A method for trajectory optimization of a composite material laying robot

Abstract

The application discloses a kind of composite material laying robot trajectory optimization methods, by combining NURBS fitting method and INGSA-Ⅱ multi-objective optimization algorithm are carried out joint parameter fitting of laying robot, realize time optimal, energy consumption minimum and impact minimum, after inverse solution of pressure vessel head joint angle optimization, joint related parameters are all smooth and continuous, pressure vessel head operating time is shorter, trajectory efficiency is high, the integral of joint acceleration and joint jerk with time is smaller, energy consumption and impact are lower;Realized in improving the work efficiency of robot while reducing the energy consumption of laying robot production core mold, reduce the impact in the movement process of laying robot, improve the smoothness of laying robot movement, prolong the service life of laying robot.

Description

TECHNICAL FIELD

[0001] The application relates to a composite material laying robot trajectory optimization method and belongs to the technical field of composite material forming. BACKGROUND

[0002] The actual working performance of a laying robot mainly depends on control and planning. Since the main body of the laying robot is a six-axis industrial robot, the autonomy of the control is reduced, so trajectory planning, which is important in planning, will directly affect the motion performance, end precision and smoothness of the laying robot. In order to meet the requirements of the laying robot in efficiency, energy consumption and the like, the application mainly optimizes the running time, running energy consumption and running smoothness of the laying robot, realizes high efficiency, low energy consumption and low impact under the premise of meeting the joint limit of the laying robot, improves the laying performance, enhances the joint smoothness and prolongs the service life of the equipment.

[0003] In order to improve the industrial production efficiency, reduce the energy consumption of the industrial production line and prolong the service life of the equipment, the application provides an optimization method for trajectory planning of a composite material laying robot, which reduces the trajectory time as much as possible under the premise of meeting the energy consumption and impact targets. Cartesian space poses are obtained through non-geodesic prepreg tape laying trajectories, discrete joint angle of each joint of the laying robot is solved by using an improved snake optimization inverse kinematics algorithm, angle, angular velocity and angular acceleration curves of each joint are fitted according to the given discrete joint angle, time, energy consumption and impact are optimized as the targets by using the strong convex hull property of the NURBS curve and the constraint condition of the laying robot, and the time nodes of the NURBS curve are optimized by using the INSGA-II multi-objective genetic optimization algorithm, so that the multi-objective optimal trajectory planning of the laying robot in the Cartesian space is realized. SUMMARY

[0004] In order to achieve the above object, as shown in the accompanying drawings, Figure 1 The application provides a composite material laying robot trajectory optimization method, which adopts the technical scheme as follows: the fastest running time is determined according to the joint angles of each joint in the eight joints of the laying robot and the robot motion parameters, and the time constraint interval is given on the basis of the fastest running time according to the task demand; time is taken as the target population to be optimized, the initial fitness value is calculated by using three target functions of time, energy consumption and impact after the initialization of the INSGA-II algorithm, the Pareto non-dominated solution set is obtained after the non-dominated sorting and congestion calculation of the INSGA-II algorithm, and the optimal solution is selected from the Pareto non-dominated solution set. The motion trajectory described by the solution meets the time-energy consumption-impact optimization of the laying robot in the laying path process.

[0005] As shown in the accompanying drawings, Figure 1 A composite material laying robot trajectory optimization method comprises the following specific steps:

[0006] Step one, establishing optimization objective function;

[0007] Laid track p(u) as shown in equation (1);

[0008]

[0009] In the formula d i The i-th control point of NURBS curve, ω i Weight factor, N i,k (u) is the base function; the NURBS curve control point d i Decide the trend of the curve fitted by the path point; the base function N i,k (u) is the k-th polynomial obtained by time node vector t i Corresponding to a B-spline curve;

[0010] According to the definition of time-energy-impact combined NURBS curve, the motion time objective function S I , joint average acceleration objective function S II And joint pulse objective function S III As shown in equation (2); the motion time objective function S I Characterizes the motion time of the joint, the joint average acceleration objective function S II Characterizes the motion energy consumption of the joint, the joint pulse objective function S III Jerk, used to characterize the motion impact of the joint;

[0011]

[0012] In the formula n is the number of track points, D is the number of robot joints, T is the laying time of the whole track, v i , a i , j i The i-th track point joint speed, joint acceleration and joint jerk on the track respectively;

[0013] For the i-th control point d i The laying robot kinematics constraint is shown in equation (3);

[0014]

[0015] Using the strong convexity of NURBS curve, the kinematics constraint of laying robot is transformed into the constraint of the i-th control point d i Of NURBS curve, as shown in equation (4);

[0016]

[0017] where and are the joint velocity, joint acceleration and joint jerk of the ith control point of the dth joint NURBS curve, K is the amplification coefficient;

[0018]

[0019] The initial velocity v s , initial acceleration a s , initial jerk j s , end velocity v e , end acceleration a e and end jerk j e of the laying robot laying trajectory p(u) are as shown in equation (6);

[0020]

[0021] where p'(u), p''(u) and p'''(u) are the first, second and third derivatives of the laying trajectory p(u), respectively;

[0022] The ith control point d i of the NURBS curve is solved by equation (5), and equation (6) is substituted into equation (2) to calculate the motion time objective function S I , the joint average acceleration objective function S II and the joint pulsation objective function S III ;

[0023] Step two, set the initial values of INSGA-II algorithm, including amplification coefficient K, population size N, maximum iteration number M, optimization precision C and mutation probability η m ;

[0024] Step three, randomly initialize the time population;

[0025] According to the given joint angle Jiont i , the joint displacement between each joint trajectory point is calculated by the Pieper criterion of inverse kinematics If the maximum joint velocity v j,max is known, the shortest motion time is obtained by equation (7)

[0026]

[0027] The longest running time allowed by the task is as shown in equation (8);

[0028]

[0029] where t is time margin;

[0030] Randomly initialize the initial time population Q using formula (9) for the optimization target of time;

[0031]

[0032] The time sequence of eight joints of a laying robot for a segment of trajectory is recorded as i = 1, 2, …, n, j = 1, 2, …, 8, i represents the position of an individual in the population, j represents the joint sequence, Q i Express the i-th individual in the initial time population Q;

[0033] Step four, calculate the motion time objective function S I , the joint average acceleration objective function S II , the joint pulsation objective function S III , and the i-th control point d of the NURBS curve i of the initial time population Q using formula (2) and formula (5);

[0034] Step five, perform non-dominated fast sorting on the individuals in the initial time population Q to obtain a Pareto non-dominated solution set;

[0035] Step six, select the individuals in the initial time population Q using binary selection method and generate a next-generation time population QE with a population size of N;

[0036] Step seven, generate offspring individuals through mutation and crossover;

[0037] Using simulated binary crossover method and polynomial mutation method, randomly select next-generation individuals QE i and QE j from the next-generation time population QE, cross them using formula (10) to generate individuals QN i and QN j in the offspring time population QN with a population size of N;

[0038]

[0039] where u is a random number in [0, 1], and the calculation of β(u) is shown in formula (11);

[0040]

[0041] where η is a distribution index used to control the distribution range of the offspring individuals;

[0042] Generate offspring mutation individuals using formula (12);

[0043]

[0044] wherein η m is the probability of variation, used to enhance the diversity of the offspring temporal population QN;

[0045] Step eight, population fusion is performed to generate the next generation temporal population QM;

[0046] The newly generated offspring temporal population QN is mixed with the initial temporal population Q to obtain a fusion temporal population QNE with a population number of 2N; the fusion temporal population QNE is re-performed non-dominated fast sorting according to step five, and the next generation temporal population QM is selected therefrom;

[0047] Step nine, steps four to eight are repeated for iteration; if the maximum iteration number M or the optimization precision C requirement is reached, the optimal time sequence Q of time-energy-impact is output N .

[0048] Beneficial effects: the composite material laying robot trajectory optimization method provided by the application realizes time optimization, minimum energy consumption and minimum impact by combining the NURBS fitting method with the INGSA-II multi-objective optimization algorithm to fit the joint parameters of the laying robot, optimizes the joint angle after the inverse solution of the pressure vessel head, the joint related parameters are all smooth and continuous, the pressure vessel head has a shorter running time, the trajectory efficiency is high, the integral of the joint acceleration and the joint jerk with time is smaller, and the energy consumption and the impact are lower; the working efficiency of the robot is improved while the energy consumption of the laying robot for producing a core mold is reduced, the impact in the movement process of the laying robot is reduced, the smoothness of the movement of the laying robot is improved, and the service life of the laying robot is prolonged. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 It is a flowchart of a composite material laying robot trajectory optimization method.

[0050] Figure 2 It is a joint angle curve diagram of an optimized pressure vessel head section.

[0051] Figure 3 It is a joint speed curve diagram of an optimized pressure vessel head section.

[0052] Figure 4 It is a joint acceleration curve diagram of an optimized pressure vessel head section.

[0053] Figure 5 It is an impact curve diagram of an optimized pressure vessel head section.

[0054] Figure 6 It is a laying speed curve diagram of an optimized pressure vessel head section.

[0055] Figure 7 It is the optimized laying position curve of the pressure vessel head section.

[0056] Figure 8 It is the optimized laying posture curve of the pressure vessel head section.

[0057] Figure 9 It is the optimized pressure vessel head section laying posture speed curve. DETAILED DESCRIPTION

[0058] Example 1 A composite material placement robot trajectory optimization method.

[0059] As attached Figure 1 As shown in FIG, a composite material placement robot trajectory optimization method, the specific steps are as follows:

[0060] Step 1: Establish the optimization objective function;

[0061] The laying trajectory p(u) is shown in formula (1);

[0062]

[0063] Where d i is the i-th control point of the NURBS curve, ω i is the weight factor, N i,k (u) is the basis function; the NURBS curve controls the fixed point d i Determines the trend of the curve fitted by the path point; the basis function N i,k (u) is the time node vector t i The obtained k-degree polynomial corresponds to a B-spline curve;

[0064] According to the definition of time-energy-impact combined with NURBS curve, the motion time objective function S is established. I , joint average acceleration objective function S II and joint pulsation objective function S III , as shown in formula (2); the motion time objective function S I Characterizing the movement time of the joint, the joint average acceleration objective function S II Characterizing the joint's motion energy consumption, the joint pulsation objective function S III is the jerk, which is used to characterize the motion impact of the joint;

[0065]

[0066] Where n is the number of trajectory points, D is the number of robot joints, T is the laying time of the entire trajectory, and v i 、a i, j i are the joint velocity, joint acceleration and joint jerk of the i th track point on the track respectively;

[0067] for the i th control point d i of the NURBS curve, the kinematic constraints of the deposition robot are shown as formula (3) ;

[0068]

[0069] By using the strong convex hull property of the NURBS curve, the kinematic constraints of the deposition robot are transformed into the constraints of the i th control point d i of the NURBS curve, which is shown as formula (4) ;

[0070]

[0071] wherein and are the joint velocity, joint acceleration and joint jerk of the i th control point of the d th joint NURBS curve respectively, and K is the amplification coefficient;

[0072]

[0073] The initial velocity v s , initial acceleration a s , initial jerk j s , end velocity v e , end acceleration a e and end jerk j e of the deposition robot deposition track p(u) are shown as formula (6) ;

[0074]

[0075] wherein p'(u), p''(u) and p'''(u) are the first derivative, second derivative and third derivative of the deposition track p(u) respectively;

[0076] The i th control point d i of the NURBS curve is solved by using formula (5), and formula (6) is substituted into formula (2) to calculate the motion time target function S I , joint average acceleration target function S II and joint pulsation target function S III ;

[0077] Step two, set the initial value of INSGA-II algorithm, including amplification coefficient K, population number N, maximum iteration number M, optimization precision C and mutation probability η m ;

[0078] Step three, time population is randomly initialized;

[0079] According to the given joint angle Jiont i The joint displacement between each joint trajectory point is calculated by the Pieper criterion of inverse kinematics If the maximum joint velocity v j,max The shortest motion time is obtained by formula (7)

[0080]

[0081] The longest running time allowed by the task As shown in formula (8);

[0082]

[0083] In the formula, t is the time margin;

[0084] The initial time population Q is obtained by randomly initializing the population with the optimization target of time using formula (9);

[0085]

[0086] The time sequence of eight joints of the laying robot for a segment of trajectory is denoted as i=1,2,…,n,j=1,2,…,8,i represents the position of the individual in the population, and j represents the joint sequence, Q i The i-th individual in the initial time population Q is denoted as

[0087] Step four, calculate the motion time objective function S of the initial time population Q using formula (2) and formula (5) I The joint average acceleration objective function S II The joint pulsation objective function S III And the i-th control point d i of the NURBS curve;

[0088] Step five, non-dominated fast sorting is performed on the individuals in the initial time population Q to obtain a Pareto non-dominated solution set;

[0089] Step six, select the individuals in the initial time population Q using binary selection method and generate a next-generation time population QE with a population size of N;

[0090] Step seven, mutation and crossover to generate offspring individuals;

[0091] Simulated binary crossover method and polynomial mutation method are used to randomly select next-generation individuals QE i and next-generation individuals QE j, the individuals in the offspring time population QN of quantity N are generated by crossing with formula (10) i and the individuals in the offspring time population QN of quantity N are generated by crossing with formula (10) j ;

[0092]

[0093] wherein u is a random number in [0, 1], and the calculation of β (u) is shown in formula (11);

[0094]

[0095] wherein η is a distribution index, used to control the distribution range of the offspring individuals;

[0096] The offspring mutation individuals are generated by formula (12);

[0097]

[0098] wherein η m is a mutation probability, used to enhance the diversity of the offspring time population QN;

[0099] Step eight, population fusion is performed to generate the next generation time population QM;

[0100] The newly generated offspring time population QN is mixed with the initial time population Q to obtain a fusion time population QNE of population quantity 2N; the fusion time population QNE is re-sorted by non-dominated fast sorting according to step five, and the next generation time population QM is selected therefrom;

[0101] Step nine, steps four to eight are repeated for iteration; if the maximum iteration number M or the optimization precision C requirement is reached, the optimal time sequence Q of time-energy-impact is output N .

[0102] For the given composite shell head joint angle to be fitted, as shown in Table 1.

[0103] Table 1 Joint angle to be fitted

[0104]

[0105]

[0106] For the laying robot kinematic limit, as shown in Table 2.

[0107] Table 2 Laying robot kinematic limit

[0108] Para(deg) v max ]]> a max ]]> j max ]]> A1 120 45 60 A2 115 40 60 A3 112 75 55 A4 179 70 70 A5 172 90 75 A6 220 80 70 A7 200 80 70 A8 180 90 75

[0109] The optimized results are shown in Figs. 1 to 3 Figure 2 toFigure 9 As shown in the results, it is shown that the composite material laying robot trajectory optimization method provided by the application realizes time optimization, minimum energy consumption and minimum impact, optimizes the joint angle after the inverse solution of the pressure vessel head, the joint related parameters are smooth and continuous, the pressure vessel head running time is shorter, the trajectory efficiency is high, the integral of joint acceleration and joint jerk with time is smaller, and the energy consumption and impact are lower.

[0110] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A composite material placement robot trajectory optimization method, characterized in that The method adopts the following technical solutions: the fastest running time is determined according to the joint angles of each of the eight joints of the placement robot and the robot motion parameters, and the task requirements provide a time constraint interval based on the fastest running time; time is used as the target population to be optimized, and after initialization of the INSGA-II algorithm, the initial fitness value is calculated using the three objective functions of time, energy consumption and impact; after the non-dominated sorting and congestion calculation strategies of the INSGA-II algorithm, the Pareto non-dominated solution set is obtained, and the optimal solution is selected from the Pareto non-dominated solution set. The motion trajectory described by the solution satisfies the time-energy consumption-impact optimization of the placement robot during the placement path process; the method includes the following steps: Step 1: Establish the optimization objective function; The laying trajectory p(u) is shown in formula (1); Where i is the index number of the control point and basis function, n is the number of trajectory points, u is the node of the NURBS curve, and d is the i is the i-th control point of the NURBS curve, ω i is the weight factor, N i,k (u) is the i-th k-order B-spline basis function; the NURBS curve controls the fixed point d i Determines the trend of the curve fitted by the path point; the basis function N i,k (u) is the time node vector t i The obtained k-degree polynomial corresponds to a B-spline curve; According to the definition of time-energy-impact combined with NURBS curve, the motion time objective function S is established. Ι , joint average acceleration objective function S ΙΙ and joint pulsation objective function S ΙIΙ , as shown in formula (2); the motion time objective function S I Characterizing the movement time of the joint, the joint average acceleration objective function S II Characterizing the joint's motion energy consumption, the joint pulsation objective function S III is the jerk, which is used to characterize the motion impact of the joint; Where Δt i is the time interval between the i-th trajectory point and the i+1-th trajectory point, D is the number of robot joints, T is the laying time of the entire trajectory, v i 、a i 、j i are the joint velocity, joint acceleration and joint jerk of the i-th trajectory point on the trajectory respectively; For the i-th control point d i The kinematic constraints of the placement robot are shown in formula (3); By using the strong convex hull property of NURBS curve, the kinematic constraints of the placement robot are transformed into the i-th control point d of the NURBS curve. i The constraint is shown in formula (4); In the formula and are the joint velocity, joint acceleration and joint jerk of the ith control point of the dth joint NURBS curve, K is the magnification factor, and k is the degree of the NURBS curve; Where u i 、u i+1 are the i-th and i+1-th node values ​​on the NURBS curve respectively; The initial velocity v of the laying robot's laying trajectory p(u) s , initial acceleration a s , initial acceleration j s , end speed v e , end acceleration a e and the end jerk j e As shown in formula (6); Where p'(u), p"(u), and p"'(u) are the first-order derivative, second-order derivative, and third-order derivative of the placement trajectory p(u), respectively; Use formula (5) to find the i-th control point d of the NURBS curve i , substitute equation (6) into equation (2) to calculate the motion time objective function S Ι , joint average acceleration objective function S ΙΙ and joint pulsation objective function S ΙIΙ ; Step 2: Set the initial values ​​of the INSGA-Ⅱ algorithm, including the amplification coefficient K, population size N, maximum number of iterations M, optimization accuracy C and mutation probability η m ; Step 3: Randomly initialize the time population; According to the given joint angle Jiont i , the joint displacement between each joint trajectory point is calculated by the Pieper criterion of inverse kinematics If the maximum joint velocity v is known j,max , then the shortest movement time is obtained from formula (7): The maximum allowed running time for a task As shown in formula (8); Where t is the time margin; The population whose optimization target is time is randomly initialized using formula (9) to obtain the initial generation time population Q; Where r is a random number in the range [0,1]; The time series of eight joints of a trajectory of the laying robot is recorded as i represents the position of the individual in the population, j represents the joint sequence, Q i Describe the i-th individual in the initial time population Q; Step 4: Use equations (2) and (5) to calculate the movement time objective function S of the initial time population Q Ι , joint average acceleration objective function S ΙΙ , joint pulsation objective function S ΙIΙ and the NURBS curve i-th control point d i ; Step 5: Perform non-dominated quick sorting on the individuals in the initial time population Q to obtain the Pareto non-dominated solution set; Step 6: Use binary selection method to select individuals from the primary time population Q and generate a secondary time population QE with a population size of N; Step 7: mutation and crossover to produce offspring individuals; Using the simulated binary crossover method and the polynomial mutation method, the next generation individual QE is randomly selected from the next generation time population QE i and next-generation individual QE j , using formula (10) to generate N number of offspring time population QN in the individual QN i and individual QN j ; Where u∈[0,1] is any random number, and the calculation of β(u) is shown in formula (11); Where η is the distribution index, which is used to control the distribution range of offspring individuals; Use formula (12) to generate offspring mutant individuals; Where η m is the mutation probability, which is used to enhance the diversity of the offspring time population QN; Step 8: Perform population fusion to generate the next generation time population QM; Mix the newly generated offspring time population QN with the initial time population Q to obtain a fused time population QNE with a population size of 2N; according to step 5, re-perform non-dominated quick sort on the fused time population QNE to select the next generation time population QM; Step 9: Repeat steps 4 to 8 for iteration. If the maximum number of iterations M or the optimization accuracy C requirement is reached, the optimal time series Q of time-energy consumption-impact is output. N .

2. A composite material placement robot trajectory optimization method according to claim 1, characterized in that This method combines NURBS fitting with the INGSA-Ⅱ multi-objective optimization algorithm to fit the joint parameters of the placement robot, achieving optimal time, lowest energy consumption and minimum impact. The joint angle is optimized after the inverse solution of the pressure vessel head. The joint-related parameters are smooth and continuous, the pressure vessel head operation time is short, the trajectory efficiency is high, the joint acceleration and the integral of the joint jerk over time are small, and the energy consumption and impact are low. This method achieves the goal of reducing the energy consumption of the placement robot in producing core molds while improving the robot's work efficiency, reducing the impact during the placement robot's movement, improving the smoothness of the placement robot's movement, and extending the service life of the placement robot.

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