Docking mechanism dynamics modeling method for cabin sections

Abstract

The application discloses a docking double-arm mechanism dynamics modeling method for cabin sections. The method adopts the Lagrange method to establish a docking mechanism dynamics model for cabin sections based on the docking double-arm mechanism for cabin sections, establishes a joint transmission error model and a force / torque disturbance model of the double-arm mechanism, and introduces a joint friction model to construct a complete compound dynamics equation of the docking double-arm mechanism for cabin sections, so as to serve as a basic model for joint tracking control of the docking mechanism mechanical arm. The application improves the efficiency and motion stability of the cabin section docking process, and has a wide application prospect.

Description

Technical Field

[0001] This invention belongs to the field of robot dynamics technology, and in particular relates to a dynamic modeling method for a dual-arm mechanism for docking of compartments. Background Technology

[0002] Regarding the docking systems and implementation methods for module components, the main methods used both domestically and internationally include docking based on the POGO column (three-coordinate system), docking based on the Stewart platform, vertical assembly via module hoisting, and horizontal docking assembly. The horizontal docking assembly method employs a decoupled design for the control of each degree of freedom, with each independent degree of freedom of the product component controlled by an independent motor control system. This decoupled structural design effectively simplifies the control algorithm and improves system stability, and is widely used both domestically and internationally in the field of weaponry and aerospace module assembly.

[0003] Dynamics analysis is fundamental for robot simulation research, dynamics optimization design, and control system design. Dynamics modeling is an essential research component for achieving high-precision control of mechanical systems. Currently, domestic module docking commonly employs overhead crane hoisting in workshops, relying on manual labor to adjust the spatial orientation of the module workpieces. This method suffers from high labor intensity, low work efficiency, and poor assembly quality. Therefore, there is an urgent need to research automated module docking mechanisms. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic modeling method for a dual-arm mechanism for module docking, thereby improving the efficiency and stability of the module docking process.

[0005] To achieve the objective of this invention, a dynamic modeling method for a dual-arm mechanism for module docking is provided, comprising the following steps:

[0006] Step 1: Define the generalized coordinate vector of the docking double-arm mechanism of the module;

[0007] Step 2: Based on the coordinate vector, determine the joint kinetic energy model of the double-arm mechanism using the mechanical kinetic energy formula, obtain the kinetic energy model of the double arms based on the joint kinetic energy, and then obtain the total kinetic energy model using the kinetic energy model of the double arms.

[0008] Step 3: Based on the coordinate vector, determine the potential energy model of the two arms using the mechanical potential energy formula, and then obtain the total potential energy model using the potential energy model of the two arms.

[0009] Step 4: Construct the Lagrange function by subtraction based on the total kinetic energy model and the total potential energy model, and differentiate the Lagrange function through the Lagrange equation to obtain the Lagrange joint dynamic torque model;

[0010] Step 5: Using the coordinate vector, based on the planetary reducer transmission error function and the mechanical joint transmission error function, and their corresponding transmission ratio, obtain the joint transmission error model of the docking manipulator arm, and obtain the joint transmission error disturbance torque model based on the joint transmission error model of the docking manipulator arm.

[0011] Step 6: Using the coordinate vectors, determine the joint friction force or friction torque model of the docking double-arm mechanism of the compartment according to the Stribeck friction model;

[0012] Step 7: Based on the Lagrange joint dynamic torque model, the joint transmission error disturbance torque model, and the joint friction force or friction torque model, sum to obtain the composite dynamic model of the docking double arm mechanism of the compartment.

[0013] Furthermore, the module docking dual-arm mechanism includes a left robotic arm, a right robotic arm, and a base. The left and right robotic arms jointly support the module components, enabling the module components to adjust their spatial position and orientation.

[0014] The single robotic arm consists of movable joints and rotary joints. The movable joints include axial movable joints, vertical lifting joints, and radial movable joints. The rotary joints include circumferential rolling joints. The axial movable joint transmission system includes a rack and pinion pair and a planetary reducer. The vertical lifting joint transmission system includes a trapezoidal lead screw pair and a planetary reducer. The radial movable joint includes a ball screw pair and a planetary reducer. The circumferential rolling joint includes a gear pair and a planetary reducer.

[0015] Step 2 includes the following steps:

[0016] Step 2-1: Based on the coordinate vector, determine the kinetic energy models of the axial translation joint, vertical translation joint, and radial translation joint of the left robotic arm according to the kinetic energy formula of the translation joint;

[0017] Step 2-2: Determine the kinetic energy model of the left robotic arm's circular rotation joint based on the kinetic energy formula of the rotation joint;

[0018] Steps 2-3: Summing up the joint kinetic energy model of the left robotic arm based on the above kinetic energy model;

[0019] Step 2-4: Repeat steps 2-1 to 2-3 above to obtain the joint kinetic energy model of the right robotic arm;

[0020] Steps 2-5: Obtain the total kinetic energy model by summing the joint kinetic energy models of the left and right robotic arms.

[0021] Step 3 includes the following steps:

[0022] Step 3-1: Based on the coordinate vector, determine the potential energy model of the left robotic arm for docking the module using the potential energy formula;

[0023] Step 3-2: Based on the coordinate vector, determine the potential energy model of the right robotic arm for docking the module using the potential energy formula;

[0024] Step 3-3: Summing up the potential energy model above yields the total potential energy model.

[0025] Step 4 includes the following steps:

[0026] Step 4-1: Obtain the two-arm Lagrangian function by subtraction based on the total potential energy model and the total kinetic energy model;

[0027] Step 4-2: Substitute the Lagrangian functions of the two arms into the Lagrangian equations and differentiate for each generalized coordinate vector of the two arms to obtain the dynamic differential equation of the two arms, which is the Lagrangian dynamic torque model of the two-arm mechanism.

[0028] Step 5 includes the following steps:

[0029] Step 5-1: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear rack transmission pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the axial translation of the left robotic arm joint;

[0030] Step 5-2: Based on the coordinate vector, according to the planetary reducer transmission error function and the trapezoidal screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the vertical translation of the left robotic arm joint;

[0031] Step 5-3: Based on the coordinate vector, according to the planetary reducer transmission error function and the ball screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the radial translation of the left robotic arm joint.

[0032] Step 5-4: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the left mechanical arm joint in circular rotation.

[0033] Step 5-5: Based on the transmission error model of the left robotic arm joint described above, obtain the transmission error disturbance torque model of the left robotic arm joint.

[0034] Steps 5-6: Repeat the above steps to obtain the transmission error disturbance torque model of the right robotic arm joint;

[0035] Steps 5-7: Based on the disturbance torque models of the left and right robotic arm joints described above, the disturbance torque model of the joint transmission error of the docking double-arm mechanism is obtained.

[0036] The significant advancement of this invention compared to existing technologies lies in:

[0037] (1) The present invention uses the Lagrange method to establish the joint torque calculation formula of the module docking mechanism. The calculation process is simpler and it is easier to apply modern control theory and optimization algorithm. It can monitor the joint displacement, joint velocity and joint acceleration in real time to ensure the stable operation of the system.

[0038] (2) The present invention establishes transmission error models for the docking mechanism of the compartment for gear rack pair, trapezoidal screw pair, ball screw pair and gear pair respectively, and calculates the disturbance force / torque formula caused by joint transmission error;

[0039] (3) The present invention introduces a joint friction model to construct a complete dynamic equation of the double-arm mechanism for docking of compartments, providing a basic theoretical model for joint tracking control of the docking mechanism of compartments and improving the working accuracy of the mechanism.

[0040] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0042] Figure 1 This is a schematic diagram of the double-arm mechanism for docking the compartments of the present invention;

[0043] Figure 2 This is a schematic diagram of the structure of a single robotic arm for docking a module of the present invention;

[0044] Figure 3 This is a flowchart of the dynamic modeling steps for the docking double-arm mechanism of the present invention.

[0045] Figure 4 (a)-(c) are the displacement curve, velocity curve and acceleration curve of the left robotic arm joint in the embodiments of the present invention;

[0046] Figure 5 (a)-(c) are the displacement curve, velocity curve and acceleration curve of the right robotic arm joint in the embodiment of the present invention;

[0047] Figure 6 (a)-(d) are the disturbance force / torque curves of the transmission error of the left robotic arm joint in the embodiments of the present invention;

[0048] Figure 7 (a)-(d) are the force / torque curves of the right robotic arm joint transmission error in the embodiments of the present invention;

[0049] Figure 8 (a)-(d) are the friction force / torque curves of the left robotic arm joint in the embodiments of the present invention;

[0050] Figure 9 (a)-(d) are the friction force / torque curves of the right robotic arm joint in the embodiments of the present invention;

[0051] Figure 10 (a)-(d) are the force / torque curves of the left robotic arm joint control in the embodiments of the present invention;

[0052] Figure 11 (a)-(d) are the control force / torque curves of the right robotic arm joint in the embodiments of the present invention. Detailed Implementation

[0053] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Combination Figure 1 The module docking dual-arm mechanism includes a left robotic arm, a right robotic arm, and a base. The left and right robotic arms jointly support the module components, enabling the module components to adjust their spatial position and orientation.

[0055] Combination Figure 2 The single robotic arm consists of three moving joints and one rotating joint. The three moving joints include an axial moving joint, a vertical lifting joint, and a radial moving joint. The rotating joint includes a circumferential rolling joint. The axial moving joint transmission system includes a rack and pinion pair and a planetary reducer. The vertical lifting joint transmission system includes a trapezoidal screw pair and a planetary reducer. The radial moving joint includes a ball screw pair and a planetary reducer. The circumferential rolling joint includes a gear pair and a planetary reducer.

[0056] Combination Figure 3 According to the above structure, the present invention provides a dynamic modeling method for a dual-arm docking mechanism for a module, comprising the following steps:

[0057] Step 1: Define the generalized coordinate vector of the docking double-arm mechanism of the module;

[0058] ;

[0059] in, , The position of the axial translation joints of the left and right robotic arms. , The vertical translation joint positions of the left and right robotic arms. , The radial translation joint positions of the left and right robotic arms. , The angle of the rolling joints of the left and right robotic arms.

[0060] Step 2: Based on the coordinate vector, determine the joint kinetic energy model of the double-arm mechanism using the mechanical kinetic energy formula, obtain the kinetic energy model of the double arms based on the joint kinetic energy, and then obtain the total kinetic energy model using the kinetic energy model of the double arms.

[0061] Step 2-1: Based on the coordinate vector, determine the kinetic energy models of the left robotic arm's axial translation joint L1, vertical translation joint L2, and radial translation joint L3 according to the translation joint kinetic energy formula. , , The specific formula is as follows:

[0062] ;

[0063] ;

[0064] ;

[0065] in, , , The masses of the axial moving joint L1, the vertical lifting joint L2, and the radial moving joint L3 are respectively. , , These are the velocity vectors of the axial moving joint L1, the vertical lifting joint L2, and the radial moving joint L3, respectively. These are the derivatives of the generalized coordinate vectors of the axial moving joint L1, the vertical lifting joint L2, and the radial moving joint L3, respectively.

[0066] Step 2-2: Determine the kinetic energy model of the L4 circumferential rotary joint of the left robotic arm according to the kinetic energy formula of the rotary joint, as shown in the following formula:

[0067] ;

[0068] in, This is the translational kinetic energy of the circular rotary joint L4. Let L4 be the rotational kinetic energy of the circular rotary joint. Let L4 be the mass of the circular rotary joint. Let L4 be the velocity vector of the circular rotary joint. Let L4 be the inertia tensor of the circular revolute joint. Let L4 be the generalized velocity vector of the circular rotary joint;

[0069] Steps 2-3: Summing up the joint kinetic energy model of the left robotic arm based on the above kinetic energy model. The specific formula is as follows:

[0070] ;

[0071] Step 2-4: Repeat steps 2-1 to 2-3 above to obtain the joint kinetic energy model of the right robotic arm. The specific formula is as follows:

[0072] ;

[0073] Steps 2-5: Develop a kinetic energy model of the joints of the left robotic arm. Joint kinetic energy model of the right robotic arm Summing yields the total kinetic energy model : .

[0074] Step 3: Based on the coordinate vector, determine the potential energy model of the two arms using the mechanical potential energy formula, and then obtain the total potential energy model using the potential energy model of the two arms.

[0075] Step 3-1: Based on the coordinate vector, determine the potential energy model of the left robotic arm for module docking using the potential energy formula. The specific formula is as follows:

[0076] ;

[0077] in, These are the geometric parameters of the joint links of the left robotic arm, in mm; Acceleration due to gravity, unit m / s² 2 ; The offset of the circumferential rotary joint link of the left robotic arm, in mm;

[0078] Step 3-2: Based on the coordinate vector, determine the potential energy model of the right robotic arm for module docking using the potential energy formula. The specific formula is as follows:

[0079] ;

[0080] in, These are the geometric parameters of the joint links of the right robotic arm, in mm; The offset of the circumferential rotary joint link of the right robotic arm, in mm;

[0081] Step 3-3: Summing up the potential energy model above yields the total potential energy model. : .

[0082] Step 4: Obtain the double-arm Lagrangian function by subtraction based on the total potential energy model and the total kinetic energy model. Substitute the double-arm Lagrangian function into the Lagrangian equation and calculate the derivative to obtain the double-arm dynamic differential equation, that is, the Lagrangian joint dynamic torque model of the double-arm mechanism.

[0083] Step 4-1: Obtain the two-arm Lagrangian function by subtraction based on the total potential energy model and the total kinetic energy model;

[0084] Step 4-2: Substitute the Lagrangian functions of the two arms into the Lagrangian equations and differentiate for each generalized coordinate vector of the two arms to obtain the dynamic differential equations of the two arms. This yields the Lagrangian dynamic models of the left robotic arm joints L1, L2, L3, and L4, as shown in the following equations:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] in, , , These are the acceleration vectors of the left robotic arm joints L1, L2, and L3, respectively. The Lagrangian dynamics model of the left robotic arm joint L1 is shown below. The Lagrangian dynamics model of the left robotic arm joint L2 is shown below. The Lagrangian dynamics model of the left robotic arm joint L3 is shown below. Let L4 be the angular acceleration vector of the left robotic arm joint. The Lagrangian dynamics model of the left robotic arm joint L4;

[0090] Simultaneously, the Lagrangian dynamic models of the right robotic arm joints R1, R2, R3, and R4 are obtained, as shown in the following equations:

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] in, , , These are the acceleration vectors of the right robotic arm joints R1, R2, and R3, respectively. , , These are the Lagrangian dynamic models of right robotic arm joint R1, right robotic arm joint R2, and right robotic arm joint R3, respectively. Let L4 be the angular acceleration vector of the left robotic arm joint. Let L4 be the inertia tensor of the left robotic arm joint. The Lagrangian dynamics model of joint R4 of the left robotic arm;

[0096] Based on the above Lagrange dynamics model, the Lagrange joint dynamics torque model is obtained, as shown in the following equation:

[0097] ;

[0098] in, The masses of each joint of the twin-arm mechanism for docking the modules form a mass matrix. For each joint acceleration matrix, It is a gravity array. This is a model of the joint driving torque of a robot based on Lagrange dynamics.

[0099] The mass array The specific formula is as follows: ;

[0100] The acceleration array of each joint The specific formula is as follows:

[0101] ;

[0102] The gravity array The specific formula is as follows:

[0103] .

[0104] Step 5: Using the coordinate vector, based on the planetary reducer transmission function and the mechanical joint transmission function, and their corresponding transmission ratios, obtain the joint transmission error model of the docking manipulator arm, and obtain the joint transmission error disturbance torque model based on the joint transmission error model of the docking manipulator arm.

[0105] Step 5-1: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear and rack transmission pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the axial translation of the left robotic arm joint;

[0106] The transmission error model of the axial translation joint L1 of the left robotic arm :

[0107] ;

[0108] Where, m g1 Let z be the module of the gear and rack pair. g1 i is the number of teeth. p1 The reduction ratio of the planetary gear reducer. Let x be the magnitude of the k-th order error component. Let j be the magnitude of the error. Let be the initial phase angle of the j-th error component. The phase angle, The harmonic order is... The number of errors. For time, This represents the maximum number of errors.

[0109] Step 5-2: Based on the coordinate vector, according to the planetary reducer transmission error function and the trapezoidal screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the vertical translation of the left robotic arm joint;

[0110] The transmission error model of the vertical translation joint L2 of the left robotic arm :

[0111] ;

[0112] Where P1 is the pitch of the trapezoidal leadscrew; i p2 This refers to the reduction ratio of the planetary gear reducer.

[0113] Step 5-3: Based on the coordinate vector, according to the planetary reducer transmission error function and the ball screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the radial translation of the left robotic arm joint.

[0114] The transmission error model of the left robotic arm radial translation joint L3 :

[0115] ;

[0116] Where P2 is the pitch of the ball screw; i p3 This refers to the reduction ratio of the planetary gear reducer.

[0117] Step 5-4: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the left mechanical arm joint in circular rotation.

[0118] The transmission error model of the L4 circumferential rotation joint of the left robotic arm :

[0119] ;

[0120] Among them, i s i is the gear reduction ratio; p4 This refers to the reduction ratio of the planetary gear reducer.

[0121] Step 5-5: Based on the transmission error model of the left robotic arm joints described above, obtain the transmission error disturbance torque models for the left robotic arm joints L1, L2, L3, and L4. , , , ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] Where, k c1 k represents the meshing stiffness of the gear and rack pair. c2 k represents the axial stiffness of the trapezoidal lead screw pair. c3 r is the axial stiffness of the ball screw pair. c k is the base circle radius of the driven gear in the gear pair; c4 This refers to the meshing stiffness of the gear and rack pair;

[0127] Steps 5-6: Repeat the above steps to obtain the transmission error disturbance torque model of the right robotic arm joints R1, R2, R3, and R4. , , , ;

[0128] Steps 5-7: Based on the disturbance torque models of the left and right robotic arm joints described above, the disturbance torque model of the joint transmission error of the docking double-arm mechanism is obtained.

[0129] Steps 5-7 are specifically shown in the following formula:

[0130] ;

[0131] in, These are the transmission error disturbance torque models for the first, second, third, and fourth left robotic arm joints, respectively. The transmission error disturbance torque models are for the first, second, third, and fourth right robotic arm joints, respectively. This is a model of the disturbance torque of transmission error in the dual-arm joint.

[0132] Step 6: Using the coordinate vectors, determine the joint friction force or friction torque model of the docking double-arm mechanism of the compartment according to the Stribeck friction model;

[0133] The specific model of joint friction force or friction torque of the docking double-arm mechanism of the compartment is determined by the Stribeck friction model, as shown in the following formula:

[0134] ;

[0135] Among them, f c f is the Coulomb friction coefficient. s f is the static friction coefficient. v v is the coefficient of viscous friction. s For Stribeck speed, For joint velocity variables, is the base of the natural logarithm. A model of the joint friction or friction torque of the twin-arm mechanism for docking of the module;

[0136] The frictional force or frictional torque models of the left arm joints L1, L2, L3, and L4 were determined using the Stribeck friction model. , , , The specific formula is as follows:

[0137] ;

[0138] ;

[0139] ;

[0140] ;

[0141] The frictional force or frictional torque models of the right arm joints R1, R2, R3, and R4 were determined using the Stribeck friction model. , , , The specific formula is as follows:

[0142] ;

[0143] ;

[0144] ;

[0145] .

[0146] Step 7: Based on the Lagrange joint dynamic torque model, the joint transmission error disturbance torque model, and the joint friction force or friction torque model, obtain the composite dynamic model of the module docking double arm mechanism;

[0147] The specific formula is as follows:

[0148] ;

[0149] in, A composite dynamic model of the dual-arm mechanism for module docking.

[0150] Example

[0151] To verify the effectiveness of this method, dynamic simulation was performed using MATLAB software, and the characteristics of the dynamic model of the docking double-arm mechanism were analyzed. The specific steps included:

[0152] 1) Set the simulation parameters. The parameters of each joint of the docking double arm mechanism of the compartment are consistent. The dynamic parameters of the axial movement joint are shown in Table 1, the dynamic parameters of the vertical lifting joint are shown in Table 2, the dynamic parameters of the radial movement joint are shown in Table 3, and the dynamic parameters of the circumferential rolling joint are shown in Table 4.

[0153] Table 1. Dynamic parameters of the axially moving joint

[0154] mass / kg 107.87 Coulomb friction coefficient 0.15 static friction coefficient 0.03 coefficient of viscous friction 0.02 Planetary gear reducer reduction ratio 15 Gear and rack pair width / mm 55 Gear and rack module / mm 5 Number of teeth in a gear and rack pair 400 Number of teeth in a gear and rack pair 20 Pitch circle radius of gear and rack pair gear / mm 50

[0155] Table 2. Dynamic parameters of the vertical lifting joint

[0156] mass / kg 49.48 Coulomb friction coefficient 0.16 static friction coefficient 0.08 coefficient of viscous friction 0.04 Planetary gear reducer reduction ratio 64 Trapezoidal lead screw length / mm 800 Trapezoidal lead screw pitch / mm 24 Trapezoidal lead screw nominal diameter / mm 80 Trapezoidal lead screw / mm 24

[0157] Table 3. Dynamic parameters of the radially moving joint

[0158] mass / kg 117.73 Coulomb friction coefficient 0.16 static friction coefficient 0.08 coefficient of viscous friction 0.04 Planetary gear reducer reduction ratio 50 Ball screw length / mm 320 Ball screw pitch / mm 10 Ball screw lead / mm 10 Ball screw nominal diameter / mm 25 Ball screw ball diameter / mm 6.35

[0159] Table 4. Dynamic parameters of the circumferential roll joint

[0160] mass / kg 107.87 Moment of inertia / kgm2 411.26 Coulomb friction coefficient 0.17 static friction coefficient 0.03 coefficient of viscous friction 0.02 Planetary gear reducer reduction ratio 64 gear pair helix angle / ° 0 Gear tooth width / mm 20 Gear module / mm 3 Pitch circle radius of the driving gear in the gear pair / mm 60 Number of teeth of the driving gear in the gear pair 20 Pitch circle radius of driven gear in gear pair / mm 1200 Number of teeth of driven gear in a gear pair 27

[0161] 2) Assume the spatial pose variables of the dual-arm robot system for module docking are: ,in The motion trajectories are respectively the coordinates of the origin of the coordinate system on the left end face of the compartment. These are the attitude motion trajectories of the cabin section at pitch, yaw, and roll angles, respectively.

[0162] Assumptions: Initial position of the module docking system ;Stop pose .

[0163] Combination Figures 4-5 Figures (a)-(c) show the displacement, velocity, and acceleration curves of each joint of the docking manipulator arm, obtained using trajectory planning. Figures 4-5 The robot arm exhibits smooth displacement and velocity trajectories, with changes in control force / torque largely consistent with changes in acceleration. Notably, the vertical lifting joint of the robot arm requires a larger control force because this joint primarily supports the movement of subsequent joints in the direction of gravity, and the total mass of these subsequent joints is substantial, necessitating a greater control force to complete this action. In contrast, the loads borne by other joints mainly originate from joint friction or frictional torque, and their values ​​are relatively smaller.

[0164] 3) Substitute the displacement, velocity, acceleration and other parameters of each joint into the dynamic equation of the docking double arm mechanism of the compartment, and calculate the changes in the transmission error disturbance force / torque of the docking mechanism, the joint friction force / torque and the joint control force / torque.

[0165] Combination Figures 6-7 As shown in Figures (a)-(d), due to the differences in the transmission structure and motion speed of each joint in the dual-arm mechanism for docking the module, the disturbance force and torque generated by the transmission error exhibit significant harmonic characteristics, becoming a crucial factor that cannot be ignored in the precise trajectory control of the module docking robot. This discovery provides a valuable reference for subsequent research on dynamic control methods and control algorithms. Among the three moving joints of the left robotic arm, the vertical lifting joint has the largest peak-to-peak value of the transmission error disturbance force, which is 10.56 N; the radial moving joint has the smallest peak-to-peak value of the transmission error disturbance force, which is 0.1933 N. The peak-to-peak value of the transmission error disturbance force of the circular rotation joint is 0.04068 Nm. The variation trend of the transmission error disturbance force / torque of the right robotic arm joints is similar.

[0166] Combination Figures 8-9 Figures (a)-(d) show that the frictional forces of the axial and radial movement joints of the docking arm mechanism exhibit a semi-trigonometric function-like variation pattern, while the variation patterns of the vertical lifting and circular rotation joints are less clear. It is particularly important to note that the frictional forces of each joint are closely related to the joint's movement speed, showing a similar trend, which inevitably affects the joint's operational state. Among the three movement joints of the left robotic arm, the vertical lifting joint has the largest peak-to-peak frictional force, at 0.3213 N; the radial movement joint has the smallest peak-to-peak frictional force, at 0.0001619 N. The peak-to-peak frictional force of the circular rotation joint is 0.1867 Nm. The frictional force variation trend of the right robotic arm joints is similar.

[0167] Combination Figures 10-11Figures (a)-(d) show that the trends of driving force and torque variation for each joint are basically consistent with the acceleration variation patterns obtained from trajectory planning. It is particularly noteworthy that the vertical lifting joint of the robotic arm requires a relatively large driving force. This is because this joint is mainly used to support the movement of subsequent joints in the direction of gravity, and the total mass of the subsequent joints is large, thus requiring a large driving force to complete this action. In contrast, other joints mainly undertake the task of driving the corresponding joints to move horizontally, bearing smaller loads, and requiring relatively smaller driving forces and torques. However, due to the influence of joint transmission errors and friction, the driving force and torque will exhibit disturbances in local forces and torques. Among the three moving joints of the left robotic arm, the vertical lifting joint has the highest control force and peak fluctuation value, with the maximum control force reaching 2458 N and the peak fluctuation value reaching 10.7 N; the radial moving joint has the lowest control force and peak fluctuation value, with the maximum control force being 0.3026 N and the peak fluctuation value being 0.2858 N. The circular rotation joint has a maximum control force of 0.826 Nm and a peak fluctuation value of 1.89 Nm. The trend of frictional force changes at the joints of the right robotic arm is similar.

[0168] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0169] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic modeling method for a dual-arm mechanism for module docking, characterized in that, Includes the following steps: Step 1: Define the generalized coordinate vector of the docking double-arm mechanism of the module; Step 2: Based on the coordinate vector, determine the joint kinetic energy model of the double-arm mechanism using the mechanical kinetic energy formula, obtain the kinetic energy model of the double arms based on the joint kinetic energy, and then obtain the total kinetic energy model using the kinetic energy model of the double arms. Step 3: Based on the coordinate vector, determine the potential energy model of the two arms using the mechanical potential energy formula, and then obtain the total potential energy model using the potential energy model of the two arms. Step 4: Construct the Lagrange function by subtraction based on the total kinetic energy model and the total potential energy model, and differentiate the Lagrange function through the Lagrange equation to obtain the Lagrange joint dynamic torque model; Step 5: Using the coordinate vector, based on the planetary reducer transmission error function and the mechanical joint transmission error function, and their corresponding transmission ratio, obtain the joint transmission error model of the docking manipulator arm, and obtain the joint transmission error disturbance torque model based on the joint transmission error model of the docking manipulator arm. Step 6: Using the coordinate vectors, determine the joint friction force or friction torque model of the docking double-arm mechanism of the compartment according to the Stribeck friction model; Step 7: Based on the Lagrange joint dynamic torque model, the joint transmission error disturbance torque model, and the joint friction force or friction torque model, sum to obtain the composite dynamic model of the docking double arm mechanism of the compartment.

2. The dynamic modeling method for a dual-arm mechanism for module docking according to claim 1, characterized in that, The module docking dual-arm mechanism includes a left robotic arm, a right robotic arm, and a base. The left and right robotic arms jointly support the module components and realize the spatial orientation adjustment function of the module components. The single robotic arm consists of movable joints and rotary joints. The movable joints include axial movable joints, vertical lifting joints, and radial movable joints. The rotary joints include circumferential rolling joints. The axial movement joint transmission system includes a gear and rack pair and a planetary reducer; the vertical lifting joint transmission system includes a trapezoidal screw pair and a planetary reducer; the radial movement joint includes a ball screw pair and a planetary reducer; and the circumferential rolling joint includes a gear pair and a planetary reducer.

3. The dynamic modeling method for a module docking double-arm mechanism according to claim 2, characterized in that, Based on the structure of the docking double-arm mechanism of the aforementioned module, its generalized coordinate vector is defined as follows: ； in, , The position of the axial translation joints of the left and right robotic arms. , The vertical translation joint positions of the left and right robotic arms. , The radial translation joint positions of the left and right robotic arms. , The angle of the rolling joints of the left and right robotic arms.

4. The dynamic modeling method for a dual-arm mechanism for module docking according to claim 3, characterized in that, Step 2 includes the following steps: Step 2-1: Based on the coordinate vector, determine the kinetic energy models of the axial translation joint, vertical translation joint, and radial translation joint of the left robotic arm according to the kinetic energy formula of the translation joint; Step 2-2: Determine the kinetic energy model of the left robotic arm's circular rotation joint based on the kinetic energy formula of the rotation joint; Steps 2-3: Summing up the joint kinetic energy model of the left robotic arm based on the above kinetic energy model; Step 2-4: Repeat steps 2-1 to 2-3 above to obtain the joint kinetic energy model of the right robotic arm; Steps 2-5: Obtain the total kinetic energy model by summing the joint kinetic energy models of the left and right robotic arms.

5. The dynamic modeling method for a dual-arm mechanism for module docking according to claim 4, characterized in that, Step 3 includes the following steps: Step 3-1: Based on the coordinate vector, determine the potential energy model of the left robotic arm for docking the module using the potential energy formula; Step 3-2: Based on the coordinate vector, determine the potential energy model of the right robotic arm for docking the module using the potential energy formula; Step 3-3: Summing up the potential energy model above yields the total potential energy model.

6. The dynamic modeling method for a module docking double-arm mechanism according to claim 5, characterized in that, Step 4 includes the following steps: Step 4-1: Obtain the two-arm Lagrangian function by subtraction based on the total potential energy model and the total kinetic energy model; Step 4-2: Substitute the Lagrangian functions of the two arms into the Lagrangian equations and differentiate for each generalized coordinate vector of the two arms to obtain the dynamic differential equation of the two arms, which is the Lagrangian dynamic torque model of the two-arm mechanism.

7. The dynamic modeling method for a module docking double-arm mechanism according to claim 6, characterized in that, The Lagrange joint dynamic moment model in step 4-2 is shown in the following equation: ； in, The masses of each joint of the twin-arm mechanism for docking the modules form a mass matrix. For each joint acceleration matrix, It is a gravity array. It is a Lagrange dynamics model.

8. The dynamic modeling method for a module docking double-arm mechanism according to claim 7, characterized in that, Step 5 includes the following steps: Step 5-1: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear and rack transmission pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the left robotic arm axial translation joint; Step 5-2: Based on the coordinate vector, according to the planetary reducer transmission error function and the trapezoidal screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the vertical translation joint of the left robotic arm; Step 5-3: Based on the coordinate vector, according to the planetary reducer transmission error function and the ball screw pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the radial translation joint of the left robotic arm; Step 5-4: Based on the coordinate vector, according to the planetary reducer transmission error function and the gear pair transmission error function, and their corresponding transmission ratio, obtain the transmission error model of the left robotic arm's circumferential rotary joint. Step 5-5: Based on the transmission error model of the left robotic arm joints described above, obtain the transmission error disturbance torque model of all joints of the left robotic arm. Steps 5-6: Repeat the above steps to obtain the transmission error disturbance torque model of all joints of the right robotic arm; Steps 5-7: Based on the disturbance torque models of all joints of the left and right robotic arms, the disturbance torque model of the joint transmission error of the docking double-arm mechanism is obtained.

9. The dynamic modeling method for a module docking double-arm mechanism according to claim 8, characterized in that, Steps 5-7 are specifically shown in the following formula: ； in, The transmission error disturbance torque models are for the first, second, third, and fourth left robotic arm joints, respectively. The transmission error disturbance torque models are for the first, second, third, and fourth right robotic arm joints, respectively. This is a model of the disturbance torque of the joint transmission error in a dual-arm mechanism.

10. The dynamic modeling method for a dual-arm mechanism for module docking according to claim 1, characterized in that, Step 6 is specifically shown in the following formula: ； Among them, f c f is the Coulomb friction coefficient. s f is the static friction coefficient. v v is the coefficient of viscous friction. s For Stribeck speed, For joint velocity variables, is the base of the natural logarithm. This is a model of joint friction or friction torque in a dual-arm mechanism.

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