A multi-joint robot trajectory planning method considering time and energy consumption optimization

Abstract

The application discloses a multi-joint robot trajectory planning method considering time and energy consumption optimization and belongs to the technical field of intelligent control of industrial robots. In view of the problems of low working efficiency, high energy consumption and high use cost of a multi-joint robot in an actual working process, the method takes time and energy consumption as optimization targets, realizes path planning in a joint space of the multi-joint robot based on a particle swarm optimization algorithm and polynomial interpolation, and realizes autonomous adjustment of the weight proportion of time and energy consumption optimization by setting a weight factor, so that the flexibility of the path planning method is improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology for industrial robots, specifically relating to a trajectory planning method for multi-joint robots that considers time and energy consumption optimization. Background Technology

[0002] The development of industrial intelligence and intelligent manufacturing has become an important trend in global manufacturing, bringing new challenges and opportunities to labor-intensive industries. With the continuous in-depth research on industrial robots and the vigorous development of related functions, the manufacturing industry has also developed rapidly, and production capacity has been significantly improved.

[0003] Multi-joint robots are characterized by their compact structure, flexible operation, and large range of motion. They are a typical form of robot with multi-joint manipulators or multiple degrees of freedom.

[0004] In practical applications of multi-joint robots, optimizing time and energy consumption are primary objectives. By simultaneously considering and optimizing both time and energy consumption, the flexibility and efficiency of trajectory planning can be improved, enabling robots to complete tasks faster and increasing productivity and service quality. Reducing energy consumption also helps lower operating costs, extend robot lifespan, and aligns with sustainable development requirements. Furthermore, trajectory optimization can reduce mechanical wear and fatigue, improving robot reliability and stability. In scenarios with high precision and safety requirements, trajectory planning methods that optimize both time and energy consumption ensure smooth robot movement, avoiding potential hazards to the surrounding environment and personnel. Finally, in complex and dynamic environments, trajectory optimization enhances the robot's adaptability and task completion capabilities. In conclusion, trajectory planning methods that consider both time and energy consumption optimization can improve the overall performance, economic efficiency, and reliability of robot systems, meeting the needs of modern industry and service sectors. Summary of the Invention

[0005] To address the problems of low working efficiency, high energy consumption, and high operating costs of multi-joint robots in actual work, this invention provides a trajectory planning method for multi-joint robots that considers time and energy consumption optimization.

[0006] To achieve the above objectives, the present invention employs the following technical solutions:

[0007] A trajectory planning method for multi-joint robots that considers time and energy consumption optimization includes the following steps:

[0008] Step 1: Obtain the current position of each joint of the multi-joint robot and set the target position of each joint. Plan the robot's motion trajectory in the joint space. Use the current position of each joint as the starting point of the trajectory planning in radians and the set target position of each joint as the ending point of the trajectory planning.

[0009] Step 2: Set the weighting factors for time and energy consumption in trajectory planning, which are used to adjust the degree of influence of the two optimization objectives of time and energy consumption on the planned trajectory when optimizing the trajectory.

[0010] Step 3: Obtain the three-dimensional particles that best fit the target trajectory through particle swarm optimization algorithm and dual-objective optimization update strategy;

[0011] Furthermore, the particle optimization algorithm in step 3 employs two fitness functions and updates the particles according to the proposed bi-objective optimization update strategy, as detailed below:

[0012] Under the premise of satisfying kinematic constraints, the optimal time is selected to minimize the motion time of the multi-joint robot; then the optimization objective function 1 for the j-th joint is expressed as:

[0013]

[0014] The optimization objective function for the j-th joint is expressed as:

[0015]

[0016] The kinematic constraints are:

[0017]

[0018]

[0019] In the formula, , , , , , V represents the magnitude of the velocity and acceleration of the first cubic polynomial, the second quintic polynomial, and the third cubic polynomial in the j-th joint as a function of time; max Indicates maximum speed, a max t represents the maximum acceleration. j1 t represents the cubic polynomial of the first segment in the j-th joint; j2 t represents the fifth-order polynomial in the j-th joint; j3 The second segment of the cubic polynomial in the j-th joint; n represents the total number of particles; E all (t) represents the total energy consumption of the multi-joint robot based on kinetic energy;

[0020] In the particle swarm optimization algorithm, when the search space is N-dimensional and the total number of particles is n, the current position of the l-th particle in the N-dimensional space is: Flight speed is Each particle has a fitness value determined by the objective function being optimized, and it clears its best position found so far. and current location Each particle clears the best position found by the entire swarm so far. Then the position of each particle is updated in the following form:

[0021]

[0022]

[0023] In the formula, Let v be the d-th component of the flight velocity v of the l-th particle during the k-th iteration. Let x be the d-th dimension component of the position x of the l-th particle during the k-th iteration. Best position for the group The d-th dimension component, The best position for particle l The d-th dimension component, and For the interval is random numbers, and As a weighting factor, This is the inertial weight.

[0024] When performing trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the objective function 1 for the j-th joint is:

[0025]

[0026] The problem of energy consumption optimization is transformed into finding a set of three-segment polynomial interpolation times that minimizes energy consumption. , , The question is: what is the kinetic energy E during the movement of the j-th joint? j Represented as:

[0027]

[0028] Where, m j Let v represent the mass of the j-th joint. j Let a represent the velocity of the j-th joint. jLet represent the acceleration of the j-th joint, and let i represent the number of polynomials currently in use. The energy consumption model of each joint is expressed as a function of time, resulting in the kinetic energy-based energy consumption model E for the multi-joint robot. all (t):

[0029]

[0030] The problem of finding the energy-optimal trajectory for a multi-joint robot on a given path is transformed into finding the particle with the least energy consumption.

[0031] When performing trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the objective function 2 for the j-th joint is:

[0032]

[0033] When optimizing trajectories, both time and energy consumption need to be considered, making the optimization of both a key challenge. For particle swarm optimization algorithms, the key lies in how to measure the quality of a particle. Although the particle itself only represents the time required for three interpolation segments, the energy consumption required for the trajectory corresponding to that particle can be obtained by using the time of the three interpolation segments through a kinetic energy-based energy consumption model.

[0034] Time and energy consumption are parameters for evaluating particle quality; therefore, the following strategy is used for particle updates:

[0035] when , If the time consumption and energy consumption of the current particle are both better than the historical best particle, then the current particle is updated to the global best particle.

[0036] when , If the current particle's time consumption is better than the historical best particle, but its energy consumption is worse than the historical best particle, then a judgment is made: when Then update the current particle to the globally optimal particle;

[0037] when , If the current particle's time consumption is worse than the historical best particle, but its energy consumption is better than the historical best particle, then a judgment is made: when If so, then update the current particle to the globally optimal particle;

[0038] in, This represents the optimal time when something appeared and was stored in the past. T represents the optimal energy consumption that appeared and was stored in the past, while T and E represent the time and energy consumption corresponding to the current particle. The weight assigned to time optimization, with a value ranging from 0 to 1. The weight assigned to energy consumption optimization.

[0039] Step 4: Use 3-5-3 polynomial interpolation to solve for the motion trajectory of each joint using the obtained three-dimensional particles;

[0040] Furthermore, the general formula for 3-5-3 polynomial interpolation is:

[0041]

[0042]

[0043]

[0044] Among them, coefficient , , It is the first The first three segments of the joint trajectory interpolation function One coefficient, Corresponding to the cubic polynomial trajectory of the first segment of the j-th joint, Corresponding to the second segment of the fifth-order polynomial trajectory of the j-th joint, This represents the third polynomial trajectory corresponding to the j-th joint, where t represents time. , This represents the number of joints;

[0045]

[0046]

[0047] In the formula, Represents the position of the j-th joint interpolation, where , representing the sequence number of the four interpolation points; in the Cartesian coordinate system These are the joint angles corresponding to the motion space coordinates of the multi-joint robot calculated using inverse kinematics; A, b, and a represent unknown coefficients. , , The relationship between the interpolation point and the interpolation point (this only represents the relationship and has no explicit definition), where T represents the transpose;

[0048] The constraint is: the starting point of the j-th joint motion of the multi-joint robot is known. End point Path points and And the velocity and acceleration at the starting and ending points (usually defaulted to 0), with the velocity and acceleration being continuous between each path point;

[0049] Based on the above conditions, the corresponding relationship between the coefficients and the interpolation points can be derived, where... - Let represent the time required for the first cubic polynomial trajectory, the second quintic polynomial trajectory, and the third cubic polynomial trajectory during the movement of the j-th joint, respectively, and then obtain the solution for the trajectory of the j-th joint.

[0050] Step 5: Discretize the motion trajectories of each joint to obtain a series of trajectory points for controlling the robot's motion;

[0051] Furthermore, the joint trajectories obtained in step 4, including the continuous functions of position, velocity, and acceleration with respect to time, are sampled to obtain discrete trajectory points for publication to the robot actuator.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] This invention proposes a trajectory planning method for multi-joint robots that considers time and energy consumption optimization. Based on trajectory planning, this method achieves dual-objective optimization of time and energy consumption. Trajectory planning is implemented in joint space using particle swarm optimization and 3-5-3 polynomial interpolation. The optimal particle is determined through a proposed particle update strategy and two fitness functions used to judge particle quality.

[0054] This invention provides a multi-joint robot trajectory planning method that considers time and energy consumption optimization. Furthermore, by setting weight factors, it can plan trajectories that emphasize different aspects, providing more choices for robot motion trajectories, increasing the robot's work flexibility and adaptability to different working states. Attached Figure Description

[0055] Figure 1 This is a flowchart of a multi-joint robot trajectory planning process that takes into account time and energy consumption optimization, based on a preferred embodiment.

[0056] Figure 2 This is a schematic diagram of the update strategy used to determine the quality of particles during particle updates.

[0057] Figure 3 for Joint trajectory diagrams at =0.2

[0058] Figure 4 for Joint trajectory diagram at 0.5

[0059] Figure 5 for Trajectory diagrams of each joint when =0.8. Detailed Implementation

[0060] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0061] A trajectory planning method for multi-joint robots that considers time and energy consumption optimization. Figure 1 The flowchart illustrates a trajectory planning method for multi-joint robots that considers time and energy consumption. The method includes the following steps:

[0062] Step 1: Obtain the current position of each joint of the multi-joint robot and set the target position of each joint. Plan the robot's motion trajectory in the joint space. Use the current position of each joint as the starting point of the trajectory planning in radians and the set target position of each joint as the ending point of the trajectory planning.

[0063] Step 2: Set the weighting factors for time and energy consumption in trajectory planning, which are used to adjust the degree of influence of the two optimization objectives of time and energy consumption on the planned trajectory when optimizing the trajectory.

[0064] Step 3: Obtain the three-dimensional particles that best fit the target trajectory through particle swarm optimization algorithm and dual-objective optimization update strategy;

[0065] Furthermore, the particle optimization algorithm in step 3 employs two fitness functions and updates the particles according to the proposed bi-objective optimization update strategy, as detailed below:

[0066] Under the premise of satisfying kinematic constraints, the optimal time is selected to minimize the motion time of the multi-joint robot; then the optimization objective function 1 for the j-th joint is expressed as:

[0067]

[0068] The optimization objective function for the j-th joint is expressed as:

[0069]

[0070] The kinematic constraints are:

[0071]

[0072]

[0073] In the formula, , , , , , V represents the magnitude of the velocity and acceleration of the first cubic polynomial, the second quintic polynomial, and the third cubic polynomial in the j-th joint as a function of time; max Indicates maximum speed, a max t represents the maximum acceleration. j1 t represents the cubic polynomial of the first segment in the j-th joint; j2 t represents the fifth-order polynomial in the j-th joint; j3 The second segment of the cubic polynomial in the j-th joint; n represents the total number of particles; E all (t) represents the total energy consumption of the multi-joint robot based on kinetic energy;

[0074] In the particle swarm optimization algorithm, when the search space is N-dimensional and the total number of particles is n, the current position of the i-th particle in the N-dimensional space is: Flight speed is Each particle has a fitness value determined by the objective function being optimized, and it clears its best position found so far. and current location Each particle clears the best position found by the entire swarm so far. Then the position of each particle is updated in the following form:

[0075]

[0076]

[0077] In the formula, Let v be the d-th component of the flight velocity v of the l-th particle during the k-th iteration. Let x be the d-th dimension component of the position x of the l-th particle during the k-th iteration. Best position for the group The d-th dimension component, The best position for particle l The d-th dimension component, and For the interval is random numbers, and As a weighting factor, This is the inertial weight.

[0078] When performing trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the objective function 1 for the j-th joint is:

[0079]

[0080] The problem of energy consumption optimization is transformed into finding a set of three-segment polynomial interpolation times that minimizes energy consumption. , , The question is: what is the kinetic energy E during the movement of the j-th joint? j Represented as:

[0081]

[0082] Where, m j Let v represent the mass of the j-th joint. j Let a represent the velocity of the j-th joint. j Let represent the acceleration of the j-th joint, and let i represent the number of polynomials currently in use. The energy consumption model of each joint is expressed as a function of time, resulting in the kinetic energy-based energy consumption model E for the multi-joint robot. all (t):

[0083]

[0084] The problem of finding the energy-optimal trajectory for a multi-joint robot on a given path is transformed into finding the particle with the least energy consumption.

[0085] When performing trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the objective function 2 for the j-th joint is:

[0086]

[0087] When optimizing trajectories, both time and energy consumption need to be considered, making the optimization of both a key challenge. For particle swarm optimization algorithms, the key lies in how to measure the quality of a particle. Although the particle itself only represents the time required for three interpolation segments, the energy consumption required for the trajectory corresponding to that particle can be obtained by using the time of the three interpolation segments through a kinetic energy-based energy consumption model.

[0088] Time and energy consumption are parameters for evaluating particle quality; therefore, the following strategy is used for particle updates:

[0089] when , If the time consumption and energy consumption of the current particle are both better than the historical best particle, then the current particle is updated to the global best particle.

[0090] when , If the current particle's time consumption is better than the historical best particle, but its energy consumption is worse than the historical best particle, then a judgment is made: when Then update the current particle to the globally optimal particle;

[0091] when , If the current particle's time consumption is worse than the historical best particle, but its energy consumption is better than the historical best particle, then a judgment is made: when If so, then update the current particle to the globally optimal particle;

[0092] in, This represents the optimal time when something appeared and was stored in the past. T represents the optimal energy consumption that appeared and was stored in the past, while T and E represent the time and energy consumption corresponding to the current particle. The weight assigned to time optimization, with a value ranging from 0 to 1. The weight assigned to energy consumption optimization.

[0093] Step 4: Use 3-5-3 polynomial interpolation to solve for the motion trajectory of each joint using the obtained three-dimensional particles;

[0094] Furthermore, the general formula for 3-5-3 polynomial interpolation is:

[0095]

[0096]

[0097]

[0098] Among them, coefficient , , It is the first The first three segments of the joint trajectory interpolation function One coefficient, Corresponding to the cubic polynomial trajectory of the first segment of the j-th joint, Corresponding to the second segment of the fifth-order polynomial trajectory of the j-th joint, This represents the third polynomial trajectory corresponding to the j-th joint, where t represents time. , This represents the number of joints;

[0099]

[0100]

[0101] In the formula, Represents the position of the j-th joint interpolation, where , representing the sequence number of the four interpolation points; in the Cartesian coordinate system These are the joint angles corresponding to the motion space coordinates of the multi-joint robot calculated using inverse kinematics; A, b, and a represent unknown coefficients. , , The relationship between the interpolation point and the interpolation point (this only represents the relationship and has no explicit definition), where T represents the transpose;

[0102] The constraint is: the starting point of the j-th joint motion of the multi-joint robot is known. End point Path points and And the velocity and acceleration at the starting and ending points (usually defaulted to 0), with the velocity and acceleration being continuous between each path point;

[0103] Based on the above conditions, the corresponding relationship between the coefficients and the interpolation points can be derived, where... - Let represent the time required for the first cubic polynomial trajectory, the second quintic polynomial trajectory, and the third cubic polynomial trajectory during the movement of the j-th joint, respectively, and then obtain the solution for the trajectory of the j-th joint.

[0104] Step 5: Discretize the motion trajectories of each joint to obtain a series of trajectory points for controlling the robot's motion;

[0105] Furthermore, the joint trajectories obtained in step 4, including the continuous functions of position, velocity, and acceleration with respect to time, are sampled to obtain discrete trajectory points for publication to the robot actuator.

[0106] by =0.2, =0.8; =0.5, =0.5; =0.8, =0.2 Multiple experiments were conducted, and the time and energy consumption were statistically analyzed. The results are shown in Tables 4-15, 4-16, and 4-17. Under the premise that the starting and ending points and the weights of each link are the same, the experiment was repeated multiple times, and nine sets of data were randomly selected to analyze the changes in weight. Increase in weight The reduction of time / energy consumption reduces the total motion time and total energy consumption of the trajectory planned by the time / energy consumption optimal controller.

[0107] Comparing Tables 1, 2, and 3, we can conclude that, with increasing weight... , Changes in exercise duration Total energy consumption There are corresponding changes, the specific changes are as follows:

[0108] (1) Optimize weights over time Improvements are made, but the time required for robot movement is reduced, while energy consumption is increased.

[0109] (2) With the weight of energy consumption optimization With the improvement of [the system / mechanics], the energy consumption of robot movement is reduced, but the time consumption is increased.

[0110] Table 1 =0.2 Time consumption and energy consumption

[0111] Serial Number 1 2 3 4 5 6 7 8 13.88 14.01 14.01 13.99 14.01 14.00 13.99 14.01 26548.9 26968.2 26510.8 26510.7 26774.5 26510.3 26546.9 26780.1

[0112] Table 2 =0.5 Time and Energy Consumption

[0113] Serial Number 1 2 3 4 5 6 7 8 9.74 9.67 9.59 9.68 9.55 9.66 9.81 9.73 97847.2 100128 100126 100425 100112 100129 93036.8 100347

[0114] Table 3 =0.8 Time and Energy Consumption

[0115] Serial Number 1 2 3 4 5 6 7 8 3.92 3.93 3.99 3.88 3.98 4.01 3.99 3.93 414951 422581 410398 389756 396576 409858 412593 405653

[0116] Optimize weights at different times The trajectory diagrams of each joint are shown below. Figure 3 , Figure 4 , Figure 5 As shown. Under the constraints of kinematics and time optimization weights... and energy consumption optimization weights Under the changed circumstances, the trajectory planned by the time / energy-optimal controller differs, as follows:

[0117] (1) Optimize weights over time As the velocity and acceleration increase, the trajectory planned by the controller shows that the velocity and acceleration increase and tend to the maximum value. , The fluctuations in speed and acceleration also become more intense, leading to a greater overall energy consumption. Increase;

[0118] (2) With the weight of energy consumption optimization As the energy density increases, the trajectory planned by the controller shows a decrease in speed and acceleration with smoother fluctuations, resulting in lower total energy consumption. Reduce, exercise duration Increase.

[0119] like Figure 3 As shown, when When the value is 0.2, the trajectory curves of each joint approximate the trajectory planned by the energy-optimal controller, with low velocity and acceleration, and smooth joint position curves.

[0120] like Figure 4 As shown, when When the value is 0.5, the trajectory curves of each joint fluctuate relatively violently, and the velocity and acceleration are relatively... When the value is increased to 0.2, the time it takes for each joint to reach the specified position from the initial position is reduced.

[0121] like Figure 5 As shown, when When the coefficient of friction is 0.8, the trajectory curves of each joint approximate the trajectory planned by the time-optimal controller, with relatively large velocities and accelerations, and the maximum values ​​approaching the constraint conditions. Compared to... When the value is 0.5, the time taken for each joint to reach the specified position from the initial position is reduced.

[0122] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A trajectory planning method for a multi-joint robot considering time and energy consumption optimization, characterized in that, The method includes the following steps: Step 1: Obtain the current position of each joint of the multi-joint robot and set the target position of each joint of the multi-joint robot; Step 2: Set the weighting factors of time and energy consumption in trajectory planning, and adjust the degree of influence of the two optimization objectives of time and energy consumption on trajectory planning when optimizing the trajectory. Step 3: Obtain the three-dimensional particles that best fit the target trajectory through the particle swarm optimization algorithm and the dual-objective optimization update strategy, and obtain the optimal trajectory that meets the optimization objective. Step 4: Use 3-5-3 polynomial interpolation to solve for the motion trajectory of each joint using the obtained three-dimensional particles; Step 5: Discretize the motion trajectories of each joint to obtain a series of trajectory points for controlling the robot's motion; The particle optimization algorithm in step 3 employs two fitness functions and updates the particles according to the proposed bi-objective optimization update strategy, as detailed below: Under the premise of satisfying kinematic constraints, select the optimal time to minimize the motion time of the multi-joint robot; Then the first The optimization objective function 1 for each joint is expressed as: ; No. The optimization objective function for each joint is expressed as: ; The kinematic constraints are: , In the formula, , , , , , Indicates the first The speed and magnitude of acceleration of the first cubic polynomial, the second quintic polynomial, and the third cubic polynomial in each joint as a function of time; Indicates the maximum speed. Indicates the maximum acceleration. Indicates the first The first segment of the joint is a cubic polynomial; Indicates the first A fifth-order polynomial in each joint; Indicates the first The second segment of the joint is a cubic polynomial; Indicates the total number of particles; This represents the total energy consumption of a multi-joint robot based on kinetic energy. In the particle swarm optimization algorithm, when the search space is Dimension, total number of particles , No. Individual particles The current position in 3D space is Flight speed is Each particle has a fitness value determined by the objective function being optimized, and it clears its best position found so far. and current location Each particle clears the best position found by the entire swarm so far. Then the position of each particle is updated in the following form: , ; In the formula, For the first The first particle Flight speed during the next iteration The dimensional components, For the first The first particle Position at the next iteration The dimensional components, Best position for the group The dimensional components, For particles Best location The dimensional components, and For the interval is random numbers, and As a weighting factor, Inertial weight; In step 3, during trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the... The optimization objective function 1 for each joint is: ; The problem of energy consumption optimization is transformed into finding a set of three-segment polynomial interpolation times that minimizes energy consumption. , , The question; then the first Kinetic energy during joint movement Represented as: ; in, Indicates the first The quality of each joint Indicates the first The speed of each joint Indicates the first The acceleration of each joint, This indicates which polynomial segment is currently in use. The energy consumption model of each joint is expressed as a function of time, resulting in the kinetic energy-based energy consumption model of the multi-joint robot. : ; The problem of finding the energy-optimal trajectory for a multi-joint robot on a given path is transformed into finding the particle with the least energy consumption. When performing trajectory planning, each joint of the multi-joint robot is planned separately. Specifically, in the trajectory optimization part, the... The optimization objective function for each joint is: , Time and energy consumption are parameters for evaluating particle quality; therefore, the following strategy is used for particle updates: when , If the time consumption and energy consumption of the current particle are both better than the historical best particle, then the current particle is updated to the global best particle. when , If the current particle's time consumption is better than the historical best particle, but its energy consumption is worse than the historical best particle, then a judgment is made: when Then update the current particle to the globally optimal particle; when , If the current particle's time consumption is worse than the historical best particle, but its energy consumption is better than the historical best particle, then a judgment is made: when If so, then update the current particle to the globally optimal particle; in, This represents the optimal time when something appeared and was stored in the past. This represents the optimal energy consumption that has appeared and been stored in the past. , This represents the time and energy consumption corresponding to the current particle. The weight assigned to time optimization, with a value ranging from 0 to 1. The weight given to energy consumption optimization; The specific operation of step 4 is as follows: The general formula for polynomial interpolation in 3-5-3 is: , , , Among them, coefficient , , It is the first The first to third segments of the interpolation function of the joint trajectory One coefficient, Corresponding to the first The first segment of the joint's cubic polynomial trajectory Corresponding to the first The second segment of the fifth-order polynomial trajectory of each joint Representing the first The third polynomial trajectory corresponding to each joint. Indicates time, , This represents the number of joints; ， ， ； In the formula, Representing the The position of each joint interpolation, where , representing the sequence number of the four interpolation points; in the Cartesian coordinate system These are the joint angles corresponding to the motion space coordinates of a multi-joint robot calculated through inverse kinematics. , , Unknown coefficients , , The relationship between the interpolation point and the interpolation point; The constraints are: given the first joint of the multi-joint robot... The starting point of each joint movement End point Path points and The velocities and accelerations at the starting and ending points are also considered, and the velocities and accelerations between each path point are continuous. The corresponding relationship between the coefficients and the interpolation points is derived, where... ~ Representing the first The time required for the first cubic polynomial trajectory, the second quintic polynomial trajectory, and the third cubic polynomial trajectory during the movement of each joint is thus obtained. The solution for the trajectory of each joint.

2. The multi-joint robot trajectory planning method considering time and energy consumption optimization according to claim 1, characterized in that, In step 1, the current position of each joint of the multi-joint robot is obtained, and the target position of each joint is set. The robot's motion trajectory is planned in the joint space. The current position of each joint is obtained in radians as the starting point of the trajectory planning, and the set target position of each joint is used as the ending point of the trajectory planning.

3. The multi-joint robot trajectory planning method considering time and energy consumption optimization according to claim 2, characterized in that, The specific steps of step 5 are as follows: the joint trajectories obtained in step 4, including the continuous functions of position, velocity, and acceleration with respect to time, are sampled to obtain discrete trajectory points.

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