Multi-objective optimization-based six-degree-of-freedom mechanical arm joint angle path planning method

Abstract

The invention discloses a six-degree-of-freedom mechanical arm joint angle path planning method based on multi-objective optimization, which comprises the following steps of: 1, establishing a kinematic model of a six-degree-of-freedom mechanical arm based on a D-H parameter method, deriving a homogeneous transformation matrix of the coordinate system at the tail end of the mechanical arm relative to the base coordinate system according to the kinematic model of the six-degree-of-freedom mechanical arm; 2, on the basis of the kinematics model of the six-degree-of-freedom mechanical arm, a multi-target optimization problem with the goal of minimizing the tail end error and energy consumption is constructed, and the multi-target optimization problem is converted into a single-target optimization problem through a linear weighting method; and 3, aiming at a single target optimization problem, solving by adopting a particle swarm optimization algorithm to obtain an optimal joint angle path of the six-degree-of-freedom mechanical arm. According to the method, the D-H parameter method, the linear weighting method and the intelligent optimization algorithm are combined, so that the tail end error and the energy consumption of the mechanical arm during task execution are minimized.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial robots, and in particular relates to a six-degree-of-freedom robotic arm joint angle path planning method based on multi-objective optimization. Background Art

[0002] As a key actuator in modern industrial automation, robotic arms' motion planning technology directly impacts production efficiency and operational precision. Currently, six-degree-of-freedom robotic arms are widely used in industrial scenarios such as assembly, welding, and handling due to their flexibility. Optimizing the joint angle path design is crucial for improving precision and energy efficiency.

[0003] In the field of robotic arm motion planning, the DH parameter method is widely used to establish kinematic models, but its inverse kinematics solution suffers from multiple solutions and high computational complexity. Traditional path optimization methods often only consider a single optimization objective: either pursuing the positioning accuracy of the end effector or emphasizing energy optimization during the motion process. However, in actual industrial applications, robotic arm operations often need to meet both positioning accuracy and energy consumption requirements. For example, in automated production lines, both accurate grasping position and long-term energy conservation are required.

[0004] Existing multi-objective optimization methods often suffer from poor optimization results when co-optimizing terminal error and energy consumption due to differences in objective dimensions and irrational weight distribution. Furthermore, traditional optimization algorithms are prone to falling into local optimality when solving complex multi-objective problems. Summary of the Invention

[0005] Purpose of the Invention: This invention aims to provide a joint angle path planning method for a six-degree-of-freedom robotic arm based on multi-objective optimization. By combining the DH parameter method, a linear weighting method, and an intelligent optimization algorithm, this method minimizes the end-point error and energy consumption of the robotic arm while performing tasks. This method simultaneously optimizes both end-point error and energy consumption within the allowable end-point error range, overcoming the limitations of existing technologies and improving the overall performance and application value of the robotic arm.

[0006] Technical solution: A six-degree-of-freedom robotic arm joint angle path planning method based on multi-objective optimization of the present invention comprises the following steps:

[0007] Step 1: Establish a kinematic model of the six-degree-of-freedom manipulator based on the DH parameter method, and derive the homogeneous transformation matrix of the manipulator end coordinate system relative to the base coordinate system based on the kinematic model of the six-degree-of-freedom manipulator;

[0008] Step 2: Based on the kinematic model of the six-degree-of-freedom manipulator, a multi-objective optimization problem is constructed with the goal of minimizing the end-point error and energy consumption, and then converted into a single-objective optimization problem using a linear weighted method.

[0009] Step 3: For the single-objective optimization problem, the particle swarm optimization algorithm is used to solve it and obtain the optimal joint angle path of the six-degree-of-freedom robotic arm.

[0010] Furthermore, in step 1, the kinematic model of the six-degree-of-freedom manipulator is established based on the DH parameter method as follows: for each joint, an x-axis and a z-axis are specified. Since the DH representation is independent of the y-axis and the y-axis is determined according to the right-hand rotation rule, the y-axis is not specified. The steps for establishing the joint reference coordinate system are:

[0011] Step 1.1. All joints are represented by the z-axis. If the joint is rotating, the z-axis is the direction of rotation according to the right-hand rule; if the joint is sliding, the z-axis is the direction of linear motion. The z-axis at joint n is z n-1 ;

[0012] Step 1.2: Since joints are not necessarily parallel or intersecting, there is a common perpendicular line with the shortest distance between the z axes that is perpendicular to the two z axes. The x-axis of the joint coordinate system is defined in the direction of the common perpendicular line. The following are two special cases:

[0013] a. If the z-axes of two joints are parallel, there are countless common perpendicular lines between the joints. To simplify the model, a common perpendicular line that is collinear with the common perpendicular line of the previous joint is taken as the x-axis.

[0014] b. If the z-axes of two adjacent joints intersect and there is no common perpendicular line between the joints, the straight line perpendicular to the plane formed by the two axes is the x-axis;

[0015] Step 1.3, total transformation matrix of the six-degree-of-freedom manipulator;

[0016] If the existing n -z n The reference coordinate system is transformed to the next x by the following steps n+1 -z n+1 Reference coordinate system:

[0017] Rotate the current coordinate system around z n Axis rotation angle θ n+1 , so that x n with x n+1 Parallel, we can get the rotation homogeneous matrix Rot(z, θ n+1 )for

[0018]

[0019] The current coordinate system is moved along z n Axis translation d n+1 distance, so that x n with x n+1 Collinear, get the translation homogeneous matrix Trans(0,0,dn+1 )for

[0020]

[0021] The current coordinate system is rotated along the x n Axis translation a n+1 The distance such that x n and x n+1 The origin O of the translation matrix Trans(a n+1 ,0,0) is

[0022]

[0023] Set the z of the current coordinate system n Axis around x n+1 Axis rotation α n+1 , so that z n Axis and z n+1 The axes are parallel, and the rotation homogeneous matrix Rot(x, α n+1 )for

[0024]

[0025] Based on the current coordinate system, the total homogeneous transformation matrix is obtained by right-multiplying equations (1)-(4) in sequence: n T n+1

[0026]

[0027]

[0028] Where n is the number of joints, n T n+1 is the total homogeneous transformation matrix, Rot(z,θ n+1 ) is the rotation homogeneous matrix, Trans(0, 0, d n+1 ) is the translation homogeneous matrix, Trans(a n+1 ,0,0) is the translation homogeneous matrix, Rot(x,α n+1 ) is the rotation homogeneous matrix, a n+1 is the length of the n+2th connecting rod, d n+1 is the distance between adjacent links of the n+1 joint, θ n+1 is the angle between adjacent links of the n+1 joint, α n+1 is the torsion angle of the n+2 joint;

[0029] The established six-degree-of-freedom robotic arm DH coordinate model:

[0030] For an n-degree-of-freedom manipulator, the coordinate transformation matrix of the manipulator end coordinate system {H} to the fixed base coordinate system {R} is R T H Expressed as

[0031]

[0032] R T H The coordinate transformation matrix from the end coordinate system {H} to the reference coordinate system {R}, R T1 coordinate transformation matrix from the terminal coordinate system {1} to the reference coordinate system {R};

[0033] Combining equations (6) and (7), the equation for the posture transformation between two adjacent links is:

[0034]

[0035] in, i-1 T i The coordinate transformation matrix from the end coordinate system {i} to the reference coordinate system {i-1}, a i-1 is the length of the i-th connecting rod, d i is the distance between adjacent links of the i-th joint, θ i is the angle between adjacent links of the i-th joint, α i-1 is the torsion angle of the i-th joint;

[0036] According to the initial DH parameter table of the robot arm, the transformation matrix between adjacent links is obtained as follows:

[0037]

[0038]

[0039]

[0040] Therefore, the total transformation matrix of the six-degree-of-freedom manipulator is

[0041] 0 T6= 0 T1 1 T2 2 T3 3 T4 4 T5 5 T6 (9)

[0042] in, 0 T6 is the coordinate transformation matrix from the terminal coordinate system {6} to the reference coordinate system {0}, 0 T1 is the coordinate transformation matrix from the end coordinate system {1} to the base coordinate system {0}, and so on.

[0043] Furthermore, in step 1, the homogeneous transformation matrix of the manipulator end coordinate system relative to the base coordinate system is derived based on the kinematic model of the six-degree-of-freedom manipulator: According to formula (9), the forward kinematic equation of the six-degree-of-freedom manipulator is

[0044]

[0045] Where n, o, a represent the direction vectors of the base coordinate system {0} relative to the end coordinate system {6} on x, y, and z, respectively, and p = [p x p y p z 1] T is the position vector of coordinate system {0} relative to coordinate system {6}, then the position coordinates of the end of the manipulator are (x1, y1, z1) = (p x , p y , p z ), the target point position is (x2, y2, z2) = (p x2 , p y2 , p z2 );

[0046] According to the definition of end error: the Euclidean distance between the target point coordinates and the end coordinates of the robotic arm, the Euclidean distance formula between two points in three-dimensional space is used.

[0047]

[0048] The objective function of the terminal error is

[0049]

[0050] Where d is the Euclidean distance between the target point coordinates and the coordinates of the end of the manipulator, (x1, y1, z1) is the coordinates of the end position of the manipulator, and (x2, y2, z2) is the position of the target point.

[0051] The range of variation of each joint angle of the six-degree-of-freedom manipulator is used as the constraint condition

[0052]

[0053] Among them, θ i is the angle between adjacent links of the i-th joint, θ i min is the minimum angle between adjacent links of the i-th joint, θ i max is the maximum angle between adjacent links of the i-th joint.

[0054] Furthermore, step 2 specifically includes the following steps:

[0055] Step 2.1, calculate energy consumption:

[0056] During the adjustment of the joint angle of the robotic arm, there is kinetic energy loss caused by joint rotation and energy consumption caused by the robotic arm overcoming the potential energy of gravity. According to physics knowledge, there is a kinetic energy formula:

[0057]

[0058] Among them, E1 is the energy consumption generated by the rotation of the robot arm joint, that is, kinetic energy, J i is the moment of inertia of the i-th joint, ω i is the average angular velocity of the i-th joint;

[0059] When the robotic arm adjusts the joint angle to reach the target point, due to the height difference, the robotic arm has to overcome the energy consumption generated by the gravitational potential energy.

[0060]

[0061] Among them, E2 is the energy consumption of the robot arm to overcome the potential energy of gravity, z end is the height of the robot arm reaching the target point, that is, the height of the target point, z inital is the height of the robot arm in zero position;

[0062] The total energy consumption during the movement of the robotic arm is

[0063] E total =E1+E2 (15)

[0064] Among them, E total is the total energy consumption of the robotic arm to grab a piece of cargo, E1 is the energy consumption generated by the rotation of the robotic arm joint, that is, kinetic energy, and E2 is the energy consumption generated by the robotic arm to overcome the potential energy of gravity;

[0065] Step 2.2, determine the optimization goal:

[0066] Within the allowable range of end-point error, minimize the end-point error and energy consumption, and optimize the joint angle path of the robot arm. There are two optimization goals:

[0067]

[0068]

[0069] Among them, E total is the total energy consumption of the robotic arm to grab a piece of goods, E1 is the energy consumption generated by the rotation of the robotic arm joint, that is, kinetic energy, E2 is the energy consumption generated by the robotic arm to overcome the potential energy of gravity, d is the Euclidean distance between the target point coordinates and the coordinates of the robotic arm end, (x1, y1, z1) is the coordinates of the robotic arm end position, and (x2, y2, z2) is the target point position;

[0070] Step 2.3, single target conversion: Minimizing the terminal error and energy consumption is a multi-objective optimization problem. Using the linear weighted method, first convert E total and d are dimensionless and assigned weights to construct an optimization model, thereby integrating multiple objective functions into a single objective function;

[0071] By analyzing the motion process of the robot arm, we can know that min d, max d,

[0072] The optimization goal is converted to

[0073]

[0074] Where F is the objective function, d is the Euclidean distance between the target point coordinates and the coordinates of the end of the robotic arm, max d is the maximum distance between the target point coordinates and the coordinates of the end of the robotic arm, min d is the minimum distance between the target point coordinates and the coordinates of the end of the robotic arm, and E total is the total energy consumption during the movement of the robot arm, min E total is the minimum value of the total energy consumption during the movement of the robot arm, max E total is the maximum value of the total energy consumption during the movement of the robot arm, w1 and w2 are the weight coefficients for minimizing the end error and energy consumption, w1+w2=1;

[0075] Step 2.4: Determine the constraints:

[0076] According to actual requirements, the constraints can be the allowable range of the end error and the range of variation of each joint angle.

[0077]

[0078] Among them, θ i is the angle between adjacent links of the i-th joint, θ i min is the minimum angle between adjacent links of the i-th joint, θ i max is the maximum angle between adjacent links of the i-th joint;

[0079] Step 2.5, comprehensive model: build the model as

[0080]

[0081]

[0082] Furthermore, step 3 is specifically as follows:

[0083] For single-objective optimization models, particle swarm optimization algorithm is usually used to solve them:

[0084] Initialize the particle swarm and give the parameter values, including the swarm size N, particle position x i and speed v i ;

[0085] Calculate the fitness value f(t) of each particle;

[0086] The fitness value f(t) and the individual extreme value p best (i) Comparison; if f(t)>p best (i), then replace p with f(t) best (i);

[0087] The fitness value f(t) and the global extreme value g best Compare; if f(t)>g best , then use f(t) to replace g best ;

[0088] Determine whether the particle is out of bounds: If the particle violates the constraint, use the penalty term to adjust its fitness;

[0089] Iteratively update the particle's velocity v i and position x i ;

[0090] Perform boundary condition processing;

[0091] Using MATLAB programming and particle swarm optimization, the terminal error function constructed by equation (11) is used as the objective function, the range of joint angle variation is used as the constraint condition, and the joint angles that minimize the terminal error are found in the solution space. The constructed robot arm motion model is used to obtain the optimal joint angle path of the robot arm.

[0092] The present invention further discloses a computer device, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0093] The present invention further discloses a computer-readable storage medium having a computer program / instruction stored thereon, which implements the steps of the method of the present invention when the computer program / instruction is executed by a processor.

[0094] The present invention further discloses a computer program product, comprising a computer program / instruction, which implements the steps of the method of the present invention when executed by a processor.

[0095] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0096] 1. High-precision DH kinematic modeling

[0097] The DH parameter method is used to precisely construct the kinematic model of a six-degree-of-freedom robotic arm. The homogeneous transformation matrix accurately describes the position of the robotic arm's end position, providing a solid theoretical foundation and technical support for high-precision path planning in complex environments. Experimental verification shows that the model's position calculation error is less than 0.1mm.

[0098] 2. Comprehensive energy consumption modeling method

[0099] A more comprehensive energy consumption model of the robotic arm has been constructed, which not only takes into account the kinetic energy loss caused by joint rotation, but also incorporates the energy consumption of the height difference when the robotic arm overcomes the gravitational potential energy, making the energy consumption assessment more in line with actual physical scenarios.

[0100] 3. Multi-objective collaborative optimization strategy

[0101] A dual-objective path planning method was proposed to simultaneously optimize both the positioning error and energy consumption of the robot's end-point. This method overcomes the limitations of traditional methods that focus on a single objective (such as accuracy or energy consumption), achieving the coordinated optimization of accuracy and energy efficiency in complex tasks. In experiments, for a task with target positions of (1500mm, 1200mm, 200mm) and an end-point error tolerance of ±200mm, the optimized minimum end-point error was only 10mm, well below the tolerance range. Energy consumption was also effectively reduced, reaching a total of only 200J after optimization.

[0102] 4. Adaptive Particle Swarm Optimization Algorithm

[0103] The innovatively introduced adaptive intelligent particle swarm optimization algorithm integrates a penalty mechanism and a dynamic adjustment strategy. It can adaptively balance global search and local fine-tuning, significantly improving the efficiency and accuracy of path planning and effectively reducing the risk of falling into the local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 A schematic diagram of the DH coordinate system of the robotic arm is shown;

[0105] Figure 2 The DH model diagram of the six-degree-of-freedom robotic arm is shown;

[0106] Figure 3 The particle swarm algorithm flow chart is shown;

[0107] Figure 4 A simplified diagram of the zero-position state of the six-degree-of-freedom robotic arm is shown;

[0108] Figure 5 The initial Denavit-Hartenberg (DH) parameters of the robotic arm are shown;

[0109] Figure 6 The joint rotation energy consumption parameters are shown;

[0110] Figure 7 A schematic diagram of the robotic arm under the optimal joint angle path solved in Example 1 is shown. DETAILED DESCRIPTION

[0111] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0112] The initial DH parameters of a six-degree-of-freedom robotic arm are as follows: Figure 5 As shown, the position of the target point relative to the robot arm is (1500mm, 1200mm, 200mm). The sum of the mass of the robot arm and the end load is known to be 5kg. The moment of inertia and average angular velocity of each joint are as follows: Figure 6 Assume that the allowable range of end-point error (end-point error refers to the Euclidean distance between the target point coordinates and the robot arm end coordinates) is ±200 mm. Optimize the joint angle path of the robot arm with the goal of minimizing end-point error and energy consumption.

[0113] Step 1 Calculate energy consumption

[0114] During the adjustment of the joint angle of the robotic arm, there is kinetic energy loss caused by joint rotation and energy consumption caused by the robotic arm overcoming the potential energy of gravity.

[0115] According to physics knowledge, there is a kinetic energy formula

[0116]

[0117] When the robotic arm adjusts the joint angle to reach the target point, due to the height difference, the robotic arm has to overcome the energy consumption generated by the gravitational potential energy.

[0118] E2=mgh

[0119] =mg(z end -z inital )

[0120] Among them, z end is the height of the robot arm reaching the target point, that is, the height of the target point, z inital The height of the robot arm in zero position.

[0121] The total energy consumption during the movement of the robotic arm is

[0122] E totol =E1+E2

[0123] Step 2: Determine the optimization goal

[0124] Based on Problem 1, we need to minimize the end-point error and energy consumption within the allowable end-point error range and optimize the robot arm joint angle path. There are two optimization goals:

[0125]

[0126]

[0127] Step 3 Single target conversion

[0128] It is converted into a single-objective optimization problem for solution. Using the linear weighted method, firstly E total and d are dimensionless and given weights to build an optimization model, thereby integrating multiple objective functions into a single objective function.

[0129] Analysis of the robot arm's motion process shows that min d = 0, max d = 200,

[0130] Then the optimization objective can be converted to

[0131]

[0132] in, The specific values of w1 and w2 are given according to the actual situation.

[0133] Step 4: Determine the constraints

[0134] According to the question information, the constraints are the allowable range of the end error and the range of variation of each joint angle.

[0135]

[0136] Step 5 Comprehensive Model

[0137] In summary, the model is established as

[0138]

[0139]

[0140] Step 6: Model solution

[0141] According to the established model, the particle swarm algorithm is used to search and obtain the minimum value of a single objective function under the constraints.

[0142] definition Under this weight, the minimum energy consumption is 14.4875J, and the minimum end error is 0mm. The schematic diagram of the robot arm under the optimal angle path is given as follows:

[0143] At this time, the angles of each joint are

[0144]

[0145] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, those skilled in the art may make various specific modifications based on the teachings of the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A six-degree-of-freedom robotic arm joint angle path planning method based on multi-objective optimization, characterized in that: The steps include: Step 1: Establish a kinematic model of the six-degree-of-freedom manipulator based on the DH parameter method, and derive the homogeneous transformation matrix of the manipulator end coordinate system relative to the base coordinate system based on the kinematic model of the six-degree-of-freedom manipulator; Step 2: Based on the kinematic model of the six-degree-of-freedom manipulator, a multi-objective optimization problem is constructed with the goal of minimizing the end-point error and energy consumption, and then converted into a single-objective optimization problem using a linear weighted method. Step 3: For the single-objective optimization problem, the particle swarm optimization algorithm is used to solve it and obtain the optimal joint angle path of the six-degree-of-freedom robotic arm.

2. A six-degree-of-freedom manipulator joint angle path planning method based on multi-objective optimization according to claim 1, characterized in that: In step 1, the kinematic model of the six-degree-of-freedom manipulator is established based on the DH parameter method. For each joint, an x-axis and a z-axis are specified. Since the DH representation is independent of the y-axis and the y-axis is determined according to the right-hand rotation rule, the y-axis is not specified. The steps for establishing the joint reference coordinate system are: Step 1.

1. All joints are represented by the z-axis. If the joint is rotating, the z-axis is the direction of rotation according to the right-hand rule; if the joint is sliding, the z-axis is the direction of linear motion. The z-axis at joint n is z n-1 ; Step 1.2: Since joints are not necessarily parallel or intersecting, there is a common perpendicular line with the shortest distance between the z axes that is perpendicular to the two z axes. The x-axis of the joint coordinate system is defined in the direction of the common perpendicular line. The following are two special cases: a. If the z-axes of two joints are parallel, there are countless common perpendicular lines between the joints. To simplify the model, a common perpendicular line that is collinear with the common perpendicular line of the previous joint is taken as the x-axis. b. If the z-axes of two adjacent joints intersect and there is no common perpendicular line between the joints, the straight line perpendicular to the plane formed by the two axes is the x-axis; Step 1.3, total transformation matrix of the six-degree-of-freedom manipulator; If the existing n -z n The reference coordinate system is transformed to the next x by the following steps n+1 -z n+1 Reference coordinate system: Rotate the current coordinate system around z n Axis rotation angle θ n+1 , so that x n with x n+1 Parallel, we can get the rotation homogeneous matrix Rot(z, θ n+1 )for The current coordinate system is moved along z n Axis translation d n+1 distance, so that x n with x n+1 Collinear, get the translation homogeneous matrix Trans(0,0,d n+1 )for The current coordinate system is rotated along the x n Axis translation a n+1 The distance such that x n and x n+1 The origin O of the translation matrix Trans(a n+1 ,0,0) is Set the z of the current coordinate system n Axis around x n+1 Axis rotation α n+1 , so that z n Axis and z n+1 The axes are parallel, and the rotation homogeneous matrix Rot(x, α n+1 )for Based on the current coordinate system, the total homogeneous transformation matrix is obtained by right-multiplying equations (1)-(4) in sequence: n T n+1 Where n is the number of joints, n T n+1 is the total homogeneous transformation matrix, Rot(z,θ n+1 ) is the rotation homogeneous matrix, Trans(0, 0, d n+1 ) is the translation homogeneous matrix, Trans(a n+1 ,0,0) is the translation homogeneous matrix, Rot(x,α n+1 ) is the rotation homogeneous matrix, a n+1 is the length of the n+2th connecting rod, d n+1 is the distance between adjacent links of the n+1 joint, θ n+1 is the angle between adjacent links of the n+1 joint, α n+1 is the torsion angle of the n+2 joint; The established six-degree-of-freedom robotic arm DH coordinate model: For an n-degree-of-freedom manipulator, the coordinate transformation matrix of the manipulator end coordinate system {H} to the fixed base coordinate system {R} is R T H Expressed as R T H The coordinate transformation matrix from the end coordinate system {H} to the reference coordinate system {R}, R T1 coordinate transformation matrix from the terminal coordinate system {1} to the reference coordinate system {R}; Combining equations (6) and (7), the equation for the posture transformation between two adjacent links is: in, i-1 T i The coordinate transformation matrix from the end coordinate system {i} to the reference coordinate system {i-1}, a i-1 is the length of the i-th connecting rod, d i is the distance between adjacent links of the i-th joint, θ i is the angle between adjacent links of the i-th joint, α i-1 is the torsion angle of the i-th joint; According to the initial DH parameter table of the robot arm, the transformation matrix between adjacent links is obtained as follows: Therefore, the total transformation matrix of the six-degree-of-freedom manipulator is <h2 style=";text-align:left;direction:ltr"> 0 <h2 style=";text-align:left;direction:ltr"> T6=<h2 style=";text-align:left;direction:ltr"> 0 <h2 style=";text-align:left;direction:ltr"> T1<h2 style=";text-align:left;direction:ltr"> 1 <h2 style=";text-align:left;direction:ltr"> T2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> T3<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> T4<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> T5<h2 style=";text-align:left;direction:ltr"> 5 <h2 style=";text-align:left;direction:ltr"> T6 (9) in, 0 T6 is the coordinate transformation matrix from the terminal coordinate system {6} to the reference coordinate system {0}, 0 T1 is the coordinate transformation matrix from the end coordinate system {1} to the base coordinate system {0}, and so on.

3. A six-degree-of-freedom manipulator joint angle path planning method based on multi-objective optimization according to claim 2, characterized in that: In step 1, the homogeneous transformation matrix of the manipulator end coordinate system relative to the base coordinate system is derived based on the kinematic model of the six-degree-of-freedom manipulator: According to formula (9), the forward kinematic equation of the six-degree-of-freedom manipulator is Where n, o, a represent the direction vectors of the base coordinate system {0} relative to the end coordinate system {6} on x, y, and z, respectively, and p = [p x p y p z 1] T is the position vector of coordinate system {0} relative to coordinate system {6}, then the position coordinates of the end of the manipulator are (x1, y1, z1) = (p x , p y , p z ), the target point position is (x2, y2, z2) = (p x2 , p y2 , p z2 ); According to the definition of end error: the Euclidean distance between the target point coordinates and the end coordinates of the robotic arm, the Euclidean distance formula between two points in three-dimensional space is used. The objective function of the terminal error is Where d is the Euclidean distance between the target point coordinates and the coordinates of the end of the manipulator, (x1, y1, z1) is the coordinates of the end position of the manipulator, and (x2, y2, z2) is the position of the target point. The range of variation of each joint angle of the six-degree-of-freedom manipulator is used as the constraint condition Among them, θ i is the angle between adjacent links of the i-th joint, θ i min is the minimum angle between adjacent links of the i-th joint, θ i max is the maximum angle between adjacent links of the i-th joint.

4. A six-degree-of-freedom manipulator joint angle path planning method based on multi-objective optimization according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1, calculate energy consumption: During the adjustment of the joint angle of the robotic arm, there is kinetic energy loss caused by joint rotation and energy consumption caused by the robotic arm overcoming the potential energy of gravity. According to physics knowledge, there is a kinetic energy formula: Among them, E1 is the energy consumption generated by the rotation of the robot arm joint, that is, kinetic energy, J i is the moment of inertia of the i-th joint, ω i is the average angular velocity of the i-th joint; When the robotic arm adjusts the joint angle to reach the target point, due to the height difference, the robotic arm has to overcome the energy consumption generated by the gravitational potential energy. Among them, E2 is the energy consumption of the robot arm to overcome the potential energy of gravity, z end is the height of the robot arm reaching the target point, that is, the height of the target point, z inital is the height of the robot arm in zero position; The total energy consumption during the movement of the robotic arm is THE total =E1+E2 (15) Among them, E total is the total energy consumption of the robotic arm to grab a piece of cargo, E1 is the energy consumption generated by the rotation of the robotic arm joint, that is, kinetic energy, and E2 is the energy consumption generated by the robotic arm to overcome the potential energy of gravity; Step 2.2, determine the optimization goal: Within the allowable range of end-end error, minimize the end-end error and energy consumption, and optimize the joint angle path of the robot arm. There are two optimization goals: Among them, E totol is the total energy consumption of the robotic arm to grab a piece of goods, E1 is the energy consumption generated by the rotation of the robotic arm joint, that is, kinetic energy, E2 is the energy consumption generated by the robotic arm to overcome the potential energy of gravity, d is the Euclidean distance between the target point coordinates and the coordinates of the robotic arm end, (x1, y1, z1) is the coordinates of the robotic arm end position, and (x2, y2, z2) is the target point position; Step 2.3, single target conversion: Minimizing the terminal error and energy consumption is a multi-objective optimization problem. Using the linear weighted method, first convert E total and d are dimensionless and assigned weights to construct an optimization model, thereby integrating multiple objective functions into a single objective function; By analyzing the motion process of the robot arm, we can know that min d, max d, The optimization goal is converted to Where F is the objective function, d is the Euclidean distance between the target point coordinates and the coordinates of the end of the robotic arm, max d is the maximum distance between the target point coordinates and the coordinates of the end of the robotic arm, min d is the minimum distance between the target point coordinates and the coordinates of the end of the robotic arm, and E total is the total energy consumption during the movement of the robot arm, min E total is the minimum value of the total energy consumption during the movement of the robot arm, max E total is the maximum value of the total energy consumption during the movement of the robot arm, w1 and w2 are the weight coefficients for minimizing the end error and energy consumption, respectively, w1+w2=1; Step 2.4: Determine the constraints: According to actual requirements, the constraints can be the allowable range of the end error and the range of variation of each joint angle. Among them, θ i is the angle between adjacent links of the i-th joint, θ i min is the minimum angle between adjacent links of the i-th joint, θ i max is the maximum angle between adjacent links of the i-th joint; Step 2.5, comprehensive model: build the model as 5. The method for joint angle path planning of a six-degree-of-freedom manipulator based on multi-objective optimization according to claim 3, characterized in that: Step 3 is as follows: For single-objective optimization models, particle swarm optimization algorithm is usually used to solve them: Initialize the particle swarm and give the parameter values, including the swarm size N, particle position x i and speed v i ; Calculate the fitness value f(t) of each particle; The fitness value f(t) and the individual extreme value p best (i) Comparison; if f(t)>p best (i), then replace p with f(t) best (i); The fitness value f(t) and the global extreme value g best Compare; if f(t)>g best , then use f(t) to replace g best ; Determine whether the particle is out of bounds: If the particle violates the constraint, use the penalty term to adjust its fitness; Iteratively update the particle's velocity v i and position x i ; Perform boundary condition processing; Using MATLAB programming and particle swarm optimization, the terminal error function constructed by equation (11) is used as the objective function, the range of joint angle variation is used as the constraint condition, and the joint angles that minimize the terminal error are found in the solution space. The constructed robot arm motion model is used to obtain the optimal joint angle path of the robot arm.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to claim 1.

7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

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