Mechanical arm track optimization method based on self-adaptive golden search algorithm

Abstract

The invention relates to the technical field of mechanical arm trajectory optimization, and discloses a mechanical arm trajectory optimization method based on a self-adaptive golden search algorithm, on the premise of establishing a kinematics model by using a DH method, the method takes a six-axis tandem type mechanical arm as a research object to establish a time optimal mathematical model, and the kinematics model is optimized. A 3-5-3 hybrid interpolation polynomial is used for carrying out trajectory planning on all joints of the mechanical arm, population diversity is increased through elite reverse strategy population initialization, a global optimal position search mechanism is achieved through self-adaption nonlinear descent factor balance function dispersion and a golden sine variation strategy, and finally the optimal trajectory planning time of the mechanical arm is achieved. The working efficiency is improved, and the angular displacement, speed and acceleration curves of the joint after algorithm optimization are smooth and continuous. The problem that in the actual working process of the industrial mechanical arm, the working efficiency is low is solved, and the energy consumption loss and the production cost are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm trajectory optimization, and in particular to a robotic arm trajectory optimization method based on an adaptive golden search algorithm. Background Technique

[0002] Robotic arm trajectory planning refers to planning a motion path from a starting point to a target point for the end effector or joints of a robotic arm, ensuring that various constraint conditions are met during the motion process, such as obstacle avoidance, smoothness, and time optimality. The quality of trajectory planning directly affects the motion efficiency, accuracy, and safety of the robotic arm.

[0003] In the field of robotic arm trajectory optimization, improvements have been made to traditional algorithms. The improvement methods include methods based on genetic algorithms, particle swarm optimization algorithms, etc. However, these technical methods still have deficiencies. The algorithms are highly sensitive to initial parameters, which easily leads to the algorithms falling into local optima. At the same time, it also causes problems such as low convergence accuracy and slow convergence speed. It is difficult to ensure time optimality in the trajectory planning of multi-degree-of-freedom robotic arms, which results in a large amount of time being spent on path planning, and the planned path is not the optimal path, making the existing industrial robotic arms inefficient in actual work and unable to meet industrial requirements. Summary of the Invention

[0004] The present invention provides a robotic arm trajectory optimization method based on an adaptive golden search algorithm to solve the problem of low working efficiency of existing industrial robotic arms in the actual working process.

[0005] To achieve the above object, the present invention is realized through the following technical solutions: In a first aspect, the present invention provides a robotic arm trajectory optimization method based on an adaptive golden search algorithm, including the following steps: Step 1: Decompose the to-be-planned actions of the robotic arm to be trajectory-optimized into three segments of actions, and then construct a time optimization mathematical model for fitness in combination with the optimization objective; Step 2: Construct a population based on fitness, adjust the individuals in the population through an adaptive inertia weight, and then construct an optimal position search formula in combination with an elite reverse strategy and a golden sine mutation strategy, calculate the optimal position, and substitute it into the time optimization mathematical model to calculate the fitness; Step 3: Repeat Step 2 until a predetermined maximum number of iterations, record the optimal fitness, and obtain the time solutions of the three segments of actions corresponding to the optimal fitness; Step 4: Obtain the kinematic parameters of the robotic arm to be optimized for the trajectory. Based on the kinematic parameters of the robotic arm, combine the forward kinematics of the robotic arm to solve for the pose and position in the joint space of the trajectory points. Construct a hybrid difference polynomial for the motion planning of the robotic arm according to the pose and position, and calculate the coefficient solutions in the hybrid difference polynomial. Substitute the time solutions of the three segments of actions to complete the trajectory optimization of the robotic arm trajectory.

[0006] Further, the construction of the optimal position search formula by combining the elite reverse strategy and the golden sine mutation strategy includes: combining the elite reverse strategy to obtain the initial population for the population adjusted by the adaptive inertia weight, introducing the golden section coefficient of the golden sine mutation strategy to obtain the optimal position search formula.

[0007] Further, the adjustment of the individuals in the population by the adaptive inertia weight includes: combining the adaptive inertia weight to adjust the initial parameters of the population so that the individuals in the population approach the optimal region; The adaptive inertia weight is expressed by the following formula: ; where, represents the adaptive inertia weight, n is the loop counter, is the maximum number of iterations, r is the damping factor, and its value range is [0, 1].

[0008] Further, in Step 2, the initial population is obtained through the following steps: Step 201: Calculate the fitness for all individuals in the population adjusted by the adaptive inertia weight, and select several individuals from largest to smallest according to the fitness. Construct an elite population based on the several individuals; Step 202: Obtain the reverse population of the elite population, and merge the initial population and the reverse population into a new initial population; Step 203: Repeat Step 201 to Step 202 to construct a new initial population.

[0009] Further, the optimal position search formula is expressed by the following formula: ; In the formula, represents the optimal position of the t th iteration of the i th population individual, and are the representation coefficients of distance and direction respectively, and take values between and respectively, represents t in thei The position of an individual in a population denotes the position of the i -th individual in the -th iteration of a population, and its expression is shown as follows: ; In the formula, is the golden ratio.

[0010] Furthermore, it further includes Step 5: Execute the trajectory of the manipulator after trajectory optimization, and obtain the speeds and accelerations of all joints when the manipulator performs actions. If the speed is greater than the preset speed value, the manipulator stops moving; If the acceleration is greater than the preset acceleration value, the manipulator stops moving.

[0011] Furthermore, the optimization objectives include: the joint angular displacement of the manipulator satisfies the maximum joint angular displacement constraint, the joint angular velocity of the manipulator satisfies the maximum joint angular velocity constraint, and the joint angular acceleration of the manipulator satisfies the maximum joint angular acceleration constraint; The time optimization mathematical model for fitness is expressed by the following formula: ; ; where, t i1 , t i2 , t i3 are the planned motion times of the i -th i ( = 1, 2,..., 6) joints of the multi-form interpolation of the three-section motion of the manipulator, , respectively represent the joint angular displacement, joint angular velocity, and joint angular acceleration. In the formula, , , are the maximum joint angular displacement constraint, the maximum joint angular velocity constraint, and the maximum joint angular acceleration constraint respectively.

[0012] Furthermore, in Step 4, the hybrid interpolation polynomial includes: a 3-5-3 hybrid interpolation polynomial for the motion planning of the manipulator constructed based on the decomposed three-section motion.

[0013] Further, in step 4, the calculation of the coefficient solution in the hybrid difference polynomial includes: based on the hybrid difference polynomial, constructing a transformation matrix of the hybrid difference polynomial and a position matrix for the manipulator trajectory planning, constructing a coefficient matrix of the polynomial interpolation function based on the transformation matrix and the position matrix, and calculating the coefficient solution in the hybrid difference polynomial based on the coefficient matrix.

[0014] Further, in step 4, the obtaining of the manipulator kinematic parameters of the manipulator to be trajectory-optimized includes: based on the manipulator to be trajectory-optimized, and in combination with the manipulator kinematic analysis method, obtaining the manipulator kinematic parameters; The manipulator kinematic parameters include: link length, link twist angle, link offset distance, and joint rotation angle.

[0015] Beneficial effects: A manipulator trajectory optimization method based on the adaptive golden search algorithm provided by the present invention. The adopted golden sine mutation strategy has its unique search mechanism. Based on the golden section ratio, the search range is continuously reduced within the search interval to approach the optimal solution, which can more accurately approach the optimal solution. It can dynamically adjust the search strategy according to the situation during the search process, reduce the probability of falling into the local optimum. By optimizing the manipulator trajectory through the adaptive golden search algorithm, a motion path that makes the joint torque more reasonable can be found, thereby reducing energy consumption. Description of the drawings

[0016] Figure 1 is a flowchart of a manipulator trajectory optimization method based on the adaptive golden search algorithm of the present invention; Figure 2 is a flowchart of obtaining the initial population in the present invention; Figure 3 is a schematic diagram of the manipulator trajectory optimization in the present invention, where (a) to (d) are the first stage to the fourth stage of the manipulator actions. Detailed implementation manners

[0017] The technical solutions of the present invention will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0018] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings as understood by those of ordinary skill in the art to which the present invention pertains. The terms "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. Similarly, the terms such as "a" or "an" do not denote a quantity limitation, but mean that there is at least one. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationships will also change accordingly.

[0019] Example 1 Please refer to Figure 1 , the embodiment of the present application provides a robotic arm trajectory optimization method based on an adaptive golden search algorithm, including the following steps: Step 1: Decompose the to-be-trajectory-optimized actions of the robotic arm into three segments of actions, and then construct a time optimization mathematical model for fitness in combination with the optimization objectives; Among them, the optimization objectives include: the joint angular displacement of the robotic arm satisfies the maximum value of the joint angular displacement constraint, the joint angular velocity of the robotic arm satisfies the maximum value of the joint angular velocity constraint, and the joint angular acceleration of the robotic arm satisfies the maximum value of the joint angular acceleration constraint; The time optimization mathematical model for fitness is represented by the following formula: ; ; Among them, t i1 , t i2 , t i3 are respectively the planned motion times of the i th i ( = 1, 2,..., 6) joints of the three-segment multi-form interpolation of the robotic arm's actions, , respectively represent the joint angular displacement, joint angular velocity and joint angular acceleration. In the formula, , , are respectively the maximum value of the joint angular displacement constraint, the maximum value of the joint angular velocity constraint and the maximum value of the joint angular acceleration constraint, means taking the maximum value under the constraint conditions, that is, taking the maximum value under each constraint in the optimization objectives.

[0020] Step 2: Construct a population based on fitness, adjust the individuals in the population through an adaptive inertia weight, then combine the elite reverse strategy and the golden sine mutation strategy to construct an optimal position search formula, calculate the optimal position, and substitute it into the time optimization mathematical model to calculate the fitness; Specifically, construct a population based on fitness, combine the adaptive inertia weight to adjust the initial parameters of the population so that the individuals in the population approach the optimal region, and then combine the business reverse strategy to obtain an initial population for the population adjusted by the adaptive inertia weight. Introduce the golden section coefficient of the golden sine mutation strategy to obtain the optimal position search formula.

[0021] The adaptive inertia weight is expressed by the following formula: ; Where, represents the adaptive inertia weight, n is the loop counter, is the maximum number of iterations, r is the damping factor, and its value range is [0, 1].

[0022] Please refer to Figure 2 , and the initial population is obtained through the following steps: Step 201: Calculate the fitness of all individuals in the population adjusted by the adaptive inertia weight, and select half of the individuals from largest to smallest, that is, individuals, and construct an elite population based on several individuals P ; Step 202: Obtain the reverse population P of the elite population , and combine the initial population with the reverse population to form a new initial population ; Step 203: Repeat Step 201 to Step 202 to construct a new initial population .

[0023] In the present invention, after constructing the initial population, the golden sine mutation strategy is adopted to define the optimal position search formula, introduce the golden section coefficient, and use it to update the optimal position of the individual. The optimal position search formula is expressed by the following formula: ; In the formula, represents the optimal position of the t th iteration of the i th population individual, and are the representation coefficients of distance and direction respectively, and are respectively in and takes values between denotes t the position of the i -th individual in the denotes the position of the i -th individual in the population in the ; In the formula, is the golden ratio number, and in this embodiment, is used, which is an irrational number.

[0024] Step 3: Repeat Step 2 until the predetermined maximum number of iterations, record the optimal fitness, and obtain the time solutions of the three segments of actions corresponding to the optimal fitness.

[0025] Step 4: Obtain the kinematic parameters of the manipulator to be trajectory-optimized. Based on the kinematic parameters of the manipulator, combine the forward kinematics of the manipulator to solve the pose and position in the joint space of the trajectory points. According to the pose and position, construct a hybrid interpolation polynomial for the manipulator motion planning, and calculate the coefficient solutions in the hybrid interpolation polynomial. Substitute the time solutions of the three segments of actions to complete the trajectory optimization of the manipulator trajectory; Based on the manipulator to be trajectory-optimized, combine the kinematic analysis method of the manipulator and obtain the kinematic parameters of the manipulator;

[0026] Based on the three segments of actions that have been decomposed, construct a 3-5-3 hybrid interpolation polynomial for the manipulator motion planning; The 3-5-3 hybrid interpolation polynomial is represented by the following formula: ; Wherein, l j1 , l j2 , l j3 respectively represent the angular displacements of the j -th joint of the 3-5-3 interpolation polynomial, a jk denotes the j -th term coefficient in the k -th segment function; Based on the hybrid interpolation polynomial, construct the transformation matrix of the hybrid interpolation polynomial and the position matrix of the manipulator trajectory planning. Based on the transformation matrix and the position matrix, construct the coefficient matrix of the polynomial interpolation function, and calculate the coefficient solutions in the hybrid interpolation polynomial based on the coefficient matrix; Wherein, the transformation matrix It is expressed by the following formula: ; Position matrix It is expressed by the following formula: ; The coefficient matrix of the polynomial interpolation function can be obtained from the transformation matrix and the position matrix : ; ; Based on the above derivation, the coefficient solutions of the 3-5-3 hybrid difference polynomial can be obtained; Step 5: Execute the trajectory of the manipulator after trajectory optimization, and obtain the speeds and accelerations of all joints when the manipulator executes actions. If the speed is greater than the speed preset value, the manipulator stops moving. If the acceleration is greater than the acceleration preset value, the manipulator stops moving.

[0027] In this embodiment, the speed preset value is ±24r / s, and the acceleration preset value is ±30r / s 2 .

[0028] Embodiment 2 Please refer to Figure 3 , and use a manipulator trajectory optimization method based on the adaptive golden search algorithm provided by the present invention to optimize the trajectory of a six-axis manipulator. Figure 3 In Figure 3 (a) to Figure 3 (d) are the entire action process for the manipulator to complete the action.

[0029] Initialize the population using the elite reverse strategy and set the maximum number of iterations to 100. Then calculate the adaptive search weight and adjust the algorithm parameters in real time. Next, perform an adaptive golden optimal position search to calculate the individual optimal position, calculate its fitness and record the better value. Determine whether to continue iterating by judging whether the number of iterations exceeds 100. Finally, output the optimal trajectory planning times t1, t2, t3; Table 1: Kinematic parameters of the six-axis manipulator

[0030] After the optimization iteration of the adaptive golden search algorithm, with the maximum number of iterations Imax = 100, a set of optimal solutions are found: t1 = 2.0979s, t2 = 1.7807s, t3 = 2.0855s, and the optimal time for the manipulator trajectory planning is 5.9641s.

[0031] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A robot arm trajectory optimization method based on an adaptive golden search algorithm, characterized in that: The steps include: Step 1: Decompose the planned action of the robot arm to be trajectory optimized into three actions, and then build a time optimization mathematical model for fitness based on the optimization goal; Step 2: Construct a population based on fitness, and adjust the individuals in the population through adaptive inertia weights. Then, combine the elite reverse strategy and the golden sine mutation strategy to construct the optimal position search formula, calculate the optimal position, and substitute it into the time optimization mathematical model to calculate the fitness; Step 3: Repeat step 2 until the maximum number of iterations is reached, and record the optimal fitness, and obtain the time solution of the three actions corresponding to the optimal fitness; Step 4: Obtain the robot kinematic parameters of the robot to be trajectory optimized, solve the posture and position in the joint space of the trajectory points based on the robot kinematic parameters combined with the robot forward kinematics, construct a mixed difference polynomial for the robot motion planning according to the posture and position, calculate the coefficient solution in the mixed difference polynomial, and substitute it into the time solution of the three actions to complete the trajectory optimization of the robot trajectory.

2. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 1 is characterized in that: The method of combining the elite reverse strategy with the golden sine mutation strategy to construct the optimal position search formula includes: combining the business reverse strategy to obtain an initialization population from the population adjusted by the adaptive inertia weight, introducing the golden section coefficient of the golden sine mutation strategy, and obtaining the optimal position search formula.

3. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 2 is characterized in that: The adjusting of individuals in the population by adaptive inertia weights includes: adjusting initial parameters of the population in combination with the adaptive inertia weights so that the individuals in the population move closer to the optimal area; The adaptive inertia weight is expressed by the following formula: ； in, represents the adaptive inertia weight, n is the loop counter, is the maximum number of iterations, r is the damping factor, and its value range is [0,1].

4. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 3 is characterized in that: In step 2, the initialization population is obtained by the following steps: Step 201: Calculate the fitness of all individuals in the population adjusted by the adaptive inertia weight, select a number of individuals from large to small according to the fitness, and construct an elite population based on the individuals; Step 202: Obtain the reverse population of the elite population, and merge the initialization population and the reverse population into a new initialization population; Step 203: Repeat steps 201 to 202 to construct a new initialization population.

5. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 1 is characterized in that: The optimal position search formula is expressed by the following formula: ； In the formula, Indicates t Iteration No. i The optimal position of an individual in a population is and are the representation coefficients of distance and direction, respectively. and Take values ​​between express t In the iteration i The location of each individual in the population, express In the iteration i The location of each individual in the population, represents the golden ratio coefficient; The expression is as follows: ； In the formula, is the golden ratio number.

6. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 1, characterized in that: The method further includes step 5: executing the trajectory of the robot arm after trajectory optimization, and obtaining the speed and acceleration of all joints when the robot arm performs the action, and if the speed is greater than the preset speed value, the robot arm stops moving; If the acceleration is greater than the preset value, the robot stops moving.

7. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to claim 1 is characterized in that: The optimization objectives include: the joint angular displacement of the robot arm satisfies the maximum value of the joint angular displacement constraint, the joint angular velocity of the robot arm satisfies the maximum value of the joint angular velocity constraint, and the joint angular acceleration of the robot arm satisfies the maximum value of the joint angular acceleration constraint; The time optimization mathematical model for fitness is expressed by the following formula: ； ； in, t i1 , t i2 , t i3 They are the multi-form interpolation of the three-stage motion of the robot arm. i ( i =1,2,…,6) joints’ planned motion time, , , Respectively represent joint angular displacement, joint angular velocity and joint angular acceleration, where , , They are the maximum value of the joint angular displacement constraint, the maximum value of the joint angular velocity constraint, and the maximum value of the joint angular acceleration constraint.

8. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to any one of claims 1 to 5, characterized in that: In step 4, the mixed difference polynomial includes: constructing a 3-5-3 mixed difference polynomial for robot arm motion planning based on the decomposed three-segment motion.

9. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to any one of claims 1 to 5, characterized in that: In step 4, the calculation of the coefficient solution in the mixed difference polynomial includes: based on the mixed difference polynomial, constructing a transformation matrix of the mixed difference polynomial and a position matrix of the robot arm trajectory planning, constructing a coefficient matrix of the polynomial interpolation function based on the transformation matrix and the position matrix, and calculating the coefficient solution in the mixed difference polynomial based on the coefficient matrix.

10. The robot arm trajectory optimization method based on the adaptive golden search algorithm according to any one of claims 1 to 5, characterized in that: In step 4, the obtaining of the kinematic parameters of the robot arm to be trajectory optimized includes: obtaining the kinematic parameters of the robot arm based on the robot arm to be trajectory optimized and in combination with the robot arm kinematic analysis method; The kinematic parameters of the robot arm include: connecting rod length, connecting rod torsion angle, connecting rod distance and joint rotation angle.

Images