A multi-objective adaptive collaborative trajectory optimization method for industrial robots and its application

Abstract

The present invention belongs to the technical field related to industrial robot trajectory planning, and discloses a multi-objective adaptive collaborative trajectory optimization method and application of an industrial robot, comprising the following steps: (1) using a parameter space mapping method to uniformly map dynamic parameters to a parameter space; (2) introducing convex optimization parameters to model the time optimal trajectory planning problem; (3) introducing an impact term into the obtained time optimal trajectory planning model; (4) selecting an optimal impact factor based on a target trade-off curve; (5) completing terminal path smoothing and continuous parameter domain discrete analysis; (6) analyzing and obtaining a parameter domain expression of the discretized parameters to obtain a multi-objective multi-constraint trajectory optimization model; (7) introducing a second-order cone parameter into the multi-objective multi-constraint trajectory optimization model to transform the target problem into a second-order cone programming problem, obtaining a final optimization model and completing the solution. The present invention is of great significance for industrial robots to achieve high-speed, high-precision, and low-impact motion.

Description

Technical Field

[0001] The present invention belongs to the technical field related to industrial robots, and more specifically, relates to a multi-objective adaptive collaborative trajectory optimization method and application of an industrial robot. Background Art

[0002] With the development of industrial robots in various manufacturing and processing fields, high speed and high precision have become the criteria for measuring robot processing performance and the direction of development. The goal of multi-objective and multi-constraint trajectory optimization of industrial robots is to shorten the running time, improve the running speed and processing efficiency. It is one of the basic theoretical studies to achieve robot high-speed processing and is also the most critical and basic function in robot applications. Trajectory optimization problems are divided into two cases: unknown path and known path. The former is mainly used for point-to-point (PTP) movement, such as palletizing and handling, and path planning is required first; the latter is widely used in non-contact processes such as welding and spraying. For industrial robot trajectory optimization technology, in order to solve the contradictory relationship between robot operation efficiency and smoothness, it is necessary to introduce multi-objective optimization and consider the planning of robots under various constraints. At present, there are two main problems with the objective equation and constraint conditions of trajectory optimization problems. One is how to quickly judge and select the optimal weight factor in the multi-objective problem; the other is how to consider the constraints so that the robot can take into account both time efficiency and smoothness.

[0003] In the field of engineering applications, the trajectory optimization problem of industrial robots generally considers various target optimal trajectories. Time optimization, energy optimization and impact optimization are the most considered solutions. Taking them into comprehensive consideration, there are many joint optimal solutions. For example, patent CN111399514A provides a robot time optimal trajectory planning method to solve the problem that the trajectory planning method in the prior art is poorly applicable in practice. Patent CN111983924A obtains the time optimal trajectory in the process of interacting with the environment based on the reinforcement learning algorithm. The above methods are all single-target time optimal trajectory planning (TOTP), and their planning results do not consider the continuity and smoothness of motion.

[0004] In order to limit the feasible domain of the TOTP problem, different factors need to be considered to constrain the planning scope. In the early days, the most considered were the robot kinematic constraints. Later, in order to give full play to the mechanical properties of each joint of the robot, dynamic constraints became the main focus. For example, patent CN110209048A introduces a robot time optimal trajectory planning method based on a dynamic model; patent CN113084821A also proposes a time optimal trajectory planning method for a spraying robot based on dynamics. At present, there are many studies on dynamic constraints in this technical field, but there is no better continuity constraint method to consider the continuity and smoothness of the planning results. Patent CN113885535A proposes a robot obstacle avoidance and time optimal trajectory planning method with impact constraints, which takes into account the efficiency and impact problems during the operation of the robot, but it is easy to fall into local optimality during the optimization process, and the practicality of the results has not been fully confirmed.

[0005] In summary, only the robot multi-objective trajectory optimization scheme that considers the smooth continuity of motion can achieve time optimization while ensuring the robot's motion accuracy and motion smoothness. Therefore, it is urgent to conduct research on the common problems in industrial robot motion planning, which is of great significance for industrial robots to achieve high-speed, high-precision, low-impact motion, as well as efficient production. Summary of the invention

[0006] In view of the above defects or improvement needs of the prior art, the present invention provides a multi-objective adaptive collaborative trajectory optimization method and application of an industrial robot, which is mainly proposed to solve the problem of how to make the industrial robot take into account both operating efficiency and smoothness in non-contact processing such as welding and spraying. The present invention can improve the robot's time efficiency while reducing process impact.

[0007] To achieve the above object, according to one aspect of the present invention, a multi-objective adaptive collaborative trajectory optimization method for an industrial robot is provided, and the method mainly comprises the following steps:

[0008] (1) The dynamic parameters are uniformly mapped to the parameter space using the parameter space mapping method;

[0009] (2) Taking the running time as the single objective, the convex optimization parameters are introduced to model the time optimal trajectory planning problem and obtain the time optimal trajectory planning model;

[0010] (3) Introducing the impact term into the time-optimal trajectory planning model to transform the single-objective optimization problem into a multi-objective optimization problem;

[0011] (4) Selecting the optimal impact factor ω based on the target trade-off curve opt ;

[0012] (5) The terminal path is smoothed based on cubic B-splines, and the equal error discretization strategy is used to perform discretization analysis on the continuous parameter domain;

[0013] (6) The pseudo-velocity and pseudo-acceleration parameters are derived and analyzed to obtain the parameter domain expression of the discretized parameters, and then the multi-objective multi-constraint trajectory optimization model is obtained; the mathematical expression of the multi-objective multi-constraint trajectory optimization model is:

[0014]

[0015] Where u is the control parameter of the optimization problem; b(u) is the convex optimization parameter, ω is the impact factor; n is the number of discrete points; τ max is the upper limit of the joint torque; τ′(u) is the first-order derivative of the joint torque; Δu k is the length of the kth discrete interval, a k is the pseudo acceleration value of the kth discrete position; F i is the force on the robot end at the ith discrete position; m x (u) is the mass matrix in parameter space; a i is the pseudo acceleration value of the ith discrete position; c x (u) is the centrifugal force coefficient matrix in parameter space; b i+0.5 is the pseudo velocity value of the ith discrete position; g x (u) is the gravity vector in parameter space; v(u) is the velocity; is the upper limit of acceleration; χ′(u) is the first-order derivative of the Cartesian space path with respect to the parameter; are the upper and lower force / torque limits;

[0016] (7) The second-order cone parameters are introduced into the multi-objective and multi-constraint trajectory optimization model to transform the objective problem into a second-order cone programming problem, obtain the final optimization model and complete the solution.

[0017] Furthermore, the parameter domain expression of the discretized parameter velocity is obtained as:

[0018]

[0019] Where n is the number of discrete points, Δu k is the length of the kth discrete interval, a k is the pseudo acceleration value of the kth discrete position.

[0020] Furthermore, before step (1), the method also includes the steps of constructing a robot kinematic model and a robot dynamic model, wherein the exponential product modeling method is used to construct the robot POE forward and inverse kinematic model, and the Newton-Euler recursion method is used to perform robot connecting rod dynamic modeling.

[0021] Furthermore, the mathematical expression of the robot dynamics model is:

[0022]

[0023] Where M is the mass matrix of the joint space; C is the centrifugal force coefficient matrix of the joint space; q(t) is the joint position; is the joint angular acceleration; G is the gravity vector in the joint space; F is the force at the end of the robot in Cartesian space; is the friction term; M x (q) is the mass matrix in Cartesian space; C x (q) is the centrifugal force coefficient matrix in Cartesian space; G x (q) is the gravity vector in Cartesian space; m x (u) is the mass matrix in parameter space; c x (u) is the centrifugal force coefficient matrix in parameter space; g x (u) is the gravity vector in parameter space; is the first-order derivative of the Cartesian space path with respect to time; is the second-order derivative of the Cartesian space path with respect to time.

[0024] Furthermore, the dynamic equation in parameter u space is:

[0025] in,

[0026]

[0027] In the formula, C x (q) is the centrifugal force coefficient matrix in Cartesian space; χ′(u) is the first-order derivative of the Cartesian space path with respect to the parameter; χ″(u) is the second-order derivative of the Cartesian space path with respect to the parameter.

[0028] Furthermore, the expression of the time optimal trajectory planning model is:

[0029]

[0030]

[0031] Where, t f is the total running time; It is the mapping function between time and space parameter u.

[0032] Furthermore, the expression corresponding to the second-order cone programming problem is:

[0033]

[0034] Where b min is the pseudo speed lower limit; F imax is the upper limit of the end force at the ith discrete position; |F i ′(u)| is the first-order derivative of the end force at the ith discrete position with respect to parameter u; F 1imax is the upper limit of the end force of the ith discrete position in one axis direction; |F 1i ′(u)| is the first-order derivative of the end force in one axis direction at the ith discrete position with respect to the parameter u; c i+1 is the second-order cone parameter; b i is a pseudo speed.

[0035] Furthermore, the tangent position of the curve tim+imp=K and the target trade-off curve is determined, and the impact factor value at the tangent point is the optimal impact factor ω opt ; The optimal impact factor ω should make the absolute value of process impact and running time smaller than the value before optimization, and the time sacrifice efficiency η tim and impact sacrifice efficiency η imp The values ​​should be relatively balanced; among them, tim is the running time; imp is the process impact; K is a parameter, indicating that this curve is dynamic and its size depends on the position of the tangent point.

[0036] The present invention also provides an industrial robot multi-objective adaptive collaborative trajectory optimization system, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the steps of the industrial robot multi-objective adaptive collaborative trajectory optimization method as described above when executing the computer program.

[0037] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the multi-objective adaptive collaborative trajectory optimization method for industrial robots as described above.

[0038] In general, compared with the prior art, the above technical solutions conceived by the present invention mainly have the following advantages in the method and application of multi-objective adaptive collaborative trajectory optimization of industrial robots provided by the present invention:

[0039] Beneficial effects:

[0040] 1. For the multi-objective optimization problem after the introduction of the impact term, the optimal impact factor is selected through a reasonable analysis of the target trade-off curve. Compared with the traditional method of continuous adjustment based on the experience of the staff, this method does not add any subjective judgment and is stable, and does not require trial and error, making the selection process more convenient.

[0041] 2. In addition to considering traditional kinematic and dynamic constraints, the acceleration continuity constraint is introduced to limit the speed and acceleration during the operation process to ensure the continuity of the planning results, thereby making the planning results smoother. This method can reduce process impact without sacrificing operation efficiency.

[0042] 3. Compared with the traditional DH modeling method, the kinematic model established by the POE kinematic modeling method has continuous expression in the entire workspace. Its kinematic parameters correspond to the posture of the workspace one by one, and there is no need to establish the local coordinate system of each joint, which simplifies the modeling process and has strong universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a multi-objective adaptive collaborative trajectory optimization method for an industrial robot provided by the present invention;

[0044] Figure 2 (a) and (b) are the kinematic parameter models of the HSR-605 robot and its exponential product, respectively;

[0045] Figure 3 (a) and (b) are schematic diagrams of the robot dynamics space mapping relationship; (a) is the mapping between spaces, and (b) is the formula corresponding to the mapping:

[0046] Figure 4 is the target trade-off curve under different shock factors;

[0047] Figure 5 (a) and (b) are schematic diagrams of joint angular velocity of the circular path under the original planning algorithm and the time optimal algorithm, respectively;

[0048] Figure 6 (a), (b), (c), and (d) are schematic diagrams of joint angular velocity and joint angular acceleration after comprehensively considering the optimal impact factor selection strategy and continuity constraints under different paths. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0050] The present invention provides a multi-objective adaptive collaborative trajectory optimization method for industrial robots. The method first models a single trajectory planning problem based on a convex optimization method, mainly including two parts: robot body modeling and trajectory planning problem modeling. A spatial nonlinear mapping method is used to solve the problem of inconsistency between the robot constraint space and the solution space. Then, in view of how to select the values ​​of each weight of the multi-objective optimization problem, a multi-objective adaptive collaborative optimization scheme is used to realize the selection of optimal parameters. In view of the problem of process impact in the optimization problem with running time as the main optimization target, the acceleration continuity constraint is used based on the path after smoothing to solve it. Finally, the target optimization problem is converted into a second-order cone programming problem by introducing a second-order cone parameter, and the solution is completed.

[0051] The optimization method mainly comprises the following steps:

[0052] S1, construct robot kinematic model and robot dynamic model.

[0053] Specifically, the modeling and analysis of the robot body mainly includes kinematic modeling and dynamic modeling. Among them, the exponential product modeling method is used to construct the robot POE forward and inverse kinematics model, and the Newton-Euler recursion method is used to perform robot link dynamics modeling.

[0054] S2, the parameter space mapping method is used to uniformly map the dynamic parameters to the parameter space.

[0055] In order to solve the inconsistency problem among the robot's constraint space, planning space and solution space, the three are unified, and the parameter space mapping method is used to transform the dynamic parameters and uniformly map them to the parameter space.

[0056] S3, taking the running time as the single objective, introduces convex optimization parameters to model the time optimal trajectory planning problem and obtains the time optimal trajectory planning model.

[0057] Taking the running time as the single goal, considering the kinematic constraints and dynamic constraints of the robot based on the above analysis, convex optimization parameters are introduced to model the time optimal trajectory planning problem, and the time optimal trajectory optimization model with parameter u as the optimization target is obtained.

[0058] S4, the impact term is introduced into the time-optimal trajectory planning model to transform the single-objective optimization problem into a multi-objective optimization problem.

[0059] Specifically, considering that the time optimization problem lacks consideration of process shocks, the impact term is introduced to transform the single-objective problem into a multi-objective problem.

[0060] S5, select the optimal impact factor ω based on the target trade-off curve opt .

[0061] Specifically, a multi-objective adaptive collaborative scheme based on the target trade-off curve is used to complete the optimal impact factor ω opt The adaptive selection ω opt The method is applicable to any path condition, and the obtained ω opt It has more practical value than artificial experience points.

[0062] S6, terminal path smoothing is completed based on cubic B-spline, and the equal error discretization strategy is used to perform discrete analysis on the continuous parameter domain.

[0063] S7, the pseudo-velocity and pseudo-acceleration parameters are derived and analyzed to obtain the parameter domain expression of the discretized parameters, and then the multi-objective multi-constraint trajectory optimization model is obtained; the mathematical expression of the multi-objective multi-constraint trajectory optimization model is:

[0064]

[0065]

[0066] Where u is the control parameter of the optimization problem; b(u) is the convex optimization parameter, ω is the impact factor; n is the number of discrete points; τ max is the upper limit of the joint torque; τ′(u) is the first-order derivative of the joint torque; Δu k is the length of the kth discrete interval, a k is the pseudo acceleration value of the kth discrete position; F i is the force on the robot end at the ith discrete position; m x (u) is the mass matrix in parameter space; a i is the pseudo acceleration value of the ith discrete position; c x (u) is the centrifugal force coefficient matrix in parameter space; b i+0.5 is the pseudo velocity value of the ith discrete position; g x (u) is the gravity vector in parameter space; v(u) is the velocity; is the upper limit of acceleration; χ′(u) is the first-order derivative of the Cartesian space path with respect to the parameter; are the upper and lower force / torque limits;

[0067] The parameter domain expression of the discretized parameter velocity is obtained as follows:

[0068]

[0069] Where n is the number of discrete points, Δu k is the length of the kth discrete interval, a k is the pseudo acceleration value of the kth discrete position.

[0070] S8, introduce the second-order cone parameters into the multi-objective multi-constraint trajectory optimization model to transform the target problem into a second-order cone programming problem, obtain the final optimization model and complete the solution.

[0071] The present invention is further described in detail below with reference to a specific embodiment.

[0072] See also Figure 1 Based on the Wasu HSR-605 six-degree-of-freedom industrial robot, the optimization method provided in this embodiment mainly includes the following steps:

[0073] Step 1: Based on the exponential product method, the kinematic modeling of HSR-605 is carried out. The POE modeling size relationship and the line vector of each joint axis are as follows: Figure 2 As shown, the coordinate axis direction of the robot base coordinate system {0} is X 0 , Y 0 , Z 0 , the coordinate axis direction of the robot end flange coordinate system {6} is X 6 , Y 6 , Z 6 .L 1 ~L 6 They represent the line vectors of each joint axis when the robot is modeled by exponential product. The exponential product kinematic equation and the positive solution mapping relationship of the six-joint robot are as follows:

[0074]

[0075] In the formula, θ 1 ~θ 6 They are the joint angles of the six-joint robot; is the rigid body motion index transformation of the i-th joint; R(θ i ) is the axial direction vector of the joint; p(θ i ) is the cross product of the position coordinates of the i-th joint axis in the base coordinate system and the axis direction vector.

[0076] Step 2: Use the Newton-Euler recursion formula to model the robot link dynamics and obtain the following dynamic expression:

[0077]

[0078] Where M is the mass matrix of the joint space; C is the centrifugal force coefficient matrix of the joint space; q(t) is the joint position; is the joint angular acceleration; G is the gravity vector in the joint space; F is the force at the end of the robot in Cartesian space; is the friction term; M x (q) is the mass matrix in Cartesian space; C x(q) is the centrifugal force coefficient matrix in Cartesian space; G x (q) is the gravity vector in Cartesian space; m x (u) is the mass matrix in parameter space; c x (u) is the centrifugal force coefficient matrix in parameter space; g x (u) is the gravity vector in parameter space; is the first-order derivative of the Cartesian space path with respect to time; is the second-order derivative of the Cartesian space path with respect to time.

[0079] The first is the dynamic equation considering viscous friction in the joint space. For the convenience of solving, this implementation will ignore Coulomb and viscous friction in subsequent calculations. The second is the expression in Cartesian space. The Jacobian matrix J(q) needs to be introduced to map the dynamic expression from the joint space to the Cartesian space. The third is the dynamic expression in the parameter space.

[0080] Step 3: Due to the inconsistency between constraint space, planning space, and solution space, the dynamic parameters in the above three spaces are spatially mapped. The [M, C, G] matrix of the joint space and the [M x , C x , G x ] matrix, parameter space [m x , c x , g x ]The spatial mapping relationship between matrices is as follows Figure 3 As shown. Convert it into parameter u space.

[0081] Among them, the dynamic equation of the joint space is Convert to The parameter mapping relationship is as follows:

[0082]

[0083] Where M(q) is the mass matrix of the joint space; is the centrifugal force coefficient matrix of the joint space; G(q) is the gravity vector of the joint space; is the joint angular acceleration; is the joint angular velocity.

[0084] Get the dynamic equations in Cartesian space Transformed into parameter space, the parameter mapping relationship is as follows:

[0085]

[0086] In the formula, C x(q) is the centrifugal force coefficient matrix in Cartesian space; χ′(u) is the first-order derivative of the Cartesian space path with respect to the parameter; χ″(u) is the second-order derivative of the Cartesian space path with respect to the parameter.

[0087] Then, according to the transformed formula, the matrix introduced in the parameter space is transformed into the dynamic equation of the parameter u space:

[0088]

[0089] Step 4: Modeling the time optimal trajectory planning problem. Introduce convex optimization parameters a(u) and b(u). Defined as follows:

[0090]

[0091] The expression with time as the single target, as well as the velocity constraint and acceleration constraint are converted to obtain the expression of the time optimal trajectory planning model in the following parameter space:

[0092]

[0093]

[0094] In the formula, are the upper and lower force / torque limits; is the upper speed limit (specified as positive); is the upper limit of acceleration (specified as positive); t f is the total running time; It is the mapping function between time and space parameter u.

[0095] Step 5: A single goal cannot achieve comprehensive consideration of efficiency and smoothness, so an impact term is added on the basis of the time term, and an impact factor ω is introduced to adjust the weight. At the same time, the value of the impact factor is determined based on the target trade-off curve.

[0096] If we consider the running time positively, the goal is to sacrifice the least running time in exchange for the impact factor of the same process impact (time sacrifice efficiency η tim ); If we consider the process impact positively, the goal is to find the process impact with the least sacrifice in exchange for the same amount of running time (impact sacrifice efficiency η imp ). Figure 4 Point A in the figure is the time optimum; η at point B is tim Relatively large, η imp Smaller; C point η tim and η imp Relative equilibrium, η at point D tim Smaller, η imp Considering ηtim and η imp When both are relatively balanced, the comprehensive sacrifice efficiency η will approach the maximum value. Therefore, the selection rules of the optimal impact factor ω are as follows: ① The absolute value of the process impact and the running time is less than the value before optimization; ②η tim and η imp The values ​​must be relatively balanced to maximize the comprehensive sacrifice efficiency value η.

[0097] In order to meet the above selection rules, based on Figure 4 The target trade-off curve shown in Figure 1 is the tangent position of the curve tim+imp=K (tim is the running time; imp is the process impact; K is a parameter, indicating that this curve is dynamic and its size depends on the tangent point position) and the target trade-off curve. The impact factor value at this point is the optimal impact factor ω. opt ,like Figure 4 The optimal impact factor in is the state where point C is located, at this time ω opt =0.038.

[0098] Step 6: In addition to the kinematic and dynamic constraints considered in Step 4, the Cartesian space velocity V(u) and acceleration expression A(u) can be obtained according to the chain rule as shown below.

[0099]

[0100] In the formula, χ(u) is the parameterized expression of the path curve chord length, and u is the control parameter of the optimization problem. First, the terminal path is smoothed using cubic B-spline fitting to ensure the continuity of χ(u); then, constraints are imposed on the parameters to ensure that the parameter acceleration is C0 continuous, parameter speed It is C1 continuous.

[0101] The pseudo acceleration a(u) is piecewise linearly interpolated to ensure that the last point of the previous segment coincides with the first point of the next segment. k-1， u k ](k=1~n), the slope of the curve K k It can be calculated from the interpolation points:

[0102]

[0103] In the formula, u k is the parameter value of the kth discrete position.

[0104] Therefore, in the interval [u k-1 ,u k ]The expressions of a(u) and b(u) on ] are as follows:

[0105]

[0106] Among them A k is a constant whose value is chosen to ensure that the parameter velocity of the last point of the kth segment and the first point of the k+1th segment are equal. The expression of a(u) can also ensure that the left and right limits of the parameter acceleration are equal. After adding and subtracting each term, the parameter domain expression of the discretized parameter velocity is obtained as follows:

[0107]

[0108] This relationship expresses a k and b k The conversion relationship between is used to replace the relationship between the convex optimization parameters a(u) and b(u). This parameter domain continuity constraint method combined with the smoothed path can ensure the continuity of the acceleration after planning.

[0109] Step 7: For the optimization problem in the discrete domain, introduce the second-order cone parameter c i d i 、e i , defined as follows. The above optimization problem is transformed into a standard second-order cone problem to complete the solution. The expression of the second-order cone problem is:

[0110]

[0111] Where b min is the pseudo speed lower limit; F imax is the upper limit of the end force at the ith discrete position; |F i ′(u)| is the first-order derivative of the end force at the ith discrete position with respect to parameter u; F 1imax is the upper limit of the end force of the ith discrete position in one axis direction; |F 1i ′(u)| is the first-order derivative of the end force in one axis direction at the ith discrete position with respect to the parameter u; c i+1 is the second-order cone parameter; b i is a pseudo speed.

[0112] The transformed standardized second-order cone optimization problem is shown in the following formula. This optimization problem is a complete model of the multi-objective adaptive trajectory optimization problem based on continuity constraints. This model is a standard second-order cone programming model and can be solved with the help of the standardized SEDUMI toolkit.

[0113] Step 8: Analyze the multi-objective adaptive collaborative trajectory optimization model considering continuity constraints obtained in Step 7. Figure 5As shown in FIG. 1 , the total running time of the robot after adopting the time optimal trajectory planning algorithm proposed in the present invention is shortened by 66.7%, and the speed amplitude is 3 times that before optimization, which has a greater impact; when the optimal impact factor adaptive selection strategy and acceleration continuity constraint proposed in the present invention are adopted, as shown in FIG. Figure 6 As shown in the figure, compared with the optimal state in time, the robot running time increased by 66.7%; but the angular velocity amplitude decreased by 50%, and the angular acceleration amplitude decreased by 72%; compared with the original planning algorithm, the efficiency was still increased by 2 times.

[0114] The expression of the complete model of the multi-objective adaptive trajectory optimization problem is:

[0115]

[0116]

[0117] In the formula, Δu i is the length of the i-th discrete interval; b k is the pseudo velocity of the ith discrete point; b i+0.5 is the pseudo velocity approximation of the ith discrete point.

[0118] After verification, it was found that the process impact of the robot was significantly improved after adopting the method proposed by the present invention, and the robot jitter was also reduced to a certain extent. Therefore, it can be concluded that in most industrial application scenarios, the optimization result is more scientific and practical.

[0119] The present invention also provides an industrial robot multi-objective adaptive collaborative trajectory optimization system, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the steps of the industrial robot multi-objective adaptive collaborative trajectory optimization method as described above when executing the computer program.

[0120] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the multi-objective adaptive collaborative trajectory optimization method for industrial robots as described above.

[0121] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-objective adaptive collaborative trajectory optimization method for industrial robots, characterized in that: The method comprises the following steps: (1) The dynamic parameters are uniformly mapped to the parameter space using the parameter space mapping method; (2) Taking the running time as the single objective, the convex optimization parameters are introduced to model the time optimal trajectory planning problem and obtain the time optimal trajectory planning model; (3) Introducing the impact term into the time-optimal trajectory planning model to transform the single-objective optimization problem into a multi-objective optimization problem; (4) Selecting the optimal impact factor ω based on the target trade-off curve opt ; (5) The terminal path is smoothed based on cubic B-splines, and the equal error discretization strategy is used to perform discretization analysis on the continuous parameter domain; (6) The pseudo-velocity and pseudo-acceleration parameters are derived and analyzed to obtain the parameter domain expression of the discretized parameters, and then the multi-objective multi-constraint trajectory optimization model is obtained; the mathematical expression of the multi-objective multi-constraint trajectory optimization model is: Where u is the control parameter of the optimization problem; b(u) is the convex optimization parameter, ω is the impact factor; n is the number of discrete points; τ max is the upper limit of joint torque; τ ′ (u) is the first-order derivative of the joint torque; Δu k is the length of the kth discrete interval, a k is the pseudo acceleration value of the kth discrete position; F i is the force on the robot end at the ith discrete position; m x (u) is the mass matrix in parameter space; a i is the pseudo acceleration value of the ith discrete position; c x (u) is the centrifugal force coefficient matrix in parameter space; b i+0.5 is the pseudo velocity value of the ith discrete position; g x (u) is the gravity vector in parameter space; is the upper limit of speed; is the upper limit of acceleration; ′ (u) is the first-order derivative of the Cartesian space path with respect to the parameter; are the upper and lower force / torque limits; (7) The second-order cone parameters are introduced into the multi-objective and multi-constraint trajectory optimization model to transform the objective problem into a second-order cone programming problem, obtain the final optimization model and complete the solution.

2. The multi-objective adaptive collaborative trajectory optimization method for industrial robots according to claim 1, characterized in that: Before step (1), the method also includes the steps of constructing a robot kinematic model and a robot dynamic model, wherein the robot POE forward and inverse kinematic model is constructed by using an exponential product modeling method, and the robot connecting rod dynamic modeling is performed by using a Newton-Euler recursion method.

3. The multi-objective adaptive collaborative trajectory optimization method for industrial robots according to claim 1, characterized in that: The mathematical expression of the robot dynamics model is: Where M is the mass matrix of the joint space; C is the centrifugal force coefficient matrix of the joint space; q(t) is the joint position; is the joint angular acceleration; G is the gravity vector in the joint space; F is the force at the end of the robot in Cartesian space; is the friction term; M x (q) is the mass matrix in Cartesian space; C x (q) is the centrifugal force coefficient matrix in Cartesian space; G x (q) is the gravity vector in Cartesian space; is the first-order derivative of the Cartesian space path with respect to time; is the second-order derivative of the Cartesian space path with respect to time.

4. The multi-objective adaptive collaborative trajectory optimization method for industrial robots according to claim 3, characterized in that: The dynamic equation in parameter u space is: in, Where χ″(u) is the second-order derivative of the Cartesian space path with respect to the parameter.

5. The method for multi-objective adaptive collaborative trajectory optimization of industrial robots according to claim 4, characterized in that: The expression of the time optimal trajectory planning model is: Where, t f is the total running time; a(u)=ü; It is the mapping function between time and space parameter u.

6. The multi-objective adaptive collaborative trajectory optimization method for industrial robots according to claim 5, characterized in that: The expression corresponding to the second-order cone programming problem is: Where b min is the pseudo speed lower limit; F imax is the upper limit of the end force at the ith discrete position; |F i ′ (u)| is the first-order derivative of the end force at the ith discrete position with respect to parameter u; F 1imax is the upper limit of the end force in one axis direction at the ith discrete position; |F 1i ′ (u)| is the first-order derivative of the end force in one axis direction at the ith discrete position with respect to the parameter u; F 6imax is the upper limit of the end force of the ith discrete position in the six-axis direction; |F 6i ′ (u)| is the first-order derivative of the end force at the i-th discrete position in the six-axis direction with respect to the parameter u; c i+1 is the second-order cone parameter; b i is a pseudo speed.

7. The multi-objective adaptive collaborative trajectory optimization method for industrial robots according to any one of claims 1 to 6, characterized in that: Determine the tangent position of the curve tim+imp=K and the target trade-off curve. The impact factor value at the tangent point is the optimal impact factor ω opt ; The optimal impact factor ω should make the absolute value of process impact and running time smaller than the value before optimization, and the time sacrifice efficiency η tim and impact sacrifice efficiency η imp The values ​​should be relatively balanced; among them, tim is the running time; imp is the process impact; K is a parameter, indicating that this curve is dynamic and its size depends on the position of the tangent point.

8. An industrial robot multi-objective adaptive collaborative trajectory optimization system, characterized by: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the steps of the industrial robot multi-objective adaptive collaborative trajectory optimization method according to any one of claims 1 to 7 when executing the computer program.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the industrial robot multi-objective adaptive collaborative trajectory optimization method according to any one of claims 1 to 7.

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