A method for generating a tri-branched robot configuration

Abstract

This invention provides a method for generating a three-branch robot configuration, comprising: generating a contact impulse solution model for the gripping truss of the three-branch robot based on the truss structure and the kinematic and dynamic equations of the three-branch robot; determining a performance evaluation index for the gripping configuration of the three-branch robot based on the contact collision impulse solution model and the truss smooth climbing task requirements; generating a multi-objective gripping configuration optimization model for the three-branch robot based on the gripping configuration performance evaluation index, wherein the multi-objective gripping configuration optimization model is used to output the optimal gripping configuration for smooth truss climbing of the three-branch robot based on the input gripping points; and performing an effectiveness test on the optimal gripping configuration for smooth truss climbing to obtain the test result of the multi-objective gripping configuration optimization model.

Description

Technical Field

[0001] This invention relates to the field of space robot technology, and in particular to a method for generating a three-branch robot configuration. Background Technology

[0002] With the development of aerospace technology and in-depth exploration of the space environment, large spacecraft such as large-aperture space telescopes and space solar power stations, due to their complex technical systems and diverse functional modules, are capable of performing a variety of tasks and operations, and have gradually become indispensable key equipment in space activities. The main structure of large spacecraft typically adopts a large-span, lightweight, and low-damping space truss structure. During the assembly process, this structure faces the challenge of long-distance and stable on-orbit transportation of various loads, including truss members, truss sections, and functional modules.

[0003] Currently, on-orbit transport and assembly tasks are mainly performed by astronauts. However, astronauts' extravehicular activities pose high safety risks and are ill-suited to handling a large number of demanding on-orbit tasks. In contrast, space robots possess strong operational capabilities, simple energy supply, and the ability to maintain stable on-orbit operation for extended periods. They can efficiently, economically, and safely replace astronauts in performing on-orbit transport and assembly tasks. In particular, to balance payload carrying and climbing requirements, designing multi-branched space robots has become an effective solution. Three-branched robots, as the simplest form of multi-branched robots, not only possess the ability to carry payloads and climb but also effectively avoid increasing system complexity due to excessive branches, making them an ideal configuration for solving on-orbit transport and assembly tasks for large spacecraft.

[0004] Due to the high flexibility and low damping characteristics of large spacecraft truss structures, the gripping configuration of a three-branch robot during load-bearing climbing can easily induce time-varying dynamic vibrations in the truss structure. This can affect the stability of the load transfer process and even threaten the safety of the spacecraft structure and load. Therefore, optimizing the gripping configuration when the three-branch robot contacts the truss is essential to ensure stable load-bearing climbing of the truss over a wide range. Current research on space robot configuration optimization mainly focuses on single-arm and dual-arm robots, primarily addressing optimization indicators such as minimum degrees of freedom, dexterity, fault tolerance, and maneuverability. However, optimizing the gripping configuration for stable load-bearing climbing of multi-branch robots remains a pressing issue. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a method for generating a three-branch robot configuration, which comprehensively considers the influence of the configuration of each branch on the gripping effect, so as to improve the three-branch robot's ability to climb with load.

[0006] This invention provides a method for generating a three-branch robot configuration, comprising:

[0007] Based on the truss structure and the kinematic and dynamic equations of the three-branch robot, a solution model for the contact impulse of the gripping truss of the three-branch robot is generated.

[0008] Based on the contact collision impulse solution model and the truss smooth climbing task requirements, the performance evaluation index of the gripping configuration of the three-branch robot is determined.

[0009] Based on the performance evaluation index of the gripping configuration, a multi-objective gripping configuration optimization model for the three-branch robot is generated. The multi-objective gripping configuration optimization model is used to output the optimal gripping configuration for the smooth climbing of the gantry of the three-branch robot based on the input gripping points.

[0010] The above method further includes:

[0011] The effectiveness of the optimal gripping configuration for smooth truss climbing is tested to obtain the test results of the multi-objective gripping configuration optimization model.

[0012] In the above method, based on the truss structure and the kinematic and dynamic equations of the three-branch robot, a solution model for the contact impulse of the gripping truss of the three-branch robot is generated, including:

[0013] The kinematic and dynamic equations are obtained as follows:

[0014]

[0015] Where M is the mass matrix of the three-branch robot, q, These represent the angles, angular velocities, and angular accelerations of each joint of the three-branch robot, respectively. C represents the nonlinear term of the three-branch robot, J1 is the generalized Jacobian matrix corresponding to the climbing arm, J2 is the generalized Jacobian matrix corresponding to the load arm, F1 represents the external force and torque acting on the gripper at the end of the climbing branch, and F2 represents the external force and torque acting on the gripper at the end of the load arm.

[0016] For the instantaneous process of the three-branch robot climbing and grasping the space truss, the end of the climbing arm will make contact and collision when grasping the truss. According to the kinematic and dynamic equations, integrating over the entire collision process δt, we get:

[0017]

[0018] Where t0 is the instant before the collision. Since the displacement, velocity, and load force are finite quantities during the collision, when δt→0, we get:

[0019]

[0020] Where p represents the external impact impulse generated at the point of contact at the moment of grasping, i.e.

[0021] The expression for obtaining the generalized joint angular velocity increment of a three-branch robot is as follows:

[0022]

[0023] The velocity increment at the collision point at the end of the three-branch robot climbing arm is obtained as follows:

[0024] δv1=J1M -1 J1 T p

[0025] When a three-branch robot encounters a contact collision while gripping a truss, the direction of the collision impulse is always along the normal direction n of the contact point. Therefore:

[0026]

[0027] Among them, J t M is the truss Jacobian matrix. t Let v be the truss mass matrix. t v1 is the velocity of the truss relative to the inertial coordinate system at the time of collision, and e (0 < e < 1) is the collision recovery coefficient.

[0028] The collision impulse p is represented as a scalar p and the unit action direction vector n∈R. 6 The product of, i.e.:

[0029] p = pn

[0030] Obtain the contact collision impulse solution model when the three-branch robot climbing arm grasps the truss:

[0031]

[0032] In the above method, based on the contact collision impulse solution model and the truss smooth climbing task requirements, the performance evaluation index of the gripping configuration of the three-branch robot is determined, including:

[0033] Based on the contact collision impulse solution model, the velocity increment generated by the contact collision at the end of the three-branch robot climbing arm is obtained, namely:

[0034] δv1=J1M -1 J1 T p

[0035] Based on the contact collision impulse solution model, the velocity increment caused by the contact collision between the end of the three-branch robot's load arm and the climbing arm is obtained, namely:

[0036] δv2=J2M -1 J1 T p

[0037] Among them, the value of δv1 reflects the degree of velocity fluctuation at the end of the climbing arm when the gripping truss collides, and the value of δv2 reflects the degree of velocity fluctuation at the end of the load arm when the gripping truss collides. The values ​​of δv1 and δv2 are directly proportional to the velocity fluctuation at the end of the branches when the three-branch robot grips the truss.

[0038] Under the condition that the two speed increments are minimized in the task requirement information of smooth truss climbing, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. The performance evaluation index of the gripping configuration includes: motion stability evaluation index, which is expressed as the end-effector speed increment of the climbing arm and the load arm generated when gripping the truss, that is:

[0039] f1=ζ1||δv1||+ζ2||δv2||

[0040] Where ||·|| represents the norm of the vector, and ζ1 and ζ2 are weighting factors used to characterize the influence of the velocity fluctuations at the ends of the climbing arm and the load arm on the climbing motion of the loaded truss.

[0041] In the above method, based on the contact collision impulse solution model and the truss smooth climbing task requirements, the performance evaluation index of the gripping configuration of the three-branch robot is determined, including:

[0042] Based on the contact collision impulse solution model, the formula for calculating the center of mass of the three-branch robot is as follows:

[0043]

[0044] Where M1, M2, and M3 are the total masses of the three branches of the three-branch robot, respectively; m 1,i m 2,j m 3,k The masses of the joint links of the robot's three branches are r, respectively. 1,i r 2,j r 3,k These are the radius vectors of the mass points of each joint link of the robot's three branches relative to the origin O;

[0045] The requirement for a stable truss climbing task is that the center of mass of the three-branch robot should be as low as possible and closer to the side to be gripped when gripping the truss. Based on the center of mass calculation formula, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. This performance evaluation index includes a gripping balance evaluation index, which is expressed as the offset of the robot's center of mass relative to the gripping points of the two trusses during the truss gripping process.

[0046] f2=λ1||r σ -r1||+λ2||r σ -r2||

[0047] Where r1 and r2 are the coordinates of the two gripping points of the climbing branch when the robot grips the truss during the climbing process, and λ1 and λ2 are the weighting factors of the robot's center of mass biased towards the two gripping points, respectively, with λ1 < λ2.

[0048] In the above method, based on the contact collision impulse solution model and the truss smooth climbing task requirements, the performance evaluation index of the gripping configuration of the three-branch robot is determined, including:

[0049] Based on the contact collision impulse solution model, the determinant of the product of the Jacobian matrix and its transpose is obtained, i.e.

[0050]

[0051] Where ω is the operability metric, det() is the determinant of the square matrix, J(q) is the Jacobian matrix, and J T (q) is the transpose of the Jacobian matrix, σ i Let m be the singular values ​​of the Jacobian matrix J(q), and m be the matrix J(q)J T The larger the value of the operability index ω, the better the flexibility of each branch of the three-branch robot. When ω = 0, the robotic arm is in a singular position.

[0052] Based on the determinant, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. The performance evaluation index of the gripping configuration of the three-branch robot includes an operability evaluation index, namely:

[0053]

[0054] In the formula, κ1 and κ2 are the weighting factors of the operability evaluation index of the climbing arm and the load arm, respectively.

[0055] In the above method, a multi-objective gripping configuration optimization model for a three-branch robot is generated based on the gripping configuration performance evaluation index, including:

[0056] The constraints for constructing a multi-objective gripping configuration optimization model include joint angle constraints, reachability constraints, and vertical constraints.

[0057] A decision variable based on the angles of each joint is established; the decision variables are selected as follows:

[0058] x=[θ1,θ2,…,θ 14 ,θ 8' ,θ 9' ,…,θ 14' ]

[0059] Where, θ i The angles of each joint of the three-branch robot;

[0060] Based on the performance evaluation indicators of the gripping configuration, the decision variables, and the constraints, a multi-objective gripping configuration optimization model for the three-branch robot is established. This model optimizes motion stability, gripping balance, and operability by minimizing the objective function.

[0061]

[0062] Where f(x) is the objective function and x is the decision variable.

[0063] In the above method, the joint angle constraint conditions are as follows:

[0064] |θ i |≤|θ imax |=180°

[0065] In the formula, θ i Let θ be the angle of the i-th joint. imax Let be the maximum rotation angle of the i-th joint.

[0066] In the above method, the reachability constraint conditions are as follows:

[0067] ||T i -T c ||≤ε p

[0068] Where T i To optimize the actual end-effector position of the three-branch robot climbing arm obtained from the kinematic derivation of the joint angle overcorrection process, T c For the target gripping position of the end effector of the climbing arm in a truss-loaded climbing task, ε p This is the allowable error.

[0069] In the above method, the effectiveness detection of the optimal gripping configuration for smooth truss climbing includes:

[0070] Four sets of gripping angle ranges were determined, including: 0–90°, 90–180°, 180–270°, and 270–360°;

[0071] Based on the optimal gripping configurations for smooth truss climbing that are not optimized and the optimal gripping configurations for smooth truss climbing that are optimized within the four groups of gripping angles, the test results of each optimal gripping configuration for smooth truss climbing on multiple specified optimization indicators are obtained, and the effectiveness of the optimal gripping configuration for smooth truss climbing is tested.

[0072] The three-branch robot configuration generation method designed in this embodiment of the invention effectively solves the problems of lack of consideration for the impact of contact collisions, single optimization index, and incomplete consideration of constraints in the traditional configuration generation process. It significantly improves the gripping configuration optimization effect of the three-branch robot in the process of stable climbing of the truss, and provides more comprehensive and efficient technical support for the application of the three-branch robot in complex truss environments. Attached Figure Description

[0073] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0074] Figure 1 This is an operation flowchart provided in the embodiments of the present invention;

[0075] Figure 2 This is a schematic diagram of the initial configuration and link coordinate system of the three-branch robot used in this embodiment of the invention;

[0076] Figure 3 This is a schematic diagram of a large spacecraft truss unit in an embodiment of the present invention;

[0077] Figure 4 This is a flowchart of the multi-objective optimization process for the three-branch robot grasping configuration in an embodiment of the present invention;

[0078] Figure 5 This is a surface plot showing the distribution of the optimization target value for the Pareto front configuration of the three-branch robot in this embodiment of the invention.

[0079] Figure 6 This is a distribution diagram of the gripping angles corresponding to the Pareto front optimization configuration of the three-branch robot in this embodiment of the invention. Detailed Implementation

[0080] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0081] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0082] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for generating a three-branch robot configuration, which includes the following steps:

[0083] Step 101: Based on the truss structure and the kinematic and dynamic equations of the three-branch robot, generate a solution model for the contact impulse of the gripping truss of the three-branch robot.

[0084] Specifically, by combining the kinematic equations, the dynamic equations of the three-branch robot can be derived as follows:

[0085]

[0086] Where M is the mass matrix of the three-branch robot, q, Let J1 represent the angle, angular velocity, and angular acceleration of each joint of the three-branch robot, respectively. Let C represent the nonlinear terms of the three-branch robot, including Coriolis force and centrifugal force terms. Let J1 be the generalized Jacobian matrix corresponding to the climbing arm, and J2 be the generalized Jacobian matrix corresponding to the load arm. Let F1 represent the external force and torque acting on the gripper at the end of the climbing branch, and F2 represent the external force and torque acting on the gripper at the end of the load arm. The generalized force / torque of the three-branch robot can be expressed as τ = [τ1, τ2, ..., τ]. 14 ,τ 8' ,τ 9' ,…,τ 14' ] T ;

[0087] For the instantaneous process of the three-branch robot climbing and grasping the space truss, the end of the climbing arm will make contact and collision when grasping the truss. According to the kinematic and dynamic equations, integrating over the entire collision process δt, we get:

[0088]

[0089] Where t0 is the instant before the collision. Since the displacement, velocity, and load force are finite quantities during the collision, when δt→0, we get:

[0090]

[0091] Where p represents the external impact impulse generated at the point of contact at the moment of grasping, i.e.

[0092] Due to the complexity of the collision mechanism and the difficulty in accurately measuring the collision time, the collision impulse *p* is used to describe the magnitude of the collision effect. Therefore, the expression for the generalized joint angular velocity increment of the three-branch robot is obtained as follows:

[0093]

[0094] The velocity increment at the collision point at the end of the three-branch robot climbing arm is obtained as follows:

[0095] δv1=J1M -1 J1 Tp

[0096] When a three-branch robot encounters a contact collision while gripping a truss, ignoring the friction on the contact surfaces, and assuming the direction of the collision impulse is always along the normal direction n at the contact point, we obtain:

[0097]

[0098] Among them, J t M is the truss Jacobian matrix. t Let v be the truss mass matrix. t v1 is the velocity of the truss relative to the inertial coordinate system at the time of collision, and e (0 < e < 1) is the collision recovery coefficient.

[0099] The collision impulse p can be expressed as a scalar p and the unit action direction vector n∈R 6 The product of, i.e.:

[0100] p = pn

[0101] Obtain the contact collision impulse solution model when the three-branch robot climbing arm grasps the truss:

[0102]

[0103] In this solution model, the velocity at the moment of collision and the magnitude of the collision impulse are decoupled. Given the relative velocity at which the end of the climbing arm contacts the truss, the magnitude of the collision impulse depends only on the configuration of the three-branch robot.

[0104] Step 102: Based on the contact collision impulse solution model and the truss smooth climbing task requirements, determine the performance evaluation index of the gripping configuration of the three-branch robot.

[0105] (1) Evaluation index of motion stability

[0106] Specifically, based on the contact collision impulse solution model, the velocity increment generated by the contact collision at the end of the three-branch robot climbing arm is obtained, i.e.:

[0107] δv1=J1M -1 J1 T p

[0108] Based on the contact collision impulse solution model, the velocity increment caused by the contact collision between the end of the three-branch robot's load arm and the climbing arm is obtained, namely:

[0109] δv2=J2M -1 J1 T p

[0110] Wherein, the value of δv1 reflects the degree of velocity fluctuation at the end of the climbing arm during the truss collision, and the value of δv2 reflects the degree of velocity fluctuation at the end of the load arm during the truss collision. The values ​​of δv1 and δv2 are directly proportional to the velocity fluctuations at the end of the branches when the three-branch robot grasps the truss. Therefore, to reduce the impact of grasping contact collisions on the velocity fluctuations at the end of the three-branch robot and thus improve motion stability, under the condition that the two velocity increments are minimized in the truss smooth climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is obtained. The grasping configuration performance evaluation index includes: a motion stability evaluation index, expressed as the velocity increments at the end of the climbing arm and load arm generated during truss grasping, i.e.:

[0111] f1=ζ1||δv1||+ζ2||δv2||

[0112] Where ||·|| represents the norm of the vector, and ζ1 and ζ2 are weighting factors used to characterize the influence of the velocity fluctuations at the ends of the climbing arm and the load arm on the climbing motion of the loaded truss.

[0113] (2) Grasp the balance evaluation indicators

[0114] Specifically, when a three-branch robot grips a truss, properly arranging the robot's center of mass is crucial for maintaining balance and stability during loaded climbing motion. Based on the contact collision impulse solution model, the formula for calculating the center of mass of the three-branch robot is as follows:

[0115]

[0116] Where M1, M2, and M3 are the total masses of the three branches of the three-branch robot, respectively; m 1,i m 2,j m 3,k The masses of the joint links of the robot's three branches are r, respectively. 1,i r 2,j r 3,k These are the radius vectors of the mass points of each joint link of the robot's three branches relative to the origin O;

[0117] The requirement for a smooth truss climbing task is that the center of gravity of the three-branch robot should be as low as possible and closer to the side to be gripped when it grasps the truss. Based on the center of gravity calculation formula, the performance evaluation index of the three-branch robot's gripping configuration is obtained. This performance evaluation index includes a gripping balance evaluation index, which is expressed as the offset of the three-branch robot's center of gravity relative to the gripping points of the two trusses during the truss gripping process.

[0118] f2=λ1||r σ -r1||+λ2||r σ -r2||

[0119] Where r1 and r2 are the coordinates of the two gripping points of the climbing branch when the robot grips the truss during the climbing process, and λ1 and λ2 are the weighting factors of the robot's center of mass biased towards the two gripping points, respectively, with λ1 < λ2.

[0120] (3) Operability evaluation indicators

[0121] Specifically, the determinant of the product of the Jacobian matrix and its transpose is defined as a measure of operability, i.e.

[0122]

[0123] Where ω is the operability metric, det() is the determinant of the square matrix, J(q) is the Jacobian matrix, and J T (q) is the transpose of the Jacobian matrix, σ i Let m be the singular values ​​of the Jacobian matrix J(q), and m be the matrix J(q)J T The larger the value of the operability index ω, the better the flexibility of each branch of the robot. When ω = 0, the robotic arm is in a singular position.

[0124] Based on the determinant and the contact collision impulse solution model, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. The performance evaluation index of the gripping configuration of the three-branch robot includes an operability evaluation index, namely:

[0125]

[0126] Wherein, κ1 and κ2 are the weighting factors of the operability evaluation index of the climbing arm and the load arm, respectively.

[0127] Step 103: Based on the performance evaluation index of the gripping configuration, generate a multi-objective gripping configuration optimization model for the three-branch robot, including:

[0128] (1) Constraints for constructing a multi-objective gripping configuration optimization model

[0129] The constraints include joint angle constraints, reachability constraints, and vertical constraints:

[0130] ① Joint angle constraint

[0131] Based on the mechanical structure, internal wiring layout, and installation location of the three-branch robot, joint angle constraints are established for the joint motion range of each branch to limit its movement space. For the three-branch robot studied in this patent, the joint angle constraints for each branch are as follows:

[0132] |θ i |≤|θ imax |=180°

[0133] Where, θ i Let θ be the angle of the i-th joint. imax The maximum rotation angle of the i-th joint;

[0134] ② Reachability constraints

[0135] Reachability constraints are one of the fundamental requirements for optimizing the gripping configuration of a three-branch robot in a space truss climbing task. It ensures that the optimized configuration enables the robot's end effector to reach the target gripping point. This patent uses the difference between the actual end effector position and the desired position of the robot's actual configuration as the reachability constraint, as shown below:

[0136] ||T i -T c ||≤ε p

[0137] Where T i To optimize the actual end-effector position of the three-branch robot climbing arm obtained from the kinematic derivation of the joint angle overcorrection process, T c For the target gripping position of the end effector of the climbing arm in a truss-loaded climbing task, ε p This is the allowable error.

[0138] ③ Vertical constraint

[0139] Based on the characteristics of the end effector and truss of the three-branch robot, in order to ensure the stability and reliability of the gripping, the robot needs to ensure that the gripper's posture is perpendicular to the truss member being gripped.

[0140] (2) Establish decision variables based on the angles of each joint; the decision variables are selected as follows:

[0141] x=[θ1,θ2,…,θ 14 ,θ 8' ,θ 9' ,…,θ 14' ]

[0142] Where, θ i The angles of each joint of the three-branch robot;

[0143] (3) Based on the performance evaluation index of the gripping configuration, the decision variables, and the constraints, a multi-objective gripping configuration optimization model for the three-branch robot is established. The multi-objective gripping configuration optimization model optimizes motion stability, gripping balance, and operability by minimizing the optimization objective function.

[0144]

[0145] Where f(x) is the objective function and x is the decision variable.

[0146] The multi-objective gripping configuration optimization model is used to output the optimal gripping configuration for the smooth gantry climbing of the three-branch robot based on the input gripping points.

[0147] Step 104: Perform an effectiveness test on the optimal gripping configuration for smooth truss climbing to obtain the test results of the multi-objective gripping configuration optimization model.

[0148] Because three-branch robots have a large number of joints, solving the kinematic position-level inverse kinematics is quite difficult. However, by setting different starting poses of the end effector of the climbing branch and different gripping angles of the given gripping point, a straight-line path planning in Cartesian space can be performed on the three-branch robot. The robot's generalized Jacobian matrix can be inverted, the joint angular velocities can be solved based on the end effector velocity, and the next joint angle can be obtained by integrating the joint angular velocities. Thus, the gripping configuration corresponding to different gripping angles can be obtained by using the velocity-level inverse kinematics method.

[0149] Four gripping angle ranges were determined, including: 0–90°, 90–180°, 180–270°, and 270–360°. Based on the optimal gripping configuration for smooth truss climbing without optimization and the optimal gripping configuration for smooth truss climbing within the four gripping angle ranges, the test results of each optimal gripping configuration for smooth truss climbing on multiple specified optimization indicators were obtained, and the effectiveness of the optimal gripping configuration for smooth truss climbing was tested.

[0150] The method for generating a three-branch robot configuration was simulated according to the method provided in the embodiments of the present invention.

[0151] The three-branch robot model used in this embodiment is as follows: Figure 2 As shown, the robot consists of three branches, each containing 7 rotational joints and a total of 21 degrees of freedom. Three grippers are located at the ends of each branch. Table 1 shows the initial DH parameters of the three-branch robot.

[0152] Table 1 DH Parameters of the Three-Branch Robot

[0153]

[0154]

[0155] Based on the contact collision impulse solution model of the three-branch robot gripping truss and the task requirements for smooth truss climbing, the performance evaluation indicators of motion stability, gripping balance, and maneuverability of the gripping configuration are determined. Using MATLAB as the foundation, according to... Figure 4 The optimization algorithm flow shown is used to conduct simulation experiments on the optimization of the NSGA-II multi-target grasping configuration.

[0156] Large spacecraft truss units, such as Figure 3 As shown in Table 2, the relevant parameters of the truss and robot are as follows:

[0157] Table 2. Parameters related to spacecraft trusses and robots

[0158]

[0159]

[0160] A reference coordinate system is constructed with the gripping point at the end of branch 1 as the origin when the three-branch robot grips the target truss. At this time, the pose of the gripper at the end of branch 1 is p1 = [0m, 0m, 0m, 0°, 0°, 0°], where the first three terms of the vector represent the end position and the last three terms represent the end pose, that is, the angles of rotation around the x, y, and z axes, respectively. The expected pose of the three-branch robot climbing the end of branch 2 (end of branch 2) is p2 = [0m, 0m, -2.5m, 0°, r°, 0°], where r is the angle of rotation around the truss when the gripper at the end of the climbing branch grips the truss.

[0161] To reduce algorithm complexity and improve optimization efficiency, and considering that different situations during handling may impose different limitations on the truss gripping angle, the range of the gripping angle r is divided into four intervals: [0°, 90°), [90°, 180°), [180°, 270°), and [270°, 360°). Then, multi-objective optimization is performed for each interval to obtain the optimal configuration and corresponding gripping angle within each interval. The multiple performance evaluation index values ​​corresponding to the obtained optimized configuration are then normalized to eliminate dimensional differences caused by different units and data scales, thereby obtaining the globally optimal configuration and corresponding gripping angle.

[0162] like Figure 4As shown, the configuration optimization process begins by creating an initial population representing the robot configuration. Then, a simulated binary crossover operator (SBX operator) is used to perform crossover operations on the population, followed by a polynomial mutation operator to generate a new offspring population. After generating offspring and before any genetic operations, each configuration is verified to meet various constraints, including whether the robot can reach the specified task point and whether the joint angles are within the allowed rotation range. Configurations that do not meet the constraints are marked as infeasible and excluded from subsequent genetic operations. Configurations that meet the constraints are then evaluated by non-dominated sorting and crowding calculation using the objective function. Based on the sorting results, superior offspring individuals are selected to combine with their parents to form the next generation population, and subsequent iterative cycles are performed until the set number of iterations is reached. For the NSGA-II multi-objective genetic optimization algorithm, real-number encoding is used, and binary tournament selection is employed. Specific parameters are shown in Table 3 below.

[0163] Table 3 Parameter settings for NSGA-II multi-objective optimization algorithm

[0164]

[0165]

[0166] After the simulation program is initialized, it is run to perform multi-objective configuration optimization of the truss gripping using the NSGA-II algorithm. The specific optimization process is as follows: Figure 4 As shown, after gen=100 iterations, the final simulation result is as follows. Figure 5 As shown, the 3D surface fitted by the scatter plot in the figure is the Pareto front of the multi-objective optimization results. The three coordinate axes in the figure represent the three objective functions of the configuration optimization. It can be seen that the distribution of the Pareto front solution set roughly presents an expanding surface, which extends from a position near the origin towards the three objective axes. However, due to the mutual constraints between the objective functions, the front does not reach the origin. This distribution characteristic shows the balance state of the optimization solution among the three objective dimensions, reflecting the inevitable trade-offs in the multi-objective optimization process, which is consistent with the theory and further verifies the rationality of the optimization process.

[0167] Simultaneously, the gripping angle distribution corresponding to the Pareto front configuration solution set for each gripping angle interval is obtained, as follows: Figure 6As shown in the figure, the optimal gripping angles for each interval are concentrated in 10–25°, 145–165°, 190–210°, and 345–360°, respectively. This indicates that the gripping angles have converged through the configuration optimization algorithm, verifying the effectiveness of the algorithm. Furthermore, when the gripping angles in a certain interval are not suitable for the current large spacecraft climbing mission requirements, this optimization method provides more references and options.

[0168] To obtain the optimal solution for the Pareto front, the magnitude of the normalized performance evaluation index value corresponding to each configuration and the error of the corresponding end pose were comprehensively considered. A comprehensive evaluation index was constructed by weighted summation of the index value and the error to measure the overall performance of the current mission configuration. Then, the configuration with the smallest comprehensive evaluation index value in each solution set was taken as the optimal configuration for that set. The specific results are shown in Table 4 below.

[0169] Table 4 Optimization results of each group's optimal configuration

[0170]

[0171] Without considering environmental collisions and gripping angle constraints, the configuration with the smallest normalized comprehensive index is selected as the optimal configuration for the current loaded climbing gripping task. The gripping angle corresponding to this optimal configuration is 199.26°, and the angles of each joint are shown in Table 5 below.

[0172] Table 5. Joint Angles Corresponding to Optimal Configurations

[0173]

[0174] As shown in Table 4, although this optimal configuration is not the best in terms of index f1 compared to the other three groups, it has significant advantages in indices f2 and f3. Specifically, index f2 is 9.76% higher than group 1, 17.03% higher than group 2, and 16.09% higher than group 4. The optimal configuration is particularly outstanding in index f3, which is 61.69% higher than group 1, 41.90% higher than group 2, and 36.55% higher than group 4. This trade-off results in the configuration corresponding to the third group having the smallest comprehensive evaluation index, making it the optimal configuration. Calculations show that this configuration achieves significant improvements in various performance evaluation indices while satisfying accessibility constraints, joint constraints, and vertical constraints, thus demonstrating the feasibility of the configuration optimization model to some extent.

[0175] Next, the effectiveness of the optimal gripping configuration for smooth climbing of the truss is tested. By setting different starting poses of the end gripper of the climbing branch and different gripping angles of the given gripping point, the three-branch robot is planned in Cartesian space straight path. The robot's generalized Jacobian matrix is ​​inverted, the joint angular velocity is solved based on the end velocity, and the next joint angle is obtained by integrating the joint angular velocity, thus obtaining the gripping configuration corresponding to different gripping angles.

[0176] Next, four sets of control experiments were set up, covering the comparison and analysis of unoptimized and optimized configurations within the gripping angle ranges of 0–90°, 90–180°, 180–270°, and 270–360°. For the unoptimized configurations, in each range, we selected the mean of the convergence intervals of each gripping angle obtained by the above-mentioned optimization algorithm as the target gripping angle, and then obtained the target configuration through Cartesian space path planning. For the optimized configurations, we selected the configuration corresponding to the minimum value of the normalized comprehensive evaluation index in each of the above ranges as the optimal configuration for the current range, and analyzed and compared the numerical performance of each configuration on multiple specified performance evaluation indicators. The specific results are shown in Table 6.

[0177] Table 6 Results of the control experiment

[0178]

[0179] As shown in Table 6, for each gripping angle range, the optimized configuration significantly improved upon the unoptimized configuration in each optimized index. For the range corresponding to the optimal configuration (180–270° group), the optimized configuration achieved an index f1 of 0.1073, a 41.21% improvement compared to the unoptimized configuration's 0.1825, indicating stronger motion stability and less disturbance when contacting the collision truss. Furthermore, the optimized configuration achieved an index f2 of 1.4894, a 57.60% improvement compared to the unoptimized configuration's 3.5128, demonstrating stronger climbing balance and improved task efficiency. Finally, the optimized configuration achieved an index f3 of 0.0441, a 65.97% improvement compared to the unoptimized configuration's 0.1296, indicating stronger speed conversion capability and greater flexibility. This indicates that the generated multi-objective configuration optimization model has good performance.

[0180] The technical solutions of the embodiments of the present invention have the following beneficial effects:

[0181] In the technical solution of this invention, a method for generating a three-branch robot configuration is designed. After modeling the known truss environment and the three-branch robot, a model for solving the contact collision impulse of the three-branch robot gripping the truss is constructed. Then, combined with the truss smooth climbing task requirements information, a performance evaluation index for the gripping configuration is constructed, decision variables and constraints are determined, and the NSGA-II algorithm is used to perform multi-objective optimization of the gripping configuration to obtain the optimal gripping configuration of the three-branch robot at a given target gripping point. Finally, the effectiveness of the optimal gripping configuration for smooth truss climbing is tested, thereby realizing the optimization of the gripping configuration of the three-branch robot during the smooth truss climbing process.

[0182] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0183] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for generating a three-branch robot configuration, characterized in that, The method includes: Based on the kinematic and dynamic equations of the truss structure and the three-branch robot, a computational model is generated to characterize the collision impulse generated during the three-branch robot's gripping of the truss. The kinematic and dynamic equations are obtained as follows: in, It is a three-branch robot mass matrix. , , These are the angles, angular velocities, and angular accelerations of each joint of the three-branch robot. For the nonlinear terms of a three-branch robot, For the generalized torque of a three-branch robot, The generalized Jacobian matrix corresponding to the climbing arm. Let Jacobian be the generalized Jacobian matrix corresponding to the load arm. This represents the external force and torque acting on the gripper at the end of the climbing branch. This indicates the external force and torque acting on the end gripper of the load arm; Regarding the instantaneous process of a three-branch robot climbing and grasping a space truss, the end of the climbing arm will make contact and collision when grasping the truss. According to the aforementioned kinematic and dynamic equations, during the entire collision process... Integrating within the inner quadratic, we get: in, At the instant before the collision, since the displacement, velocity, and load force are finite quantities during the collision, when At that time, we obtained: in, This represents the external impact impulse generated at the point of contact at the moment of grasping, i.e. ; The expression for obtaining the generalized joint angular velocity increment of a three-branch robot is as follows: The velocity increment at the collision point at the end of the three-branch robot climbing arm is obtained as follows: When a contact collision occurs during the gripping of a truss by a three-branch robot, the direction of the collision impulse is always along the normal direction of the contact point. ,get: in, For the truss Jacobian matrix, Here is the truss mass matrix. Let be the velocity of the truss relative to the inertial coordinate system at the time of the collision. The velocity of the climbing arm tip relative to the inertial coordinate system at the time of collision. The coefficient of restitution is the collision recovery factor. Gain collision momentum Represented as a scalar With unit direction vector The product of, i.e.: Obtain the collision impulse calculation model when the three-branch robot climbing arm grasps the truss: Based on the collision impulse calculation model and the truss smooth climbing task requirements, the performance evaluation index of the gripping configuration of the three-branch robot is determined. Based on the performance evaluation index of the gripping configuration, a multi-objective gripping configuration optimization model for the three-branch robot is generated. The multi-objective gripping configuration optimization model is used to output the optimal gripping configuration for the smooth climbing of the gantry of the three-branch robot based on the input gripping points.

2. The method according to claim 1, characterized in that, The method further includes: The effectiveness of the optimal gripping configuration for smooth truss climbing is tested to obtain the test results of the multi-objective gripping configuration optimization model.

3. The method according to claim 1, characterized in that, Based on the collision impulse calculation model and the requirements for the truss smooth climbing task, the performance evaluation indicators for the gripping configuration of the three-branch robot are determined, including: Based on the collision impulse calculation model during the gripping process, the velocity increment generated by the contact collision at the end of the three-branch robot climbing arm is obtained, namely: Based on the collision impulse calculation model during the gripping process, the velocity increment caused by the contact collision between the end of the three-branch robot's load arm and the gripping arm is obtained, namely: in, The value reflects the degree of velocity fluctuation at the end of the climbing arm during a collision with the grab truss. The value reflects the degree of velocity fluctuation at the end of the load arm during the collision of the gripping truss. Value and The value is directly proportional to the speed fluctuation at the end of the branch when the three-branch robot grasps the truss; Under the condition that the two speed increments are minimized in the task requirement information of smooth truss climbing, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. The performance evaluation index of the gripping configuration includes: motion stability evaluation index, which is expressed as the end-effector speed increment of the climbing arm and the load arm generated when gripping the truss, that is: in, The norm of a vector , As a weighting factor, it is used to characterize the influence of the velocity fluctuations at the ends of the climbing arm and load arm on the climbing motion of the loaded truss.

4. The method according to claim 1, characterized in that, Based on the collision impulse calculation model and the requirements for the truss smooth climbing task, the performance evaluation indicators for the gripping configuration of the three-branch robot are determined, including: Based on the collision impulse calculation model during the grasping process, the formula for calculating the center of mass of the three-branch robot is as follows: in, These represent the total mass of the three branches of the three-branch robot; , , These represent the masses of the joint links of the robot's three branches. , , The mass points of each joint link of the robot's three branches relative to the origin. The radius vector; The task requirement for a stable truss climbing operation is that the center of mass of the three-branch robot should be as low as possible and closer to the side to be gripped when gripping the truss. Based on the center of mass calculation formula, the performance evaluation index of the three-branch robot's gripping configuration is obtained. This performance evaluation index includes a gripping balance evaluation index, which is expressed as the offset of the three-branch robot's center of mass relative to the gripping points of the two trusses during the truss gripping operation. in, , These are the coordinates of the gripping points of the two climbing branches when the robot grips the truss during the climbing process. , The weighting factors for the robot's center of mass shifting towards the two gripping points are respectively. .

5. The method according to claim 1, characterized in that, Based on the collision impulse calculation model and the requirements for the truss smooth climbing task, the performance evaluation indicators for the gripping configuration of the three-branch robot are determined, including: Based on the collision impulse calculation model during the grasping process, the determinant of the product of the Jacobian matrix and its transpose is obtained, i.e. in, As a metric for operability, The determinant of a square matrix. For Jacobian matrices, This is the transpose of the Jacobian matrix. Jacobian matrix singular values, For matrix Number of rows, operational indicators The larger the value, the better the flexibility of each branch of the three-branch robot. At that time, the robotic arm was in a singular position; Based on the determinant, the performance evaluation index of the gripping configuration of the three-branch robot is obtained. The performance evaluation index of the gripping configuration of the three-branch robot includes an operability evaluation index, namely: in, , These are the weighting factors for the operability evaluation indicators of the climbing arm and the load arm, respectively.

6. The method according to claim 1, characterized in that, Based on the aforementioned gripping configuration performance evaluation indicators, a multi-objective gripping configuration optimization model for the three-branch robot is generated, including: The constraints for constructing a multi-objective gripping configuration optimization model include joint angle constraints, reachability constraints, and vertical constraints. Establish decision variables based on the angles of each joint; the decision variables are selected as follows: in, The angles of each joint of the three-branch robot; Based on the performance evaluation indicators of the gripping configuration, the decision variables, and the constraints, a multi-objective gripping configuration optimization model for the three-branch robot is established. This model optimizes motion stability, gripping balance, and operability by minimizing the objective function. in, To optimize the objective function, These are decision variables.

7. The method according to claim 6, characterized in that, The joint angle constraints are as follows: In the formula, For the first Each joint angle; For the first The maximum rotation angle of each joint.

8. The method according to claim 6, characterized in that, The reachability constraints are as follows: in To optimize the robot's joint angle overcorrection during the kinematic derivation, the actual end position of the three-branch robot climbing arm was obtained. The target gripping position of the end gripper at the end of the climbing arm for truss-loaded climbing tasks. This is the allowable error.

9. The method according to claim 2, characterized in that, The effectiveness test of the optimal gripping configuration for stable truss climbing includes: Four sets of gripping angle ranges were determined, including: 0~90°, 90~180°, 180~270° and 270~360°; Based on the optimal gripping configurations for smooth truss climbing that are not optimized and the optimal gripping configurations for smooth truss climbing that are optimized within the four groups of gripping angles, the test results of each optimal gripping configuration for smooth truss climbing on multiple specified optimization indicators are obtained, and the effectiveness of the optimal gripping configuration for smooth truss climbing is tested.

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