Motion control method of flexible continuum robot based on improved horned lizard optimization algorithm

Abstract

The present invention discloses a motion control method for a flexible continuum robot based on an improved horned lizard optimization algorithm, comprising a novel 3D printed structure for a flexible continuum robot and a closed-loop model-free control method based on the improved horned lizard optimization algorithm. The present invention introduces an improved horned lizard optimization algorithm, which, on the basis of the original algorithm, respectively introduces the Henon chaos mapping theory, linear adaptive weights, and mirror reflection learning models. The improvement increases the diversity of population initialization, improves the optimization accuracy of the algorithm, balances the global search capability and local search capability of the algorithm at each stage, effectively increases the convergence speed, and prevents the algorithm from falling into a local optimum. By combining the above-mentioned improved horned lizard optimization algorithm with the closed-loop model-free control method proposed in the present invention, path planning and posture adjustment of the novel flexible continuum robot are achieved, providing a guarantee for high-precision control of the novel flexible continuum robot.

Description

Technical Field

[0001] The present 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 excellent motion characteristics, environmental adaptability, and structural compliance, becoming a research hotspot in fields such as environmental exploration, biomedicine, and social services. Unlike existing rigid continuum robots, the structural units of SCRs are mostly made of flexible intelligent materials, which generate less reaction force during the execution of tasks, effectively reducing collision damage during the grasping process. At the same time, the rise of soft robotics and 3D / 4D printing technologies has brought many possibilities to the design of SCRs. Among them, origami technology stands out due to its excellent 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] Prior art, such as publication number CN113580119A, discloses a pneumatic continuum mechanism based on an origami structure. The mechanism comprises 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 comprises multiple origami structures supported in parallel between the base plate and the control box, each foldable and foldably connected to the base plate and the control box. The air drive assembly comprises multiple bellows supported in parallel between the base plate and the control box, each equipped with a connector for air supply and exhaust. This prior art, based on an air drive mechanism, complexly controls a multi-layer preform module with multiple degrees of freedom, freeing up workspace and the environment, and addressing the challenges of requiring a large number of drive units and achieving lightweight design. This achieves a foldable structure that is both lightweight and compact, yet also scalable and miniaturized, while maintaining its motion performance. However, designs combining origami structures with SCRs often rely on inherent folds for motion and still suffer from the limitations of limited degrees of freedom. Secondly, research on modeling and control has mostly focused on dynamic models or static deformation models, thereby designing corresponding control methods. Furthermore, the nonlinearity and fatigue effects of soft materials can easily lead to uncertain changes in the relevant parameters of the mechanical model, which greatly complicates the modeling and control of SCRs.

[0004] In recent years, meta-heuristic algorithms have been widely used in various optimization problems. In 2024, Delgado proposed a Horned Lizard Optimization Algorithm (Horned Lizard Optimization Algorithm). This algorithm simulates the passive defense behavior and living habits of horned lizards, has strong adaptability, and demonstrates effectiveness in balancing exploitation and exploration mechanisms, enabling effective search capabilities in optimization problems. However, the algorithm itself is prone to falling into local optimality, has high initialization uncertainty, and still has some issues with convergence speed and 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 realize high-precision motion control of the new flexible continuum robot along the expected trajectory.

[0006] The present invention achieves the above-mentioned object through the following technical solutions: a motion control method for a flexible continuum robot based on an improved horned lizard optimization algorithm, comprising a novel 3D printed structure of the flexible continuum robot and a closed-loop model-free control method based on the improved horned lizard optimization algorithm, wherein the novel 3D printed structure of the flexible continuum robot comprises a flexible telescopic unit and a flexible bending unit, both of which 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 it is in and 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. Based on the improved horned lizard optimization algorithm, the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed part structure are optimized and selected, and the new flexible continuum robot 3D printed part 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 serial coupling of a flexible telescopic unit and a flexible bending unit; the flexible telescopic unit and the flexible bending unit are both designed based on a double-layer Kresling origami configuration, and the flexible telescopic unit has an origami plane pattern of the same chirality in its unfolded state, and the flexible bending unit has an origami plane pattern of the opposite chirality in its unfolded state.

[0014] As a further solution of the present invention: the motion 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 3D-printed structure of the new flexible continuum robot. This motion 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 3D-printed structure of the new flexible continuum robot. 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, causing the surface stiffness of the unit to increase, resulting in a stiffness difference in the flexible bending unit, causing the entire unit to bend toward 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 deviation; 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 , which brings a larger pressure compensation P to the main chamber of the new flexible continuum robot 3D printing 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 novel flexible continuum robot 3D printed structure 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 realizes the state change of the terminal through a solenoid 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 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 single chip computer changes 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:

[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 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 serves as the feedback variable 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 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, blood flow injection behavior, escape behavior, and temperature regulation behavior;

[0030] Hiding behavior refers to the horned lizard's ability to mimic environmental features and blend in with its surroundings, making it difficult for prey and predators to detect it and increasing its chances of survival in the wild. The behavioral formula is as follows:

[0031]

[0032] Where t is the current number of iterations and T is the maximum number of iterations; is the latest search agent of Horned Lizard in the search space of generation t+1, is the best search agent of the horned lizard in generation t, r1, r2, r3, and 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, which is obtained as follows:

[0033]

[0034] Changing skin brightness behavior means that horned lizards change their skin color by increasing or decreasing sunlight gain. Darker colors absorb more heat, while lighter colors reflect more heat. The mathematical model for the darkening and lightening of horned lizards' 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 refers to the horned lizard's eyes being able to eject blood to defend against enemies. The blood jet mainly moves in a projectile motion, and the motion 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 diversion escape behavior refers to the horned lizard's need to move quickly to avoid predators. The diversion formula is as follows:

[0041]

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

[0043] Thermoregulation refers to the horned lizard's ability to adjust its body temperature to change its skin color in response to various emergencies. The mathematical formula for the entire 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: Based on 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 constants 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, nonlinear adaptive weights are introduced into the horned lizard color iteration stage; the nonlinear adaptive weights are as follows:

[0052]

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

[0054]

[0055] The introduction of this 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, Learning 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] Where rand1 and rand2 are both random numbers between 0 and 1, φ is the elastic coefficient, and N0 is the radius of the mirror.

[0061] 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 making it better able to 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 NSCR end moves to the target position by using airbags 1 to 4. 1～4 Compensate and control the pressure of airbags 1 to 4;

[0066] 2) To address the uncertainty of the NSCR's operating environment, a closed-loop model-free control system was established, and parameter tuning and adaptive optimization were performed. The parameters of the NSCR closed-loop model-free control system controller were selected to enable the NSCR to move along the desired trajectory. An improved horned lizard optimization algorithm was introduced for the NSCR closed-loop model-free control method. This algorithm, based on the original algorithm, incorporates Henon chaos mapping theory, linear adaptive weights, and a mirror reflection learning model.

[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 A brief flow chart of the closed-loop model-free control method of the present invention;

[0071] Figure 3 Schematic diagram of the working principle 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 a flow chart of the improved horned lizard optimization algorithm of the present invention;

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

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

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

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

[0078] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0079] Example 1, as Figures 1 to 5 As shown, a motion control method for a flexible continuum robot 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. 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 it is in and 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, the airbags 1 to 2 are controlled separately so that the X at the end e ,Y e To X t ,Y t , move closer. At the same time, control FTU 1～4 Make Z e To Z t to move 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 part structure 1-1;

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

[0086] Example 2. In addition to all the technical features of Example 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 motions 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 novel flexible continuum robot 3D printed structure 1-1, driven by the air pressure in the unit chamber and capable of achieving 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 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, causing the surface stiffness of the unit to increase, resulting in a stiffness difference in the flexible bending unit 1-3 unit, thereby causing the unit as a whole to bend toward the opposite side of the action surface.

[0090] In addition to all the technical features of the first embodiment, 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 deviation; 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 , which brings 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 consisting of four two-position two-way valves and one two-position three-way valve, among which 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 part 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 part 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-holding 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 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 1-1, the visual system will provide it with the end position coordinates (X e ,Y e ,Z e ), and serves as the feedback variable 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 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] In addition to all the technical features of the first embodiment, 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, blood flow behavior, transfer escape behavior and body temperature regulation behavior;

[0105] Hiding behavior refers to the horned lizard's ability to mimic environmental features and blend in with its surroundings, making it difficult for prey and predators to detect it and increasing its chances of survival in the wild. The behavioral formula is as follows:

[0106]

[0107] Where t is the current number of iterations and T is the maximum number of iterations; is the latest search agent of Horned Lizard in the search space of generation t+1, is the best search agent of the horned lizard in generation t, r1, r2, r3, and 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, which is obtained as follows:

[0108]

[0109] Changing skin brightness behavior means that horned lizards can change their skin color by increasing or decreasing sunlight gain. Darker colors absorb more heat, while lighter colors reflect more heat. The mathematical model for how horned lizards' skin darkens and lightens 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 refers to the horned lizard's eyes being able to eject blood to defend against enemies. The blood jet mainly moves in a projectile motion, and the motion 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 diversion escape behavior refers to the horned lizard's need to move quickly to avoid predators. The diversion formula is as follows:

[0116]

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

[0118] Thermoregulation refers to the horned lizard's ability to adjust its body temperature to change its skin color in response to various emergencies. The mathematical formula for the entire 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, based on 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 HLOA population initialization and improves the search efficiency of the HLOA algorithm. The mapping model is shown below:

[0124]

[0125] Among them, x n 、y n is the initial position parameter of HLOA; when the mapping randomness constants 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 this 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, Learning 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] Where rand1 and rand2 are both random numbers between 0 and 1, φ is the elastic coefficient, and N0 is the radius of the mirror.

[0136] 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 making it better able to 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 this function is 0. The improved horned lizard optimization algorithm (MHLOA) is compared with the original horned lizard optimization algorithm (HLOA), the Panthera kingfisher optimization algorithm (PKO), the coot optimization algorithm (COOT), the red-billed blue magpie optimization algorithm (RBMO), the parrot optimization algorithm (PO), the frost and ice optimization algorithm (RIME), the black-winged kite optimization algorithm (BKA), the vector weighted average algorithm (INFO), the gray wolf optimization algorithm (GWO), and the particle swarm optimization algorithm (PSO). To ensure fairness in 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 in the figure, it can be seen that the improved horned lizard optimization algorithm has greater 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 this function is 1. The improved horned lizard optimization algorithm (MHLOA) is compared with the original horned lizard optimization algorithm (HLOA), the Panthera kingfisher optimization algorithm (PKO), the coot optimization algorithm (COOT), the red-billed blue magpie optimization algorithm (RBMO), the parrot optimization algorithm (PO), the frost and ice optimization algorithm (RIME), the black-winged kite optimization algorithm (BKA), the vector weighted average algorithm (INFO), the gray wolf optimization algorithm (GWO), and the particle swarm optimization algorithm (PSO). To ensure fairness in 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 in the figure, it can be seen that the improved horned lizard optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with other algorithms.

[0143] Example 7, a flexible continuum robot control method based on the improved horned lizard optimization algorithm, using the basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function was -10.1532. The improved horned lizard optimization algorithm (MHLOA) was compared with the original horned lizard optimization algorithm (HLOA), the Panthera kingfisher optimization algorithm (PKO), the coot optimization algorithm (COOT), the red-billed blue magpie optimization algorithm (RBMO), the parrot optimization algorithm (PO), the frost and ice optimization algorithm (RIME), the black-winged kite optimization algorithm (BKA), the vector weighted average algorithm (INFO), the gray wolf optimization algorithm (GWO), and the particle swarm optimization algorithm (PSO). To ensure fairness in the test, the population size of each algorithm was set to 30, and the maximum number of iterations was set to 400.

[0144] like Figure 8 As shown in the figure, it can be seen that the improved horned lizard optimization algorithm has greater 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. The quadrant of the target position is determined and the FTU is controlled. 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. 1～4, and compensate for the pressure of airbags 1-4. An improved horned lizard optimization algorithm was used to tune the parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1, achieving adaptive optimization. Optimizing the parameters of the controller of the closed-loop model-free control system of the new flexible continuum robot 3D printed structure 1-1 ensures that the new flexible continuum robot 3D printed structure 1-1 moves along the expected trajectory.

[0146] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0147] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method 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 can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A motion control method for a flexible continuum robot 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 the 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 both the flexible telescopic unit (1-2) and the flexible bending unit (1-3) adopt 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: Set the coordinates (X t , Y t , Z t ); and obtain the coordinates (X) of the end position of the new flexible continuum robot 3D printed structure (1-1) through the visual system. e , Y e , Z e ); Step 2: Based on the horizontal and vertical coordinates X of the initial target position t and Y t The quadrant in which the robot is located is determined, and the auxiliary airbags of the flexible telescopic unit (1-2) and the flexible bending unit (1-3) are controlled to move the end of the novel flexible continuum robot 3D printed part structure (1-1) toward the set initial target position; 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); 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); The basic algorithm of the improved horned lizard optimization algorithm is calculated based on the passive defense behavior of the horned lizard, which includes: hiding behavior, changing skin brightness behavior, blood flow behavior, transfer escape behavior and regulating body temperature behavior. Step 5: Optimize and select parameters of the closed-loop model-free control system of the new flexible continuum robot 3D printed part structure (1-1) according to the improved horned lizard optimization algorithm, and make the new flexible continuum robot 3D printed part structure (1-1) move along the expected trajectory; On the basis of improving the horned lizard optimization algorithm, the Henon chaos mapping theory is introduced into the initialization stage of the horned lizard population. The mapping model is as follows: Among them, x n 、y n is the initial position parameter of HLOA; the random mapping constants are a=1.4,b=0.3,x n+1 、y n+1 is the position after chaos mapping.

2. The flexible continuum robot motion control method according to claim 1, characterized in that: The novel flexible continuum robot 3D printed part 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; the flexible telescopic unit (1-2) has an origami plane pattern (1-4) of the same chirality when in its unfolded state, and the flexible bending unit (1-3) has an origami plane pattern (1-5) of the opposite chirality when 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 in 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) achieves flexible adjustment of the surface stiffness by changing the expansion or 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 toward the opposite side of the action surface.

4. The flexible continuum robot motion control method according to claim 1, characterized in that: The formula for the hidden behavior is as follows: Where t is the current number of iterations and T is the maximum number of iterations; is the latest search agent of Horned Lizard in the search space of generation t+1, is the best search agent of the horned lizard in generation t, r1, r2, r3 and r4 are random integers between the maximum population size N and 1, and r1≠r2≠r3≠r4; and are the selected r1-th, r2-th, r3-th, and r4-th search agents, β is set to 2, and k1 and k2 are random numbers selected from the standardized color palette; λ1 is the binary value obtained, and its acquisition formula is as follows: Among them, rand is a random number between 0 and 1; The mathematical model for changing skin brightness is as follows: in, and are the worst and best search agents found, respectively, and are the selected search agents r1, r2, r3, and r4, respectively. 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 formula for the ejection blood flow behavior is as follows: Among them, v0 is the initial velocity, which is set to 1, ω is set to π / 2, μ is 1E-6, g is the acceleration of the earth, t is the current number of iterations, and T is the maximum number of iterations. is the latest search agent of Horned Lizard in the search space of generation t+1, It is the latest search agent for Horned Lizard in the T-generation search space; The transfer formula for the escape behavior is as follows: Where wk is a random number between -1 and 1, ε is a random mean generated by the Cauchy distribution, is the latest search agent of Horned Lizard in the search space of generation t+1, is the latest search agent for Horned Lizard in the T-generation search space, is the best search agent; The formula for the thermoregulatory behavior is as follows: 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.

5. The flexible continuum robot motion control method according to claim 4, characterized in that: For the formula for regulating body temperature, when M(i)≤0.3, the following formula is used to complete the position update: in, is the latest search agent for Horned Lizard in the T-generation search space, is the best search agent, and They are the selected r1th and r2th search agents respectively.

6. The flexible continuum robot motion control method according to claim 5, characterized in that: Based on the improved 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, Learning solution for mirror reflection, V max and V min are the upper and lower limits of the population information after a single iteration, and λ2 is the parameter that controls the degree of reflection; Among them, rand1 and rand2 are both random numbers from 0 to 1. is the elastic coefficient, N0 is the field radius of the mirror; The upper and lower limits of the population information after a single iteration are processed according to the following formula: Among them, F U and F L are the upper and lower limit judgment results of the population information after a single iteration, is the mirror reflection learning solution, ~ is the negation operation, ub and lb are the upper and lower limits of the population information after a single iteration.

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