Robot inverse solution optimization method and system based on multi-target Pareto optimization-particle swarm mixing

Abstract

The invention discloses a robot inverse solution optimization method and system based on multi-target Pareto optimization-particle swarm mixing, and the method comprises the following steps: constructing a kinematics model of a 7R redundant robot, and calculating an inverse kinematics analytical solution; constraint conditions and optimization targets of an inverse kinematics analytical solution of the robot are set, the constraint conditions include obstacle avoidance, singularity avoidance and joint limit, and the optimization targets include jump optimization, time optimization and curvature optimization; and optimizing the inverse kinematics analytical solution based on the constraint condition and the optimization target to obtain an inverse kinematics optimal solution. According to the method, inverse solution and optimization can be carried out on the determined trajectory, so that the joint space can be smoother, flexibility, energy consumption and arm curvature are considered while abrupt change does not exist, and the performance target of optimal joint space planning is achieved to the maximum extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of motion control for redundant robot inverse solution optimization, and in particular relates to a robot inverse solution optimization method and system based on multi-objective Pareto optimal-particle swarm mixing. Background Art

[0002] There are a large number of pipelines in large ships and boiler plants, but the free space is small. It is difficult for welders to maintain a good welding posture and operation during the welding process, which affects the welding quality and efficiency. At present, most of the pipeline welding work is done manually, with a low degree of mechanization and low production efficiency. In addition, the welding process usually needs to be carried out in a high temperature and harmful environment. Long-term exposure to high temperature welding will have an adverse effect on the health of welders and increase the risk of operation. In recent years, with the development of automation technology, welding automation technology has also developed rapidly, and many automatic welding equipment have emerged, such as automatic welding machines, welding carriages, laser welding machines, welding robots, etc., to achieve parameter adjustment of the welding process, welding path control, etc., to improve the quality and efficiency of welding.

[0003] However, for all-position multi-pass welding at pipe joints, as well as the need for repair welding of defective pipes in service in large ships and boiler plants, the current related automated welding equipment is difficult to meet the requirements in terms of welding space flexibility. Compared with the traditional non-redundant 6-DOF manipulator, the 7R redundant robot has greater flexibility. The terminal posture of the 7R redundant robot corresponds to countless joint combinations, which allows the 7R redundant robot to keep the end unchanged while the joints still move. This is a unique adaptive feature of the redundant robot, so its advantages include obstacle avoidance, singularity avoidance, and enhanced operability. Based on the above advantages, it can better meet the requirements of welding flexibility. However, this feature makes the inverse solution of the 7R redundant robot multi-solution, which increases the complexity of inverse kinematics.

[0004] At present, the main inverse kinematics solution algorithms for 7R redundant robots include geometric method, weighted minimum norm method, neural network method, genetic algorithm, particle swarm, etc. However, when ensuring accuracy, the adaptive performance of redundant robots is often lost. However, when relying solely on intelligent algorithms to ensure its flexibility, the solution accuracy and calculation time will contradict each other and it is difficult to ensure them at the same time. Summary of the invention

[0005] The present invention aims to solve the deficiencies of the prior art and provides the following solutions:

[0006] A robot inverse solution optimization method based on multi-objective Pareto optimal-particle swarm hybrid includes the following steps:

[0007] Construct the kinematic model of the 7R redundant robot and calculate the inverse kinematics analytical solution;

[0008] Setting constraints and optimization goals of the inverse kinematics analytical solution of the robot, wherein the constraints include: obstacle avoidance, singularity avoidance and joint limit, and the optimization goals include: optimal jump, optimal time and optimal curvature;

[0009] The inverse kinematics analytical solution is optimized based on the constraint conditions and the optimization target to obtain an inverse kinematics optimal solution.

[0010] Preferably, the process of calculating the inverse kinematics analytical solution includes:

[0011] Construct the kinematic model of the 7R redundant robot:

[0012]

[0013] Among them, r 11 、r 12 、r 13 ...r 33 Indicates the posture of the robot end flange coordinate system, px e ,py e 、pz e represents the position vector of the origin of the connecting rod 7;

[0014] Move the origin of the robot end flange coordinate system to the intersection center of the last three joints, and use the inverse transformation method to obtain the angle value of joint 1:

[0015] θ1=a tan 2(py,px)

[0016] px=px e -r 13 d7

[0017] py=py e -r 23 d7

[0018] Wherein, θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the link 7 coordinate system relative to the link 6 coordinate system in the Z-axis direction;

[0019] The angle value θ3 of joint 3 is taken as a known value, and joint 2 and joint 3 are equivalent to an equivalent joint θ eq :

[0020] θ eq =-atan2(d5,a5)±acos(temp)

[0021] temp=(BT - DT 2 -CT 2) / (2*DT*CT)

[0022] BT=sqrt(P 2 +Q 2 )

[0023] P=px*c1+py*s1-a2

[0024] Q=BT=pz-d1

[0025]

[0026] Wherein, c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents square root calculation, a2 represents the length of connecting rod 2, a3 represents the length of connecting rod 3, a4 represents the length of connecting rod 4, a5 represents the length of connecting rod 5, d1 represents the distance between connecting rod 1 and connecting rod 0, and d5 represents the distance between connecting rod 5 and connecting rod 4;

[0027] Calculate the equivalent joint θ eq Middle value of middle joint 2:

[0028] θ 2m =a tan2(-(P*k4+Q*k3),P*k3-Q*k4)

[0029] k3=DT+a5*c4-d5*s4

[0030] k4=d5*s4+d5*c4

[0031] Wherein, c4 represents the cosine value of θ4, and s4 represents the sine value of θ4;

[0032] According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated:

[0033] θ2=θ 2m ±(θ3-temp2)

[0034] θ4=θ eq ±temp2

[0035] temp2=a sin(temp1*a4)

[0036] temp1=abs(s3) / DT

[0037] Where, s3 represents the sine value of θ3, and abs represents the absolute value;

[0038] According to the known origin of the robot end flange coordinate system and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6:

[0039]

[0040] m 23 =-c234*r 33 -c1*r 13 *s234-r 23 *s1*s234

[0041] C234=C23*C4-S23*S4

[0042] s234=s23*c4+c23*s4

[0043] c23=c2*c3-s2*s3

[0044] s23=s2*c3+c2*s3

[0045] Wherein, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2;

[0046] When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is:

[0047] θ7=a tan 2(-m 13 , m 11 )-θ5

[0048] m 11 =c1*c234*r 11 -r 31 *s234+c234*r 21 *s1

[0049] m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1

[0050] Wherein, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7;

[0051] When joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as:

[0052] θ5=a tan 2(m 33 , ±m 13 )

[0053] θ7=a tan 2(m 22 , ±m 21 )

[0054] m 21 =-c234*r 31 -cl*r 11 *s234-s234*r 21 *s1

[0055] m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1

[0056] m 33 =c1*r 23 -r 13 *s1.

[0057] Preferably, the optimization objectives include: optimal jump, optimal time and optimal curvature;

[0058] The optimal index function is:

[0059]

[0060] Where k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient, and q j，i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the range of motion of joint i;

[0061] The time-optimal index function is:

[0062]

[0063] t_d(j,i)=impW(i)*abs(q j，i -q j-1，i )

[0064]

[0065] Wherein, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, and t max(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution;

[0066] The optimal index function for the curvature is:

[0067]

[0068] Among them, bW1 and bW2 represent weight coefficients.

[0069] Preferably, the method for obtaining the optimal solution of inverse kinematics includes:

[0070] Determine the target trajectory machine interpolation number n and the constrained angle segment number m of the robot grasping the target;

[0071] Based on the time-optimal index function, the continuous interpolation points are determined, and the number of effective segments is k, then the initial solution set is m*(k)n;

[0072] Eliminate the inferior solutions where obstacles and singular points are located and obtain the feasible solution set F_set;

[0073] Based on the optimal jump, the optimal time and the optimal curvature, the Pareto optimal frontier is constructed using the quick sorting method, and the optimality of each solution of the frontier, opti_b, is calculated:

[0074]

[0075] Among them, Opti_b(i) represents the optimality of each solution;

[0076] Sort the optimality of each solution from small to large, select the numth one as the Pareto optimal solution F_best, generate an initial population of 100*(100*θ2) according to the variation range of joint 2 and joint 3 in F_best, and obtain the position and speed limits;

[0077] The fitness of the initial population is calculated based on the optimal index function of the curvature. When the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, the optimal solution F_best can be updated and the current optimality opti_b can be calculated. Otherwise, the speed and position are updated.

[0078] It is determined whether the optimality opti_b≤0.9 is satisfied. If yes, the optimal solution of the inverse kinematics is output.

[0079] The present invention also provides a robot inverse solution optimization system based on multi-objective Pareto optimal-particle swarm hybrid, the system applying any of the above methods, including: an analytical solution calculation module, a constraint module and an optimization module;

[0080] The analytical solution calculation module is used to construct a kinematic model of the 7R redundant robot and calculate an inverse kinematics analytical solution;

[0081] The constraint module is used to set the constraint conditions and optimization goals of the inverse kinematics analytical solution of the robot, the constraint conditions include: obstacle avoidance, singularity avoidance and joint limit, and the optimization goals include: optimal jump, optimal time and optimal curvature;

[0082] The optimization module optimizes the inverse kinematics analytical solution based on the constraint conditions and the optimization target to obtain the inverse kinematics optimal solution.

[0083] Preferably, the workflow of the analytical solution calculation module includes:

[0084] Construct the kinematic model of the 7R redundant robot:

[0085]

[0086] Among them, r 11 、r 12 、r 13 ...r 33 Indicates the posture of the robot end flange coordinate system, px e 、py e 、pz e represents the position vector of the origin of the connecting rod 7;

[0087] Move the origin of the robot end flange coordinate system to the intersection center of the last three joints, and use the inverse transformation method to obtain the angle value of joint 1:

[0088] θ1=a tan 2(py,px)

[0089] px=px e -r 13 d7

[0090] py=py e -r 23 d7

[0091] Wherein, θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the link 7 coordinate system relative to the link 6 coordinate system in the Z-axis direction;

[0092] The angle value θ3 of joint 3 is taken as a known value, and joint 2 and joint 3 are equivalent to an equivalent joint θ eq :

[0093] θ eq =-atan2(d5,a5)±acos(temp)

[0094] temp=(BT 2 -DT 2 -CT 2 ) / (2*DT*CT)

[0095] BT=sqrt(P 2 +Q 2 )

[0096] P=px*c1+py*s1-a2

[0097] Q=BT=pz-d1

[0098]

[0099] Wherein, c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents square root calculation, a2 represents the length of connecting rod 2, a3 represents the length of connecting rod 3, a4 represents the length of connecting rod 4, a5 represents the length of connecting rod 5, d1 represents the distance between connecting rod 1 and connecting rod 0, and d5 represents the distance between connecting rod 5 and connecting rod 4;

[0100] Calculate the equivalent joint θ eq Middle value of middle joint 2:

[0101] θ 2m =a tan 2(-(P*k4+Q*k3),P*k3-Q*k4)

[0102] k3=DT+a5*c4-d5*s4

[0103] k4=d5*s4+d5*c4

[0104] Wherein, c4 represents the cosine value of θ4, and s4 represents the sine value of θ4;

[0105] According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated:

[0106] θ2=θ 2m ±(θ3-temp2)

[0107] θ4=θ eq ±temp2

[0108] temp2=asin(temp1*a4)

[0109] temp1=abs(s3) / DT

[0110] Where, s3 represents the sine value of θ3, and abs represents the absolute value;

[0111] According to the known origin of the robot end flange coordinate system and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6:

[0112]

[0113] m 23 =-c234*r 33 -c1*r13 *s234-r 23 *s1*s234

[0114] C234=C23*C4-S23*S4

[0115] s234=s23*c4+c23*s4

[0116] c23=c2*c3-s2*s3

[0117] s23=s2*c3+c2*s3

[0118] Wherein, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2;

[0119] When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is:

[0120] θ7=a tan 2(-m 13 , m 11 )-θ5

[0121] m 11 =c1*c234*r11-r 31 *s234+c234*r 21 *s1

[0122] m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1

[0123] Wherein, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7;

[0124] When joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as:

[0125] θ5=a tan 2(m 33 , ±m 13 )

[0126] θ7=a tan 2(m 22 , ±m 21 )

[0127] m 21 =-c234*r 31 -c1*r 11 *s234-s234*r 21 *s1

[0128] m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1

[0129] m 33 =c1*r 23 -r 13 *s1.

[0130] Preferably, the optimal index function is:

[0131]

[0132] Where k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient, and q j，i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the range of motion of joint i;

[0133] The time-optimal index function is:

[0134]

[0135] t_d(j,i)=impW(i)*abs(q j，i -q j-1，i )

[0136]

[0137] Wherein, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, and t max(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution;

[0138] The optimal index function for the curvature is:

[0139]

[0140] Among them, bW1 and bW2 represent weight coefficients.

[0141] Preferably, the workflow of the optimization module includes:

[0142] Determine the target trajectory machine interpolation number n and the constrained angle segment number m of the robot grasping the target;

[0143] Based on the time-optimal index function, the continuous interpolation points are determined, and the number of effective segments is k, then the initial solution set is m*(k)n;

[0144] Eliminate the inferior solutions where obstacles and singular points are located and obtain the feasible solution set F_set;

[0145] Based on the optimal jump, the optimal time and the optimal curvature, the Pareto optimal frontier is constructed using the quick sorting method, and the optimality of each solution of the frontier, opti_b, is calculated:

[0146]

[0147] Among them, Opti_b(i) represents the optimality of each solution;

[0148] Sort the optimality of each solution from small to large, select the numth one as the Pareto optimal solution F_best, generate an initial population of 100*(100*θ2) according to the variation range of joint 2 and joint 3 in F_best, and obtain the position and speed limits;

[0149] The fitness of the initial population is calculated based on the optimal index function of the curvature. When the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, the optimal solution F_best can be updated and the current optimality opti_b can be calculated. Otherwise, the speed and position are updated.

[0150] It is determined whether the optimality opti_b≤0.9 is satisfied. If yes, the optimal solution of the inverse kinematics is output.

[0151] Compared with the prior art, the present invention has the following beneficial effects:

[0152] The present invention firstly aims at the inverse solution problem, and gives a calculation method of the analytical solution by constraining a joint value. Then, according to the inverse solution optimization goal, a robot inverse solution intelligent optimization algorithm based on a multi-objective Pareto optimal-particle swarm hybrid algorithm is proposed. The algorithm is suitable for offline programming optimizers with determined operation objects and occasions with high requirements for spatial flexibility. The present invention can perform inverse solution and optimization on the determined trajectory, so that the joint space can be smoother, without mutations, while taking flexibility, energy consumption, and arm bending into consideration, thereby achieving the optimal performance goal of joint space planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0153] In order to more clearly illustrate the technical solution 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 creative labor.

[0154] Figure 1 A schematic diagram of a method flow chart of an embodiment of the present invention;

[0155] Figure 2 Schematic diagram of a 7R redundant robot according to an embodiment of the present invention;

[0156] Figure 3 A schematic diagram of a method for obtaining an optimal solution for inverse kinematics according to an embodiment of the present invention;

[0157] Figure 4 Schematic diagram of robot posture interpolation according to an embodiment of the present invention, wherein a is a schematic diagram of robot trajectory and posture requirements, and b is a schematic diagram of joint information corresponding to the best interpolation point of the robot. DETAILED DESCRIPTION

[0158] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the 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.

[0159] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0160] First of all, it should be noted that m 11 、m 13 、m 21 、m 22 、m 23 、m 33 It only appears as an intermediate value in other formulas and has no specific meaning.

[0161] Embodiment 1

[0162] In this embodiment, if Figure 1 As shown, a robot inverse solution optimization method based on multi-objective Pareto optimal-particle swarm hybrid includes the following steps:

[0163] S1. Construct the kinematic model of the 7R redundant robot and calculate the inverse kinematics analytical solution.

[0164] In this embodiment, the MDH parameter table established in Table 1 and Figure 2 The configuration characteristics of the redundant robot shown are used to calculate the analytical solution of inverse kinematics;

[0165] Table 1

[0166] link <![CDATA[α i ]]> <![CDATA[a i ]]> <![CDATA[d i ]]> <![CDATA[θ i ]]> 1 0 0 <![CDATA[d1]]> <![CDATA[θ1]]> 2 -90° <![CDATA[a2]]> 0 <![CDATA[θ2(-90°)]]> 3 0 <![CDATA[a3]]> 0 <![CDATA[θ3]]> 4 0 <![CDATA[a4]]> 0 <![CDATA[θ1]]> 5 -90° <![CDATA[a5]]> <![CDATA[d5]]> <![CDATA[θ5]]> 6 90° 0 0 <![CDATA[θ6]]> 7 -90° 0 <![CDATA[d7]]> <![CDATA[θ7]]>

[0167] The process of calculating the analytical solution of inverse kinematics includes: building the kinematic model of the 7R redundant robot:

[0168]

[0169] Among them, r 11 、r 12 、r 13 ...r 33 The 3*3 matrix is ​​a rotation matrix, which represents the posture of the robot end flange coordinate system (i.e., the connecting rod coordinate system 7), r 11 、r 21 、r 31 The normal vector, r 12 、r 22 、r 32 The direction vector, r 13 、r 23 、r 33 The approach vector is formed; pxe, pye, and pze represent the position vector of the origin of the connecting rod 7; the origin of the robot end flange coordinate system is moved to the intersection center of the last three joints, and the angle value of joint 1 is obtained by the inverse transformation method:

[0170] θ1=a tan 2(py,px)

[0171] px=px e -r 13 d7

[0172] py=py e -r 23 d7

[0173] Where θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the coordinate system of link 7 relative to the coordinate system of link 6 in the Z-axis direction; the angle value θ3 of joint 3 is taken as a known value, and joints 2 and 3 are equivalent to an equivalent joint θ eq :

[0174] θ eq =-atan2(d5,a5)±acos(temp)

[0175] temp=(BT 2 -DT 2 -CT 2 ) / (2*DT*CT)

[0176] BT=sqrt(P 2 +Q 2 )

[0177] P=px*c1+py*s1-a2

[0178] Q=BT=pz-d1

[0179]

[0180] Where c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents the square root calculation, a2 represents the length of link 2, a3 represents the length of link 3, a4 represents the length of link 4, a5 represents the length of link 5, d1 represents the distance between link 1 and link 0, and d5 represents the distance between link 5 and link 4; Calculate the equivalent joint θ eq Middle value of middle joint 2:

[0181] θ 2m =a tan 2(-(P*k4+Q*k3),P*k3-Q*k4)

[0182] k3=DT+a5*c4-d5*s4

[0183] k4=a5*s4+d5*c4

[0184] Where c4 represents the cosine value of θ4, and s4 represents the sine value of θ4. According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated:

[0185] θ2=θ 2m ±(θ3-temp2)

[0186] θ4=θ eq ±temp2

[0187] temp2=a sin(temp1*a4)

[0188] temp1=abs(s3) / DT

[0189] Where s3 represents the sine value of θ3, and abs represents the absolute value. According to the known origin of the robot end flange coordinate system and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6:

[0190]

[0191] m 23 =-c234*r 33 -c1*r 13 *s234-r 23 *s1*s234

[0192] C234=C23*C4-S23*S4

[0193] s234=s23*c4+c23*s4

[0194] c23=c2*c3-s2*s3

[0195] s23=s2*c3+c2*s3

[0196] Among them, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2. When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is:

[0197] θ7=a tan 2(-m 13 , m 11 )-θ5

[0198] m 11 =c1*c234*r 11 -r 31 *s234+c234*r 21 *s1

[0199] m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1

[0200] Among them, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7; when joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as follows:

[0201] θ5=a tan 2(m 33 , ±m 13 )

[0202] θ7=a tan 2(m 22 , ±m 21 )

[0203] m 21 =-c234*r 31 -c1*r 11 *s234-s234*r 21 *s1

[0204] m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1

[0205] m33 =c1*r 23 -r 13 *s1.

[0206] S2. Set the constraints and optimization goals of the robot's inverse kinematics analytical solution. The constraints include: obstacle avoidance, singularity avoidance and joint limits. The optimization goals include: optimal jump, optimal time and optimal curvature.

[0207] In this embodiment, as described in S1, for this type of 7R redundant robot, when a certain joint value is constrained, such as constraining joint 3 in the above, an accurate analytical solution can be obtained, so joint 3 can be used as a redundant angle. Of course, joints 2 and 4 also have the same function, and one of them can be selected. How to constrain the redundant angle needs to be adaptively adjusted according to rules such as constraint conditions and optimization objectives. Combined with the application scenario analysis rules, the redundant robot needs to complete a continuous motion trajectory of a section of the pipeline that is not less than 180°, and can complete 360° full-position welding in two steps, so multiple constraints and optimization problems need to be considered. The first is constraint, including three constraints: obstacle avoidance, singularity avoidance, and joint limit; the second is optimization: including three aspects: optimal jump, optimal time, and optimal curvature. The optimal jump means that the entire trajectory is completed, and all joints deviate from the zero center to the minimum. The optimal time means that the cumulative sum of the corresponding joint differences between the front and rear interpolation points is the minimum, and the optimal curvature is combined with the structural characteristics of the 7R robot. The flexibility mainly comes from the elbow flexibility formed by the up and down swing of joints 2 and 3, and the function is similar to the bending ability of the continuous robot.

[0208] The optimization objectives include: optimal jump, optimal time and optimal curvature; the index function for optimal jump is:

[0209]

[0210] Wherein, k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient. In this embodiment, the weight coefficient is set to impW(i) = [0.1, 0.3, 0.25, 0.15, 0.15, 0.05], q j，i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the motion range of joint i; the optimal index function for time is:

[0211]

[0212] t_d(j,i)=impW(i)*abs(q j，i -q j-1，i )

[0213]

[0214] Among them, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, t max(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution; the index function for the optimal curvature is:

[0215]

[0216] Among them, bW1 and bW2 represent weight coefficients. The value range of each indicator function is

[01] , and the smaller the value, the better the indicator.

[0217] S3. Optimize the inverse kinematics analytical solution based on constraints and optimization objectives to obtain the optimal inverse kinematics solution.

[0218] The method to obtain the optimal solution of inverse kinematics is as follows Figure 3 As shown, it includes: determining the target trajectory machine interpolation number n and the constrained angle segment number m of the robot grasping the target; determining the continuous interpolation point based on the time-optimal indicator function, the latter effective segment number is k, then the initial solution set is m*(k)n; eliminating the inferior solutions where the obstacles and singular points are located, and obtaining the feasible solution set F_set; based on the optimal jump, optimal time and optimal curvature, the Pareto optimal frontier is constructed using the quick sorting method, and the optimality of each solution on the frontier is calculated opti_b:

[0219]

[0220] Among them, Opti_b(i) represents the optimality of each solution; the optimality of each solution is sorted from small to large, and the numth position is selected as the Pareto optimal solution F_best (initial num=1), and according to the change range of joints 2 and 3 in F_best, an initial population of 100*(100*θ2) is generated to obtain the position and speed limits; the fitness of the initial population is calculated based on the indicator function with the best curvature, and when the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, the optimal solution F_best can be updated, and the current optimality opti_b is calculated, otherwise the speed and position are updated; it is determined whether the optimality opti_b≤0.9 is satisfied, if so, the inverse kinematics optimal solution is output, otherwise num++ is updated.

[0221] Embodiment 2

[0222] In this embodiment, the application process of the present invention will be described in detail.

[0223] First, when one degree of freedom is constrained, the exact inverse solution is calculated using the analytical solution method. As for how to constrain this degree of freedom, three external and internal constraints and three optimization objectives are combined, such as Figure 3 As shown in the figure, a robot inverse solution intelligent optimization algorithm based on multi-objective Pareto optimal-particle swarm (MPO-PSO) hybrid algorithm is proposed to obtain the optimal inverse solution set.

[0224] When facing a known pipeline welding trajectory, the MPO-PSO hybrid inverse solution algorithm of the present invention is used to make the three indicators of optimal jump, optimal time and optimal curvature reach the optimal state under the consideration of the three constraints of obstacle avoidance, singularity avoidance and joint limit. Figure 4 As shown in (a), the robot end posture still always points to the center of the circle, and the number of interpolation points is 2738. Then, the MPO-PSO hybrid inverse solution algorithm is used for forward planning to obtain the joint information corresponding to the best interpolation point, as shown in Figure 4 As shown in (b), the calculation time of each inverse solution is 2.5s, and the solution accuracy is guaranteed to be within 10-12mm. Compared with the three commonly used classical intelligent inverse solution optimization algorithms, namely Adaptive Particle Swarm Optimization (APSO), Improved Butterfly Optimization (IBO), and Improved Fruit-fly optimization (IFO), it has relatively better solution accuracy and calculation speed. Based on the PQArt robot motion simulation platform, the 7R redundant robot can achieve continuous welding of about 190° of the pipeline circumference through its own flexibility during pipeline welding. Since the full-position pipeline welding has a 360° requirement, a ground rail needs to be added in the design to assist in completion. When optimized into a 7+1 composite redundant robot, it can easily and flexibly complete the 360° full-position pipeline welding requirements. The MPO-PSO hybrid inverse solution algorithm proposed in the present invention is applied to the motion forward planning layer, and the actual trajectory of the pipeline full-position welding is simulated. The robot has successfully passed various basic function tests, proving the feasibility and reliability of the method proposed in the present invention.

[0225] Embodiment 3

[0226] In this embodiment, a robot inverse solution optimization system based on multi-objective Pareto optimal-particle swarm hybrid includes: an analytical solution calculation module, a constraint module and an optimization module.

[0227] The analytical solution calculation module is used to construct the kinematic model of the 7R redundant robot and calculate the inverse kinematics analytical solution.

[0228] The workflow of the analytical solution calculation module includes: Building the kinematic model of the 7R redundant robot:

[0229]

[0230] Among them, r 11 、r 12 、r 13 ...r 33 Indicates the posture of the robot end flange coordinate system, px e ,py e 、pz e Represents the position vector of the origin of connecting rod 7; move the end position to the intersection center of the last three joints, and use the inverse transformation method to obtain the angle value of joint 1:

[0231] θ1=a tan 2(py,px)

[0232] px=px e -r 13 d7

[0233] py=py e -r 23 d7

[0234] Where θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the coordinate system of link 7 relative to the coordinate system of link 6 in the Z-axis direction; the angle value θ3 of joint 3 is taken as a known value, and joints 2 and 3 are equivalent to an equivalent joint θ eq :

[0235] θ eq =-atan2(d5,a5)±acos(temp)

[0236] temp=(BT 2 -DT 2 -CT 2 ) / (2*DT*CT)

[0237] BT=sqrt(P 2 +Q 2 )

[0238] P=px*c1+py*s1-a2

[0239] Q=BT=pz-d1

[0240]

[0241] Where c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents the square root calculation, a2 represents the length of link 2, a3 represents the length of link 3, a4 represents the length of link 4, a5 represents the length of link 5, d1 represents the distance between link 1 and link 0, and d5 represents the distance between link 5 and link 4; Calculate the equivalent joint θ eq Middle value of middle joint 2:

[0242] θ 2m =a tan 2(-(P*k4+Q*k3),P*k3-Q*k4)

[0243] k3=DT+a5*c4-d5*s4

[0244] k4=a5*s4+d5*c4

[0245] Where c4 represents the cosine value of θ4, and s4 represents the sine value of θ4. According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated:

[0246] θ2=θ 2m ±(θ3-temp2)

[0247] θ4=θ eq ±temp2

[0248] temp2=a sin(temp1*a4)

[0249] temp1=abs(s3) / DT

[0250] Where s3 represents the sine value of θ3, and abs represents the absolute value. Based on the known end position and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6:

[0251]

[0252] m 23 =-c234*r 33 -c1*r 13 *s234-r 23 *s1*s234

[0253] C234=C23*C4-S23*S4

[0254] s234=s23*c4+c23*s4

[0255] c23=c2*c3-s2*s3

[0256] s23=s2*c3+c2*s3

[0257] Among them, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2. When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is:

[0258] θ7=a tan2(-m 13 , m 11 )-θ5

[0259] m 11 =c1*c234*r 11 -r 31 *s234+c234*r 21 *s1

[0260] m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1

[0261] Among them, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7; when joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as follows:

[0262] θ5=a tan 2(m 33 , ±m 13 )

[0263] θ7=a tan 2(m 22 , ±m 21 )

[0264] m 21 =-c234*r 31 -c1*r 11 *s234-s234*r 21 *s1

[0265] m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1

[0266] m 33 =c1*r 23 -r 13 *s1.

[0267] The constraint module is used to set the constraint conditions and optimization objectives of the robot's inverse kinematics analytical solution. The constraint conditions include: obstacle avoidance, singularity avoidance and joint limits, and the optimization objectives include: optimal jump, optimal time and optimal curvature.

[0268] The optimal index function is:

[0269]

[0270] Where k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient, and q j，i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the motion range of joint i; the optimal index function for time is:

[0271]

[0272] t_d(j,i)=impW(i)*abs(q j，i -q j-1，i )

[0273]

[0274] Among them, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, t max(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution; the index function for the optimal curvature is:

[0275]

[0276] Among them, bW1 and bW2 represent weight coefficients.

[0277] The optimization module optimizes the inverse kinematics analytical solution based on constraints and optimization objectives to obtain the optimal inverse kinematics solution.

[0278] The workflow of the optimization module includes: determining the target trajectory machine interpolation number n and the constrained angular segment number m of the robot's grasping target; determining the number of effective segments of the continuous interpolation points based on the time-optimal indicator function is k, then the initial solution set is m*(k)n; eliminating the inferior solutions where obstacles and singular points are located, and obtaining the feasible solution set F_set; based on the optimal jump, time and curvature, using the quick sorting method to construct the Pareto optimal frontier, and calculate the optimality of each solution on the frontier opti_b:

[0279]

[0280] Among them, Opti_b(i) represents the optimality of each solution; sort the optimality of each solution from small to large, select the numth one as the Pareto optimal solution F_best, generate an initial population of 100*(100*θ2) according to the change range of joints 2 and 3 in F_best, and obtain the position and speed limits; calculate the fitness of the initial population based on the index function with the best curvature, and when the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, update the optimal solution F_best and calculate the current optimality opti_b, otherwise update the speed and position; determine whether the optimality opti_b≤0.9 is satisfied, and if so, output the inverse kinematics optimal solution.

[0281] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A robot inverse optimization method based on multi-objective Pareto optimal-particle swarm hybrid, characterized in that: The following steps are involved: Construct the kinematic model of the 7R redundant robot and calculate the inverse kinematics analytical solution; Setting constraints and optimization goals of the inverse kinematics analytical solution of the robot, wherein the constraints include: obstacle avoidance, singularity avoidance and joint limit, and the optimization goals include: optimal jump, optimal time and optimal curvature; The inverse kinematics analytical solution is optimized based on the constraint conditions and the optimization target to obtain an inverse kinematics optimal solution.

2. According to claim 1, a robot inverse optimization method based on multi-objective Pareto optimal-particle swarm hybrid is characterized in that: The process of calculating the analytical solution of the inverse kinematics includes: Construct the kinematic model of the 7R redundant robot: Among them, r 11 、r 12 、r 13 ...r 33 Indicates the posture of the robot end flange coordinate system, px e 、py e 、pz e represents the position vector of the origin of the connecting rod 7; Move the origin of the robot end flange coordinate system to the intersection center of the last three joints, and use the inverse transformation method to obtain the angle value of joint 1: θ1=a tan2(py,px) px=px e -r 13 d7 py=py e -r 23 d7 Wherein, θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the link 7 coordinate system relative to the link 6 coordinate system in the Z-axis direction; The angle value θ3 of joint 3 is taken as a known value, and joint 2 and joint 3 are equivalent to an equivalent joint θ eq : <h2 style=";text-align:left;direction:ltr">θ<h2 style=";text-align:left;direction:ltr"> eq <h2 style=";text-align:left;direction:ltr"> =-atan2(d5,a5)±acos(temp) temp=(BT 2 -DT 2 -CT 2 ) / (2*DT*CT) BT=sqrt(P 2 +Q 2 ) P=px*c1+py*s1-a2 Q=BT=pz-d1 Wherein, c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents square root calculation, a2 represents the length of connecting rod 2, a3 represents the length of connecting rod 3, a4 represents the length of connecting rod 4, a5 represents the length of connecting rod 5, d1 represents the distance between connecting rod 1 and connecting rod 0, and d5 represents the distance between connecting rod 5 and connecting rod 4; Calculate the equivalent joint θ eq Middle value of middle joint 2: θ 2m =a tan2(-(P*k4+Q*k3),P*k3-Q*k4) k3=DT+a5*c4-d5*s4 k4=d5*s4+d5*c4 Wherein, c4 represents the cosine value of θ4, and s4 represents the sine value of θ4; According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated: θ2=θ 2m ±(θ3-temp2) θ4=θ eq ±temp2 temp2=a sin(temp1*a4) temp1=abs(s3) / DT Where, s3 represents the sine value of θ3, and abs represents the absolute value; According to the known origin of the robot end flange coordinate system and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6: m 23 =-c234*r 33 -c1*r 13 *s234-r 23 *s1*s234 C234=C23*C4-S23*S4 s234=s23*c4+c23*s4 c23=c2*c3-s2*s3 s23=s2*c3+c2*s3 Wherein, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2; When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is: θ7=a tan2(-m 13 ,m 11 )-θ5 m 11 =c1*c234*r 13 -r 31 *s234+c234*r 21 *s1 m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1 Wherein, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7; When joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as: θ5=a tan2(m 33 ,±m 13 ) θ7=a tan2(m 22 ,±m 21 ) m 21 =-c234*r 31 -c1*r 11 *s234-s234*r 21 *s1 m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1 m 33 =c1*r 23 -r 13 *s1。 3. According to claim 1, a robot inverse optimization method based on multi-objective Pareto optimal-particle swarm hybrid is characterized in that: The optimization objectives include: optimal jump, optimal time and optimal curvature; The optimal index function is: Where k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient, and q j,i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the range of motion of joint i; The time-optimal index function is: t_d(j,i)=impW(i)*abs(q j，i -q j-1，i ) Wherein, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, and tmax(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution; The optimal index function for the curvature is: Among them, bW1 and bW2 represent weight coefficients.

4. According to claim 1, a robot inverse optimization method based on multi-objective Pareto optimal-particle swarm hybrid is characterized in that: The method for obtaining the optimal solution of inverse kinematics includes: Determine the target trajectory machine interpolation number n and the constrained angle segment number m of the robot grasping the target; Based on the time-optimal index function, the continuous interpolation points are determined, and the number of effective segments is k, then the initial solution set is m*(k)n; Eliminate the inferior solutions where obstacles and singular points are located and obtain the feasible solution set F_set; Based on the optimal jump, the optimal time and the optimal curvature, the Pareto optimal frontier is constructed using the quick sorting method, and the optimality of each solution of the frontier, opti_b, is calculated: Among them, Opti_b(i) represents the optimality of each solution; Sort the optimality of each solution from small to large, select the numth one as the Pareto optimal solution F_best, generate an initial population of 100*(100*θ2) according to the variation range of joint 2 and joint 3 in F_best, and obtain the position and speed limits; The fitness of the initial population is calculated based on the optimal index function of the curvature. When the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, the optimal solution F_best can be updated and the current optimality opti_b can be calculated. Otherwise, the speed and position are updated. It is determined whether the optimality opti_b≤0.9 is satisfied. If yes, the optimal solution of the inverse kinematics is output.

5. A robot inverse optimization system based on multi-objective Pareto optimal-particle swarm hybrid, the system applying the method described in any one of claims 1 to 4, characterized in that: include: Analytical solution calculation module, constraint module and optimization module; The analytical solution calculation module is used to construct a kinematic model of the 7R redundant robot and calculate an inverse kinematics analytical solution; The constraint module is used to set the constraint conditions and optimization goals of the inverse kinematics analytical solution of the robot, the constraint conditions include: obstacle avoidance, singularity avoidance and joint limit, and the optimization goals include: optimal jump, optimal time and optimal curvature; The optimization module optimizes the inverse kinematics analytical solution based on the constraint conditions and the optimization target to obtain the inverse kinematics optimal solution.

6. The robot inverse optimization system based on multi-objective Pareto optimal-particle swarm hybrid according to claim 5, characterized in that: The workflow of the analytical solution calculation module includes: Construct the kinematic model of the 7R redundant robot: Among them, r 11 、r 12 、r 13 ...r 33 Indicates the posture of the robot end flange coordinate system, px e 、py e 、pz e represents the position vector of the origin of the connecting rod 7; Move the origin of the robot end flange coordinate system to the intersection center of the last three joints, and use the inverse transformation method to obtain the angle value of joint 1: θ1=atan2(py,px) px=px e -r 13 d7 py=py e -r 23 d7 Wherein, θ1 represents the angle value of joint 1, atan2 represents the inverse tangent function, and d7 represents the offset of the link 7 coordinate system relative to the link 6 coordinate system in the Z-axis direction; The angle value θ3 of joint 3 is taken as a known value, and joint 2 and joint 3 are equivalent to an equivalent joint θ eq : <h2 style=";text-align:left;direction:ltr">θ<h2 style=";text-align:left;direction:ltr"> eq <h2 style=";text-align:left;direction:ltr"> =-atan2(d5, a5)±acos(temp) temp=(BT 2 -DT 2 -CT 2 ) / (2*DT*CT) BT=sqrt(P 2 +Q 2 ) P=px*c1+py*s1-a2 Q=BT=pz-d1 Wherein, c1 represents the cosine value of θ1, s1 represents the sine value of θ1, c3 represents the cosine value of θ3, sqrt represents square root calculation, a2 represents the length of connecting rod 2, a3 represents the length of connecting rod 3, a4 represents the length of connecting rod 4, a5 represents the length of connecting rod 5, d1 represents the distance between connecting rod 1 and connecting rod 0, and d5 represents the distance between connecting rod 5 and connecting rod 4; Calculate the equivalent joint θ eq Middle value of middle joint 2: θ 2m =atan2(-(P*k4+Q*k3),P*k3-Q*k4) k3=DT+a5*c4-d5*s4 k4=a5*s4+d5*c4 Wherein, c4 represents the cosine value of θ4, and s4 represents the sine value of θ4; According to the direction of joint 3, the equivalent joint and the intermediate value of joint 2, the actual values ​​of joint 2 and joint 4 are calculated: θ2=θ 2m ±(θ3-temp2) θ4=θ eq ±temp2 temp2=asin(temp1*a4) temp1=abs(s3) / DT Where, s3 represents the sine value of θ3, and abs represents the absolute value; According to the known origin of the robot end flange coordinate system and the values ​​of joints 1, 2, 3, and 4, calculate the angle value of joint 6: m 23 =-c234*r 33 -c1*r 13 *s234-r 23 *s1*s234 C234=C23*C4-S23*S4 s234=s23*c4+c23*s4 c23=c2*c3-s2*s3 c23=c2*c3+s2*s3 Wherein, θ6 represents the angle value of joint 6, c3 represents the cosine value of θ3, and s2 represents the sine value of θ2; When the angle value of joint 6 is equal to 0 or ±180°, the axes of joints 5 and 7 coincide and are in a singular position. At this time, let joint 5 keep the previous position unchanged, and the angle value of joint 7 is: θ7=a tan2(-m 13 ,m 11 )-θ5 m 11 =c1*c234*r 11 -r 31 *s234+c234*r 21 *s1 m 13 =c1*c234*r 13 -r 33 *s234+c234*r 23 *s1 Wherein, θ5 represents the angle value of joint 5, and θ7 represents the angle value of joint 7; When joint 6 is not equal to 0 or ±180°, the angle values ​​of joint 5 and joint 7 are calculated as: θ5=a tan2(m 33 ,±m 13 ) θ7=a tan2(m 22 ,±m 21 ) m 21 =-c234*r 31 -c1*r 11 *s234-s234*r 21 *s1 m 22 =-c234*r 32 -c1*r 12 *s234-s234*r 22 *s1 m 33 =c1*r 23 -r 13 *s1。 7. The robot inverse optimization system based on multi-objective Pareto optimal-particle swarm hybrid according to claim 5, characterized in that: The optimal index function is: Where k represents the kth group of inverse solutions, i represents the i-th joint, j represents the j-th interpolation point, n represents the total number of interpolation points, impW(i) represents the weight coefficient, and q j,i represents the angle value corresponding to the j-th interpolation point of the i-th joint, represents the maximum value of the range of motion of joint i, represents the minimum value of the range of motion of joint i; The time-optimal index function is: t_d(j,i)=impW(i)*abs(q j，i -q j-1，i ) Wherein, t_d(j, i) represents the product of the joint difference of the j-th interpolation point of the i-th joint relative to the previous interpolation point and the weight coefficient, and tmax(i) represents the value corresponding to the maximum time index of a joint trajectory of the m-group solution; The optimal index function for the curvature is: Among them, bW1 and bW2 represent weight coefficients.

8. The robot inverse optimization system based on multi-objective Pareto optimal-particle swarm hybrid according to claim 5, characterized in that: The workflow of the optimization module includes: Determine the target trajectory machine interpolation number n and the constrained angle segment number m of the robot grasping the target; Based on the time-optimal index function, the continuous interpolation points are determined, and the number of effective segments is k, then the initial solution set is m*(k)n; Eliminate the inferior solutions where obstacles and singular points are located and obtain the feasible solution set F_set; Based on the optimal jump, the optimal time and the optimal curvature, the Pareto optimal frontier is constructed using the quick sorting method, and the optimality of each solution of the frontier, opti_b, is calculated: Among them, Opti_b(i) represents the optimality of each solution; Sort the optimality of each solution from small to large, select the numth one as the Pareto optimal solution F_best, generate an initial population of 100*(100*θ2) according to the variation range of joint 2 and joint 3 in F_best, and obtain the position and speed limits; The fitness of the initial population is calculated based on the optimal index function of the curvature. When the maximum number of iterations is reached or the fitness value between two iterations is the minimum difference, the optimal solution F_best can be updated and the current optimality opti_b can be calculated. Otherwise, the speed and position are updated. It is determined whether the optimality opti_b≤0.9 is satisfied. If yes, the optimal solution of the inverse kinematics is output.

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