A method for calculating a driving rope of a snake robot based on statics analysis

Abstract

The algorithm discloses a calculation method of a driving rope of a snake robot based on static analysis, the joints of the snake robot are driven to move by the rope, each joint is relatively rotated and is mutually coupled to affect each other, so that a predetermined working pose is achieved. The algorithm performs front-end traversal on kinematics to obtain joint pose information of the snake robot and a conversion matrix of adjacent joints, rear-end traversal is performed on force analysis of the joints, a nonlinear optimization method is used to optimize force of the driving rope, so that the maximum value of the force of the three driving ropes directly acting on the connecting rod is minimized under the premise of meeting the motion of the snake robot, and the minimum value of the force of the three driving ropes meets the required pre-tightening force of the connecting rod, the mechanical property of the driving rope is improved by reducing the maximum value. Finally, the optimization force conditions of all the driving ropes of the snake robot under the static condition are obtained through the result of the rear-end traversal.

Description

Technical Field

[0001] This invention relates to the field of static optimization design, specifically to a calculation method for the driving rope of a snake robot based on static analysis. Background Technology

[0002] The snake-like robot is a multi-jointed, highly redundant robot capable of operating in confined spaces. As the robot's joints rotate, the drive cables passing through the robotic arm's turntable generate enormous frictional forces. These forces become even more pronounced with increasing rotation angles, causing irreversible damage to the drive cables. When this damage reaches a certain threshold, the drive cables may break, severely damaging the entire mechanical structure and leading to a safety accident. Therefore, from a safety perspective, analyzing the mechanics of the snake-like robot is crucial.

[0003] For snake robots, there is a lot of research on forward and inverse kinematics, but relatively little research on mechanics. Since the force on the drive rope is a nonlinear constraint problem, it is impossible to directly solve the force on the drive rope using a specific formula. In this case, nonlinear optimization algorithms can be used to obtain the optimized force on the drive rope based on the constraint conditions, thereby improving the reliability of the snake robot. Summary of the Invention

[0004] This application provides a method for calculating the driving rope of a snake robot based on static analysis. A nonlinear optimization method is used to constrain the maximum force on the driving rope in the static model, obtaining the model's output, i.e., the force condition of the driving rope. The technical solution is as follows:

[0005] According to one aspect of this application, a calculation method for the driving rope of a snake robot based on static analysis is provided, the method comprising:

[0006] Obtain the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities;

[0007] Based on geometric information, a static model of the snake robot and a frictional force solution model for the driving rope are constructed.

[0008] A nonlinear optimization method is used to constrain the maximum force on the driving rope in the static model, thereby obtaining the output of the model, i.e., the force condition of the driving rope.

[0009] According to one aspect of this application, a computational device for driving a snake-like robot's cable based on static analysis is provided, the device comprising:

[0010] Acquisition Module: Acquires the known quantities of the statics problem to be solved, as well as the model input quantities obtained by dephysicalizing the known quantities.

[0011] Building modules: Based on geometric information, constructing a static model of the snake robot and a model for solving the frictional force of the driving rope;

[0012] Solution module: Using a nonlinear optimization method, the maximum force on the driving rope in the static model is constrained to obtain the output of the model, i.e. the force situation of the driving rope.

[0013] According to one aspect of this application, a computational device for a snake-like robot's driving rope based on static analysis is provided, applied to a computational statics solution system. The nonlinear optimization algorithm is used to solve the statics model of the snake-like robot. The device includes:

[0014] Acquisition module: Acquires the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities;

[0015] Building modules: Based on geometric information, constructing a static model of the snake robot and a model for solving the frictional force of the driving rope;

[0016] Solution module: Using a nonlinear optimization method, the maximum force on the driving rope in the static model is constrained to obtain the output of the model, i.e. the force situation of the driving rope.

[0017] According to one aspect of this application, a computer device is provided, the computer device including a processor and a memory, the memory storing at least one piece of program code, the program code being loaded by the processor and executed as described above for the static optimization calculation method of a robot.

[0018] According to one aspect of this application, a computer-readable storage medium is provided, which stores at least one piece of program code, which is loaded and executed by a processor to implement the static optimization calculation method for a snake robot as described above.

[0019] The beneficial effects of the technical solutions provided in this application include at least the following:

[0020] By employing a nonlinear optimization method, the forces acting on the drive cables are optimized to ensure that the maximum forces on the three drive cables directly acting on the link are minimized while still satisfying the motion requirements of the snake robot. Furthermore, the minimum forces on the three drive cables must meet the preload requirements of the link. The mechanical properties of the drive cables are improved by reducing the maximum values. Finally, the optimized force distribution of all drive cables for the snake robot under stationary conditions is obtained through backend traversal. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 A block diagram of a snake robot structure design provided for an exemplary embodiment of this application;

[0023] Figure 2 A schematic diagram of the overall model of a snake-like robot provided as an exemplary embodiment of this application;

[0024] Figure 3 A schematic diagram of the snake robot body structure provided as an exemplary embodiment of this application;

[0025] Figure 4 A schematic diagram of a single joint structure of a snake robot provided as an exemplary embodiment of this application;

[0026] Figure 5 A schematic diagram of the force on the drive rope of a snake robot provided as an exemplary embodiment of this application;

[0027] Figure 6 A schematic diagram of a statics optimization process is provided as an exemplary embodiment of this application;

[0028] Figure 7 A schematic diagram of the frictional force model of a drive rope at a single joint, provided as an exemplary embodiment of this application;

[0029] Figure 8 A flowchart of nonlinear statics optimization is provided as an exemplary embodiment of this application;

[0030] Figure 9 A structural block diagram of a computer device provided for an exemplary embodiment of this application.

[0031] In the diagram: 1-Secondary lifting device, 2-Drive compartment, 3-Base, 4-Power distribution box, 5-Visual detection equipment, 6-Serpentine arm, 7-Cross shaft gasket, 8-Cross shaft sleeve, 9-Cross shaft seat, 10-Cross shaft. Detailed Implementation

[0032] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0033] This invention utilizes the MATLAB nonlinear solver module to optimize the static model and obtain the optimized driving force of the snake robot's drive ropes. This ensures that the maximum force on the three drive ropes directly acting on the link is minimized while still satisfying the snake robot's motion requirements. Furthermore, it ensures that the minimum force on the three drive ropes satisfies the preload required by the link. By reducing the maximum value, the mechanical properties of the snake robot's drive ropes are improved.

[0034] This invention provides a static model and a friction model for a snake-like robot. The pose information of the snake-like robot and the transformation matrix between the arms are obtained by forward traversal using joint angles and geometric information. Then, the force on the driving rope is optimized and solved using force balance equations and torque balance equations. A friction solution model is added at the joint angles to compensate for the force balance equations and torque balance equations.

[0035] The mechanical system of the snake robot consists of a manipulator arm that performs the task and a drive box at its root that provides power and trajectory planning. The kinematic mapping for trajectory planning is given based on a kinematic model of the manipulator arm's mechanical structure, obtained by decoupling the joint and cable-driven spatial mappings. The joint design is based on the configuration of degrees of freedom and uses linkage cables as a medium to transmit the motion between them. The arm design needs to consider the envelope size and overall length, while also setting up the cable routing channels; the manipulator arm's motion originates from the extension and retraction of the drive cables. Based on the design concept of the snake robot's structural parts and the design requirements of the snake robot mechanism, the following is obtained: Figure 1 The diagram shows the design block diagram of the snake-shaped robot structure.

[0036] The complete set of equipment consists of the snake-arm robot body, base 3, secondary lifting device 1, lifting electric cylinder, vision detection device 5, control system, etc. Figure 2 As shown. Through human-machine interaction control, the front articulated arm is remotely controlled to pass through a narrow entrance, reach the designated work space, complete the visual inspection task, acquire video and image information within the narrow space, and transmit it back to the back-end video monitoring equipment in real time.

[0037] The snake-arm robot body mainly consists of two parts: the drive compartment 2 and the snake arm 6. The drive compartment 2 houses the motor and transmission mechanism, providing power for the movement of the front snake arm; the snake arm 6 is composed of multiple rigid links connected by Hooke joints. (See schematic diagram of the snake robot body structure.) Figure 3 As shown below.

[0038] To better understand the forces acting on the drive cables, a physical model of a single joint is performed and stress analysis is conducted. The schematic diagram of the single joint structure of the snake robot and the force diagram of the drive cables acting on the joint are shown below. Figure 4 and Figure 5 As shown.

[0039] Based on the above, Figure 8 This is a flowchart of nonlinear statics optimization provided in one embodiment of this application. This method can be implemented in... Figure 3 In the application scenario of the snake-like robot body, the method includes the following steps:

[0040] S102, obtain the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities.

[0041] Schematic, the geometric information includes, but is not limited to, at least one of the following: joint angles and link configuration information of the robot. Link configuration information refers to geometric information related to the robot's links, including at least one of shape and position.

[0042] Optionally, geometric information includes joint angles, link lengths, and relative pose descriptions between joints. Here, pose refers to the robot's position and orientation. Robots are typically composed of a series of components and kinematic pairs, capable of performing various complex movements and predetermined operations in three-dimensional space. The relative pose description between joints is used to describe the movement between two joints.

[0043] An illustrative kinematic model can be constructed based on the transformation matrix between adjacent links of the robot.

[0044] S104 uses geometric information to build a static model of the snake robot and a frictional force solution model for the driving rope.

[0045] An illustrative static model used to describe the forces acting on a robot when it is in static equilibrium.

[0046] Among them, the equilibrium state is determined with the Earth as the reference frame, which refers to the state in which an object is at rest or in uniform linear motion relative to the inertial reference frame, that is, the state in which the acceleration is zero.

[0047] Indicatively, step S104 can be implemented as follows:

[0048] Based on the geometric information, determine the mass parameters and the position parameters of the centroid;

[0049] Based on the mass parameters and center of mass position parameters, the center of mass parameter item of the robot is generated. The center of mass parameter item is used to describe the equilibrium state of each link in the robot.

[0050] Based on the center of mass parameter terms and the center of mass dynamic equation, a static model is constructed;

[0051] Here, the mass parameter can be represented by m, and the center of mass position parameter can be represented by r. Taking geometric information including joint angles and link shape and position information as an example, the mass parameter and the center of mass position parameter can be represented by matrix T, where matrix T... Let be the position of the robot's center of mass in the world coordinate system. The world coordinate system is the robot's absolute coordinate system. Other coordinate systems can be transformed to and from the world coordinate system. Any coordinate system relative to the world coordinate system has the following relationships:

[0052]

[0053] To simplify the force model, the following assumptions are made:

[0054] The quality of each module is uniform;

[0055] The frictional force generated by the drive rope is the maximum static frictional force generated by the normal pressure exerted by the drive rope on the joint.

[0056] The drive rope is thin enough that its weight can be ignored.

[0057] The drive rope only generates tension, not thrust, and the direction of the tension is along the rope direction.

[0058] A static model is constructed using the center of mass parameters and the center of mass dynamic equations, forward kinematic ergonomics, mechanical equilibrium, and backward torque equilibrium ergonomics. Specifically, the static model of the serpentine arm 6 is constructed as follows: Figure 6 As shown.

[0059] 1) Force analysis of the end module

[0060] Based on the above assumptions, the force analysis of the end module is first performed, where the end module is subjected to its own weight m. 12 g and the weight m0g of the end effector, and the tension T of the drive rope acting on the end face. 12-1-12 T 12-2-12 T 12-3-12 This affects the Hooke's hinge angle β, thus changing the working direction of the end link. Force analysis of the end module is performed, such as... Figure 6 As shown.

[0061] A moment balance analysis of the end effector module in the coordinate system of joint 12 yields the following equation:

[0062]

[0063] O 12 P is the origin of the sixth joint coordinate system. 12 P0 and P1 are the points of application of the self-weight and load of the sixth joint arm, respectively, and T is the point of application of the load. 12-i-12Let be the tension in the i-th rope of the 12th rope group at the 12th joint, r be the radius of the circumference of the rope group, l be the relative length between the two joints, and h be the joint half-length. Where:

[0064]

[0065] 2) Intermediate joint analysis (taking the penultimate joint as an example)

[0066] A force balance analysis was performed on the twelfth joint arm, and its mechanical equilibrium equations are as follows:

[0067]

[0068] This can be derived through end-point model analysis, and F can be calculated using the above formula. 12 The matrix F 12 The transpose of F 12 Same size, opposite direction.

[0069] Torque balance analysis of joint 11:

[0070]

[0071] Where, d 12-i-12 'The coordinates O from the pressure point at the upper end of the eleventh joint to the joint center are...' 11 The vector distance, N 12-i-12 'and N 12-i-11 T respectively 12-i-12 and T 12-i-11 The projection onto the end face of the articulated arm has a direction determined by the articulated arm's pose, such as... Figure 7 As shown, the deflection angle β is determined by θ and α.

[0072] Based on the static calculation of the angle of the driving rope at the joint, a friction model of the snake robot is constructed.

[0073] By analyzing the forces acting on the driving rope on the flange, a frictional force model is constructed, as shown in the model below. Figure 7 As shown.

[0074] Drive rope k through flange hole H n-1,k Pressure is generated subsequently, and due to the tendency of motion, a corresponding static friction force f is generated. Therefore, the frictional force acting on the driving rope can be defined as:

[0075] ||F fr2,n,k ||=|N fr2,n,k |*k

[0076] In the formula, F fr2,n,k For disk D 2,n-1 Kong H n-1,k The action of Ck The estimated static friction force is given by k, where k is the static friction coefficient, taken as k = 0.2. Since the geometric relationship of the serpentine arm 6 can be used to solve for the static friction force using the law of cosines, C... 2,n-1,k It is the driving rope k (i.e. e) t2,n-1,k ,e t1,n,k The angle between the directions of the tension and the direction of the force can be determined as:

[0077] C 2,n-1,k =cos -1 (e t2,n-1,k ,e t1,n,k )

[0078] |F t2,n-1,k | 2 +(|F t2,n-1,k |+|N fr2,n,k |*k) 2 -2*|F t2,n-1,k |*(|F t2,n-1,k |+|N fr2,n,k |*k)*cosC 2,n-1,k =(|N fr2,n,k |*k) 2 +|N fr2,n,k | 2 |F t1,n,k |=|F t2,n-1,k |+|N fr2,n,k |*k

[0079] The magnitude of the pressure and the magnitude of the friction can be determined by solving the above formula. Similarly, for disk D... 1,n Kong H n,k The action of C k The estimated static friction force can also be calculated using the above formula.

[0080] S106 uses a nonlinear optimization method to constrain the maximum force on the driving rope in the static model, and obtains the output of the model, i.e. the force situation of the driving rope.

[0081] The forces acting on the driving rope are solved using a nonlinear method. The objective function and constraint functions are listed below:

[0082]

[0083] The equation contains three unknowns, and the coefficient matrix of the equation system is not full rank, making it impossible to obtain an accurate value for the traction force of the driving rope. To achieve better mechanical performance of the driving rope's traction force, an optimization objective is established: minimizing the traction force. In the calculation, f(F) is used as the objective function, and st is used as the constraint function. The built-in fmincon function in MATLAB is used to optimize the solution for the traction force of each driving rope at the end.

[0084] In MATLAB, the `fmincon` function can be used to find the minimum value of a constrained nonlinear multivariable function, i.e., it can be used to solve nonlinear programming problems. The syntax for a nonlinear programming model in MATLAB is as follows:

[0085] minf(x)

[0086]

[0087] Where f(x) is a scalar function, x, b, and bep are vectors, A and Aep are matrices, and c(x) and cep(x) are vector functions.

[0088] In summary, the embodiments of this application provide a calculation method for the driving rope of a snake robot based on static analysis. By using a nonlinear optimization method, the force on the driving rope is optimized, and the corresponding force situation is obtained.

[0089] Figure 9 This application provides a computational device for driving a snake-like robot's cable based on static analysis, according to one embodiment of the present application. The device includes:

[0090] Acquisition Module 122: Acquires the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities.

[0091] Module 124: Based on geometric information, build a static model of the snake robot and a frictional force solution model for the driving rope.

[0092] Solution module 126: Using a nonlinear optimization method, the maximum force on the driving rope in the static model is constrained to obtain the output of the model, i.e. the force situation of the driving rope.

[0093] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by computer-controlled devices. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. The storage medium can be a memory, a disk, an optical disk, etc.

[0094] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0095] The above description is merely illustrative of the invention. The invention is not limited to the above embodiments; various changes and modifications can be made without departing from the spirit and scope of the invention, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A calculation method for the driving rope of a snake-like robot based on static analysis, characterized in that, The method includes: Obtain the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities; Based on geometric information, a static model of the snake-like robot and a friction model for solving the driving ropes are constructed; including: constructing a static model of the snake-like robot based on the geometric information; constructing a friction model of the snake-like robot based on the static model; the friction model of the snake-like robot includes constructing the friction model of the snake-like robot based on the mass parameters and center of mass position parameters in the static model, as well as the angle data of the driving ropes at the joints calculated by statics; the friction model of the snake-like robot includes: Based on the force information of the driving rope obtained from the kinematic parameters in the static model, and the geometric chamfer information of the snake robot, the angle information of the driving rope at the joint in static calculation is obtained; based on the geometric and physical information of the snake robot, a single-joint friction model is constructed. A nonlinear optimization method is used to constrain the maximum force on the driving rope in the static model, thereby obtaining the output of the model, i.e., the force condition of the driving rope.

2. The calculation method according to claim 1, characterized in that, The nonlinear optimization method is used to constrain the maximum force on the driving rope in the static model, thereby obtaining the model's output, i.e., the force condition of the driving rope, including: Torque data obtained from statics, and preload data required to drive the rope; Based on the data information, the force balance equation of the driving rope in the static model is subjected to nonlinear optimization to obtain the force information of the driving rope after the model is optimized.

3. The calculation method according to claim 2, characterized in that, The data information is used to perform nonlinear optimization on the force balance equation of the driving rope in the static model to obtain the force information of the driving rope after optimization, including: Substitute the data information into the statics model to obtain the updated statics model; The updated static model is processed using a nonlinear optimization algorithm to obtain the force information of the optimized driving rope.

4. The calculation method according to claim 1, characterized in that, The static model of the snake-like robot includes: Based on the geometric information, determine the mass parameters and the centroid position parameters; Based on the mass parameters and the center of mass position parameters, a center of mass parameter item for the snake robot is generated, which is used to describe the equilibrium state of each link in the snake robot; Based on the centroid parameter terms and the centroid kinematic equations, the static model is constructed.

5. The calculation method according to claim 2, characterized in that, The nonlinear optimization method is used to constrain the maximum force on the driving rope in the static model, thereby obtaining the model's output, i.e., the force condition of the driving rope, including: The mass parameters and the center of mass position parameters determined based on the geometric information, along with the data information, are used to describe the equilibrium state of each link in the snake robot, in order to construct a static model.

6. The calculation method according to any one of claims 1 to 3, characterized in that, The method includes a kinematic model of a snake-like robot, determining the geometric information of the snake-like robot, including: Determine the transformation matrix between adjacent links of the snake-like robot; Based on the transformation matrix, construct the kinematic model of the snake robot.

7. The calculation method according to claim 6, characterized in that, The step of constructing the kinematic model of the snake robot based on the transformation matrix includes: The kinematic model is constructed based on the transformation matrix and the pose transformation equation of the snake robot.

8. A computational device for driving a snake-like robot's rope based on static analysis, applied to the computational method described in claim 1, characterized in that, The device, which is applied to a computational statics solution system, uses a nonlinear optimization algorithm to solve the statics model of the snake-like robot. The device includes: Acquisition module: Acquires the known quantities of the statics problem to be solved, and the model input quantities obtained by dephysicalizing the known quantities; Building modules: Based on geometric information, constructing a static model of the snake robot and a model for solving the frictional force of the driving rope; Solution module: Using a nonlinear optimization method, the maximum force on the driving rope in the static model is constrained to obtain the output of the model, i.e. the force situation of the driving rope.

9. A computer device, characterized in that... The computer device includes a processor and a memory, the memory storing at least one piece of program code, the program code being loaded and executed by the processor to implement the calculation method for the snake robot driving rope based on static analysis as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one piece of program code, which is loaded and executed by a processor to implement the calculation method for the snake robot driving rope based on static analysis as described in any one of claims 1 to 7.

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