Multi-mode paper folding holder and optimization control method thereof

Abstract

The invention discloses a multi-mode paper folding clamping device and an optimization control method thereof. The clamping device adopts four-finger diagonal layout, each finger is composed of double-layer Kresling paper folding units, a three-stable-state structure is formed by splicing opposite chiral paper folding cylinders and square finger strips, and symmetrical air bag sets are arranged on the inner side special edge faces. The improved MRBMO algorithm is combined with the closed-loop control method, high-precision control over the movement direction and posture adjustment of the single finger of the clamp holder is achieved, the grabbing capacity of the clamp holder is further guaranteed, meanwhile, through the synergistic effect of MRBMO-PID closed-loop control and the multi-strategy optimization algorithm, the movement precision of the single finger of the clamp holder under the complex working condition is effectively guaranteed, and the grabbing precision of the single finger of the clamp holder under the complex working condition is effectively improved. And high-reliability grabbing operation is achieved.

Description

Technical Field

[0001] The present invention relates to an origami gripper, in particular to a multi-modal origami gripper and an optimization control method thereof, belonging to the technical field of continuum control. Background Art

[0002] Traditional grippers can be divided into rigid and flexible grippers. Flexible grippers have become a hot topic in gripper research due to their ability to protect workpieces and personnel, as well as their adaptability to a variety of environments. Generally speaking, there are two ways to achieve flexible gripping: control and drive. Among them, the drive method mainly uses pneumatic or linear motion to construct the single-finger movement of the gripper. The soft pneumatic "fingers" can adaptively wrap the target object, thus getting rid of the constraints of the size and shape of the clamped object. At the same time, the flexible surface makes the clamped object evenly stressed, with less variation, and is more capable of grasping fragile objects.

[0003] The end-position of a typical gripper is the result of coordinated motion of each joint. Due to errors in the serial structure, the actual end-position will deviate from the theoretical value calculated by each joint. Research in the field of gripper control focuses on how to quickly and accurately move the end of the gripper from the starting position to the target position, and how to control the end-position during movement. PID compensation control of the airbag pressure and its parameter adjustment can achieve closed-loop control of the gripper, and optimizing its parameters through optimization algorithms is key to achieving high-precision motion of a single finger of the gripper. However, when dealing with complex conditions and real-time changes, optimization algorithms are prone to low search efficiency and local optimality. Summary of the Invention

[0004] The purpose of the present invention is to provide a multimodal origami gripper and an optimized control method thereof in order to solve at least one of the above-mentioned technical problems. The multimodal origami gripper adopts a closed-loop control algorithm based on position feedback to achieve accurate and efficient movement of the single-finger end of the gripper during the control process, thereby coping with complex changes in the working environment.

[0005] The present invention achieves the above-mentioned object through the following technical solutions: a multimodal origami gripper, comprising a gripper, the gripper comprising gripper fingers and a connecting assembly, the gripper fingers being provided with four, the connecting assembly being provided with four centrally symmetrical bases, and the bottom ends of the gripper fingers being respectively connected to the bases of the connecting assembly by interference fit;

[0006] The single-finger gripper includes an origami unit and an intermediate connector, which is connected between two origami units. The origami unit includes a Kresling origami tube and a square paper strip. The Kresling origami tube is provided with two upper and lower Kresling origami tubes of opposite chirality, and the square paper strip is connected between the two Kresling origami tubes of opposite chirality. A chamber is provided inside the Kresling origami tube of the origami unit, and an air bag is connected to the inner side of the Kresling origami tube. The Kresling origami tube and the air bag are respectively connected to an external air source.

[0007] The inner unit surface of the Kresling origami tube is formed into a special facet by reducing the area of two symmetrical triangles, and the airbags are located on the inner special facet. Four airbags are distributed in a cross shape on the tube body of the Kresling origami tube. The airbags on two sides are responsible for the bending of the origami unit in the x-axis direction, and the airbags on the other two sides are responsible for the bending of the origami unit in the y-axis direction.

[0008] As a further solution of the present invention: the multiple air bags connected to each Kresling origami tube are respectively connected to an external air source through separate connecting pipes, and each connecting pipe is connected to a solenoid valve group.

[0009] An optimization control method for a multimodal origami gripper, comprising the multimodal origami gripper, the optimization control method comprising the following steps:

[0010] Step 1: Based on the piecewise constant curvature model, a kinematic model of a single gripper finger is constructed to derive the quantitative relationship between the airbag pressure change ΔP and the end arc angle θ, providing an inverse solution theoretical basis for subsequent closed-loop control.

[0011] Step 2: Taking the single finger of the multimodal origami gripper as the research object, set the coordinates of the initial target position (X d ,Y d ,Z d ) and obtain the coordinates of the end position of the single finger of the gripper through the visual system (X t ,Y t ,Z t ) According to visual feedback, the arc angle θ is changed by changing the expansion size of the airbag, where the larger θ is, the greater the expansion degree of the airbag;

[0012] Step 3: Based on the horizontal and vertical coordinates X of the target position d and Y d Determine the quadrant it is in and control the airbag to achieve the position of the end of the gripper's single finger (X t ,Y t ,Z t ) to the target position (X d ,Y d ,Zd )sports;

[0013] Step 4: Use a PID controller to compensate and control the pressure in the airbag;

[0014] Step 5: Introduce the multi-strategy improved red-billed blue magpie optimization algorithm to adaptively optimize the closed-loop control system of the gripper's single finger;

[0015] Step 6: Correspond to the parameters of the four-finger parallel closed-loop control system of the gripper so that it moves along the expected trajectory.

[0016] As a further solution of the present invention, a kinematic model of a single finger of the gripper is modeled using the constant curvature method (CC), specifically including:

[0017] The o-xyz system is established with the bottom center of the component of the gripper as the reference. Its working space can be defined by the arc parameters, arc radius ρ, arc angle θ, and the angle δ between the projection of the arc radius on the o-xy plane and the x-axis. The center of the uppermost component K(x, y, z) is defined as the farthest end of the working space, and the other endpoints on the center arc path are defined as K n (x n ,y n ,z n ), n=1,2,3, the thickness of the structural part is defined as s, then the working space of point K3(x3,y3,z3) can be defined as:

[0018]

[0019] x2=x3+2ssinθcosδ

[0020] y2=y3+2ssinθsinδ

[0021] z2=z3+2scosθ

[0022]

[0023] At the same time, a second set of arc parameters is created to describe the motion of the above origami unit. The working space of point K1 (x1, y1, z1) is expressed as:

[0024]

[0025]

[0026] At the same time, since the working space of the upper and lower origami units is affected by different airbags, the arc parameters will vary in actual operation. The final working space of point K (x, y, z) is:

[0027] x=x1+ssinθ1cosδ

[0028] y=y1+ssinθ1sinδ

[0029] z=z1+scosθ1

[0030] In this kinematic model, the order of the lowest origami unit driving line in space is defined as 1 to 8 in the clockwise direction from x to y, and the length of the line can be expressed as l base =[l1,l2,l3,l4,l5,l6,l7,l8]; Similarly, the length of the top layer can be expressed as l top =[l9,l 10 ,l 11 ,l 12 ,l 13 ,l 14 ,l 15 ,l 16 ]; K(x,y,z) are the known input variables, the arc parameters (ρ,ρ1,θ,θ1,δ) are the resulting output variables, and the number of unknowns (x,y,z,x2,y2,z2,ρ,ρ1,θ,θ1,δ) is equal to the number of solved formulas;

[0031] Therefore, the above unknowns can be solved using the least squares method, and the lengths of the two origami unit drive lines can be solved according to the PCC model as follows:

[0032]

[0033] Where r is the distribution radius of the component.

[0034] As a further solution of the present invention: in step 4, the pressure compensation formula is as follows:

[0035]

[0036] Among them, e Θ =Θ e -Θ t (Θ=x,y,z) is the end of the single finger of the gripper (X t ,Y t ,Z t ) and the target position (X d ,Y d ,Z d ) 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 large coordinate error e Θ , bringing a larger pressure compensation P to the chamber of the gripperΘ ; 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.

[0037] As a further solution of the present invention: the initial pressure (P x,out,k ,P y,out,k ,P z,out,k) All are set to 0kpa;

[0038] When the air pump as an external air source starts to provide pressure to the gripper's single finger, the vision system will provide it with the end position coordinates (X t ,Y t ,Z t ) and used as the feedback variable of the PID controller to calculate the pressure compensation result of the current iteration step in real time;

[0039] In this control system, a single-chip microcomputer is used to control three groups of solenoid valves. One group is used to control the pressure in the cavity of the gripper's single finger, thereby driving its movement in the Z direction; the other two groups are mainly used to control the pressure of the airbag during the bending process of the single finger, thereby driving the movement of the end of the gripper's single finger in the X and Y directions.

[0040] As a further solution of the present invention: in step 5, the basic algorithm process of the red-billed blue magpie optimization algorithm is as follows:

[0041] Its foraging strategy mainly includes: population initialization, searching for food, attacking prey, and storing food;

[0042] (1) Population initialization

[0043] Like most algorithms, the initial search agent for RBMO is generated by the following formula:

[0044] x i,j =(ub-lb)×rand1+lb

[0045] Where i and j represent a single index and a dimension index respectively; ub represents the upper bound of the problem, lb represents the lower bound of the problem, and rand represents a random number between 0 and 1;

[0046] (2) Searching for food

[0047] In the process of searching for food, red-billed blue magpies usually move in small groups (2 to 5) or large groups (more than 10) to improve search efficiency. When exploring food in small groups, the following formula is used for iteration:

[0048]

[0049] Among them, t represents the current iteration number, X i (t+1) represents the i-th new search agent position, k represents the number of 2 to 5 red-billed blue magpie groups randomly selected from all searched individuals, X m represents the randomly selected mth individual, X i represents the i-th individual, X rs represents the randomly selected search agent in the current iteration;

[0050] When forming groups, the following formula is used for iteration:

[0051]

[0052] Where c represents the number of search agents that the cluster has when exploring for food, ranging from 10 to n;

[0053] (3) Attacking prey

[0054] In small group movements, the main target is usually small prey or plants; the corresponding mathematical model is shown in the following formula; when the red-billed blue magpie moves in a group, the mathematical expression of this behavior is:

[0055]

[0056] Among them, X Food (t) represents the location of the food, KF = (1-t / T) 2t / T , randn represents the random number used to generate the standard normal distribution (mean 0, standard deviation 1);

[0057] (4) Food storage

[0058] This process retains information about the solution, making it easier for individuals to find the global optimal value; the mathematical model is shown as follows:

[0059]

[0060] in, and Respectively represent the fitness values of the i-th red-billed blue magpie before and after the position update.

[0061] As a further solution of the present invention: based on the red-billed blue magpie optimization algorithm, the node set initialization theory is introduced into the initialization stage of the red-billed blue magpie population, which effectively increases the diversity of RBMO population initialization and improves the search efficiency of the RBMO algorithm; specifically, it includes:

[0062] Suppose there is a unit cube in s-dimensional Euclidean space with a set of points:

[0063]

[0064] Its deviation satisfies:

[0065]

[0066] Among them, C(r,ε) is a constant that is only related to r and ε (ε>0); then P n (k) is called the good point set, r is called the good point; the value of the good point r is:

[0067]

[0068] Where q is the smallest prime number that satisfies (q-3) / 2≥s;

[0069] Therefore, based on the good point set theory, the new initialization strategy is:

[0070] x i,j (k) = (ub-lb) {P n (k)}+lb

[0071] Among them, ub is the upper bound and lb is the lower bound.

[0072] As a further solution of the present invention: the Red-billed Blue Magpie Optimization Algorithm uses the Weibull distribution to improve the algorithm's search accuracy and efficiency. The Weibull distribution is used to measure the time until a failure occurs, or conversely, to measure reliability. Random numbers are generated based on the probability density function of the Weibull distribution and applied to the attack phase of the RBMO population, which can enhance the capabilities of the algorithm development phase. Specifically, the following methods are included:

[0073] The probability density function of the Weibull distribution is as follows:

[0074]

[0075] Where x is a random variable, β is a shape statement, η is a scale factor, γ is a location parameter (threshold parameter), and γ can be 0. When γ is equal to 0, it is called a two-parameter Weibull cumulative distribution function.

[0076] At the same time, for the probability density function of the Weibull distribution, the continuous random variable X1 has the following conditions:

[0077]

[0078] Among them, β is the shape parameter (also known as Weibull slope), η is the scaling parameter, and γ is the location parameter.

[0079] As a further solution of the present invention: the red-billed blue magpie optimization algorithm introduces a reverse learning competition strategy, through which disadvantaged individuals can obtain a second learning opportunity, which improves the ability of the algorithm to escape the local optimum to a certain extent. The calculation formula is as follows:

[0080] R p (i+1)=(ub+lb){P n (k)}-X i (t+1)

[0081] Among them, R p (i+1) is the opposite learning solution, by calculating R p (i+1) and X i The overall fitness of (t+1) can be used to obtain the output position of this iteration.

[0082] The beneficial effects of the present invention are:

[0083] 1) The gripper disclosed in this invention adopts a four-fingered diagonal layout, with each finger composed of a double-layer Kresling origami unit. A tristable structure is formed by splicing origami tubes of opposite chirality and square finger strips. A symmetrical airbag group is arranged on a special facet inside. A single finger of the origami gripper is used as the research object, and a kinematic model of the gripper finger is established based on the piecewise constant curvature model (PCC). The mapping relationship between the arc angle θ and the degree of airbag expansion is obtained. The spatial coordinates of the target object are fed back in real time by a visual system, and the control system dynamically adjusts the air pressure parameters of each motion unit to guide the end of the gripper to approach the target position along the planned trajectory.

[0084] 2) The present invention uses a PID controller to compensate for the gripper's motion parameters. To address the uncertainty of the gripper's working environment, a closed-loop control system based on position feedback is established. Control parameter tuning is performed to achieve adaptive optimization and select the optimal control parameters of the system, ensuring that the gripper's single finger can move precisely along the intended trajectory.

[0085] 3) To further optimize the control effect, the present invention introduces a multi-strategy improved Red-billed Blue Magpie Optimization (MRBMO) algorithm. Based on the original RBMO algorithm, the initialization phase introduces the focus set initialization theory, Weibull distribution function theory, and reverse learning competition strategy theory. These improvements significantly enhance the diversity of the original RBMO population initialization, improve the algorithm's local search capability, and reduce the possibility of the population falling into the local optimum. The results of the test function verify the superiority of the MRBMO algorithm and its optimization effect on the gripper control.

[0086] 4) By combining the improved MRBMO algorithm with the closed-loop control method proposed in the present invention, high-precision control of the movement direction and posture adjustment of a single finger of the gripper is achieved, thereby ensuring the gripping ability of the gripper. At the same time, through the synergistic effect of the MRBMO-PID closed-loop control and the multi-strategy optimization algorithm, the motion accuracy of the single finger of the gripper under complex working conditions is effectively ensured, and a high-reliability gripping operation is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 Schematic diagram of the working space and application location of the "multimodal origami gripper" as the research object of the present invention;

[0088] Figure 2 Schematic diagram of the research object "multimodal origami gripper" of the present invention and its connecting components and intermediate connecting parts;

[0089] Figure 3 This is a schematic diagram of a single-finger three-dimensional structure of the clamp of the present invention;

[0090] Figure 4 The Kresling multimodal origami single finger of the gripper and the airbag installation position thereof in the present invention;

[0091] Figure 5 A two-dimensional plan view of the Kresling origami structure and the airbag installation position thereof in the present invention;

[0092] Figure 6 A kinematic model diagram based on the piecewise constant curvature model introduced in the present invention;

[0093] Figure 7 A brief flow chart of the closed-loop control method of the present invention;

[0094] Figure 8 Schematic diagram of the working principle of the closed-loop control method of the present invention;

[0095] Figure 9 This is a flow chart of the algorithm for the multi-strategy improved red-billed blue magpie optimization algorithm of the present invention;

[0096] Figure 10 This is a convergence curve diagram of the first test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0097] Figure 11 This is a convergence curve diagram of the second test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0098] Figure 12This is a convergence curve diagram of the third test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0099] Figure 13 This is a convergence curve diagram of the fourth test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0100] Figure 14 This is a convergence curve diagram of the fifth test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0101] Figure 15 This is a convergence curve diagram of the sixth test function in an embodiment of the present invention under the multi-strategy improved red-billed blue magpie optimization algorithm, the red-billed blue magpie algorithm, and no algorithm optimization;

[0102] In the figure: 1. Gripper; 11. Single finger of the gripper; 111. Paper-folding unit; 1101. Kresling origami tube; 1102. Square paper strip; 112. Intermediate connecting piece; 113. Airbag; 12. Connecting assembly; 2. Robotic arm. DETAILED DESCRIPTION

[0103] 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.

[0104] Example 1, as Figures 1 to 3 As shown, this embodiment provides a multimodal origami gripper, including a gripper 1, the gripper 1 including a gripper finger 11 and a connecting assembly 12, wherein four gripper fingers 11 are provided, and the connecting assembly 12 is provided as four centrosymmetrical bases, and the bottom ends of the gripper fingers 11 are respectively connected to the bases of the connecting assembly 12 by interference fit;

[0105] The single finger 11 of the clamp includes an origami unit 111 and an intermediate connecting member 112. The intermediate connecting member 112 is connected between the two origami units 111. The origami unit 111 includes a Kresling origami tube 1101 and a square paper strip 1102. The Kresling origami tube 1101 is provided with two upper and lower Kresling origami tubes 1101 of opposite chirality, and the square paper strip 1102 is connected between the two Kresling origami tubes 1101 of opposite chirality. A cavity is provided inside the Kresling origami tube 1101 of the origami unit 111. The inner side of the Kresling origami tube 1101 is connected to the inner side of the tube body of the Kresling origami tube 1101. The Kresling origami tube 1101 and the airbag 113 are connected to an external air source. The driving force of the chamber and the selective expansion of the airbag enable the origami gripper to achieve a tri-stable state. The first stable state is achieved by folding the origami downward through torsional compression on the basis of the second stable state until it reaches the extreme position where it maintains a constant state. The third stable state is achieved by further torsional stretching on the basis of the second stable state, transforming the valley fold into an arc-shaped mountain fold with high stiffness. The remaining transient processes are also achieved by coupled expansion / contraction and torsion motion under the auxiliary driving action of the airbag.

[0106] The inner unit surface of the Kresling origami tube 1101 is formed into a special facet by reducing the area of two symmetrical triangles, and the airbag 113 is located on the inner special facet. Four airbags 113 are arranged in a cross shape on the body of the Kresling origami tube 1101. The airbags 113 on two sides are responsible for the bending of the origami unit 111 in the x-axis direction, and the airbags 113 on the other two sides are responsible for the bending of the origami unit 111 in the y-axis direction. A Kresling double-layer origami unit is formed by connecting the double-layer origami units 111 end to end and the interference fit of the connecting component 12. The Kresling double-layer origami unit The four-side airbags are designed and installed based on the double-layer Kresling origami configuration. Local stiffness is formed by inflating the auxiliary airbag 113 on one side. Then, by evacuating the chamber, the bending of the clamper finger 11 is achieved through the stiffness difference and height difference formed by itself. The four clamper fingers 11 are bent toward the center or toward the outside to achieve the clamping of objects of various shapes. At the same time, the Kresling structure can give the fingers a larger expansion and contraction ratio. The clamper finger 11 is initially in an extended state. When the main chamber is evacuated, the clamper finger 11 can achieve axial contraction. When the chamber is depressurized and the airbag 113 is contracted, the clamper finger 11 extends and returns to its original state.

[0107] The multiple air bags 113 connected to each Kresling origami tube 1101 are respectively connected to the external air source through a separate connecting pipe, and each connecting pipe is connected to a solenoid valve group. The four gripper fingers 11 of the gripper 1 are placed diagonally, and the four fingers are controlled and driven by pneumatic means, but they move independently of each other, so that the expansion of the multiple air bags 113 does not affect each other, and the four fingers of the gripper can be bent in various directions to achieve the gripping of objects of various shapes.

[0108] like Figures 4 and 5 As shown, the gripper 1 is driven by pneumatic means. By applying different pressures to the chamber of the origami unit, the gripper finger can be switched between torsional contraction and torsional bending states. An airbag is installed at a specific position inside to control the change in its stiffness. As the airbag inflates, the valley crease in a specific plane of the gripper finger gradually bends outward until it becomes a curved mountain crease. During this conversion process, nonlinear forces that promote bending naturally occur at the valley crease, giving the Kresling origami significant stiffness and load capacity in this area. At this point, the height difference between the specific plane and its opposite side causes the origami unit to exhibit a novel bending motion mode.

[0109] like Figure 4 As shown, a single gripper finger is composed of two double-layer Kresling origami units.

[0110] like Figure 5 As shown, one of the double-layer origami units is equipped with four pairs of airbags, each consisting of the airbags on the top layer of the unit. top and the bottom airbag base Working together to achieve bending. Airbags 1 & 2 base&topx Jointly control the bending of the unidirectional x-axis in the positive and negative directions, airbags 1 & 2 base&topy Together control the bending of the unidirectional x-axis in the positive and negative directions. Taking the four quadrants of the o-xy coordinate system as an example, for airbags 1 & 2 base&topx and airbags 1&2 base&topy Pressurizing the airbag and then evacuating the main chamber will achieve bending in the first quadrant. The structures and movement modes of the remaining three quadrants and the remaining three fingers are similar. Pressurizing the same airbag to different degrees will cause it to bend in a certain direction to different degrees. Figure 6 shown.

[0111] Example 2, as Figures 7 to 9 As shown, an optimization control method for a multimodal origami gripper includes the multimodal origami gripper of embodiment 1, and the optimization control method includes the following steps:

[0112] Step 1: Based on the piecewise constant curvature model (PCC), a kinematic model of the gripper's single finger is constructed to derive the quantitative relationship between the airbag pressure change ΔP and the end arc angle θ, providing a theoretical basis for the inverse solution of the subsequent closed-loop control.

[0113] Step 2: Taking the single finger of the multimodal origami gripper as the research object, set the coordinates of the initial target position (X d ,Y d ,Z d ) and obtain the coordinates of the end position of the single finger of the gripper through the visual system (X t ,Y t ,Z t ), the arc angle θ is changed by changing the airbag expansion size according to visual feedback. The larger θ is, the greater the airbag expansion degree is;

[0114] Step 3: Based on the horizontal and vertical coordinates X of the target position d and Y d Determine the quadrant it is in and control the airbag to achieve the position of the end of the gripper's single finger (X t ,Y t ,Z t ) to the target position (X d ,Y d ,Z d )sports;

[0115] Step 4: Use a PID controller to compensate and control the pressure in the airbag;

[0116] Step 5: Introduce the multi-strategy improved red-billed blue magpie optimization algorithm to adaptively optimize the closed-loop control system of the gripper's single finger;

[0117] Step 6: Correspond to the parameters of the four-finger parallel closed-loop control system of the gripper so that it moves along the expected trajectory.

[0118] In addition to the technical solutions in Example 2, this embodiment further includes: a single finger of the gripper is modeled using the constant curvature method (CC) for kinematic modeling, specifically including:

[0119] The o-xyz system is established with the bottom center of the component of the gripper as the reference. Its working space can be defined by the arc parameters, arc radius ρ, arc angle θ, and the angle δ between the projection of the arc radius on the o-xy plane and the x-axis. The center of the uppermost component K(x, y, z) is defined as the farthest end of the working space, and the other endpoints on the center arc path are defined as K n (x n ,y n ,z n )(n=1,2,3), the thickness of the structural part is defined as s, then the working space of point K3(x3,y3,z3) can be defined as:

[0120]

[0121] x2=x3+2ssinθcosδ (2)

[0122] y2=y3+2ssinθsinδ (3)

[0123] z2=z3+2scosθ (4)

[0124]

[0125] At the same time, create a second set of arc parameters to describe the movement of the above origami unit, K1(x1, y1, z 1) The working space of a point is expressed as:

[0126]

[0127] At the same time, since the working space of the upper and lower origami units is affected by different airbags, the arc parameters will vary in actual operation. The final working space of point K (x, y, z) is:

[0128] x=x1+ssinθ1cosδ (9)

[0129] y=y1+ssinθ1sinδ (10)

[0130] z=z1+scosθ1 (11)

[0131] In this kinematic model, the order of the lowest origami unit driving line in space is defined as 1 to 8 in the clockwise direction from x to y, and the length of the line can be expressed as l base =[l1,l2,l3,l4,l5,l6,l7,l8]; Similarly, the length of the top layer can be expressed as l top =[l9,l 10 ,l 11 ,l 12 ,l 13 ,l 14 ,l 15 ,l 16 ]; K(x,y,z) are known input variables, arc parameters (ρ,ρ 1, θ, θ1, δ) are the resulting output variables. The number of unknowns (x, y, z, x2, y2, z2, ρ, ρ1, θ, θ1, δ) is equal to the number of solved formulas; therefore, these unknowns can be solved using the least squares method. The lengths of the two origami unit drive lines can be solved using the PCC model as follows:

[0132]

[0133] Where r is the distribution radius of the component.

[0134] Example 4: In addition to the technical solution in Example 2, this example also includes the following steps:

[0135] Fourth, the pressure compensation formula is as follows:

[0136]

[0137] Among them, e Θ =Θ e -Θ t (Θ=x,y,z) is the end of the single finger of the gripper (X t ,Y t ,Z t ) and the target position (X d ,Y d ,Z d ) 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 large coordinate error e Θ , bringing a larger pressure compensation P to the chamber of the gripper 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.

[0138] Initial pressure of one finger of the gripper (P x,out,k ,P y,out,k ,P z,out,k ) are all set to 0kPa;

[0139] When the air pump as an external air source starts to provide pressure to the gripper's single finger, the vision system will provide it with the end position coordinates (X t ,Y t ,Z t ) 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 single-finger chamber of the gripper, thereby driving its movement in the Z direction; the other two groups are mainly used to control the pressure of the airbag during the bending process of the single finger, thereby driving the movement of the end of the single finger of the gripper in the X and Y directions.

[0140] In the fifth embodiment, in step five, the basic algorithm process of the red-billed blue magpie optimization algorithm is as follows:

[0141] Its foraging strategy mainly includes: population initialization, searching for food, attacking prey, and storing food;

[0142] (1) Population initialization

[0143] Like most algorithms, the initial search agent for RBMO is generated by the following formula:

[0144] x i,j =(ub-lb)×rand1+lb (14)

[0145] Where i and j represent a single index and a dimension index respectively; ub represents the upper bound of the problem, lb represents the lower bound of the problem, and rand represents a random number between 0 and 1;

[0146] (2) Searching for food

[0147] In the process of searching for food, red-billed blue magpies usually move in small groups (2 to 5) or large flocks (more than 10) to improve search efficiency;

[0148] When the small group explores the food, it iterates using the following formula:

[0149]

[0150] Among them, t represents the current iteration number, X i (t+1) represents the i-th new search agent position, k represents the number of 2-5 red-billed blue magpie groups randomly selected from all searched individuals, X m represents the randomly selected mth individual, X i represents the i-th individual, X rs represents the randomly selected search agent in the current iteration;

[0151] When forming groups, the following formula is used for iteration:

[0152]

[0153] Where c represents the number of search agents that the cluster has when exploring for food, ranging from 10 to n;

[0154] (3) Attacking prey

[0155] In small group movements, the main target is usually small prey or plants; the corresponding mathematical model is shown in the following formula; when the red-billed blue magpie moves in a group, the mathematical expression of this behavior is:

[0156]

[0157] Among them, X Food(t) represents the location of the food, KF = (1-t / T) 2t / T , randn represents the random number used to generate the standard normal distribution (mean 0, standard deviation 1);

[0158] (4) Food storage

[0159] This process preserves information about the solution, making it easier for individuals to find the global optimum;

[0160] The mathematical model is shown as follows:

[0161]

[0162] in, and Respectively represent the fitness values of the i-th red-billed blue magpie before and after the position update.

[0163] Based on the Red-billed Blue Magpie Optimization Algorithm, the node set initialization theory is introduced into the initialization stage of the Red-billed Blue Magpie population, which effectively increases the diversity of RBMO population initialization and improves the search efficiency of the RBMO algorithm. Specifically,

[0164] Suppose there is a unit cube in s-dimensional Euclidean space with a set of points:

[0165]

[0166] Its deviation satisfies:

[0167]

[0168] Among them, C(r,ε) is a constant that is only related to r and ε (ε>0); then P n (k) is called the good point set, r is called the good point; the value of the good point r is:

[0169]

[0170] Where q is the smallest prime number that satisfies (q-3) / 2≥s;

[0171] Therefore, based on the good point set theory, the new initialization strategy is:

[0172] x i,j (k) = (ub-lb) {P n (k)}+lb (23)

[0173] Among them, ub is the upper bound and lb is the lower bound; using the distribution of the good point set to initialize the RBMO population can effectively improve the uniformity of the individual distribution of the population, and enhance the search efficiency and global optimization ability of the algorithm.

[0174] The Red-billed Blue Magpie Optimization Algorithm uses the Weibull distribution to improve its search accuracy and efficiency. The Weibull distribution is used to measure the time until a failure occurs, or conversely, to measure reliability. Generating random numbers based on the probability density function of the Weibull distribution and applying it to the attack phase of the RBMO population can enhance the capabilities of the algorithm development phase, including:

[0175] The probability density function of the Weibull distribution is as follows:

[0176]

[0177] Where x is a random variable, β is a shape statement, η is a scale factor, γ is a location parameter (threshold parameter), and γ can be 0. When γ is equal to 0, it is called a two-parameter Weibull cumulative distribution function.

[0178] At the same time, for the probability density function of the Weibull distribution, the continuous random variable X1 has the following conditions:

[0179]

[0180] Among them, β is the shape parameter (also known as the Weibull slope), η is the scaling parameter, and γ is the location parameter. According to the Weibull distribution, the behavioral formula of the RBMO algorithm attacking prey can be updated as follows:

[0181] X i (t+1)=Formula(17)×f(t;β,η,γ) (26)

[0182] X i (t+1)=Formula(18)×f(t;β,η,γ) (27)

[0183] The red-billed blue magpie optimization algorithm introduces a reverse learning competition strategy. This strategy allows disadvantaged individuals to gain a second learning opportunity, which improves the algorithm's ability to escape local optimality to a certain extent. The calculation formula is as follows:

[0184] R p (i+1)=(ub+lb){P n (k)}-X i (t+1) (28)

[0185] Among them, R p (i+1) is the opposite learning solution, by calculating R p (i+1) and X i The overall fitness of (t+1) can be used to obtain the output position of this iteration.

[0186] Example 6: An optimization control method for a multi-modal origami gripper, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function is 0. The Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) is compared with the original Red-billed Blue Magpie Algorithm (RBMO). This verifies the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. 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 300.

[0187] like Figure 10 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0188] Example 7, an optimization control method for a multi-modal origami gripper, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function is 0. The Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) is compared with the original Red-billed Blue Magpie Algorithm (RBMO). This verifies the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. 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 300.

[0189] like Figure 11 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0190] Example 8: An optimization control method for a multi-modal origami gripper, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function is 0. The Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) is compared with the original Red-billed Blue Magpie Algorithm (RBMO). This verifies the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. 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 300.

[0191] like Figure 12 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0192] Example 9: A closed-loop control method for origami continuum book grabbing based on a multi-strategy improved red-billed blue magpie 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 Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) is compared with the original Red-billed Blue Magpie Algorithm (RBMO). This verifies the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. 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 300.

[0193] like Figure 13 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0194] Example 10: An optimization control method for a multi-modal origami gripper, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function was -10.1532. The Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) was compared with the original Red-billed Blue Magpie Algorithm (RBMO). This validated the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. To ensure fairness in the test, the population size for each algorithm was set to 30, and the maximum number of iterations was set to 300.

[0195] like Figure 14 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0196] Example 11: An optimization control method for a multi-modal origami gripper, using a basic test function To verify the performance of the improved algorithm, the theoretical optimization value of this function was -10.4028. The Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm (MRBMO) was compared with the original Red-billed Blue Magpie Algorithm (RBMO). This validated the performance of the Multi-Strategy Improved Red-billed Blue Magpie Optimization Algorithm. 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 300.

[0197] like Figure 15 As shown in the figure, it can be seen that the multi-strategy improved red-billed blue magpie optimization algorithm has greater advantages in convergence speed and convergence accuracy compared with the original algorithm.

[0198] A multimodal origami gripper consists of four Kresling double-layer origami units. A single finger of the multimodal origami gripper was used as the research object. A kinematic model of the gripper finger was established based on the piecewise constant curvature (PCC) model, and the initial target position coordinates were set. A position feedback system was used to obtain the coordinates of the gripper finger's end position in real time, determine the quadrant of the target position, and control each of the gripper finger's motion units to move the end toward the target position. A closed-loop control method was used to precisely control the gripper finger's motion.

Claims

1. A novel multimodal origami gripper, comprising a gripper (1), characterized in that: The clamper (1) comprises a clamper finger (11) and a connecting assembly (12), wherein four clamper fingers (11) are provided, and the connecting assembly (12) is provided as four centrosymmetrical bases, and the bottom ends of the clamper fingers (11) are respectively connected to the bases of the connecting assembly (12) by interference fit; The single finger (11) of the clamp comprises a paper folding unit (111) and an intermediate connecting member (112), wherein the intermediate connecting member (112) is connected between two paper folding units (111), wherein the paper folding unit (111) comprises a Kresling paper folding tube (1101) and a square paper strip (1102), wherein the Kresling paper folding tube (1101) is provided with two upper and lower Kresling paper folding tubes (1101) of opposite chirality, and the square paper strip (1102) is connected between the two Kresling paper folding tubes (1101) of opposite chirality, wherein a chamber is provided inside the Kresling paper folding tube (1101) of the paper folding unit (111), wherein an air bag (113) is connected to the inner side surface of the tube body of the Kresling paper folding tube (1101), and wherein the Kresling paper folding tube (1101) and the air bag (113) are respectively connected to an external air source; The inner unit surface of the Kresling paper-folding tube (1101) is formed into an angular face by reducing the area of two symmetrical triangles, and the airbags (113) are located on the inner angular face. Four airbags (113) are arranged in a cross-shaped distribution on the body of the Kresling paper-folding tube (1101). The airbags (113) located on two sides are responsible for the bending of the paper-folding unit (111) in the x-axis direction, and the airbags (113) located on the other two sides are responsible for the bending of the paper-folding unit (111) in the y-axis direction.

2. The multimodal origami gripper according to claim 1, characterized in that: The multiple air bags (113) connected to each of the Kresling origami tubes (1101) are respectively connected to an external air source through a separate connecting pipe, and each connecting pipe is connected to a solenoid valve group.

3. An optimization control method for a multimodal origami gripper, comprising the multimodal origami gripper according to any one of claims 1 to 2, characterized in that: The optimization control method comprises the following steps: Step 1: Construct a kinematic model of a single finger of the gripper based on the piecewise constant curvature model, and derive the quantitative relationship between the airbag pressure change ΔP and the end arc angle θ; Step 2: Taking the single finger of the multimodal origami gripper as the research object, set the coordinates of the initial target position (X d ,Y d ,Z d ) and obtain the coordinates of the end position of the single finger of the gripper through the visual system (X t ,Y t ,Z t ), the arc angle θ is changed by changing the size of the airbag expansion according to visual feedback; Step 3: Based on the horizontal and vertical coordinates X of the initial target position d and Y d Determine the quadrant it is in and control the airbag to achieve the position of the end of the gripper's single finger (X t ,Y t ,Z t ) to the initial target position (X d ,Y d ,Z d )sports; Step 4: Use a PID controller to compensate and control the pressure in the airbag; Step 5: Introduce the multi-strategy improved red-billed blue magpie optimization algorithm to adaptively optimize the closed-loop control system of the gripper's single finger; Step 6: Correspond to the parameters of the four-finger parallel closed-loop control system of the gripper so that it moves along the expected trajectory.

4. The optimization control method according to claim 3, characterized in that: The kinematic model of the gripper is modeled using a constant curvature method, specifically including: The o-xyz system is established with the bottom center of the component of the gripper as the reference. Its working space is defined by the arc parameters, arc radius ρ, arc angle θ, and the angle δ between the projection of the arc radius on the o-xy plane and the x-axis. The center of the uppermost component K(x, y, z) is defined as the farthest end of the working space, and the other endpoints on the center arc path are defined as K n (x n ,y n ,z n ), n=1,2,3, the thickness of the structural part is defined as s, then the working space of the definition point K3(x3,y3,z3) is: x2=x3+2ssinθcosδ y2=y3+2ssinθsinδ z2=z3+2scosθ At the same time, a second set of arc parameters is created to describe the motion of the above origami unit. The working space of point K1 (x1, y1, z1) is expressed as: The final working space of point K(x,y,z) is: x=x1+ssinθ1cosδ y=y1+ssinθ1sinδ z=z1+scosθ1 In the kinematic model, the order of the lowest origami unit driving line in space is defined as 1 to 8 in the clockwise direction from x to y, and the length of the line is represented by l base =[l1,l2,l3,l4,l5,l6,l7,l8]; the length of the top layer is represented by l top =[l9,l 10 ,l 11 ,l 12 ,l 13 ,l 14 ,l 15 ,l 16 ]; K(x,y,z) are the known input variables, the arc parameters (ρ,ρ1,θ,θ1,δ) are the resulting output variables, and the number of unknowns (x,y,z,x2,y2,z2,ρ,ρ1,θ,θ1,δ) is equal to the number of solved formulas; The unknown quantities are solved using the least squares method, and the lengths of the two origami unit drive lines are solved according to the PCC model as follows: Where r is the distribution radius of the component.

5. The optimization control method according to claim 3, characterized in that: In step 4, the pressure compensation formula is as follows: Among them, e Θ =Θ e -Θ t (Θ=x,y,z) is the end of the single finger of the gripper (X t ,Y t ,Z t ) and the target position (X d ,Y d ,Z d ) 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 existing coordinate error e Θ , brings pressure compensation P to the chamber of the gripper Θ .

6. The optimization control method according to claim 5, characterized in that: The initial pressure of the gripper finger (P x,out,k ,P y,out,k ,P z,out,k ) are all set to 0kPa; The air pump provides pressure for the gripper's single finger to start, and the vision system provides the end position coordinates (X t ,Y t ,Z t ) 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 this control system, a single-chip microcomputer is used to control three groups of solenoid valves. One group is used to control the pressure in the cavity of the gripper's single finger, thereby driving its movement in the Z direction; the other two groups are used to control the pressure of the airbag during the bending process of the single finger, thereby driving the movement of the end of the gripper's single finger in the X and Y directions.

7. The optimization control method according to claim 3, characterized in that: In step 5, the basic algorithm process of the red-billed blue magpie optimization algorithm is as follows: Its foraging strategy includes: population initialization, searching for food, attacking prey, and storing food; (1) Population initialization The initial search agent of RBMO is generated by the following formula: x i,j =(ub-lb)×rand1+lb Where i and j represent a single index and a dimension index respectively; ub represents the upper bound of the problem, lb represents the lower bound of the problem, and rand represents a random number between 0 and 1; (2) Searching for food In their search for food, red-billed blue magpies move in small flocks or groups; When the small group explores the food, it iterates using the following formula: Among them, t represents the current iteration number, X i (t+1) represents the i-th new search agent position, k represents the number of 2-5 red-billed blue magpie groups randomly selected from all searched individuals, X m represents the randomly selected mth individual, X i represents the i-th individual, X rs represents the randomly selected search agent in the current iteration; When forming groups, the following formula is used for iteration: Where c represents the number of search agents that the cluster has when exploring for food, ranging from 10 to n; (3) Attacking prey When blue magpies move in groups, the mathematical expression for this behavior is: Among them, X Food (t) represents the location of the food, KF = (1-t / T) 2t / T , randn represents the random number used to generate the standard normal distribution; (4) Food storage The mathematical model is shown as follows: in, and Respectively represent the fitness values of the i-th red-billed blue magpie before and after the position update.

8. The optimization control method according to claim 7, characterized in that: On the basis of the above-mentioned red-billed blue magpie optimization algorithm, the good point set initialization theory is introduced into the initialization stage of the red-billed blue magpie population, specifically including: The unit cube of s-dimensional Euclidean space has a set of points: Its deviation satisfies: Among them, C(r,ε) is a constant that is only related to r and ε (ε>0); then P n (k) is called the good point set, and r is called the good point; The value of the optimal point r is: Where q is the smallest prime number that satisfies (q-3) / 2≥s; Based on the good point set theory, the new initialization strategy is: x i,j (k)=(ub-lb){P n (k)}+lb Among them, ub is the upper bound and lb is the lower bound.

9. The optimization control method according to claim 8, characterized in that: The red-billed blue magpie optimization algorithm uses Weibull distribution to improve the search accuracy and efficiency of the algorithm, specifically including: The probability density function of the Weibull distribution is as follows: Where x is a random variable, β is a shape statement, η is a scale factor, γ is a location parameter, and γ can be 0. When γ is equal to 0, it is called a two-parameter Weibull cumulative distribution function. At the same time, for the probability density function of the Weibull distribution, the continuous random variable X1 has the following conditions: Among them, β is the shape parameter, η is the scaling parameter, and γ is the location parameter.

10. The optimization control method according to claim 9, characterized in that: The red-billed blue magpie optimization algorithm introduces a reverse learning competition strategy, and the calculation formula is as follows: R p (i+1)=(ub+lb){P n (k)}-X i (t+1) Among them, R p (i+1) is the opposite learning solution, by calculating R p (i+1) and X i The overall fitness of (t+1) is used to obtain the output position of this iteration.

Images