered off, R3 is powered off, R4 is powered on, and R5 is powered on, the end of the 3D printed structure of the new flexible continuum robot is in a positive pressure state.

[0023] When R1 is powered off, R2 is powered on, R3 is powered on, R4 is powered off, and R5 is powered on, the end of the 3D printed structure of the new flexible continuum robot is in a negative pressure state.

[0024] When R1 is powered off, R2 is powered off, R3 is powered on, R4 is powered on, and R5 is powered off, the end of the 3D printed structure of the new flexible continuum robot is in a pressure-maintaining state;

[0025] The microcontroller changes the pressure P from the air pump to the end chamber through the coordination of the solenoid valve group and the air pressure sensor. out The output pressure P at the end of the solenoid valve group at the current iteration step Θ,out,k for:

[0026] P Θ,out,k =P Θ,out,k-1 +P Θ ,Θ=x,y,z

[0027] Among them, P Θ ,out,k-1 is the output pressure at the end of the solenoid valve group in the last iteration step;

[0028] Initial pressure (P) of the new flexible continuum robot 3D printed structure x,out,k ,P y,out,k ,P z,out,k ) are all set to 0kpa; when the air pump starts to provide pressure for the new flexible continuum robot 3D printed structure, the visual system will provide it with the end position coordinates (X e ,Y e ,Z e ), and used as the feedback variable of the PID controller to calculate the pressure compensation result of the current iteration step in real time; in the control system, a single-chip microcomputer is used to control three groups of solenoid valves, one of which is used to control the pressure of the main chamber of the new flexible continuum robot 3D printed structure, thereby driving its movement in the Z direction; the other two groups are mainly used to control the pressure of the airbag in the flexible bending unit, thereby driving the movement of the end of the new flexible continuum robot 3D printed structure in the X and Y directions.

[0029] As a further solution of the present invention: in step 4, the basic algorithm of the horned lizard optimization algorithm is calculated based on the passive defense behavior of the horned lizard, wherein the passive defense behavior of the horned lizard includes: hiding behavior, changing skin brightness behavior, ejecting blood flow behavior, transferring escape behavior and regulating body temperature behavior;

[0030] Hiding behavior refers to the horned lizard mimicking environmental features and blending in with the surrounding environment, making it difficult for prey and predators to find it, increasing its chances of survival in the wild. The behavioral formula is as follows:

[0031]

[0032] Among them, t is the current iteration number, T is the maximum iteration number; is the latest search agent of the horned lizard in the search space of generation t+1, is the best search agent of the horned lizard in the tth generation, r1, r2, r3, r4 are random integers between the maximum population size N and 1, and r1≠r2≠r3≠r4; β is set to 2, k1 and k2 are random numbers selected from the standardized color palette; λ is the binary value obtained, and its acquisition formula is as follows:

[0033]

[0034] Changing skin brightness behavior means that the horned lizard changes the color of its skin by increasing or decreasing the sunlight gain. Darker colors can absorb more heat, and lighter colors can reflect more heat. The mathematical model of the darkening and lightening of the horned lizard's skin is as follows:

[0035]

[0036] Among them, Da1 and Da2 are random numbers generated between 0.5440510 and 1, and Li1 and Li2 are random numbers generated between 0 and 0.4046661;

[0037] Blood jet behavior means that the horned lizard's eyes can resist enemies by ejecting blood. The blood flow mainly moves in a parabolic motion, and the trajectory can be expressed as:

[0038]

[0039] Where v0 is the initial velocity, set to 1, ω is set to π / 2, μ is 1E-6, and g is the acceleration of the earth;

[0040] The transfer escape behavior refers to the horned lizard's need to move quickly to avoid predators. The transfer formula is as follows:

[0041]

[0042] Where wk is a random number between -1 and 1, and ε is a random mean generated by the Cauchy distribution;

[0043] Thermoregulation behavior refers to the horned lizard changing its skin color by regulating its own body temperature to cope with various emergencies. The mathematical formula of the whole process can be expressed as:

[0044]

[0045] Among them, M(i) is the color cell of the horned lizard skin, Fit max and Fit min are the best fitness and the worst fitness at the current iteration number, and Fit(i) is the current fitness of the i-th horned lizard.

[0046] As a further solution of the present invention: for the algorithm for regulating body temperature behavior, when M(i)≤0.3, the following formula is used to complete the position update:

[0047]

[0048] As a further solution of the present invention: on the basis of the horned lizard optimization algorithm, the Henon chaos mapping theory is introduced into the initialization stage of the horned lizard population, which effectively increases the diversity of the HLOA population initialization and improves the search efficiency of the HLOA algorithm; the mapping model is as follows:

[0049]

[0050] Among them, x n ,y nis the initial position parameter of HLOA; when the mapping randomness constant a=1.4, b=0.3, the mapping sequence can be guaranteed to have strong randomness, x n+1 ,y n+1 is the position after chaos mapping.

[0051] As a further solution of the present invention: based on the horned lizard optimization algorithm, a nonlinear adaptive weight is introduced into the horned lizard color iteration stage; the nonlinear adaptive weight is as follows:

[0052]

[0053] Based on the above weights, the updated color iteration formula is as follows:

[0054]

[0055] The introduction of the adaptive weight enables the color iteration method of the horned lizard to achieve a reasonable balance in each stage, which can greatly improve the optimization accuracy of the horned lizard algorithm and supplement the algorithm's need for global and local search capabilities at each stage.

[0056] As a further solution of the present invention: based on the horned lizard optimization algorithm, a mirror reflection learning model is introduced for the output stage of the horned lizard population; the mathematical model is as follows:

[0057]

[0058] in, Learn the solution for mirror reflection, V max and V min are the upper and lower limits of the population information after a single iteration, and λ is the parameter that controls the degree of reflection;

[0059]

[0060] Among them, rand1 and rand2 are both random numbers between 0 and 1, φ is the elastic coefficient, and N0 is the field radius of the mirror;

[0061] In order to ensure that the upper and lower limits of the mirror reflection learning solution do not exceed the upper and lower limits of the population itself, the upper and lower limits are processed according to the following formula:

[0062]

[0063] Among them, F U and F L are the judgment results of the upper and lower limits respectively, and ~ is the negation operation; the introduction of this model can enable the algorithm to explore a wider range of possibilities and avoid falling into suboptimal solutions, ultimately enabling it to better handle complex function problems.

[0064] The beneficial effects of the present invention are:

[0065] 1) Set the initial target position coordinates and obtain the NSCR end position coordinates based on the visual system, determine the quadrant of the target position, and control the FTU 1～4 The PID controller is used to control the FTU 1～4 Compensation control with the pressure of airbags 1 to 4;

[0066] 2) In view of the uncertainty of the NSCR working environment, a closed-loop model-free control system is established, and parameters are adjusted to achieve adaptive optimization. The parameters of the NSCR closed-loop model-free control system controller are selected to enable the NSCR to move along the expected trajectory. An improved horned lizard optimization algorithm is introduced for the closed-loop model-free control method of the NSCR. Based on the original algorithm, this algorithm introduces the Henon chaos mapping theory, linear adaptive weight and mirror reflection learning model respectively;

[0067] 3) Through the above improvements, the diversity of population initialization is increased, the optimization accuracy of the algorithm is improved, the global search ability and local search ability of the algorithm at each stage are balanced, the convergence speed is effectively improved, and the algorithm is prevented from falling into the local optimum;

[0068] 4) The improved horned lizard optimization algorithm is used to realize path planning and posture adjustment of the new flexible continuum robot, which provides a guarantee for high-precision control of the new flexible continuum robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The three-dimensional model diagram of the research object of the present invention is "a new type of flexible continuum robot";

[0070] Figure 2 is a brief flow chart of the closed-loop model-free control method of the present invention;

[0071] Figure 3 It is a working principle diagram of the closed-loop model-free control method in the present invention;

[0072] Figure 4 It is the solenoid valve working diagram of the closed-loop model-free control system in the present invention;

[0073] Figure 5 This is an algorithm flow chart of the improved horned lizard optimization algorithm of the present invention;

[0074] Figure 6 It is a convergence curve diagram of the first test function in the embodiment of the present invention under the improved horned lizard optimization algorithm and other multiple intelligent optimization algorithms;

[0075] Figure 7It is a convergence curve diagram of the second test function in the embodiment of the present invention under the improved horned lizard optimization algorithm and other multiple intelligent optimization algorithms;

[0076] Figure 8 It is a convergence curve diagram of the third test function in the embodiment of the present invention under the improved horned lizard optimization algorithm and other multiple intelligent optimization algorithms.

[0077] In the figure: 1-1, new flexible continuum robot 3D printed structure, 1-2, flexible telescopic unit, 1-3, flexible bending unit, 1-4, origami plane pattern with same chirality, 1-5, origami plane pattern with opposite chirality. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] Embodiment 1, as Figures 1 to 5 As shown, a flexible continuum robot motion control method based on an improved horned lizard optimization algorithm includes a new flexible continuum robot 3D printed structure 1-1 and a closed-loop model-free control method based on the improved horned lizard optimization algorithm. The new flexible continuum robot 3D printed structure 1-1 includes a flexible telescopic unit 1-2 and a flexible bending unit 1-3. The flexible telescopic unit 1-2 and the flexible bending unit 1-3 both use Kresling origami with tristable characteristics as structural units, and the flexible bending unit 1-3 is equipped with a deformable auxiliary airbag;

[0080] The closed-loop model-free control method includes the following steps:

[0081] Step 1: Take the new flexible continuum robot 3D printed structure 1-1 as the research object and set the coordinates of the initial target position (X t ,Y t ,Z t ); and obtain the coordinates of the end position of the new flexible continuum robot 3D printed structure 1-1 through the visual system (X e ,Y e ,Z e );

[0082] Step 2: Based on the horizontal and vertical coordinates X of the initial target position t and Y tDetermine the quadrant in which it is located, control the auxiliary airbags of the flexible telescopic unit 1-2 and the flexible bending unit 1-3 to realize the position of the end of the new flexible continuum robot 3D printed structure 1-1 (X e ,Y e ,Z e ) to set the initial target position (X t ,Y t ,Z t ) movement; for example, if the target position is exposed in the 12th quadrant, then control the airbags 1 to 2 respectively so that the end X e ,Y e To X t ,Y t At the same time, control FTU 1～4 Make Z e To Z t to get closer;

[0083] Step 3: Using a PID controller to compensate and control the pressure in the auxiliary airbags of the flexible telescopic unit 1-2 and the flexible bending unit 1-3;

[0084] Step 4: Introduce the improved horned lizard optimization algorithm to adaptively optimize the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1;

[0085] Step 5: According to the improved horned lizard optimization algorithm, the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1 are optimized and selected, and the new flexible continuum robot 3D printed structure 1-1 is made to move along the expected trajectory.

[0086] Embodiment 2. In addition to all the technical features of Embodiment 1, this embodiment also includes: a new flexible continuum robot 3D printed structure 1-1 is formed by a flexible telescopic unit 1-2 and a flexible bending unit 1-3 coupled in series; the flexible telescopic unit 1-2 and the flexible bending unit 1-3 are both designed based on a double-layer Kresling origami configuration, and the unfolded state of the flexible telescopic unit 1-2 is an origami plane pattern 1-4 of the same chirality, and the unfolded state of the flexible bending unit 1-3 is an origami plane pattern 1-5 of the opposite chirality.

[0087] The specific movements achieved by the new flexible continuum robot 3D printed structure 1-1 are:

[0088] The flexible bending unit 1-3 controls the telescopic and torsional coupled motion of the new flexible continuum robot 3D printed structure 1-1, which is driven by the air pressure of the unit chamber and can achieve a large contraction ratio;

[0089] The flexible bending unit 1-3 controls the bending movement of the new flexible continuum robot 3D printed structure 1-1. The flexible bending unit 1-3 realizes flexible adjustment of the surface stiffness by changing the expansion / contraction state of the airbag. When the unit chamber is in a negative pressure state, the airbag expands, which increases the surface stiffness of the unit and causes a stiffness difference in the flexible bending unit 1-3, thereby causing the unit as a whole to bend to the opposite side of the action surface.

[0090] Embodiment 3: In addition to all the technical features of Embodiment 1, this embodiment also includes:

[0091] In step 3, the pressure compensation formula of the PID controller is:

[0092]

[0093] Among them, e Θ =Θ e -Θt (Θ=x,y,z) is the new flexible continuum robot 3D printed structure 1-1 end (X e ,Y e ,Z e ) and the target position (X t ,Y t ,Z t ) between the two; K P , K I , K D are the proportional coefficient, integral coefficient and differential coefficient of the PID controller respectively; dt represents the time interval between iteration steps; K P The existence of will compensate for the possible large coordinate error e Θ , bringing a larger pressure compensation P to the main chamber of the new flexible continuum robot 3D printed structure 1-1 Θ ; At the same time, when the coordinate deviation is small or close to 0, K I and K D This will help eliminate steady-state errors and avoid overshoot, respectively.

[0094] Furthermore, the main chamber of the new flexible continuum robot 3D printed structure 1-1 requires three states: positive pressure, negative pressure, and steady pressure; the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1 realizes the state change of the terminal through a solenoid valve group composed of four two-position two-way valves and one two-position three-way valve, wherein R1 to R4 are two-position two-way valves, and R5 is a two-position three-way valve; R1 and R2 are arranged in parallel, R1 and R3 are connected in series, R2 and R5 are connected in series, and the parallel circuit of R1 and R2 is connected in series with R4;

[0095] The closed-loop model-free control system works as follows:

[0096] When R1 is powered on, R2 is powered off, R3 is powered off, R4 is powered on, and R5 is powered on, the end of the new flexible continuum robot 3D printed structure 1-1 is in a positive pressure state.

[0097] When R1 is powered off, R2 is powered on, R3 is powered on, R4 is powered off, and R5 is powered on, the end of the new flexible continuum robot 3D printed structure 1-1 is in a negative pressure state.

[0098] When R1 is powered off, R2 is powered off, R3 is powered on, R4 is powered on, and R5 is powered off, the end of the new flexible continuum robot 3D printed part structure 1-1 is in a pressure-maintaining state;

[0099] The microcontroller can change the pressure P from the air pump to the end chamber through the cooperation of the solenoid valve group and the air pressure sensor. out The output pressure P at the end of the solenoid valve group at the current iteration step Θ,out,k for:

[0100] P Θ,out,k =P Θ,out,k-1 +P Θ ,Θ=x,y,z (2)

[0101] Among them, P Θ,out,k-1 is the output pressure at the end of the solenoid valve group in the previous iteration step;

[0102] Initial pressure (P) of the new flexible continuum robot 3D printed structure 1-1 x,out,k ,P y,out,k ,P z,out,k ) are all set to 0kpa; when the air pump starts to provide pressure to the new flexible continuum robot 3D printed structure 1-1, the visual system will provide it with the end position coordinates (X e ,Y e ,Z e ), and used as the feedback variable of the PID controller to calculate the pressure compensation result of the current iteration step in real time; in the control system, a single-chip microcomputer is used to control three groups of solenoid valves, one of which is used to control the pressure of the main chamber of the new flexible continuum robot 3D printed structure 1-1, thereby driving its movement in the Z direction; the other two groups are mainly used to control the pressure of the airbag in the flexible bending unit, thereby driving the movement of the end of the new flexible continuum robot 3D printed structure 1-1 in the X and Y directions.

[0103] Embodiment 4: In addition to all the technical features of Embodiment 1, this embodiment also includes:

[0104] In step 4, the basic algorithm of the horned lizard optimization algorithm is calculated based on the passive defense behavior of the horned lizard, wherein the passive defense behavior of the horned lizard includes: hiding behavior, changing skin brightness behavior, ejecting blood flow behavior, transferring escape behavior and regulating body temperature behavior;

[0105] Hiding behavior refers to the horned lizard mimicking environmental features and blending in with the surrounding environment, making it difficult for prey and predators to find it, increasing its chances of survival in the wild. The behavioral formula is as follows:

[0106]

[0107] Among them, t is the current iteration number, T is the maximum iteration number; is the latest search agent of the horned lizard in the search space of generation t+1, is the best search agent of the horned lizard in the tth generation, r1, r2, r3, r4 are random integers between the maximum population size N and 1, and r1≠r2≠r3≠r4; β is set to 2, k1 and k2 are random numbers selected from the standardized color palette; λ is the binary value obtained, and its acquisition formula is as follows:

[0108]

[0109] Changing skin brightness behavior means that horned lizards can change the color of their skin by increasing or decreasing the sunlight gain. Darker colors can absorb more heat, and lighter colors can reflect more heat. The mathematical model of the darkening and lightening of the horned lizard's skin is as follows:

[0110]

[0111] Among them, Da1 and Da2 are random numbers generated between 0.5440510 and 1, and Li1 and Li2 are random numbers generated between 0 and 0.4046661;

[0112] Blood jet behavior means that the horned lizard's eyes can resist enemies by ejecting blood. The blood flow mainly moves in a parabolic motion, and the trajectory can be expressed as:

[0113]

[0114] Where v0 is the initial velocity, set to 1, ω is set to π / 2, μ is 1E-6, and g is the acceleration of the earth;

[0115] The transfer escape behavior refers to the horned lizard's need to move quickly to avoid predators. The transfer formula is as follows:

[0116]

[0117] Where wk is a random number between -1 and 1, and ε is a random mean generated by the Cauchy distribution;

[0118] Thermoregulation behavior refers to the horned lizard changing its skin color by regulating its own body temperature to cope with various emergencies. The mathematical formula of the whole process can be expressed as:

[0119]

[0120] Among them, M(i) is the color cell of the horned lizard skin, Fit max and Fit min are the best fitness and the worst fitness at the current iteration number, and Fit(i) is the current fitness of the i-th horned lizard.

[0121] Furthermore, for the algorithm for regulating body temperature behavior, when M(i)≤0.3, the following formula is used to complete the position update:

[0122]

[0123] Furthermore, on the basis of the horned lizard optimization algorithm, the Henon chaos mapping theory is introduced into the initialization stage of the horned lizard population, which effectively increases the diversity of the HLOA population initialization and improves the search efficiency of the HLOA algorithm; the mapping model is as follows:

[0124]

[0125] Among them, x n ,y n is the initial position parameter of HLOA; when the mapping randomness constant a=1.4, b=0.3, the mapping sequence can be guaranteed to have strong randomness, x n+1 ,y n+1 is the position after chaos mapping.

[0126] Furthermore, based on the horned lizard optimization algorithm, nonlinear adaptive weights are introduced into the horned lizard color iteration stage; the nonlinear adaptive weights are as follows:

[0127]

[0128] Based on the above weights, the updated color iteration formula is as follows:

[0129]

[0130] The introduction of the adaptive weight enables the color iteration method of the horned lizard to achieve a reasonable balance in each stage, which can greatly improve the optimization accuracy of the horned lizard algorithm and supplement the algorithm's need for global and local search capabilities at each stage.

[0131] Furthermore, based on the horned lizard optimization algorithm, a mirror reflection learning model is introduced for the output stage of the horned lizard population; the mathematical model is as follows:

[0132]

[0133] in, Learn the solution for mirror reflection, V max and V min are the upper and lower limits of the population information after a single iteration, and λ is the parameter that controls the degree of reflection;

[0134]

[0135] Among them, rand1 and rand2 are both random numbers between 0 and 1, φ is the elastic coefficient, and N0 is the field radius of the mirror;

[0136] In order to ensure that the upper and lower limits of the mirror reflection learning solution do not exceed the upper and lower limits of the population itself, the upper and lower limits are processed according to the following formula:

[0137]

[0138] Among them, F U and F L are the judgment results of the upper and lower limits respectively, and ~ is the negation operation; the introduction of this model can enable the algorithm to explore a wider range of possibilities and avoid falling into suboptimal solutions, ultimately enabling it to better handle complex function problems.

[0139] Example 5: A novel flexible continuum robot control method based on an improved horned lizard optimization algorithm, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of the function is 0. The improved horned lizard optimization algorithm (MHLOA) is compared with the original horned lizard optimization algorithm (HLOA), Kingfisher optimization algorithm (PKO), White-bone chicken optimization algorithm (COOT), Red-billed blue magpie optimization algorithm (RBMO), Parrot optimization algorithm (PO), Frost and ice optimization algorithm (RIME), Black-winged kite optimization algorithm (BKA), Vector weighted average algorithm (INFO), Gray wolf optimization algorithm (GWO), Particle swarm optimization algorithm (PSO) to verify the performance of the improved horned lizard optimization algorithm. To ensure the fairness of the test, the population size of each algorithm is set to 30 and the maximum number of iterations is set to 400.

[0140] like Figure 6 As shown, it can be seen that the improved horned lizard optimization algorithm has great advantages in convergence speed and convergence accuracy compared with other algorithms.

[0141] Example 6: A flexible continuum robot control method based on an improved horned lizard optimization algorithm, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of the function is 1. The improved horned lizard optimization algorithm (MHLOA) is compared with the original horned lizard optimization algorithm (HLOA), Kingfisher optimization algorithm (PKO), White-bone chicken optimization algorithm (COOT), Red-billed blue magpie optimization algorithm (RBMO), Parrot optimization algorithm (PO), Frost and ice optimization algorithm (RIME), Black-winged kite optimization algorithm (BKA), Vector weighted average algorithm (INFO), Gray wolf optimization algorithm (GWO), Particle swarm optimization algorithm (PSO) to verify the performance of the improved horned lizard optimization algorithm. To ensure the fairness of the test, the population size of each algorithm is set to 30 and the maximum number of iterations is set to 400.

[0142] like Figure 7 As shown, it can be seen that the improved horned lizard optimization algorithm has great advantages in convergence speed and convergence accuracy compared with other algorithms.

[0143] Example 7, a flexible continuum robot control method based on an improved horned lizard optimization algorithm, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of the function is -10.1532. The improved horned lizard optimization algorithm (MHLOA) is compared with the original horned lizard optimization algorithm (HLOA), Kingfisher optimization algorithm (PKO), White-bone chicken optimization algorithm (COOT), Red-billed blue magpie optimization algorithm (RBMO), Parrot optimization algorithm (PO), Frost and ice optimization algorithm (RIME), Black-winged kite optimization algorithm (BKA), Vector weighted average algorithm (INFO), Gray wolf optimization algorithm (GWO), Particle swarm optimization algorithm (PSO) to verify the performance of the improved horned lizard optimization algorithm. To ensure the fairness of the test, the population size of each algorithm is set to 30 and the maximum number of iterations is set to 400.

[0144] like Figure 8 As shown, it can be seen that the improved horned lizard optimization algorithm has great advantages in convergence speed and convergence accuracy compared with other algorithms.

[0145] The new flexible continuum robot 3D printed structure 1-1 is used as the research object, the initial target position coordinates are set and the end position coordinates of the new flexible continuum robot 3D printed structure 1-1 are obtained through the visual system. Determine the quadrant of the target position and control the FTU 1～4 , and airbags 1 to 4 make the end of the new flexible continuum robot 3D printed structure 1-1 move to the target position. The PID controller is used to control the FTU 1～4, and the pressure of airbags 1 to 4 is compensated and controlled. The improved horned lizard optimization algorithm is used to adjust the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1 to achieve adaptive optimization. The parameters of the controller of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1 are optimized to enable the new flexible continuum robot 3D printed structure 1-1 to move in the expected trajectory.

[0146] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0147] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A flexible continuum robot motion control method based on an improved horned lizard optimization algorithm, comprising a novel flexible continuum robot 3D printed structure (1-1) and a closed-loop model-free control method based on an improved horned lizard optimization algorithm, characterized in that: The novel flexible continuum robot 3D printed part structure (1-1) comprises a flexible telescopic unit (1-2) and a flexible bending unit (1-3), wherein the flexible telescopic unit (1-2) and the flexible bending unit (1-3) both use Kresling origami with tristable characteristics as structural units, and the flexible bending unit (1-3) is equipped with a deformable auxiliary airbag; The closed-loop model-free control method comprises the following steps: Step 1: Taking the new flexible continuum robot 3D printed structure (1-1) as the research object, set the coordinates of the initial target position (Xt, Yt, Zt); and obtain the coordinates of the end position of the new flexible continuum robot 3D printed structure (1-1) as (Xe, Ye, Ze) through the visual system; Step 2: Determine the quadrant of the initial target position according to the horizontal and vertical coordinates Xt and Yt of the initial target position, and control the auxiliary airbags of the flexible telescopic unit (1-2) and the flexible bending unit (1-3) to realize the movement of the position (Xe, Ye, Ze) of the end of the new flexible continuum robot 3D printed structure (1-1) to the set initial target position (Xt, Yt, Zt); Step 3: Using a PID controller to perform compensation control on the pressure in the auxiliary airbags of the flexible telescopic unit (1-2) and the flexible bending unit (1-3); Step 4: Introduce the improved horned lizard optimization algorithm to adaptively optimize the closed-loop model-free control system of the new flexible continuum robot 3D printed structure (1-1); Step 5. According to the improved horned lizard optimization algorithm, the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure (1-1) are optimized and selected, and the new flexible continuum robot 3D printed structure (1-1) is made to move along the expected trajectory.

2. The flexible continuum robot motion control method according to claim 1, characterized in that: The novel flexible continuum robot 3D printed structure (1-1) is formed by coupling a flexible telescopic unit (1-2) and a flexible bending unit (1-3) in series; the flexible telescopic unit (1-2) and the flexible bending unit (1-3) are both designed based on a double-layer Kresling origami configuration; the flexible telescopic unit (1-2) is an origami plane pattern (1-4) of the same chirality in its unfolded state, and the flexible bending unit (1-3) is an origami plane pattern (1-5) of the opposite chirality in its unfolded state.

3. The flexible continuum robot motion control method according to claim 1, characterized in that: The motion achieved by the novel flexible continuum robot 3D printed structure (1-1) is specifically: The flexible bending unit (1-3) controls the telescopic and torsional coupled motion of the novel flexible continuum robot 3D printed structure (1-1), which is driven by the air pressure of the unit chamber and can achieve a contraction ratio; The flexible bending unit (1-3) controls the bending movement of the new flexible continuum robot 3D printed structure (1-1). The flexible bending unit (1-3) realizes flexible adjustment of the surface stiffness by changing the expansion / contraction state of the airbag. When the unit chamber is in a negative pressure state, the airbag expands, causing the surface stiffness of the unit to increase, resulting in a stiffness difference in the flexible bending unit (1-3), thereby causing the unit as a whole to bend to the opposite side of the action surface.

4. The flexible continuum robot motion control method according to claim 1, characterized in that: In step 3, the pressure compensation formula of the PID controller is: Among them, e Θ =Θe-Θt (Θ=x, y, z) is the deviation between the end (Xe, Ye, Ze) of the new flexible continuum robot 3D printed structure (1-1) and the target position (Xt, Yt, Zt); K P , K I , K D are the proportional coefficient, integral coefficient and differential coefficient of the PID controller respectively; dt represents the time interval between iteration steps; K P The existence of will compensate for the possible large coordinate error e Θ , bringing a larger pressure compensation P to the main chamber of the new flexible continuum robot 3D printed structure (1-1) Θ ; At the same time, when the coordinate deviation is small or close to 0, K I and K D This will help eliminate steady-state errors and avoid overshoot, respectively.

5. The flexible continuum robot motion control method according to claim 4, characterized in that: The main chamber of the novel flexible continuum robot 3D printed structure (1-1) requires three states: positive pressure, negative pressure, and steady pressure; the closed-loop model-free control system of the novel flexible continuum robot 3D printed structure (1-1) realizes the state change of the terminal through an electromagnetic valve group consisting of four two-position two-way valves and one two-position three-way valve, wherein R1 to R4 are two-position two-way valves, and R5 is a two-position three-way valve; R1 and R2 are arranged in parallel, R1 and R3 are connected in series, R2 and R5 are connected in parallel, and the parallel circuit of R1 and R2 is connected in series with R4; The closed-loop model-free control system works as follows: When R1 is powered on, R2 is powered off, R3 is powered off, R4 is powered on, and R5 is powered on, the end of the new flexible continuum robot 3D printed structure (1-1) is in a positive pressure state; When R1 is powered off, R2 is powered on, R3 is powered on, R4 is powered off, and R5 is powered on, the end of the new flexible continuum robot 3D printed structure (1-1) is in a negative pressure state; When R1 is powered off, R2 is powered off, R3 is powered on, R4 is powered on, and R5 is powered off, the end of the new flexible continuum robot 3D printed structure (1-1) is in a pressure-maintaining state; The single chip microcomputer changes the pressure Pout of the air pump to the end chamber through the cooperation of the solenoid valve group and the air pressure sensor; the output pressure Pout of the end of the solenoid valve group at the current iteration step Θ ,out,k is: P Θ,out,k =P Θ,out,k-1 +P Θ ,Θ=x,y,z Among them, P Θ ,out,k-1 is the output pressure at the end of the solenoid valve group in the last iteration step; The initial pressures (Px,out,k, Py,out,k, Pz,out,k) of the new flexible continuum robot 3D printed structure (1-1) are all set to 0kpa; when the air pump starts to provide pressure to the new flexible continuum robot 3D printed structure (1-1), the visual system will provide it with the end position coordinates (Xe, Ye, Ze) in real time, and use them as feedback variables of the PID controller to calculate the pressure compensation result of the current iteration step in real time; in this control system, a single-chip microcomputer is used to control three groups of solenoid valve groups, one of which is used to control the pressure of the main chamber of the new flexible continuum robot 3D printed structure (1-1), thereby driving its movement in the Z direction; the other two groups are mainly used to control the pressure of the airbag in the flexible bending unit, thereby driving the end of the new flexible continuum robot 3D printed structure (1-1) to move in the X and Y directions.

6. The flexible continuum robot motion control method according to claim 1, characterized in that: In the step 4, the basic algorithm of the horned lizard optimization algorithm is calculated based on the passive defense behavior of the horned lizard, wherein the passive defense behavior of the horned lizard includes: hiding behavior, changing skin brightness behavior, ejecting blood flow behavior, transferring escape behavior and regulating body temperature behavior; The hiding behavior refers to the horned lizard simulating environmental features and blending in with the surrounding environment, making it difficult for prey and predators to find it, increasing its chances of survival in the wild. The behavior formula is as follows: Among them, t is the current iteration number, T is the maximum iteration number; is the latest search agent of the horned lizard in the search space of generation t+1, is the best search agent of the horned lizard in the tth generation, r1, r2, r3, r4 are random integers between the maximum population size N and 1, and r1≠r2≠r3≠r4; β is set to 2, k1 and k2 are random numbers selected from the standardized color palette; λ is the binary value obtained, and its acquisition formula is as follows: The behavior of changing skin brightness refers to that the horned lizard changes the color of its skin by increasing or decreasing the sunlight gain. Darker colors absorb more heat, and lighter colors reflect more heat. The mathematical model of the darkening and lightening of the horned lizard's skin is as follows: Among them, Da1 and Da2 are random numbers generated between 0.5440510 and 1, and Li1 and Li2 are random numbers generated between 0 and 0.4046661; The blood jetting behavior refers to the horned lizard's eyes jetting blood to defend against enemies. The blood jet mainly moves in a parabolic motion, and the motion trajectory is expressed as: Where v0 is the initial velocity, set to 1; ω is set to π / 2, μ is 1E-6, and g is the acceleration of the earth; The transfer escape behavior refers to the horned lizard's need to move quickly to avoid predators. The transfer formula is as follows: Where wk is a random number between -1 and 1, and ε is a random mean generated by the Cauchy distribution; The thermoregulation behavior refers to the horned lizard changing its skin color by regulating its own body temperature to cope with various emergencies. The mathematical formula of the whole process is expressed as: Among them, M(i) is the color cell of the horned lizard's skin, Fitmax and Fitmin are the best fitness and the worst fitness at the current iteration number, and Fit(i) is the current fitness of the i-th horned lizard.

7. The flexible continuum robot motion control method according to claim 6, characterized in that: For the algorithm for regulating body temperature behavior, when M(i)≤0.3, the following formula is used to complete the position update:

8. The flexible continuum robot motion control method according to claim 7, characterized in that: On the basis of the optimization algorithm for horned lizards, the Henon chaos mapping theory is introduced into the initialization stage of the horned lizard population. The mapping model is as follows: Among them, xn and yn are the initial position parameters of HLOA; when the mapping randomness constants a=1.4 and b=0.3, the mapping sequence is guaranteed to have strong randomness, xn +1 , yn +1 is the position after chaos mapping.

9. The flexible continuum robot motion control method according to claim 8, characterized in that: Based on the horned lizard optimization algorithm, nonlinear adaptive weights are introduced into the horned lizard color iteration stage; the nonlinear adaptive weights are as follows: Based on the above weights, the updated color iteration formula is as follows: The introduction of the adaptive weight enables the color iteration method of the horned lizard to achieve a reasonable balance in each stage, improves the optimization accuracy of the horned lizard algorithm, and supplements the algorithm's need for global and local search capabilities at each stage.

10. The flexible continuum robot motion control method according to claim 9, characterized in that: Based on the horned lizard optimization algorithm, a mirror reflection learning model is introduced for the output stage of the horned lizard population; the mathematical model is as follows: in, is the mirror reflection learning solution, Vmax and Vmin are the upper and lower limits of the population information after a single iteration, and λ is the parameter that controls the degree of reflection; Among them, rand1 and rand2 are both random numbers between 0 and 1, φ is the elastic coefficient, and N0 is the field radius of the mirror; In order to ensure that the upper and lower limits of the mirror reflection learning solution do not exceed the upper and lower limits of the population itself, the upper and lower limits are processed according to the following formula: Among them, F U and F L are the judgment results of the upper and lower limits respectively, and ~ is the negation operation.

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