A Disturbance Resistance Method for Space Robot Base Based on Tribal Migration Algorithm

Abstract

This invention relates to a method for resisting disturbances on the base of a space robot based on a tribal migration algorithm. The purpose of this invention is to solve the problem of base offset caused by the joint movement of the robotic arm in existing free-floating space robots. The process is as follows: 1. Based on the motion relationship equations between the base and the robotic arm of the free-floating space robot, define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance, and construct the objective function of the free-floating space robot base attitude disturbance based on these two amplitudes; 2. Parameterize the trajectory of the i-th joint angle of the free-floating space robot using a seventh-order sine polynomial, converting the seventh-order sine polynomial into a polynomial represented by only two unknown parameters; 3. Obtain the robotic arm joint angle that minimizes the objective function value of the base attitude disturbance. This invention belongs to the field of space robot control.

Description

Technical Field

[0001] This invention relates to a method for preventing disturbances to a space robot base. This invention belongs to the field of space robot control. Background Technology

[0002] According to the European Space Agency (ESA), as of June 2023, approximately 36,500 pieces of space debris larger than 10 centimeters had been discovered. The total number of objects larger than 1 centimeter in Earth orbit exceeds one million. The continuous generation of space debris can lead to unintended space collisions, threaten astronaut safety, affect communications and observation, increase operating costs, and potentially have long-term impacts on future space activities. In past space missions, launch vehicle malfunctions were the most common cause of space debris failures, but since 2008, the number of on-orbit malfunctions has exceeded the number of launch malfunctions, undoubtedly causing enormous losses.

[0003] Utilizing robotics to assist or even replace humans in performing space missions such as on-orbit servicing and deep space exploration is of great significance. Free-floating space robots, as a type of space robot with a special operating mode, have no driving force generated by any of their base's drive mechanisms. They can only change the posture of the base and end effector through the movement of the robotic arm joints. This control strategy can reduce energy consumption, extend on-orbit service time, and save costs. Despite these advantages, the underactuated nature of their base and their unique kinematic and dynamic characteristics compared to other space robots present numerous challenges to their application. Changes in base posture not only affect the accuracy of space mission execution and increase mission time, but also increase the difficulty of communication between the ground station and the base spacecraft. Furthermore, excessive changes in base posture can easily lead to collisions between the robotic arm and the base, causing damage to space equipment. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of base displacement caused by the joint movement of the robotic arm in existing free-floating space robots, and to propose a disturbance-resistant method for the base of space robots based on the tribal migration algorithm.

[0005] The specific process of a disturbance resistance method for a space robot base based on a tribal migration algorithm is as follows:

[0006] Step 1: Based on the motion relationship equations of the free-floating space robot base and the robotic arm, define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance. Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance, construct the objective function of the free-floating space robot base attitude disturbance.

[0007] Step 2: The seventh-order sine polynomial method is used to parameterize the trajectory of the i-th joint of the free-floating space robot, converting the seventh-order sine polynomial into a polynomial represented by only two unknown parameters.

[0008] Step 3: Optimize the two unknown parameters in the polynomial using the tribal migration algorithm to reduce the value of the objective function of the base attitude disturbance, and obtain the robot arm joint angle that minimizes the value of the objective function of the base attitude disturbance.

[0009] Preferably, in step one, based on the motion relationship equations of the free-floating space robot base and the robotic arm, the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance are defined, and the objective function of the base attitude disturbance of the free-floating space robot is constructed based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance; the specific process is as follows:

[0010] Step 11: The equations of motion between the free-floating space robot base and the robotic arm are expressed as follows:

[0011]

[0012] Where v0 is the linear velocity of the free-floating space robot base, ω0 is the angular velocity of the free-floating space robot base, M is the total mass of the robot, I3 is the third-order identity matrix, and r 0g The vector representation of the center of mass of the base pointing towards the center of mass of the freely floating robot in space. For r 0g The antisymmetric matrix; is the angular velocity matrix of the joints of the free-floating space robot, and J is the Jacobian matrix describing the motion relationship between the base and each robotic arm joint;

[0013] H M H MV H MW It is a coefficient matrix;

[0014] Steps 1 and 2: Assume the initial angular momentum of the freely floating space robot is zero;

[0015] During the motion, the base will be constantly subjected to instantaneous perturbations. The defined attitude perturbation function for the space robot base is:

[0016]

[0017] in, Let t represent the base angular velocity of the freely floating space robot at time t;

[0018] J ω Let J be the matrix consisting of rows 4 to 6 of the Jacobian matrix.

[0019] Let represent the angular velocity matrix of the joints of the robotic arm of the robot that is freely floating in space at time t;

[0020] Step 13: Define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Construct the objective function P for the base attitude perturbation of the free-floating space robot;

[0021] Step 14: Based on the objective function P of the base attitude disturbance of the free-floating space robot, the trajectory planning problem that minimizes the base attitude disturbance of the free-floating space robot is expressed as the following nonlinear constraint optimization problem.

[0022] Preferably, the coefficient matrix H M The expression is:

[0023]

[0024] Among them, I i For the i-th rigid body B of the free-floating space robot i The inertia matrix, m i For the i-th rigid body B of the free-floating space robot i quality, r i Let B be the rigid body B of the freely floating robot, origin of the inertial coordinate system. i Vector representation of the centroid, r 0i Let the center of mass of the base point to the i-th rigid body B of the freely floating space robot. i Vector representation of the centroid.

[0025] Preferably, the coefficient matrix H MW The expression is:

[0026]

[0027] Where, r i0 B is the i-th rigid body of the free-floating space robot. i Vector representation of the centroid pointing towards the base centroid;

[0028] For r i0 The antisymmetric matrix;

[0029] J ωi J represents the components of the Jacobian matrix associated with rotational motion, specifically the Jacobian matrix corresponding to the joint angular velocity. ωi =[z1,z2,…,z i [,0,…,0];

[0030] J vi The components of the Jacobian matrix associated with linear motion, i.e., the Jacobian matrix J corresponding to the joint linear velocities. vi =[z1×(r) i -p1),z2×(r i -p2),…,z i ×(r i -p i ),0,…,0];

[0031] z i For joint J i The rotation axis vector representation, p i From the origin of the inertial coordinate system to joint J i Vector representation of .

[0032] Preferably, the coefficient matrix H MV The expression is:

[0033]

[0034] Preferably, the objective function P in steps one and three is:

[0035]

[0036] Where P represents the objective function for perturbing the base attitude of the free-floating space robot, t0 represents the start time of the free-floating space robot mission, and t f Indicates the end time of the free-floating space robot mission. Let t represent the base angular velocity of the freely floating space robot at each moment, t represent the current moment, a represent the process disturbance weight, and b represent the final process disturbance weight.

[0037] Preferably, in step one and four, based on the objective function P of the base attitude disturbance of the free-floating space robot, the trajectory planning problem that minimizes the base attitude disturbance of the free-floating space robot is expressed as a nonlinear constrained optimization problem, with the following expression:

[0038]

[0039] stq T =q d

[0040]

[0041] q min ≤q n (t)≤q max

[0042]

[0043] Where, q T q represents the joint angle of the robotic arm at the end of the task. d Indicates the target joint angle of the robotic arm;

[0044] This indicates the angular velocity of the robotic arm joints at the end of the task. This indicates the target joint angular velocity of the robotic arm;

[0045] q min q is the lower limit of the joint angle constraint for the robotic arm. max Limit the upper limit of the joint angle of the robotic arm;

[0046] The lower limit of the joint angular velocity of the robotic arm. The upper limit of the angular velocity of the articulated robotic arm;

[0047] q n (t) is the joint angle of the robotic arm at time t. It is the angular velocity of the robotic arm joint at time t.

[0048] Preferably, in step two, a seventh-order sine polynomial method is used to parameterize the trajectory of the i-th joint angle of the free-floating space robot, converting the seventh-order sine polynomial into a polynomial represented by only two unknown parameters; the specific process is as follows:

[0049] Set the end angular velocity of the robotic arm joint and angular acceleration for:

[0050]

[0051] Meanwhile, the limit values ​​for the joint angles of the robotic arm are set as follows:

[0052] q i_min ≤q i (t)≤q i_max i = 1, ..., n

[0053] Where, q i (t) represents the joint angle of the i-th robotic arm at the current moment;

[0054] n represents the total number of links or joints of the free-floating space robot;

[0055] q i_min and q i_max Let represent the minimum and maximum achievable angles of the i-th robotic arm joint, respectively.

[0056] Let the expected value of the angle of the i-th robotic arm joint be: q i (t f )=q id ;

[0057] The seventh-order sine polynomial method is used to parameterize the trajectory of the i-th joint angle of the free-floating space robot, transforming the seventh-order sine polynomial into one consisting only of a. i7 ,a i6 A polynomial represented by two unknown parameters;

[0058] q i (t)=Δ i1 sin(a i7 t 7 +a i6 t 6 +a i5 t 5 +a i4 t 4 +a i3 t 3 +a i2 t 2 +a i1 t+a i0 )+Δ i2

[0059] Among them, a i0 a i1 a i2 a i3 a i4 a i5 a i6 a i7 Indicates the parameter, Δ i1 Δ i2 Indicates intermediate variables;

[0060]

[0061] a i0 =sin -1 [(q i0 -Δ i2 ) / Δ i1 ]

[0062] a i1 =a i2 =0

[0063]

[0064] Where, q i0 This represents the initial angle of the i-th joint.

[0065] Preferably, in step three, the tribal migration algorithm is used to optimize two unknown parameters in the polynomial to reduce the value of the objective function for base attitude disturbance, thereby obtaining the joint angle trajectory that minimizes the objective function value for base attitude disturbance; the specific process is as follows:

[0066] Step 31: Set the iteration count j = 0;

[0067] Generate a population of M individuals, where each individual is a parameter set (a i6 ,a i7 );

[0068] Each individual is randomly distributed within the search space:

[0069] x s,j =lb + r × (ub - lb)

[0070] Where, x s,j Let j represent an individual with index s, where s∈{0,1,2,...,M}, j∈{0,1,2,...,L}, and L is the total number of iterations;

[0071] r is a random number that satisfies 0 ≤ r ≤ 1;

[0072] lb is the lower boundary of the optimization, and ub is the upper boundary of the optimization.

[0073] Step 3.2: Divide the population into N clusters using the DBSCAN clustering algorithm. Where g∈[0,N];

[0074] Based on clustering Clustering is derived from the average position of individuals. center

[0075] Step 3: Adaptively adjust the exploration factor I and the random factor R according to the current algebra j;

[0076]

[0077] Where I(j) represents the value of the exploration factor I in the j-th iteration;

[0078] R(j) represents the value of the random factor R in the j-th iteration;

[0079] j∈{0,1,2,...,L}, where L is the maximum number of iterations;

[0080] w is the initial value of the exploration factor I, and c is the initial value of the random factor R;

[0081] Steps 3 and 4: Generate chaotic sequences. The definition of a chaotic sequence is as follows:

[0082] r(s+1)=μr(s)(1-r(s))

[0083] Where r(s+1) is the chaotic sequence generated through iteration, r(0) is a random number between 0 and 1, and μ represents the chaotic coefficient;

[0084] Step 35: Assign the parameter group (a) to each individual. i6 ,a i7 Substituting into the seventh-degree sine polynomial Obtain the motion trajectories of all joints of the space robot;

[0085] Then, through the defined space robot base attitude perturbation function Calculate the fitness function J for each individual. s,j :

[0086]

[0087] Where a represents the process disturbance weight, and b represents the final process disturbance weight;

[0088] Let represent the base angular velocity of individual s at time t during the j-th iteration;

[0089] This represents the set of joint angular velocities of individual s at time t during the j-th iteration. This represents the set of joint angles of individual s at time t during the j-th iteration;

[0090] This represents the angular velocity of joint i corresponding to individual s at time t during the j-th iteration. This represents the angle of joint i corresponding to individual s at time t during the j-th iteration;

[0091] Clustering The individual with the highest fitness is defined as the cluster. Leaders in

[0092] Step 36: Each cluster Individuals within Clustering The individual with the highest fitness Movement, if individual Fitness value of the new position Fitness value J greater than the original position s,j Then the individual Values If individual Fitness value of the new position Fitness value J less than or equal to the original positions,j Then the individual Values

[0093] The expression is:

[0094]

[0095] in, This indicates clustering at stage P1, during the j-th iteration. The inner individual s of (a) i7 ,a i6 ) value;

[0096] Clustering Individuals within;

[0097] r(j) is the chaos coefficient at the j-th iteration;

[0098] Clustering The individual with the highest fitness;

[0099] Step 37: Calculate Clustering The average fitness value of all individuals and clustering center Distance to other clusters Distance from the center

[0100] in, N represents the total number of clusters;

[0101] based on and Calculate the attractiveness index The expression is:

[0102]

[0103] in, It is clustering Leader fitness value, It is clustering center Distance to other clusters The maximum distance from the center;

[0104] By analyzing attractiveness indicators Sorting, Clustering Individuals within Towards Clustering corresponding to the maximum value If individuals move closer to the center, Fitness value of the new position Larger than an individual fitness value of the original position Individual Values If individual Fitness value of the new position Less than or equal to individuals fitness value of the original position Individual Values

[0105] The expression is:

[0106]

[0107] in, This indicates clustering at stage P2, during the j-th iteration. The inner individual s of (a) i7 ,a i6 ) value;

[0108] Step 38: During one cycle, either a threat avoidance situation or a hunting situation will occur randomly;

[0109] 1) In a threat-avoidance situation, an individual will randomly move from its original location, as represented by the following formula:

[0110]

[0111] in, This indicates clustering at stage P3, during the j-th iteration. Individual with s sequence number The value obtained after avoiding threats during migration;

[0112] 2) In a hunting scenario, randomly select an individual from each cluster as the target. The remaining individuals will attack the attacked individual. Approach;

[0113] If the individual's fitness at the new location Fitness greater than the original position Individual Values If the individual's fitness at the new location Fitness less than or equal to the original position Individual Values

[0114] The process is represented as

[0115]

[0116] Step 39: Check if all individuals have completed the position update. If not, let s = s + 1 and execute Step 34; otherwise, retain the parameter set (a) corresponding to the individual with the highest fitness. i6 ,a i7 ), proceed to step thirty;

[0117] Step 30: Randomly select a portion of individuals for reinitialization:

[0118] Each randomly selected individual is randomly distributed within the search space, and each individual receives a new corresponding set of parameters (a). i6 ,a i7 );

[0119] individual The probability T of being selected s,j And the corresponding roulette betting range U s,j for:

[0120]

[0121] Among them, T y,j This refers to individuals whose index is less than s. The probability of being selected is y = [0, 1, ..., s-1], where y represents the individual. The serial number;

[0122] Generate e random numbers r between 0 and 1. p , p∈{0,1,2,....e};

[0123] Find the satisfaction of U c-1,j <r p ≤U c,j Corresponding individuals The serial number of the selected individual;

[0124] Reinitialization:

[0125] x c,j+1 =lb + r × (ub - lb)

[0126] Step 31: Check if the specified number of iterations has been completed. If not, let j = j + 1 and jump to step 32; otherwise, jump to step 33.

[0127] Step 32: Check if j = L. If they are equal, perform DBSCAN clustering again on all M individuals and jump to step 32. If they are not equal, no re-clustering is needed and jump to step 33.

[0128] Step 33: Complete the optimization process to obtain the individual that minimizes the objective function of the base disturbance, and then obtain the motion trajectory of the robot arm joint angle.

[0129] The beneficial effects of this invention are as follows:

[0130] To improve the stability of a free-floating space robot base, shorten its task execution time, and enhance its accuracy and safety, it is necessary to reduce the disturbance caused by the robotic arm's movements on the base. Appropriate trajectory planning can minimize the disturbance caused by the robotic arm's movements on the base while simultaneously achieving the task objectives and satisfying various constraints.

[0131] 1. This invention proposes a Tribal Migration Algorithm (TMA), which uses the migration and adaptation behavior of natural populations as the algorithmic idea to solve relatively complex optimization problems.

[0132] 2. The tribal migration algorithm incorporates chaotic strategies, adaptive strategies, and the idea of ​​maintaining population diversity. Compared with other existing methods, this method can avoid the adverse effects of getting trapped in local optima and premature convergence, thus achieving better optimization results.

[0133] 3. This invention applies the tribal migration algorithm to the base anti-disturbance task of a free-floating space robot, optimizing the trajectory of the robotic arm joints, which can achieve a better anti-disturbance effect.

[0134] 4. The objective function defined in this invention consists of the instantaneous disturbance and the cumulative disturbance of the space robot base. The parameters can be freely adjusted according to the mission objective to achieve different effects. Attached Figure Description

[0135] Figure 1 This is a flowchart of the present invention;

[0136] Figure 2 This is a structural model diagram of a space robotic arm. ΣB, ΣI, and ΣE represent the base coordinate system, the inertial coordinate system, and the robotic arm end effector coordinate system, respectively. The center of mass of the base is the origin ΣB, and X... B Y B Z B Let X be the coordinate axis of ΣB; I Y I Z I Let X be the coordinate axis of ΣI; the center of the gripper is the origin of ∑E, and X is the coordinate axis of ΣI. E Y E Z E Let C be the coordinate system of ∑E; g r is the system's centroid; g B is the position vector of the system's center of mass; B0 is the rigid body 0, i.e., the base; B i(i = 1, 2, ..., n) represents rigid body i, which is also the i-th link of the robotic arm; C i (i = 1, 2, ..., n) represents rigid body B. i The center of mass; J i (i = 1, 2, ..., n) is the connection B i-1 and B i The joint; b0 is the position vector from the base center of mass to joint J1; a i ,b i (i = 1, 2, ..., n) represent the numbers starting from J. i Pointing to C i C i Pointing to J i+1 The position vector; r0 is the position vector of the base centroid; p i (i = 1, 2, ..., n) is J i Position vector; r i (i = 1, 2, ..., n) is C i Position vector;

[0137] Figure 3 This is a flowchart of the Tribal Migration Algorithm (TMA), where == indicates whether the pairs are equal.

[0138] Figure 4 Fitness curves for the tribal migration algorithm;

[0139] Figure 5a This is a graph showing the joint angles of a two-bar linkage space robot.

[0140] Figure 5b This is a graph showing the angular velocity curves of the joints of a two-bar linkage space robot.

[0141] Figure 5c This is a graph showing the joint angular acceleration curves of a two-bar linkage space robot.

[0142] Figure 6a An angle curve of the base of a two-bar linkage space robot;

[0143] Figure 6b This is a graph showing the angular velocity of the base of a two-bar linkage space robot. Detailed Implementation

[0144] Specific Implementation Method 1: The specific process of this implementation method for an anti-disturbance method for a space robot base based on a tribal migration algorithm is as follows:

[0145] This invention enables a free-floating space robot arm to reduce disturbance to the base posture while completing its motion objectives by intelligently optimizing joint trajectories.

[0146] Step 1: Based on the motion relationship equations of the free-floating space robot base and the robotic arm, define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance. Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance, construct the objective function of the free-floating space robot base attitude disturbance.

[0147] Step 2: The objective function for the attitude disturbance of the free-floating space robot base is related to the joint angles and angular velocities of the free-floating space robot. The method of using a seventh-order sine polynomial is used to parameterize the trajectory of the i-th manipulator joint angle of the free-floating space robot, and the seventh-order sine polynomial is converted into a polynomial represented by only two unknown parameters.

[0148] By defining the mission objectives and joint constraints, the trajectories of joint angles, angular velocities, and angular accelerations can be transformed into expressions affected by only two unknown parameters.

[0149] Step 3: Based on the mission of the free-floating space robot, the initial joint angle, angular velocity, final joint angle and angular acceleration, and mission time are known. The seventh-degree sine polynomial can be expressed as a polynomial with only two unknown parameters. The tribal migration algorithm is used to optimize these two unknown parameters to reduce the base attitude disturbance objective function value, thus obtaining the robot arm joint angle that minimizes the base attitude disturbance objective function value (obtaining parameter 'a' that minimizes the base attitude disturbance objective function). i7 a i6 Substituting the equation into a seventh-order sine polynomial yields the joint motion trajectory, minimizing the impact of disturbance on the base.

[0150] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step one, the motion relationship equations between the free-floating space robot base and the robotic arm are used... Define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Construct the objective function P for the base attitude perturbation of the free-floating space robot;

[0151] The specific process is as follows:

[0152] Step 11, as follows Figure 1 As shown, Figure 1 This is a general structural diagram of a space robot. B0 represents the base of the free-floating space robot, B... i J represents the i-th rigid body of the free-floating space robot, i.e., the i-th link of the free-floating space robot, where i = 1, 2, ..., n; i Indicates connection B i-1 and B iThe i-th robotic arm joint, i = 1, 2...n;

[0153] n represents the total number of links or joints of the free-floating space robot;

[0154] The equations of motion relating the base and the robotic arm of the free-floating space robot are expressed as follows:

[0155]

[0156] Where v0 is the linear velocity of the free-floating space robot base, ω0 is the angular velocity of the free-floating space robot base, M is the total mass of the robot, I3 is the third-order identity matrix, and r 0g The vector representation of the center of mass of the base pointing towards the center of mass of the freely floating robot in space. For r 0g The antisymmetric matrix; H M H MV H MW This is a coefficient matrix describing the relationship between the base state and the joint angular velocity. is the angular velocity matrix of the joints of the free-floating space robot, and J is the Jacobian matrix describing the motion relationship between the base and each robotic arm joint;

[0157] Steps 1 and 2: Assume the initial angular momentum of the freely floating space robot is zero;

[0158] During the motion, the base will be constantly subjected to instantaneous perturbations. The defined attitude perturbation function for the space robot base is:

[0159]

[0160] in, Let t represent the base angular velocity of the freely floating space robot at time t;

[0161] J ω Let J be the matrix consisting of rows 4 to 6 of the Jacobian matrix.

[0162] Let represent the angular velocity matrix of the joints of the robotic arm of the robot that is freely floating in space at time t;

[0163] Step 13: To reduce the attitude disturbance of the base caused by the movement of the robotic arm, the amplitude of the base attitude disturbance process is defined. and the final amplitude of the base attitude perturbation Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Construct the objective function P for the base attitude perturbation of the free-floating space robot;

[0164] Step 14: Based on the objective function P of the base attitude disturbance of the free-floating space robot, the trajectory planning problem that minimizes the base attitude disturbance of the free-floating space robot is expressed as the following nonlinear constraint optimization problem.

[0165] The other steps and parameters are the same as in Specific Implementation Method 1.

[0166] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that: the coefficient matrix H... M The expression is:

[0167]

[0168] Among them, I i For the i-th rigid body B of the free-floating space robot i The inertia matrix, m i For the i-th rigid body B of the free-floating space robot i quality, r i Let B be the rigid body B of the freely floating robot, origin of the inertial coordinate system. i Vector representation of the centroid, r 0i Let the center of mass of the base point to the i-th rigid body B of the freely floating space robot. i Vector representation of the centroid.

[0169] Other steps and parameters are the same as in specific implementation method one or two.

[0170] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: the coefficient matrix H... MW The expression is:

[0171]

[0172] Where, r i0 B is the i-th rigid body of the free-floating space robot. i Vector representation of the centroid pointing towards the base centroid;

[0173] For r i0 The antisymmetric matrix;

[0174] J ωi J represents the components of the Jacobian matrix associated with rotational motion, specifically the Jacobian matrix corresponding to the joint angular velocity. ωi =[z1,z2,…,z i [,0,…,0];

[0175] J vi The components of the Jacobian matrix associated with linear motion, i.e., the Jacobian matrix J corresponding to the joint linear velocities. vi =[z1×(r)i -p1),z2×(r i -p2),…,z i ×(r i -p i ),0,…,0];

[0176] z i For joint J i The rotation axis vector representation, p i From the origin of the inertial coordinate system to joint J i Vector representation of .

[0177] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0178] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: the coefficient matrix H... MV The expression is:

[0179]

[0180] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0181] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that the objective function P in step one through three is:

[0182]

[0183] Where P represents the objective function for perturbing the base attitude of the free-floating space robot, t0 represents the start time of the free-floating space robot mission, and t f Indicates the end time of the free-floating space robot mission. Let t represent the base angular velocity of the freely floating space robot at each moment, t represent the current moment, a represent the process disturbance weight, and b represent the final process disturbance weight.

[0184] Among them, the first item It is the absolute value of the integral of the base angular velocity at the end time relative to the initial time over time. The purpose is to limit the large swing of the base during the motion, which could lead to dangerous situations such as communication disruptions.

[0185] The next item It is the integral of the base angular velocity at the end time relative to the initial time over time. The purpose is to limit the attitude disturbance of the base in the final state to be too large, which may cause the robotic arm to collide with the base, reduce the efficiency of space mission execution, or even damage the spacecraft.

[0186] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0187] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step one four, based on the objective function P of the free-floating space robot's base attitude disturbance, the trajectory planning problem that minimizes the base attitude disturbance of the free-floating space robot is expressed as the following nonlinear constraint optimization problem, with the expression being:

[0188]

[0189] stq T =q d

[0190]

[0191] q min ≤q n (t)≤q max

[0192]

[0193] Where, q T q represents the joint angle of the robotic arm at the end of the task. d Indicates the target joint angle of the robotic arm;

[0194] This indicates the angular velocity of the robotic arm joints at the end of the task. This indicates the target joint angular velocity of the robotic arm;

[0195] q min q is the lower limit of the joint angle constraint for the robotic arm. max Limit the upper limit of the joint angle of the robotic arm;

[0196] The lower limit of the joint angular velocity of the robotic arm. The upper limit of the angular velocity of the articulated robotic arm;

[0197] q n (t) is the joint angle of the robotic arm at time t. It is the angular velocity of the robotic arm joint at time t.

[0198] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0199] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that: in step two, the objective function for the attitude disturbance of the free-floating space robot base is related to the joint angle and angular velocity of the free-floating space robot. The method of using a seventh-order sine polynomial is used to parameterize the trajectory of the i-th mechanical arm joint of the free-floating space robot, and the seventh-order sine polynomial is converted into a polynomial represented by only two unknown parameters.

[0200] The objective function for perturbation of the base of the free-floating space robot is related to the joint angles and angular velocities of the free-floating space robot. Therefore, a seventh-order sine polynomial is used to approximate the highly nonlinear trajectory of the joint angles, angular velocities, and angular accelerations.

[0201] By defining the mission objectives and joint constraints, the trajectories of joint angles, angular velocities, and angular accelerations can be transformed into expressions affected by only two unknown parameters.

[0202] The specific process is as follows:

[0203] Set the end angular velocity of the robotic arm joint and angular acceleration for:

[0204]

[0205] Meanwhile, the limit values ​​for the joint angles of the robotic arm are set as follows:

[0206] q i_min ≤q i (t)≤q i_max i = 1, ..., n

[0207] Where, q i (t) represents the joint angle of the i-th robotic arm at the current moment;

[0208] n represents the total number of links or joints of the free-floating space robot;

[0209] q i_min and q i_max Let represent the minimum and maximum achievable angles of the i-th robotic arm joint, respectively.

[0210] Let the expected value of the angle of the i-th robotic arm joint be: q i (t f )=q id ;

[0211] The seventh-order sine polynomial method is used to parameterize the trajectory of the i-th joint angle of the free-floating space robot, transforming the seventh-order sine polynomial into one consisting only of a. i7 ,a i6 A polynomial represented by two unknown parameters;

[0212] q i (t)=Δ i1 sin(a i7 t 7 +a i6 t 6 +a i5 t5 +a i4 t 4 +a i3 t 3 +a i2 t 2 +a i1 t+a i0 )+Δ i2

[0213] Among them, a i0 a i1 a i2 a i3 a i4 a i5 a i6 a i7 Indicates the parameter, Δ i1 Δ i2 Indicates intermediate variables;

[0214]

[0215] a i0 =sin -1 [(q i0 -Δ i2 ) / Δ i1 ]

[0216] a i1 =a i2 =0

[0217]

[0218] Where, q i0 This represents the initial angle of the i-th joint.

[0219] Given the joint start angle, start angular velocity, target angle, target angular velocity, and termination time based on the space mission objective, transform the seventh-degree sine polynomial into a polynomial consisting only of a. i7 ,a i6 A polynomial represented by two unknown parameters can be solved by optimizing a. i7 ,a i6 By altering the joint trajectories, the objective function can be reduced, thereby decreasing the disturbance to the space robot's base.

[0220] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0221] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that: in step three, based on the task of the free-floating space robot, the joint's initial angle, angular velocity, final angle and angular acceleration, and task time are known. The seventh-degree sine polynomial can be expressed as a polynomial with only two unknown parameters. The tribal migration algorithm is used to optimize the two unknown parameters in the polynomial to reduce the value of the base attitude disturbance objective function, thus obtaining the joint angle trajectory that minimizes the base attitude disturbance objective function value (obtaining parameter 'a' that minimizes the base attitude disturbance objective function). i7 a i6 Substituting the seventh-order sine polynomial into the equation yields the joint motion trajectory, minimizing the impact of disturbance on the base.

[0222] The specific process is as follows:

[0223] This invention proposes an optimization method called the Tribal Migration Algorithm, which aims to simulate the migration and adaptation behavior of groups in nature in order to solve complex optimization problems. Figure 2 This is a flowchart of the Tribal Migration Algorithm (TMA).

[0224] Step 31: Set the iteration count j = 0;

[0225] Generate a population of M individuals, where each individual is a parameter set (a i6 ,a i7 );

[0226] Each individual is randomly distributed within the search space (a is the parameter set corresponding to each individual). i6 ,a i7 Randomly assigned values, one individual corresponds to one x. s,j Value, x s,j The value is the value of parameter set (ai6, ai7):

[0227] x s,j =lb + r × (ub - lb)

[0228] Where, x s,j Let j represent an individual with index s, where s∈{0,1,2,...,M}, j∈{0,1,2,...,L}, and L is the total number of iterations;

[0229] r is a random number that satisfies 0 ≤ r ≤ 1;

[0230] lb is the lower boundary of the optimization, and ub is the upper boundary of the optimization (set; the wider the boundary, the greater the difficulty of optimization and the longer the time).

[0231] Step 3.2: Divide the population into N clusters using the DBSCAN clustering algorithm. Where g∈[0,N];

[0232] Based on clustering Clustering is derived from the average position of individuals. center

[0233] Step 3: Adaptively adjust the exploration factor I and the random factor R according to the current algebra j. By adaptively adjusting the values ​​of I (exploration factor) and R (random factor), these parameters are dynamically adjusted according to the algebra and optimization effect as the iteration process progresses, so as to help the algorithm obtain better optimization results.

[0234]

[0235] Where I(j) represents the value of the exploration factor I in the j-th iteration;

[0236] R(j) represents the value of the random factor R in the j-th iteration;

[0237] j∈{0,1,2,...,L}, where L is the maximum number of iterations;

[0238] w is the initial value of the exploration factor I, and c is the initial value of the random factor R;

[0239] Steps 3 and 4: Generate a chaotic sequence and update it using logical mapping. This sequence is used to increase randomness and diversity in individual tribe defense or exploration. The chaotic sequence is defined as follows:

[0240] r(s+1)=μr(s)(1-r(s))

[0241] Where r(s+1) is the chaotic sequence generated through iteration, r(0) is a random number between 0 and 1, and μ represents the chaotic coefficient;

[0242] Step 35: Assign the parameter group (a) to each individual. i6 ,a i7 Substituting into the seventh-degree sine polynomial Obtain the motion trajectories of all joints of the space robot (an individual obtains the motion trajectories of all joints of the space robot);

[0243] Then, through the defined space robot base attitude perturbation function Calculate the fitness function J for each individual. s,j :

[0244]

[0245] Where a represents the process disturbance weight, and b represents the final process disturbance weight;

[0246] Let represent the base angular velocity of individual s at time t during the j-th iteration;

[0247] This represents the set of joint angular velocities of individual s at time t during the j-th iteration. This represents the set of joint angles of individual s at time t during the j-th iteration;

[0248] This represents the angular velocity of joint i corresponding to individual s at time t during the j-th iteration. This represents the angle of joint i corresponding to individual s at time t during the j-th iteration;

[0249] Clustering The individual with the highest fitness in a cluster is defined as that cluster. Leaders in

[0250] Step 36: Each cluster Individuals within Clustering The individual with the highest fitness Movement, mimicking the behavior of individuals gathering towards a leader in nature, if individuals Fitness value of the new position Fitness value J greater than the original position s,j Then the individual Values If individual Fitness value of the new position Fitness value J less than or equal to the original position s,j Then the individual Values

[0251] The expression is:

[0252]

[0253] in, This indicates clustering at stage P1, during the j-th iteration. The inner individual s of (a) i7 ,a i6 ) value;

[0254] Clustering Individuals within;

[0255] r(j) is the chaos coefficient at the j-th iteration;

[0256] Clustering The individual with the highest fitness;

[0257] Step 37: Calculate Clustering The average fitness value of all individuals and clustering center Distance to other clusters Distance from the center

[0258] in, N represents the total number of clusters;

[0259] based on and Calculate the attractiveness index The expression is:

[0260]

[0261] in, It is clustering Leader fitness value, It is clustering center Distance to other clusters The maximum distance from the center;

[0262] By analyzing attractiveness indicators Sorting, Clustering Individuals within Towards Clustering corresponding to the maximum value If individuals move closer to the center, Fitness value of the new position Larger than an individual fitness value of the original position Individual Values If individual Fitness value of the new position Less than or equal to individuals fitness value of the original position Individual Values This reflects the aggregation behavior of groups towards resource-rich areas and the mutual learning and adaptation processes among groups;

[0263] The expression is:

[0264]

[0265] in, This indicates clustering at stage P2, during the j-th iteration. The inner individual s of (a) i7 ,a i6Values ​​(clustering at the j-th iteration) Individual with internal s serial number Towards the most attractive cluster centers (Values ​​after convergence);

[0266] Step 38: During migration, individuals may encounter attacks from other creatures, representing random events or challenges in the environment. Faced with these challenges, groups may move randomly to avoid threats or gather to hunt, symbolizing how groups in the real world respond to unexpected events through cooperation or escape.

[0267] During one cycle, either a threat-avoidance situation or a hunting situation occurs randomly.

[0268] 1) In a threat-avoidance situation, an individual will randomly move from its original location, as represented by the following formula:

[0269]

[0270] in, This indicates clustering at stage P3, during the j-th iteration. Individual with s sequence number The value obtained after avoiding threats during migration;

[0271] 2) In a hunting scenario, randomly select an individual from each cluster as the target. The remaining individuals will attack the attacked individual. Approach;

[0272] If the individual's fitness at the new location Fitness greater than the original position Individual Values If the individual's fitness at the new location Fitness less than or equal to the original position Individual Values

[0273] The process is represented as

[0274]

[0275] Step 39: Check if all individuals have completed the position update. If not, let s = s + 1 and execute Step 34; otherwise, retain the parameter set (a) corresponding to the individual with the highest fitness. i6 ,a i7 ), proceed to step thirty;

[0276] Step 30: Randomly select a subset of individuals (from M individuals) for reinitialization:

[0277] Each randomly selected individual is randomly distributed within the search space, and each individual receives a new corresponding set of parameters (a). i6 ,a i7 );

[0278] individual The probability T of being selected s,j And the corresponding roulette betting range U s,j for:

[0279]

[0280] Among them, T y,j This refers to individuals whose index is less than s. The probability of being selected is y = [0, 1, ..., s-1], where y represents the individual. The serial number;

[0281] Generate e random numbers r between 0 and 1. p , p∈{0,1,2,....e};

[0282] Find the satisfaction of U c-1,j <r p ≤U c,j Corresponding individuals The serial number of the selected individual;

[0283] Reinitialization:

[0284] x c,j+1 =lb + r × (ub - lb)

[0285] This step simulates the elimination and addition of new individuals in the process of natural selection, which helps maintain the diversity and adaptability of the group;

[0286] Step 31: Check if the specified number of iterations has been completed. If not, let j = j + 1 and jump to step 32; otherwise, jump to step 33.

[0287] Step 32: Check if j = L. If they are equal, it can be considered that the population has undergone significant changes after multiple iterations. Then, perform DBSCAN clustering on all M individuals again and jump to step 32. If they are not equal, then there is no need to re-cluster and jump to step 33.

[0288] Step 33: Complete the optimization process and obtain the individual that minimizes the objective function of the base perturbation (the parameter set corresponding to the individual with the highest fitness retained in Step 39 (a)). i6 ,ai7 ), parameter group (a i6 ,a i7 Input the polynomial and get q. n (t), based on calculate based on Substitute The individual that minimizes the objective function of the base disturbance is obtained, and then the motion trajectory of the robot arm joint angle is obtained.

[0289] In addressing the problem of disturbance immunity of space robot bases, the Tribal Migration Algorithm (TMA) demonstrates outstanding performance, effectively finding optimized control parameters and minimizing the cost function, thereby optimizing the disturbance immunity of the base.

[0290] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0291] The beneficial effects of the present invention are verified using the following embodiments:

[0292] Example 1:

[0293] A planar two-link free-floating space robot was selected for simulation analysis. Compared with other space robots, the attitude and position of the planar two-link free-floating space robot are relatively easy to describe and control, and it has better mechanical performance and higher application value. It is also widely used in the aerospace field.

[0294] Step 1: Assume that the rigid body B of the spatial two-bar linkage robot can be obtained. i mass m i Rigid body B i Moment of inertia I i Joint J i To rigid body B i The length of the centroid a i Rigid body B i Center of mass to joint J i+1 Length b i Furthermore, the task objective of the end controller is known.

[0295]

[0296] Step 2: When the space robot moves into the working area of ​​the robotic arm, the position of the target is observed through the onboard camera, and then the target angle of the robotic arm is obtained. Assuming the current state of the robot and the target state are as follows:

[0297]

[0298] Step 3: Initialize algorithm parameters. Set the population size N to 100, the number of iterations L to 30, the total simulation time tf = 5, the time step dt = 0.01, and initialize the population. Each individual x... s,j s∈[0,100], j∈[0,30] are four random numbers (a,j) in the interval [-3,3]. 17 ,a 16 ,a 27 ,a 26 )constitute.

[0299] Step 4: Divide the population into 5 clusters using the DBSCAN clustering algorithm. The center of each cluster can be determined based on the average position of individuals within the cluster.

[0300] Step 5: Adaptively adjust parameters I(j) and R(j) based on the current algebra j:

[0301]

[0302] Step 6: Generate a chaotic sequence:

[0303] r(s+1)=4×r(s)(1-r(s))

[0304] A chaotic sequence r(s) can be generated by using a random number r(0) between 0 and 1.

[0305] Step 7: Based on individual x s,j Substituting the values ​​into the seventh-order sine polynomial yields the joint angles, angular velocities, and angular accelerations of the two joints of the space robot. Using the kinematic formulas for the base, the angular velocity of the base rotation can be calculated. Setting a = 0.2 and b = 0.8, the base perturbation fitness function can then be calculated.

[0306]

[0307] Step 6: Sort by fitness function and find each cluster. The individual with the highest fitness function is selected as the pioneer zebra.

[0308] Step 7: In the P1 phase, each cluster... Individuals within the leadership Approach:

[0309]

[0310] If the fitness value of the new position after the move is higher than that of the original position, then the move is retained.

[0311] Step 8: In the P2 phase, obtain the cluster by summing the fitness values ​​of all individuals within the cluster and dividing by the number of individuals in the cluster. Average fitness value Then calculate the different cluster centers. Distance between This leads to the attraction index:

[0312]

[0313] Individuals in a cluster will gravitate towards those with higher attractiveness indices, i.e.:

[0314]

[0315] If the fitness value of the new position after the move is higher than that of the original position, then the move is retained.

[0316] Step 9: In Phase 3, each cluster has a 50% chance of encountering a ferocious animal, and the cluster enters a hiding state, that is, it randomly relocates from its original position:

[0317]

[0318] There is also a 50% probability that joint defense will be needed, meaning all attackers will converge on a randomly generated target.

[0319]

[0320] If the fitness value of the new position after the move is higher than that of the original position, then the move is retained.

[0321] Step 11: Check if all individuals have been updated. If not, continue updating individuals and jump to step 5; otherwise, retain the individual with the highest fitness and jump to step 12.

[0322] Step 12: Eliminate a portion of individuals based on the elimination probability:

[0323]

[0324] Generate 5 random numbers r between 0 and 1. p For p∈{0,1,2,....4}, find the expression U c-1,j <r p ≤U c,j individual Reinitialization:

[0325] x c,j+1 =lb + r × (ub - lb)

[0326] Step 13: If the specified algebraic iterations are completed, proceed to step 15 to obtain the optimal joint parameters (a). 17 ,a 16 ,a 27 ,a 26 ).

[0327] Conversely, if the condition is not met, then j+1, jump to step 14, and proceed to the next iteration.

[0328] Step 14: If 5 algebraic iterations have been performed since the last clustering, skip to Step 5, perform DBSCAN clustering again to generate 5 new clusters, and continue the loop. Otherwise, skip to Step 6 and continue the algebraic iterations.

[0329] Step 15: Complete the tribal migration algorithm's iterative process to obtain the individual with the highest fitness (a 17 ,a 16 ,a 27 ,a 26 This parameter minimizes the objective function of the space robot's base disturbance. For example... Figure 3 , Figure 4 This is the optimal trajectory planning curve obtained by the tribal migration algorithm under these parameters. At this time, the optimal individual is [0.00220103 -0.0357294 0.03085508-0.5366869], and the fitness value is 6.675770203470313.

[0330] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A disturbance resistance method for a space robot base based on a tribal migration algorithm, characterized in that: The specific process of the method is as follows: Step 1: Based on the motion relationship equations of the free-floating space robot base and the robotic arm, define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance. Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance, construct the objective function of the free-floating space robot base attitude disturbance. Step 2: Using the seventh-order sine polynomial method to analyze the free-floating space robot's... The trajectory of the joint angles of the robotic arm is parameterized, and the seventh-degree sine polynomial is transformed into a polynomial represented by only two unknown parameters. Step 3: Optimize the two unknown parameters in the polynomial using the tribal migration algorithm to reduce the value of the objective function of the base attitude disturbance, and obtain the robot arm joint angle that minimizes the value of the objective function of the base attitude disturbance. In step one, based on the motion equations of the free-floating space robot's base and robotic arm, the amplitude of the base attitude disturbance process and the final amplitude of the base attitude disturbance are defined. Based on these amplitudes, the objective function for the base attitude disturbance of the free-floating space robot is constructed. The specific process is as follows: Step 11: The equations of motion between the free-floating space robot base and the robotic arm are expressed as follows: in, The linear velocity of the free-floating space robot base. The angular velocity of the free-floating space robot base. For the total mass of the robot, It is a third-order identity matrix. The vector representation of the center of mass of the base pointing towards the center of mass of the freely floating robot in space. for The antisymmetric matrix; It is the angular velocity matrix of the joints of a free-floating space robot. The Jacobian matrix describes the motion relationship between the base and each robotic arm joint; , , It is a coefficient matrix; Steps 1 and 2: Assume the initial angular momentum of the freely floating space robot is zero; During the motion, the base will be constantly subjected to instantaneous perturbations. The defined attitude perturbation function for the space robot base is: in, express The angular velocity of the base of the constantly floating space robot; Jacobian matrix The matrix from the fourth to the sixth row; express Angular velocity matrix of the joints of the robotic arm of a space robot that is constantly floating in space; Step 13: Define the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Based on the amplitude of the base attitude disturbance process and the final amplitude of the base attitude perturbation Constructing the objective function for the base attitude perturbation of a free-floating space robot ; Step 1.4: Objective function for base attitude perturbation of a free-floating space robot The trajectory planning problem that minimizes the base attitude disturbance of a free-floating space robot can be expressed as a nonlinear constrained optimization problem to be solved as follows: The coefficient matrix The expression is: in, For the first free-floating space robot rigid body The inertia matrix, For the first free-floating space robot rigid body quality From the origin of the inertial coordinate system to the free-floating space robot rigid body Vector representation of the centroid The base's center of mass points towards the free-floating space robot. rigid body Vector representation of the centroid; The coefficient matrix The expression is: in, It is the first free-floating space robot rigid body Vector representation of the centroid pointing towards the base centroid; for The antisymmetric matrix; The components of the Jacobian matrix related to rotational motion, i.e., the Jacobian matrix corresponding to the joint angular velocity. ; The components of the Jacobian matrix associated with linear motion, i.e., the Jacobian matrix corresponding to joint linear velocities. ; For joints The rotation axis vector representation, From the origin of the inertial coordinate system to the joint Vector representation; The coefficient matrix The expression is: ； The objective function in steps one and three for: in, Let represent the objective function for perturbing the base attitude of a free-floating space robot. Indicates the start time of the free-floating space robot mission. Indicates the end time of the free-floating space robot mission. This represents the angular velocity of the base of the freely floating space robot at each moment. Indicates the current moment. Indicates the process disturbance weights. Indicates the final process perturbation weights; In step three, the tribal migration algorithm is used to optimize two unknown parameters in the polynomial to reduce the value of the objective function for base attitude disturbance, thereby obtaining the joint angle trajectory that minimizes the objective function value for base attitude disturbance; the specific process is as follows: Step 31: Let the number of iterations be... ; Generate a population consisting of M individuals, where each individual is a parameter set. ; Each individual is randomly distributed within the search space: in, express generation Individual number , , This represents the total number of iterations. To meet Random numbers; To find the optimal lower boundary, To find the optimal upper boundary; Step 3.2: Use the DBSCAN clustering algorithm to divide the population into groups. Clusters , ; Based on clustering Clustering is derived from the average position of individuals. center ; Step 3: Adaptively adjust the exploration factor based on the current algebra j. and random factors ; in, Indicates the first Exploring factors during the next iteration The value; Indicates the first Random factor at the next iteration The value; L is the maximum number of iterations; It is an exploration factor initial value, It is a random factor The initial value; Steps 3 and 4: Generate chaotic sequences. The definition of a chaotic sequence is as follows: in, The chaotic sequence is generated through iteration. A random number between 0 and 1 Represents the chaos coefficient; Step 35: Set the parameter group for each individual. Substituting into the seventh-degree sine polynomial This allows us to obtain the motion trajectories of all joints of the space robot. Then, through the defined space robot base attitude perturbation function Calculate the fitness function for each individual. : in, Indicates the process disturbance weights. Indicates the final process perturbation weights; Indicates the first In the next iteration, the individual exist The base angular velocity at time t; Indicates the first In the next iteration, the individual exist The set of joint angular velocities at each moment. Indicates the first In the next iteration, the individual exist The set of joint angles corresponding to each moment; Indicates the first In the next iteration, the individual exist The joint corresponding to the moment angular velocity, Indicates the first In the next iteration, the individual exist The joint corresponding to the moment Angle; Clustering The individual with the highest fitness is defined as the cluster. Leaders in ; Step 36: Each cluster Individuals within Clustering The individual with the highest fitness Movement, if individual Fitness value of the new position Fitness value greater than the original position Then the individual The value is If individuals Fitness value of the new position Fitness value less than or equal to the original position Then the individual The value is ; The expression is: in, This indicates that in stage P1, the first... Clustering at the next iteration Inner individual of Values; Clustering Individuals within; For the first Chaos coefficient at the next iteration; Clustering The individual with the highest fitness; Step 37: Calculate Clustering The average fitness value of all individuals and clustering center Distance to other clusters Distance from the center ; in, , ; Represents the total number of clusters; based on and Calculate the attractiveness index The expression is: in, It is clustering Leader fitness value, It is clustering center Distance to other clusters The maximum distance from the center; By analyzing attractiveness indicators Sorting, Clustering Individuals within Towards Clustering corresponding to the maximum value If individuals move closer to the center, Fitness value of the new position Larger than an individual Fitness value of the original position Then the individual Values If an individual Fitness value of the new position Less than or equal to individuals Fitness value of the original position Then the individual Values ; The expression is: in, This indicates that in stage P2, the... Clustering at the next iteration Inner individual of Values; Step 38: During one cycle, either a threat avoidance situation or a hunting situation will occur randomly; 1) In a threat-avoidance situation, an individual will randomly move from its original location, as represented by the following formula: in, This indicates that in stage P3, the... Clustering at the next iteration In Individual number The value obtained after avoiding threats during migration; 2) In a hunting scenario, randomly select an individual from each cluster as the target. The remaining individuals will attack the attacked individual. Approach; If the individual's fitness at the new location Fitness greater than the original position Then the individual Values If the fitness of an individual in its new location Fitness less than or equal to the original position Then the individual Values ; The process is represented as Step 39: Check if all individuals have completed their location updates. If not all have, then... Perform steps three and four; otherwise, retain the parameter set corresponding to the individual with the highest fitness. Proceed to step thirty; Step 30: Randomly select a portion of individuals for reinitialization: Each randomly selected individual is randomly distributed within the search space, and each individual receives a new set of corresponding parameters. ; individual Probability of being selected and the corresponding roulette betting range for: in, Indicates that the individual serial number is less than individual The probability of being selected. , Represents an individual The serial number; Randomly generated A random number between 0 and 1 , ; Find satisfaction Corresponding individuals , The serial number of the selected individual; Reinitialization: Step 31: Check if the specified number of iterations has been completed. If not, then let... If yes, proceed to step 32; otherwise, proceed to step 33. Step 32: Check if If they are equal, perform DBSCAN clustering again on all M individuals and jump to step 32; if they are not equal, no re-clustering is needed and jump to step 33. Step 33: Complete the optimization process to obtain the individual that minimizes the objective function of the base disturbance, and then obtain the motion trajectory of the robot arm joint angle.

2. The disturbance resistance method for a space robot base based on a tribal migration algorithm according to claim 1, characterized in that: The objective function for base attitude perturbation of the free-floating space robot in step one four is as follows. The trajectory planning problem that minimizes the base attitude disturbance of a free-floating space robot can be expressed as a nonlinear constrained optimization problem, with the following expression: in, This indicates the angle of the robotic arm joints at the end of the task. Indicates the target joint angle of the robotic arm; This indicates the angular velocity of the robotic arm joints at the end of the task. This indicates the target joint angular velocity of the robotic arm; This sets the lower limit for the joint angle of the robotic arm. Limit the upper limit of the joint angle of the robotic arm; The lower limit of the angular velocity limit for the robotic arm joints. The upper limit of the angular velocity of the articulated robotic arm; yes The joint angles of the robotic arm are constantly monitored. yes The angular velocity of the robotic arm joints at all times.

3. The disturbance resistance method for a space robot base based on a tribal migration algorithm according to claim 2, characterized in that: In step two, the seventh-order sine polynomial method is used to analyze the free-floating space robot. The trajectory of each robotic arm joint angle is parameterized, transforming the seventh-degree sine polynomial into a polynomial represented by only two unknown parameters; the specific process is as follows: Set the end angular velocity of the robotic arm joint and angular acceleration for: Meanwhile, the limit values ​​for the joint angles of the robotic arm are set as follows: in, Indicates the current time. The joint angles of a robotic arm; This indicates the total number of links or joints in a free-floating space robot. and They represent the first The minimum and maximum achievable joint angles of a robotic arm; Setting the first The expected value of each robotic arm joint angle is: ; The method of using a seventh-order sine polynomial is selected to study the first... The trajectory of each robotic arm joint angle is parameterized, transforming the seventh-order sine polynomial into one derived solely from... A polynomial represented by two unknown parameters; in, , , , , , , , Indicates parameters, , Indicates intermediate variables; in, Indicates the first The initial angle of each joint.

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