Three-branch robot configuration generation method

Abstract

The embodiment of the invention provides a three-branch robot configuration generation method. The three-branch robot configuration generation method comprises the steps that a contact impulse solving model of a grabbing truss of a three-branch robot is generated according to a truss structure and a three-branch robot kinematics and dynamics equation; determining grasping configuration performance evaluation indexes of the three-branch robot according to the contact collision impulse solving model and the truss stable climbing task demand information; generating a multi-target grasping configuration optimization model of the three-branch robot according to the grasping configuration performance evaluation index, wherein the multi-target grasping configuration optimization model is used for outputting an optimal grasping configuration for stable climbing of a truss of the three-branch robot according to the input grasping points; and performing effectiveness detection on the optimal grabbing configuration for stable climbing of the truss to obtain a detection result of the multi-target grabbing configuration optimization model.

Description

Technical Field

[0001] The invention relates to the technical field of space robots, and in particular to a method for generating a three-branch robot configuration. Background Art

[0002] With the development of aerospace technology and in-depth exploration of the space environment, large-aperture space telescopes, space solar power stations and other large spacecraft are able to perform a variety of tasks and operations due to their complex technical systems and diverse functional modules, and have gradually become indispensable key equipment in aerospace activities. The main structure of large spacecraft usually adopts a large-span, light-weight, low-damping space truss structure. This structure faces the problem of long-distance and stable on-orbit transportation of various loads such as trusses, truss segments and functional modules during the assembly process.

[0003] At present, on-orbit handling and assembly tasks are mainly completed by astronauts, but astronauts' extravehicular activities have high safety risks and are difficult to cope with a large number of heavy on-orbit tasks. In contrast, space robots have strong operational capabilities and simple energy supply. They can be on duty in orbit for a long time and stably. They can efficiently, economically and safely replace astronauts to perform on-orbit handling and assembly tasks. In particular, in order to take into account the needs of both payload carrying and climbing, designing a multi-branch space robot has become an effective solution. As the simplest form of a multi-branch robot, the three-branch robot not only has the ability to carry payloads and climb, but also can effectively avoid increasing system complexity due to too many branches. It is an ideal configuration solution for solving the on-orbit handling and assembly tasks of large spacecraft.

[0004] Since the truss structure of large spacecraft has the characteristics of high flexibility and low damping, when the three-branch robot grasps the truss during the loaded climbing process, it is easy to cause time-varying dynamic truss structure vibration, which affects the stability of the load handling process and even threatens the safety of the spacecraft structure and payload. Therefore, in order to ensure that the three-branch robot can climb the truss stably with loads over a large range, it is necessary to optimize its grasping configuration when it contacts the truss. At present, the research on the configuration optimization of space robots is mostly focused on single-arm and dual-arm robots, focusing on optimization indicators such as minimum degree of freedom, dexterity, fault tolerance, and operability. However, the optimization of the grasping configuration of multi-branch robots when they climb stably with loads is an urgent problem to be solved. Summary of the invention

[0005] In view of this, an embodiment of the present invention provides a method for generating a three-branch robot configuration, which comprehensively considers the influence of the configuration of each branch on the grasping effect, so as to improve the load-carrying climbing ability of the three-branch robot.

[0006] An embodiment of the present invention provides a method for generating a three-branch robot configuration, comprising:

[0007] According to the truss structure and the kinematic and dynamic equations of the three-branch robot, a contact impulse solution model for the three-branch robot to grasp the truss is generated;

[0008] Determine the grasping configuration performance evaluation index of the three-branch robot according to the contact collision impulse solution model and the truss stable climbing task requirement information;

[0009] According to the grasping configuration performance evaluation index, a multi-objective grasping configuration optimization model of the three-branch robot is generated. The multi-objective grasping configuration optimization model is used to output the optimal grasping configuration of the three-branch robot for truss smooth climbing according to the input grasping points.

[0010] In the above method, the method further comprises:

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

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

[0013] The kinematic and dynamic equations are obtained:

[0014]

[0015] Where M is the mass matrix of the three-branch robot, q, are the joint angles, angular velocities, and angular accelerations of the three-branch robot, respectively; C is 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 end gripper of the climbing branch; and F2 represents the external force and torque acting on the end gripper 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 have a contact collision when grasping the truss. According to the kinematic and dynamic equations, the integration within the entire collision process δt gives:

[0017]

[0018] Among them, t0 is the instantaneous moment before the collision. Since the displacement, velocity and load force are limited during the collision process, when δt→0, we get:

[0019]

[0020] Among them, p represents the external collision impulse generated at the contact point at the moment of grasping, that is,

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

[0022]

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

[0024] δv1=J1M -1 J1 T p

[0025] When the three-branch robot grasps the truss and a contact collision occurs, the direction of the collision impulse is always along the normal direction n of the contact point, and the following is obtained:

[0026]

[0027] Among them, J t is the truss Jacobian matrix, M t is the truss mass matrix, v t is the velocity of the truss relative to the inertial coordinate system at the time of collision, v1 is the velocity of the end of the climbing arm 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 expressed as a scalar p and a unit action direction vector n∈R 6 The product of, that is:

[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, according to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including:

[0033] According to the contact collision impulse solution model, the velocity increment caused by the contact collision at the end of the three-branch robot climbing arm is obtained, that is:

[0034] δv1=J1M -1 J1 T p

[0035] According to the contact collision impulse solution model, the velocity increment caused by the contact collision of the climbing arm at the end of the three-branch robot load arm is obtained, that is:

[0036] δv2=J2M -1 J1 T p

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

[0038] When the requirement information of the truss stable climbing task is that the two speed increments are as small as possible, the grasping configuration performance evaluation index of the three-branch robot is obtained, and the grasping configuration performance evaluation index includes: a motion stability evaluation index, which is expressed as the terminal speed increment of the climbing arm and the load arm generated when grasping the truss, that is:

[0039] f1=ζ1||δv1||+ζ2||δv2||

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

[0041] In the above method, according to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including:

[0042] According to the contact collision impulse solution model, the center of mass calculation formula of the three-branch robot is obtained as follows:

[0043]

[0044] Among them, M1, M2, and M3 are the total masses of the three branches of the three-branch robot; m 1,i , m 2,j , m 3,k are the masses of the joint links of the three branches of the robot, r 1,i , r 2,j , r 3,k are the radius vectors of the mass points of the joint links of the three branches of the robot relative to the origin O;

[0045] The requirement information of the truss stable climbing task is that the height of the center of mass of the three-branch robot when grasping the truss is as low as possible and closer to the side to be grasped. According to the center of mass calculation formula, the grasping configuration performance evaluation index of the three-branch robot is obtained. The grasping configuration performance evaluation index of the three-branch robot includes a grasping balance evaluation index, which is expressed as the offset of the center of mass of the three-branch robot relative to the grasping points of the two trusses when grasping the truss, that is:

[0046] f2=λ1||r σ -r1||+λ2||r σ -r2||

[0047] Among them, r1 and r2 are the coordinates of the two climbing branch grasping points when the robot clamps the truss during the climbing process, λ1 and λ2 are the weighting factors of the robot's center of mass biased toward the two grasping points, λ1<λ2.

[0048] In the above method, according to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including:

[0049] According to the contact collision impulse solution model, the determinant of the product of the Jacobian matrix and its transpose is obtained, that is,

[0050]

[0051] Among them, ω is the measure of operability, 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 is the singular value of the Jacobian matrix J(q), m is the matrix J(q)J T (q) 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 robot arm is in a singular position;

[0052] According to the determinant, the grasping configuration performance evaluation index of the three-branch robot is obtained, and the grasping configuration performance evaluation index of the three-branch robot includes an operability evaluation index, which is:

[0053]

[0054] Where 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 grasping configuration optimization model of a three-branch robot is generated according to the grasping configuration performance evaluation index, including:

[0056] Constructing constraint conditions of a multi-objective grasping configuration optimization model, wherein the constraint conditions include joint angle constraint conditions, reachability constraint conditions, and vertical constraint conditions;

[0057] Establish a decision variable based on the angle of each joint; the decision variables are selected as follows:

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

[0059] Among them, θ i is the angle of each joint of the three-branch robot;

[0060] According to the grasping configuration performance evaluation index, the decision variables and the constraint conditions, a multi-objective grasping configuration optimization model of the three-branch robot is established, wherein the multi-objective grasping configuration optimization model optimizes motion stability, grasping balance and operability by minimizing the optimization objective function:

[0061]

[0062] Among them, f(x) is the optimization objective function and x is the decision variable.

[0063] In the above method, the joint angle constraint condition is as follows:

[0064] |θ i |≤|θ imax |=180°

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

[0066] In the above method, the reachability constraint condition is as follows:

[0067] ||T i -T c ||≤ε p

[0068] Where T i The actual position of the end of the three-branch robot climbing arm derived from the kinematics of the robot's joint angles during the optimization process, T c is the target gripping position of the gripper at the end of the climbing arm for the truss-loaded climbing task, ε p For the allowable error.

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

[0070] Determine 4 groups of grip angle ranges, including: 0-90°, 90-180°, 180-270°, and 270-360°;

[0071] According to the unoptimized truss smooth climbing optimal grasping configurations and the optimized truss smooth climbing optimal grasping configurations within the four groups of grasping angle ranges, the test results of each truss smooth climbing optimal grasping configuration on the specified multiple optimization indicators are obtained, and the test results of the effectiveness of the truss smooth climbing optimal grasping configurations are obtained.

[0072] The three-branch robot configuration generation method designed in the embodiment of the present invention effectively solves the problems of lack of consideration of the impact of contact collision, single optimization index, and incomplete consideration of constraint conditions in the traditional configuration generation process, and significantly improves the grasping configuration optimization effect of the three-branch robot during the smooth climbing of the truss, providing more comprehensive and efficient technical support for the application of the three-branch robot in complex truss environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creativity and labor.

[0074] Figure 1 is an operation flow chart provided by an embodiment of the present invention;

[0075] Figure 2 Schematic diagram of the initial configuration and connecting rod coordinate system of the three-branch robot used in the embodiment of the present invention;

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

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

[0078] Figure 5 is a distribution surface diagram of the optimized target value of the Pareto frontier configuration of the three-branch robot in an embodiment of the present invention;

[0079] Figure 6 It is a distribution diagram of grasping angles corresponding to the Pareto frontier optimization configuration of the three-branch robot in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] In order to better understand the technical solution of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0081] It should be clear that the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0083] Step 101, generating a contact impulse solution model for the three-branch robot to grasp the truss according to the truss structure and the kinematic and dynamic equations of the three-branch robot.

[0084] Specifically, firstly, combined with the kinematic equation, the dynamic equation of the three-branch robot can be derived as follows:

[0085]

[0086] Where M is the mass matrix of the three-branch robot, q, are the joint angles, angular velocities, and angular accelerations of the three-branch robot, respectively. C is the nonlinear term of the three-branch robot, including the Coriolis force and centrifugal force terms. J1 is the generalized Jacobian matrix corresponding to the climbing arm, and J2 is the generalized Jacobian matrix corresponding to the load arm. F1 represents the external force and torque acting on the end gripper of the climbing branch, and F2 represents the external force and torque acting on the end gripper 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 have a contact collision when grasping the truss. According to the kinematic and dynamic equations, the integration within the entire collision process δt gives:

[0088]

[0089] Among them, t0 is the instantaneous moment before the collision. Since the displacement, velocity and load force are limited during the collision process, when δt→0, we get:

[0090]

[0091] Among them, p represents the external collision impulse generated at the contact point at the moment of grasping, that is,

[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 during the collision process. The expression of 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

[0095] δv1=J1M -1 J1 Tp

[0096] When the three-branch robot grasps the truss and a contact collision occurs, ignoring the friction of the contact surface, the direction of the collision impulse is always along the normal direction n of the contact point, and the following is obtained:

[0097]

[0098] Among them, J t is the truss Jacobian matrix, M t is the truss mass matrix, v t is the velocity of the truss relative to the inertial coordinate system at the time of collision, v1 is the velocity of the end of the climbing arm 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 a unit action direction vector n∈R 6 The product of, that is:

[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 time of collision is decoupled from the magnitude of the collision impulse. Given the magnitude of the relative velocity when the end of the climbing arm contacts the truss, the magnitude of the collision impulse is only related to the configuration of the three-branch robot.

[0104] Step 102: Determine the grasping configuration performance evaluation index of the three-branch robot according to the contact collision impulse solution model and the truss stable climbing task requirement information.

[0105] (1) Motion stability evaluation index

[0106] Specifically, according to the contact collision impulse solution model, the velocity increment caused by the contact collision at the end of the three-branch robot climbing arm is obtained, that is:

[0107] δv1=J1M -1 J1 T p

[0108] According to the contact collision impulse solution model, the velocity increment caused by the contact collision of the climbing arm at the end of the three-branch robot load arm is obtained, that is:

[0109] δv2=J2M -1 J1 T p

[0110] Among them, the value of δv1 reflects the degree of speed fluctuation of the end of the climbing arm when the grasping truss collides, and the value of δv2 reflects the degree of speed fluctuation of the end of the load arm when the grasping truss collides. The values ​​of δv1 and δv2 are directly proportional to the speed fluctuation of the end of the branch when the three-branch robot grasps the truss. Therefore, in order to reduce the impact of grasping contact collision on the fluctuation of the end speed of the three-branch robot and thus improve the motion stability, the grasping configuration performance evaluation index of the three-branch robot is obtained when the truss stable climbing task requirement information is that the two speed increments are as small as possible. The grasping configuration performance evaluation index includes: motion stability evaluation index, which is expressed as the end speed increment of the climbing arm and the load arm generated when grasping the truss, that is:

[0111] f1=ζ1||δv1||+ζ2||δv2||

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

[0113] (2) Grip balance evaluation index

[0114] Specifically, when the three-branch robot grasps the truss, it is crucial to reasonably arrange the center of mass position of the robot to maintain the balance and stability of the loaded climbing motion. According to the contact collision impulse solution model, the center of mass calculation formula of the three-branch robot is:

[0115]

[0116] Among them, M1, M2, and M3 are the total masses of the three branches of the three-branch robot; m 1,i , m 2,j , m 3,k are the masses of the joint links of the three branches of the robot, r 1,i , r 2,j , r 3,k are the radius vectors of the mass points of the joint links of the three branches of the robot relative to the origin O;

[0117] The requirement information for the stable truss climbing task is that the center of mass height of the three-branch robot when grasping is as low as possible and closer to the side to be grasped. According to the center of mass calculation formula, the grasping configuration performance evaluation index of the three-branch robot is obtained. The grasping configuration performance evaluation index of the three-branch robot includes a grasping balance evaluation index, which is expressed as the offset of the center of mass of the three-branch robot relative to the grasping points of the two trusses when grasping the truss, that is:

[0118] f2=λ1||r σ -r1||+λ2||r σ -r2||

[0119] Among them, r1 and r2 are the coordinates of the two climbing branch grasping points when the robot clamps the truss during the climbing process, λ1 and λ2 are the weighting factors of the robot's center of mass biased toward the two grasping points, 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, that is,

[0122]

[0123] Among them, ω is the measure of operability, 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 is the singular value of the Jacobian matrix J(q), m is the matrix J(q)J T The larger the value of the operability index ω is, the better the flexibility of each branch of the robot is. When ω=0, the robot arm is in a singular position.

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

[0125]

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

[0127] Step 103, generating a multi-objective grasping configuration optimization model of a three-branch robot according to the grasping configuration performance evaluation index, including:

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

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

[0130] ① Joint angle constraints

[0131] According to the mechanical structure of the three-branch robot, the layout of the robot's internal circuits, and the installation position, joint angle constraints are set for the joint motion range of each branch of the three-branch robot to limit its motion space. For the three-branch robot studied in this patent, the joint angle constraints for each branch of the three-branch robot are set as follows:

[0132] |θ i |≤|θ imax |=180°

[0133] Among them, θ i is the i-th joint angle; θ imax is the maximum rotation angle of the i-th joint;

[0134] ② Reachability constraints

[0135] The reachability constraint is one of the basic requirements for the optimization of the grasping configuration of the three-branch robot in the space truss climbing task. It ensures that the obtained optimized configuration can make the end position of the robot reach the target grasping point. This patent uses the difference between the end position corresponding to the actual configuration of the robot and the expected position as the reachability constraint condition, as shown below:

[0136] ||T i -T c ||≤ε p

[0137] Where T i The actual position of the end of the three-branch robot climbing arm derived from the kinematics of the robot's joint angles during the optimization process, T c is the target gripping position of the gripper at the end of the climbing arm for the truss-loaded climbing task, ε p For the allowable error.

[0138] ③Vertical constraints

[0139] According to the characteristics of the three-branch robot end gripper and the truss, in order to ensure the stability and reliability of grasping, the robot needs to ensure that the posture of the gripper is perpendicular to the grasped truss rod.

[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] Among them, θ i is the angle of each joint of the three-branch robot;

[0143] (3) Based on the grasping configuration performance evaluation index, the decision variables and the constraint conditions, a multi-objective grasping configuration optimization model of the three-branch robot is established, wherein the multi-objective grasping configuration optimization model optimizes motion stability, grasping balance and operability by minimizing the optimization objective function:

[0144]

[0145] Among them, f(x) is the optimization objective function and x is the decision variable.

[0146] The multi-objective grasping configuration optimization model is used to output the optimal grasping configuration for the three-branch robot's truss stable climbing according to the input grasping points.

[0147] Step 104 , performing validity detection on the optimal gripping configuration for steady climbing of the truss to obtain detection results of the multi-objective gripping configuration optimization model.

[0148] Due to the large number of joints in the three-branch robot, it is difficult to solve the inverse solution of the kinematic position level. By setting different starting positions of the climbing branch end clamp and different grasping angles of a given grasping point, the three-branch robot can be planned in Cartesian space straight line path, and the generalized Jacobian matrix of the robot can be inverted. The joint angular velocity is solved according to the terminal velocity, and the next joint angle is calculated by integrating the joint angular velocity. Therefore, the grasping configuration corresponding to different grasping angles can be obtained by using the velocity level inverse solution method.

[0149] Determine 4 groups of gripping angle ranges, including: 0-90°, 90-180°, 180-270° and 270-360°; based on the unoptimized truss steady climbing optimal gripping configurations and the optimized truss steady climbing optimal gripping configurations within the 4 groups of gripping angle ranges, obtain test results of each truss steady climbing optimal gripping configuration on multiple specified optimization indicators, and obtain test results of the effectiveness of the truss steady climbing optimal gripping configuration.

[0150] According to the above method provided by the embodiment of the present invention, a three-branch robot configuration generation method is simulated.

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

[0152] Table 1 DH parameters of three-branch robot

[0153]

[0154]

[0155] According to the three-branch robot grasping truss contact collision impulse solution model and the truss stable climbing task requirement information, the motion stability, grasping balance and operability grasping configuration performance evaluation indicators are determined based on MATLAB language. Figure 4 The optimization algorithm process shown in the figure is used to carry out the NSGA-Ⅱ multi-objective grasping configuration optimization simulation experiment as follows.

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

[0157] Table 2 Spacecraft truss and robot related parameters

[0158]

[0159]

[0160] The reference coordinate system is constructed with the grasping point at the end of branch 1 when the three-branch robot grasps the target truss as the origin. At this time, the position 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 posture, that is, the angles of rotation around the x, y, and z axes respectively. The expected position of the end of the climbing branch (the end of branch 2) of the three-branch robot 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 grasps the truss.

[0161] In order to reduce the complexity of the algorithm and improve the optimization efficiency, and considering that different situations in the handling process may have different restrictions on the truss gripping angle, the range of the gripping angle r is evenly divided into 4 intervals: [0°, 90°), [90°, 180°), [180°, 270°), [270°, 360°). Then, multi-objective optimization is performed for each interval to obtain the optimal configuration and the corresponding gripping angle in each interval; and the multiple performance evaluation index values ​​corresponding to the obtained optimized configuration are normalized to eliminate the dimensional differences caused by different units and data scales, so as to obtain the global optimal configuration and the corresponding gripping angle.

[0162] like Figure 4As shown in the figure, the configuration optimization process starts with creating an initial population representing the robot configuration. Then, the simulated binary crossover operator (SBX operator) is used to perform a crossover operation on the population, and the polynomial mutation operator is used to perform a mutation operation on the population to generate a new offspring population. After the offspring is generated and before any genetic operation is performed, it is first verified whether each configuration meets the various constraints, including whether the robot can reach the specified task point and whether each joint angle is within the allowable rotation range. For configurations that do not meet the constraints, they are marked as infeasible solutions and excluded from subsequent genetic operations. Configurations that meet the constraints will be judged by optimizing the objective function for non-dominated sorting and crowding calculation to determine their quality. According to the sorting results, excellent offspring individuals are selected to combine with parent individuals 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 coding is adopted, and the selection method adopts binary tournament selection. The specific relevant parameters are shown in Table 3 below:

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

[0164]

[0165]

[0166] After the simulation program is initialized, the simulation program is run and the multi-objective configuration optimization of the truss grip is performed using the NSGA-Ⅱ algorithm. The specific optimization process is as follows: Figure 4 As shown in Figure 2, after gen = 100 iterations, the final simulation results are as follows: Figure 5 As shown in the figure, the three-dimensional surface fitted by the scatter plot in the figure is the Pareto frontier surface of the multi-objective optimization result. 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 frontier solution set roughly presents an extended surface, which extends from the position close to the origin to the direction of the three objective axes, but due to the mutual constraints between the objective functions, the frontier surface will not reach the origin. This distribution characteristic shows the equilibrium state of the optimization solution between the three objective dimensions, reflects the inevitable compromise and trade-off in the multi-objective optimization process, is consistent with the theory, and further verifies the rationality of the optimization process.

[0167] At the same time, the grasping angle distribution corresponding to the Pareto frontier configuration solution set of each grasping angle interval is obtained as follows: Figure 6As shown in the figure, it can be observed that the optimal gripping angles in each interval are concentrated in 10-25°, 145-165°, 190-210°, and 345-360°. This shows that the gripping angle has converged through the configuration optimization algorithm, which verifies the effectiveness of the algorithm. When the gripping angle in a certain interval is not suitable for the current large spacecraft climbing mission requirements, the optimization method provides more references and options.

[0168] In order to obtain the optimal solution of the Pareto frontier, the normalized performance evaluation index values ​​corresponding to each configuration and the error of the corresponding terminal posture are comprehensively considered. A comprehensive evaluation index is constructed by weighted summing the index value and the error to measure the overall performance of the current task configuration. Then, the configuration with the smallest corresponding comprehensive evaluation index value in each group of solutions is taken as the optimal configuration of the group. The specific results are shown in Table 4 below.

[0169] Table 4 Optimization results of the best configurations of each group

[0170]

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

[0172] Table 5 Optimal configuration corresponding to joint angles

[0173]

[0174] As can be seen from Table 4, although the index f1 of this optimal configuration is not the best compared with the other three groups, considering that the indexes f2 and f3 have significant advantages, the index f2 is 9.76% higher than that of the first group, 17.03% higher than that of the second group, and 16.09% higher than that of the fourth group; the optimal configuration is particularly outstanding in the index f3, which is 61.69% higher than that of the first group, 41.90% higher than that of the second group, and 36.55% higher than that of the fourth group. This trade-off makes the comprehensive evaluation index of the corresponding configuration of the third group the smallest, becoming the optimal configuration. After calculation, the configuration has achieved significant improvements in various performance evaluation indicators under the premise of satisfying accessibility constraints, joint constraints, and vertical constraints, which to a certain extent illustrates the feasibility of the configuration optimization model.

[0175] Next, the effectiveness of the optimal grasping configuration for smooth climbing of the truss is tested. By setting different starting positions of the end clamp of the climbing branch and different grasping angles of a given grasping point, the three-branch robot is planned in Cartesian space. The generalized Jacobian matrix of the robot is inverted, the joint angular velocity is solved according to the terminal velocity, and the next joint angle is calculated by integrating the joint angular velocity, so as to obtain the grasping configuration corresponding to different grasping angles.

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

[0177] Table 6 Control experiment results

[0178]

[0179] It can be seen from Table 6 that for each grasping angle interval, the configuration after multi-objective optimization has significantly improved in each optimization index compared with the unoptimized configuration. For the interval corresponding to the optimal configuration obtained above (180-270° group), the optimized configuration is 0.1073 in the index f1, which is 41.21% higher than 0.1825 without configuration optimization, indicating that the robot has strong motion stability under this configuration and is less disturbed when contacting and colliding with the truss; in addition, the index f2 under this configuration is 1.4894, which is 57.60% higher than 3.5128 without configuration optimization, indicating that the robot has strong climbing balance under this configuration, which is conducive to the next step of climbing and has high task efficiency; finally, the index f3 under this configuration is 0.0441, which is 65.97% higher than 0.1296 without configuration optimization. Under this configuration, the robot has strong speed conversion ability and greater flexibility. This shows that the generated multi-objective configuration optimization model has good results.

[0180] The technical solution of the embodiment of the present invention has the following beneficial effects:

[0181] In the technical scheme of the embodiment of the present invention, a three-branch robot configuration generation method is designed. After modeling the known truss environment and the three-branch robot, a contact collision impulse solution model for the three-branch robot grasping the truss is constructed; then, the grasping configuration performance evaluation index is constructed in combination with the truss smooth climbing task requirement information, and the decision variables and constraints are determined. The NSGA-Ⅱ algorithm is used to perform multi-objective optimization on the grasping configuration to obtain the optimal configuration of the three-branch robot grasping the truss under a given target grasping point; then, the effectiveness of the optimal grasping configuration for the smooth climbing of the truss is tested to achieve the optimization of the grasping configuration of the three-branch robot during the smooth climbing of the truss.

[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 in the scope of protection of the present invention.

[0183] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A three-branch robot configuration generation method, characterized in that: The method comprises: According to the truss structure and the kinematic and dynamic equations of the three-branch robot, a contact impulse solution model for the three-branch robot to grasp the truss is generated; Determine the grasping configuration performance evaluation index of the three-branch robot according to the contact collision impulse solution model and the truss stable climbing task requirement information; According to the grasping configuration performance evaluation index, a multi-objective grasping configuration optimization model of the three-branch robot is generated. The multi-objective grasping configuration optimization model is used to output the optimal grasping configuration of the three-branch robot for truss smooth climbing according to the input grasping points.

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

3. The method according to claim 1, characterized in that According to the truss structure and the kinematic and dynamic equations of the three-branch robot, a contact impulse solution model for the grasping truss of the three-branch robot is generated, including: The kinematic and dynamic equations are obtained: Where M is the mass matrix of the three-branch robot, q, are the joint angles, angular velocities, and angular accelerations of the three-branch robot, respectively; C is 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 end gripper of the climbing branch; and F2 represents the external force and torque acting on the end gripper of the load arm; For the instantaneous process of the three-branch robot climbing and grasping the space truss, the end of the climbing arm will have a contact collision when grasping the truss. According to the kinematic and dynamic equations, the integration within the entire collision process δt gives: Among them, t0 is the instantaneous moment before the collision. Since the displacement, velocity and load force are limited during the collision process, when δt→0, we get: Among them, p represents the external collision impulse generated at the contact point at the moment of grasping, that is, The expression for obtaining the generalized joint angular velocity increment of the three-branch robot is: The velocity increment at the collision point at the end of the three-branch robot climbing arm is obtained as δv1=J1M -1 J1 T p When the three-branch robot grasps the truss and a contact collision occurs, the direction of the collision impulse is always along the normal direction n of the contact point, and the following is obtained: Among them, J t is the truss Jacobian matrix, M t is the truss mass matrix, v t is the velocity of the truss relative to the inertial coordinate system at the time of collision, v1 is the velocity of the end of the climbing arm relative to the inertial coordinate system at the time of collision, and e (0<e<1) is the collision recovery coefficient; The collision impulse p is expressed as a scalar p and a unit action direction vector n∈R 6 The product of, that is: p=pn Obtain the contact collision impulse solution model when the three-branch robot climbing arm grasps the truss:

4. The method according to claim 3, characterized in that According to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including: According to the contact collision impulse solution model, the velocity increment caused by the contact collision at the end of the three-branch robot climbing arm is obtained, that is: δv1=J1M -1 J1 T p According to the contact collision impulse solution model, the velocity increment caused by the contact collision of the climbing arm at the end of the three-branch robot load arm is obtained, that is: δv2=J2M -1 J1 T p Among them, the value of δv1 reflects the degree of velocity fluctuation of the end of the climbing arm when the grasping truss collides, and the value of δv2 reflects the degree of velocity fluctuation of the end of the load arm when the grasping truss collides. The values ​​of δv1 and δv2 are directly proportional to the velocity fluctuation of the end of the branch when the three-branch robot grasps the truss. When the requirement information of the truss stable climbing task is that the two speed increments are as small as possible, the grasping configuration performance evaluation index of the three-branch robot is obtained, and the grasping configuration performance evaluation index includes: a motion stability evaluation index, which is expressed as the terminal speed increment of the climbing arm and the load arm generated when grasping the truss, that is: f1=ζ1||δv1||+ζ2||δv2|| Here, ||·|| represents the norm of the vector, and ζ1 and ζ2 are weighting factors, which are used to characterize the influence of the velocity fluctuation at the end of the climbing arm and the load arm on the climbing motion of the loaded truss.

5. The method according to claim 3, characterized in that: According to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including: According to the contact collision impulse solution model, the center of mass calculation formula of the three-branch robot is obtained as follows: Among them, M1, M2, and M3 are the total masses of the three branches of the three-branch robot; m 1,i , m 2,j , m 3,k are the masses of the joint links of the three branches of the robot, r 1,i , r 2,j , r 3,k are the radius vectors of the mass points of the joint links of the three branches of the robot relative to the origin O; The requirement information of the truss stable climbing task is that the height of the center of mass of the three-branch robot when grasping the truss is as low as possible and closer to the side to be grasped. According to the center of mass calculation formula, the grasping configuration performance evaluation index of the three-branch robot is obtained. The grasping configuration performance evaluation index of the three-branch robot includes a grasping balance evaluation index, which is expressed as the offset of the center of mass of the three-branch robot relative to the grasping points of the two trusses when grasping the truss, that is: f2=λ1||r σ -r1||+λ2||r σ -r2|| Among them, r1 and r2 are the coordinates of the two climbing branch grasping points when the robot clamps the truss during the climbing process, λ1 and λ2 are the weighting factors of the robot's center of mass biased toward the two grasping points, λ1<λ2.

6. The method according to claim 3, characterized in that According to the contact collision impulse solution model and the truss stable climbing task requirement information, the grasping configuration performance evaluation index of the three-branch robot is determined, including: According to the contact collision impulse solution model, the determinant of the product of the Jacobian matrix and its transpose is obtained, that is, Among them, ω is the measure of operability, 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 is the singular value of the Jacobian matrix J(q), m is the matrix J(q)J T (q) 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 robot arm is in a singular position; According to the determinant, the grasping configuration performance evaluation index of the three-branch robot is obtained, and the grasping configuration performance evaluation index of the three-branch robot includes an operability evaluation index, which is: Among them, κ1 and κ2 are weighted factors of the operability evaluation index of the climbing arm and the load arm, respectively.

7. The method according to claim 1, characterized in that According to the grasping configuration performance evaluation index, a multi-objective grasping configuration optimization model of the three-branch robot is generated, including: Constructing constraint conditions of a multi-objective grasping configuration optimization model, wherein the constraint conditions include joint angle constraint conditions, reachability constraint conditions, and vertical constraint conditions; Establish decision variables based on the angles of each joint; the decision variables are selected as follows: x=[θ1,θ2,…,θ 14 ,i 8' ,i 9' ,…,θ 14' ] Among them, θ i is the angle of each joint of the three-branch robot; According to the grasping configuration performance evaluation index, the decision variables and the constraint conditions, a multi-objective grasping configuration optimization model of the three-branch robot is established, wherein the multi-objective grasping configuration optimization model optimizes motion stability, grasping balance and operability by minimizing the optimization objective function: minf(x)=min[f1(x),f2(x),f3(x)] Among them, f(x) is the optimization objective function and x is the decision variable.

8. The method according to claim 7, characterized in that The joint angle constraints are as follows: |θ i |≤|θ imax |=180° In the formula, θ i is the i-th joint angle; θ imax is the maximum rotation angle of the i-th joint.

9. The method according to claim 7, characterized in that: The reachability constraints are as follows: ||T i -T c ||≤ε p Where T i The actual position of the end of the three-branch robot climbing arm derived from the kinematics of the robot's joint angles during the optimization process, T c is the target gripping position of the gripper at the end of the climbing arm for the truss-loaded climbing task, ε p For the allowable error.

10. The method according to claim 2, characterized in that The effectiveness detection of the optimal gripping configuration for steady truss climbing includes: Determine 4 groups of grip angle ranges, including: 0-90°, 90-180°, 180-270°, and 270-360°; According to the unoptimized truss smooth climbing optimal grasping configurations and the optimized truss smooth climbing optimal grasping configurations within the four groups of grasping angle ranges, the test results of each truss smooth climbing optimal grasping configuration on the specified multiple optimization indicators are obtained, and the test results of the effectiveness of the truss smooth climbing optimal grasping configurations are obtained.

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