A mechanical arm motion planning method and system based on error-driven adaptive gradient dynamics model

Abstract

This invention belongs to the technical field of robotic arm motion planning and discloses a robotic arm motion planning method and system based on an error-driven adaptive gradient model. The method includes: S1 establishing the joint velocity at two adjacent moments with respect to the adaptive coefficient λ based on a Lyapunov function. n The gradient relationship is obtained; S2. The joint velocity at time n+1 is calculated using the gradient relationship, and the error between the calculated joint velocity at time n+1 and the adaptive coefficient is updated using the central finite difference method; S3. n = n+1; return to step S2 until the joint velocities at all times are obtained; S4. The joint position is calculated using the relationship between the joint velocity and position; the velocity of the end effector is calculated using the robotic arm motion planning model and the joint velocities at each time, thereby realizing the motion planning of the robotic arm. This invention solves the problem of low computational efficiency in robotic arm motion planning.

Description

Technical Field

[0001] This invention belongs to the technical field of robotic arm motion planning, and more specifically, relates to a robotic arm motion planning method and system based on an error-driven adaptive gradient dynamics model. Background Technology

[0002] Robotic arm motion planning has always been a focus of attention in modern industrial society. With the rapid development of robotics, computer technology, and servo control technology, robotic arm motion planning has become a focal point for scholars in various fields. Research and applications in this area cover many important sectors, including industrial production, medical surgery, and transportation assembly. In today's highly automated production environment, robotic arm motion planning is not only a necessary means to improve production efficiency but also one of the key technologies for achieving complex tasks and precision operations. By accurately planning the motion trajectory of the robotic arm, complex operations can be completed in confined spaces, improving the flexibility and adaptability of production lines. In the medical field, the application of robotic arm motion planning supports precise surgical procedures, reduces invasiveness to patients, and improves the safety and success rate of surgeries. Furthermore, the widespread application of robotic arms in transportation and assembly has brought higher efficiency and quality assurance to logistics and manufacturing. Overall, the continuous innovation and application of robotic arm motion planning has driven the technological development of modern society, bringing more intelligent, efficient, and safe solutions to various fields.

[0003] Neurodynamic models possess powerful fitting and parallel processing capabilities and are now widely used in the field of robotic arm motion planning and control. It is worth noting that in solving robotic arm motion planning problems, the computational issues of differentiating and finding the pseudo-inverse of the Jacobian matrix (the relationship matrix between the actual space and the robotic arm joint space) are unavoidable. Furthermore, improving the efficiency of solving neurodynamic models applied to robotic arm motion planning has always been one of the cutting-edge directions in this field. In other words, developing an acceleration method for robotic arm motion planning suitable for neurodynamic models is particularly important. Currently, there are two main types of acceleration methods for robotic arm motion planning based on neurodynamic models: 1) using activation functions; 2) introducing time-varying coefficients. Although these two methodologies and mathematical theories have achieved constructive and forward-looking results, they still have their own shortcomings. For example, the acceleration method using activation functions has specific requirements for discretization and step size; otherwise, it is easy to produce deviations, and it does not fully explore and utilize the potential maximum descent characteristics of the error variables in the system. On the other hand, the current mainstream types of time-varying coefficients are mainly exponential and error-based. Among them, the disadvantage of exponential time-varying coefficients is that their corresponding values ​​increase over time, so when the time is large, the computation will overflow. Error-type time-varying coefficients are determined solely by the error norm at the current moment and do not contain relevant dynamic information about higher-order errors or Lyapunov functions. This means their acceleration performance is not further evaluated through these potential dynamics. Neither of the two acceleration methods for time-varying coefficients mentioned above considers the impact of the accumulation of higher-order and historical errors on the solution speed, which undoubtedly wastes these two parameters with potential acceleration properties.

[0004] Based on the above explanation and analysis, it is necessary to develop a method for robotic arm motion planning that can utilize the potential parameter information and dynamic characteristics of an adaptive gradient model. Summary of the Invention

[0005] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a method and system for robotic arm motion planning based on an error-driven adaptive gradient dynamics model, thus solving the problem of long computation time for robotic arm motion planning.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for planning the motion of a robotic arm based on an error-driven adaptive gradient dynamics model is provided, the method comprising the following steps:

[0007] S1 establishes the joint velocity at two adjacent moments with respect to the adaptive coefficient λ based on the Lyapunov function. n The adaptive gradient relationship is determined by setting an initial value λ for the adaptive coefficient. n ;

[0008] S2 uses the aforementioned adaptive gradient relationship to solve for the joint velocity at time n+1. The joint velocity at time n+1 was calculated using the central finite difference approximation method. calculate and The error between them is used to update the adaptive coefficients;

[0009] S3n = n + 1; Return to step S2 until the joint velocities at all times are obtained;

[0010] S4 uses the relationship between joint velocity and joint position to solve for the joint position at each moment; it uses the robotic arm motion planning model and the joint velocity at each moment to calculate the velocity of the end effector, thereby realizing the motion planning of the robotic arm.

[0011] More preferably, in step S1, the adaptive gradient relationship between the joint velocities at two adjacent time points with respect to the adaptive coefficients is as follows:

[0012]

[0013] in, It is the velocity information of each joint at the nth sampling time. It is the velocity information of each joint at the (n+1)th sampling time, θ n It represents the position information of each joint at the nth sampling time, λ. n These are the adaptive coefficients at the nth sampling time, and ω1 and ω2 are the first and second gain coefficients, respectively. It is the gradient of the Lyapunov function at the nth sampling time. It is the gradient of the Lyapunov function at the i-th sampling time.

[0014] More preferably, in step S2, the gradient of the Lyapunov function at the nth sampling time is calculated using the following formula:

[0015]

[0016] in, It is the gradient of the Lyapunov function at the nth sampling time. This represents the expected velocity information of the robotic arm's end effector at the nth sampling time, indicated by the superscript (·). d It is the expected value. It is the expected position information at the nth sampling time, J(θ) n ) is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, ||·||2 is the L2 norm of the vector, and the superscript... The transpose operator for vectors.

[0017] More preferably, in step S2, the joint velocity at time n is calculated using the central finite difference approximation method, and the calculation formula is as follows:

[0018]

[0019] in, It is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method. It is the velocity of each joint at the (n-1)th sampling time, λ n These are the adaptive coefficients at the nth sampling time, ω1 and ω2 are the first and second gain coefficients, and vec(·) represents the vectorization operator. It is the gradient of the Lyapunov function at the nth sampling time, V i It is the gradient of the Lyapunov function at the i-th sampling time.

[0020] More preferably, in step S2, the formula for calculating the error is as follows:

[0021]

[0022] Where, δ n+1 The error is calculated at the (n+1)th sampling time. It is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method. It represents the velocity of each joint at the (n+1)th sampling time, indicated by the superscript (·). C The calculation method is the central finite difference approximation method, E n+1 To correct the error at the (n+1)th sampling time, δ n+1 The error δ is calculated at the (n+1)th sampling time. i η1 is the error calculated at the i-th sampling time, and η2 and η3 both represent the gain coefficients.

[0023] More preferably, in step S2, the formula for updating the adaptive coefficients is as follows:

[0024]

[0025] Where, λ n+1 These are the adaptive coefficients at the (n+1)th sampling time, γ is the expected error calculated using the two methods, η1 is the gain coefficient, and E n+1 It is the error at the (n+1)th sampling time after correction, λ n It is the adaptive coefficient at the nth sampling time.

[0026] More preferably, in step S3, the formula for calculating the joint position at each moment is as follows:

[0027]

[0028] in, This refers to the velocity information of each joint at the (n+1)th sampling time, where τ represents the sampling interval and θ... n It represents the position information of each joint at the nth sampling time, θ n+1 It represents the position information of each joint at the (n+1)th sampling time.

[0029] More preferably, in step S4, the formula for calculating the speed of the end effector is as follows:

[0030]

[0031] Wherein, J(θ) n Let be the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time. It contains the velocity information of each joint at the nth sampling time. The speed information calculated for the end effector of the robotic arm.

[0032] According to another aspect of the present invention, a robotic arm motion planning system based on an error-driven adaptive gradient dynamics model is provided. The system includes an actuator for executing the above-described robotic arm motion planning method based on an error-driven adaptive gradient dynamics model.

[0033] According to another aspect of the present invention, a computer storage medium is provided, on which a computer program is disposed, which, when executed by an executor, is used to implement the above-described method for planning motion of a robotic arm based on an error-driven adaptive gradient dynamics model.

[0034] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0035] 1. This invention proposes an accelerated motion planning method for robotic arms based on an error-driven adaptive gradient dynamics model. This method not only avoids the computationally intensive process of finding the derivative and pseudo-inverse of the Jacobian matrix, but also enables the accelerated solution of the robotic arm motion planning using the adaptive gradient dynamics model. These advantages have extremely significant practical implications for real-time industrial production operations and military applications.

[0036] 2. The adaptive update formula of this invention is based on a proportional controller (P controller). By integrating the core control concept of proportional and integral dual elements, it achieves precise adaptation to joint motion characteristics: the dynamic response of the proportional term ensures rapid tracking in real time, and the adaptive adjustment of the integral term eliminates steady-state error, which significantly improves the dynamic performance of the system, greatly improves the trajectory tracking accuracy, and enhances the robustness to load changes and modeling errors.

[0037] 3. The adaptive coefficient construction scheme proposed in this invention constructs a new high-order error compensation term by performing difference operations between high-order and low-order errors. It has the following advantages: 1) Asymptotic convergence of errors is achieved by increasing the order of the error term; 2) The introduction of the compensation term effectively suppresses low-order error components; 3) The adaptive mechanism can dynamically adjust the compensation intensity according to the system state.

[0038] 4. The present invention proposes an accelerated motion planning method for robotic arms based on an error-driven adaptive gradient dynamics model. The method uses an error-driven approach to design and analyze the adaptive gradient dynamics model. The adaptive error-driven scheme utilizes the potential acceleration properties of the sum of higher-order errors and historical errors in the adaptive gradient dynamics model. The coefficients in the adaptive gradient neural network are determined through the adaptive error-driven scheme, which greatly improves the timeliness and convergence of the adaptive gradient neural network for robotic arm motion planning.

[0039] 5. This invention combines the practical application requirements of the current adaptive gradient dynamics model for robotic arm motion planning, and constructs an accelerated method for robotic arm motion planning based on the error-driven adaptive gradient dynamics model. This method realizes robotic arm motion planning based on the adaptive gradient dynamics model, and has the advantages of fast convergence speed, short computation time, and high solution accuracy. Attached Figure Description

[0040] Figure 1 This is a flowchart of a robotic arm motion planning acceleration method based on an error-driven adaptive gradient dynamics model, constructed according to a preferred embodiment of the present invention.

[0041] Figure 2 It is the motion generation trajectory of the robotic arm end effector constructed according to the preferred embodiment of the present invention, and the motion state of each joint.

[0042] Figure 3 It refers to the state of each error component in two-dimensional space between the motion generation trajectory of the robotic arm end effector constructed according to the preferred embodiment of the present invention and the ideal trajectory.

[0043] Figure 4 This refers to the positional state of each joint angle of the robotic arm constructed according to a preferred embodiment of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0045] A method for planning the motion of a robotic arm based on an error-driven adaptive gradient dynamics model, comprising the following steps:

[0046] S1 constructs an adaptive gradient dynamics model to solve the Lyapunov function of the robotic arm motion planning model, determines the adaptive gradient dynamics model, and initializes its parameters.

[0047] For the above robotic arm motion planning model, an adaptive gradient dynamics model is constructed to solve the Lyapunov function of the robotic arm motion planning, as shown below.

[0048]

[0049] Among them, the subscript (·) n V represents the nth sampling time. n It is the Lyapunov function at the nth sampling time, with the superscript (·). d Indicates the expected value. For the desired speed information of the robotic arm end effector at the nth sampling time, For the velocity information of each joint at the nth sampling time, θ n For the position information of each joint at the nth sampling time, J(θ) n ) is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, vec(·) represents the vectorization operator, and ||·||2 represents the L2 norm of the vector.

[0050] Obtain the adaptive coefficients λ0 and λ1, and the gain coefficients ω1 and ω2. For the Lyapunov function described above, determine the adaptive gradient dynamics model used to solve it, as shown below.

[0051]

[0052] Among them, the subscript (·) n This indicates the nth sampling time, indicated by the superscript (·). d Indicates the expected value. For the desired speed information of the robotic arm end effector at the nth sampling time, For the desired location information at the nth sampling time, For the velocity information of each joint at the nth sampling time, θ n For the position information of each joint at the nth sampling time, J(θ) n V is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, vec(·) represents the vectorization operator, ||·||2 represents the L2 norm of the vector, and V n It is the Lyapunov function at the nth sampling time. The superscript represents the gradient of the Lyapunov function at the nth sampling time. The transpose operator represents a vector, where ω1 and ω2 both represent gain coefficients, and λ n This represents the adaptive coefficient at the nth sampling time.

[0053] The variables and hyperparameters of the determined adaptive gradient dynamics model are initialized, including the initial Jacobian matrix J(θ0) of the robotic arm and the initial velocity of the robotic arm's end effector. initial position Initial velocity of each joint Initial position θ0, gain coefficients ω1, ω2, η1, η2 and η3, expected error γ, initial iteration number n = 0, initial adaptive coefficients λ0 and λ1, initial time t0 = 0, sampling interval τ, termination time t f .

[0054] S2, the speed information of each joint of the robotic arm is calculated using the Euler method and the central finite difference approximation method respectively.

[0055] The velocity information of each joint of the robotic arm was calculated using the Euler method and the central finite difference approximation method, as shown below.

[0056]

[0057] The subscript (·) n This indicates the nth sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the (n-1)th sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the nth sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the (n+1)th sampling time, indicated by the superscript (·). C The calculation method is the central finite difference approximation method. This indicates that the velocity information of each joint is calculated using the central finite difference approximation method at the nth sampling time, λ. n These are the adaptive coefficients at the nth sampling time, vec(·) represents the vectorization operator, and ω1 and ω2 are the first and second gain coefficients, respectively. It is the gradient of the Lyapunov function at the nth sampling time. It is the gradient of the Lyapunov function at the i-th sampling time.

[0058] Compare the errors of the two sets of errors and sum them over the historical errors.

[0059] The calculation errors of the Euler method and the central finite difference approximation method are compared, and the historical error information is summed, as shown below:

[0060]

[0061] Among them, the subscript (·) n This indicates the nth sampling time. This is the joint velocity at the (n+1)th sampling time, calculated using the central finite difference approximation method, indicated by the superscript (·). C The calculation method is the central finite difference approximation method, δ n The error δ is calculated at the nth sampling time. i The error δ is calculated at the i-th sampling time. n+1 E is the error calculated at the (n+1)th sampling time. n To correct the error at the nth sampling time, E n+1 To correct the error at the (n+1)th sampling time, η2 and η3 both represent gain coefficients, and vec(·) represents the vectorization operator.

[0062] Execute the adaptive coefficient update scheme;

[0063] The adaptive update scheme is executed as follows:

[0064]

[0065] Among them, the subscript (·) n Let E represent the nth sampling time, γ represent the expected error calculated using the two methods, and η1 represent the gain coefficient. n+1 To correct the error at the (n+1)th sampling time, λ n It is the adaptive coefficient at the nth sampling time, λ n+1 It is the adaptive coefficient at the (n+1)th sampling time.

[0066] S3n = n + 1; Return to step S2 until the joint velocities at all times are obtained.

[0067] If t n ≥t f Stop calculation and output the velocity sequence information of each joint of the robotic arm. Position sequence information {θ0,θ1,…,θ f Based on the relationship between the velocities of each joint of the robotic arm and the velocity of the end effector in the robotic arm motion planning model of step 1, the velocity sequence information of the end effector can be obtained. Integrating the velocity sequence information of the robotic arm's end effector can yield the position sequence information {r0, r1, ..., r}. f Otherwise, jump to S2);

[0068] S4 uses the relationship between joint velocity and joint position to solve for the joint position at each moment; it uses the robotic arm motion planning model and the joint velocity at each moment to calculate the velocity of the end effector, thereby realizing the motion planning of the robotic arm.

[0069]

[0070] Among them, the subscript (·) n This represents the nth sampling time, and τ represents the sampling interval. It is the velocity information of each joint at the (n+1)th sampling time, θ n It represents the position information of each joint at the nth sampling time, θ n+1 It represents the position information of each joint at the (n+1)th sampling time.

[0071] The steps for calculating the speed of the end effector are as follows:

[0072] Obtain relevant information about the robotic arm and construct a motion planning model for the robotic arm.

[0073] Obtain the desired speed information of the robotic arm end effector Expected location information r d (t), superscript (·) d This represents the expected value, and the velocity information of each joint. Given position information θ(t), robotic arm kinematic information f(θ(t)), calculate the corresponding Jacobian matrix J(θ(t)), and construct the robotic arm motion planning model as follows:

[0074]

[0075] Discretizing the constructed robotic arm motion planning model yields...

[0076]

[0077] Among them, the subscript (·) n Let J(θ) represent the nth sampling time. n Let be the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time. It contains the velocity information of each joint at the nth sampling time. This represents the expected velocity information of the robotic arm's end effector at the nth sampling time, indicated by the superscript (·). d This represents the expected value.

[0078] The solution results are converted into control signals for robotic arm motion planning and transmitted to the lower-level controller to realize the robotic arm motion planning task.

[0079] The present invention will be further described below with reference to specific embodiments.

[0080] 1. Experimental Procedure

[0081] The following section combines a specific simulation operation with the attached... Figure 1 The operational process of this invention is described below;

[0082] The method of the present invention is simulated by using MATLAB software and a five-degree-of-freedom robotic arm to repeatedly generate motion along the same path.

[0083] Step 1: Obtain the desired initial velocity of the robotic arm's end effector. Expected initial position Initial velocity of each joint Initial position θ0, initial Jacobian matrix J(θ0)

[0084]

[0085] Next, based on the existing parameter information, the initial motion planning model of the robotic arm can be constructed:

[0086]

[0087] Where J(θ0) is the initial Jacobian matrix, and θ0 is the initial position of each joint of the robotic arm. The initial velocities of each joint of the robotic arm are indicated by the superscript (·). d Indicates the expected value. This provides the expected initial velocity information for the robotic arm's end effector.

[0088] Step 1: For the above robotic arm motion planning model, construct an adaptive gradient dynamics model to solve the Lyapunov function of the robotic arm motion planning, as shown below.

[0089]

[0090] Among them, the subscript (·) n V represents the nth sampling time. n It is the Lyapunov function at the nth sampling time, with the superscript (·). d Indicates the expected value. For the desired speed information of the robotic arm end effector at the nth sampling time, For the velocity information of each joint at the nth sampling time, θ n For the position information of each joint at the nth sampling time, J(θ) n ) is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, vec(·) represents the vectorization operator, and ||·||2 represents the L2 norm of the vector.

[0091] For the Lyapunov function described above, an adaptive gradient dynamics model for solving it is determined as follows:

[0092]

[0093] Among them, the subscript (·) n This indicates the nth sampling time, indicated by the superscript (·). d Indicates the expected value. For the desired speed information of the robotic arm end effector at the nth sampling time, For the desired location information at the nth sampling time, For the velocity information of each joint at the nth sampling time, θ n For the position information of each joint at the nth sampling time, J(θ) n V is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, vec(·) represents the vectorization operator, ||·||2 represents the L2 norm of the vector, and V n It is the Lyapunov function at the nth sampling time. The superscript represents the gradient of the Lyapunov function at the nth sampling time. The transpose operator represents a vector, where ω1 and ω2 both represent gain coefficients, and λ n This represents the adaptive coefficient at the nth sampling time; initialize the relevant variables and hyperparameters of the determined adaptive gradient dynamics model, including the initial iteration number n = 0, the initial time t0 = 0 s (seconds), the gain coefficients ω1 = ω2 = η1 = 0.1, η2 = η3 = 1, the expected error γ = 0.1, the initial adaptive coefficients λ0 = λ1 = 1, the sampling interval τ = 0.001 s (seconds), and the termination time t. f = 7s (seconds);

[0094] Step 2: Calculate the velocity information of each joint of the robotic arm using the Euler method and the central finite difference approximation method, as shown below.

[0095]

[0096] The subscript (·) n This indicates the nth sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the (n-1)th sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the nth sampling time. This indicates that the velocity information of each joint was calculated using the Euler method at the (n+1)th sampling time, indicated by the superscript (·). C The calculation method is the central finite difference approximation method. This indicates that the velocity information of each joint is calculated using the central finite difference approximation method at the nth sampling time, λ.n These are the adaptive coefficients at the nth sampling time, vec(·) represents the vectorization operator, and ω1 and ω2 are the first and second gain coefficients, respectively. It is the gradient of the Lyapunov function at the nth sampling time. It is the gradient of the Lyapunov function at the i-th sampling time.

[0097] The computational errors of the Euler method and the central finite difference approximation method are compared, and the historical error information is summed, as shown below.

[0098]

[0099] Among them, the subscript (·) n This indicates the nth sampling time. This is the joint velocity at the (n+1)th sampling time, calculated using the central finite difference approximation method, indicated by the superscript (·). C The calculation method is the central finite difference approximation method, δ n The error δ is calculated at the nth sampling time. i The error δ is calculated at the i-th sampling time. n+1 E is the error calculated at the (n+1)th sampling time. n To correct the error at the nth sampling time, E n+1 To correct the error at the (n+1)th sampling time, η2 and η3 both represent gain coefficients, and vec(·) represents the vectorization operator.

[0100] The adaptive update scheme is executed as follows:

[0101]

[0102] Among them, the subscript (·) n Let E represent the nth sampling time, γ represent the expected error calculated using the two methods, and η1 represent the gain coefficient. n+1 To correct the error at the (n+1)th sampling time, λ n λ is the adaptive coefficient at the nth sampling time. n+1 It is the adaptive coefficient at the (n+1)th sampling time.

[0103] Step 3: n = n + 1; Return to step 2 until the joint velocities at all times are obtained.

[0104] If t n ≥t f Stop calculation and output the velocity sequence information of each joint of the robotic arm. Position sequence information {θ0,θ1,…,θ fBased on the relationship between the velocities of each joint of the robotic arm and the velocity of the end effector in the robotic arm motion planning model of step 1, the velocity sequence information of the end effector can be obtained. Integrating the velocity sequence information of the robotic arm's end effector can yield the position sequence information {r0, r1, ..., r}. f Otherwise, proceed to step 2).

[0105] Step 4: Solve for the joint position at each moment by using the relationship between joint velocity and joint position; calculate the velocity of the end effector using the robotic arm motion planning model and the joint velocity at each moment, thereby realizing the motion planning of the robotic arm.

[0106]

[0107] Among them, the subscript (·) n This represents the nth sampling time, and τ represents the sampling interval. It is the velocity information of each joint at the (n+1)th sampling time, θ n It represents the position information of each joint at the nth sampling time, θ n+1 It represents the position information of each joint at the (n+1)th sampling time.

[0108] Obtain the initial velocity of the robotic arm's end effector Initial position r0, initial velocities of each joint Initial position θ0, initial Jacobian matrix J(θ0)

[0109]

[0110] Next, based on the existing parameter information, the initial motion planning model of the robotic arm can be constructed:

[0111]

[0112] Wherein, the subscript (·)1 indicates the first sampling time. The speed information calculated by the robotic arm's end effector at the first sampling time is indicated by the superscript (·). c The calculated value is represented by J(θ1), which is the Jacobian matrix corresponding to the kinematic information of the robotic arm at the first sampling time. It contains the velocity information of each joint at the first sampling time.

[0113] The solution results are converted into control signals for robotic arm motion planning and transmitted to the lower-level controller to realize the robotic arm motion planning task.

[0114] Figure 2To achieve the motion generation trajectory of the end effector of the robotic arm and the motion state of each joint, the following method for accelerating the motion planning of a robotic arm based on an error-driven adaptive gradient dynamics model is applied. Figure 2 In the process, the end effector of the robotic arm successfully generated the fish-shaped trajectory, and the angles of each joint moved reasonably, demonstrating the feasibility and efficiency of the invention.

[0115] Figure 3 To realize the loss component states of the motion generation trajectory and the ideal trajectory of the robotic arm end effector based on the error-driven adaptive gradient dynamics model in the two-dimensional space, the green dashed line e x This represents the error component state in the horizontal direction in two-dimensional space, with a maximum positional error not exceeding 9 × 10⁻⁶. -4 (meters), yellow dashed line e Y This represents the error component state in the vertical direction in two-dimensional space, with a maximum positional error not exceeding 5 × 10⁻⁶. -4 (meters) demonstrates the feasibility and superiority of this invention.

[0116] Figure 4 To achieve the joint angular position states corresponding to the motion generation trajectory of the robotic arm end effector based on an error-driven adaptive gradient dynamics model, the blue solid line θ1(t) is used in this invention. n ), yellow dashed line θ2(t n ), orange dashed line θ3(t n ), purple dashed line θ4(t n ) and the green dashed line θ5(t n The five states represent the motion trajectories of the first, second, third, fourth, and fifth joints of the robotic arm as a function of time. The smooth and continuous nature of these five trajectories demonstrates the rationality and effectiveness of the invention.

[0117] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0118] Those skilled in the art will readily understand that the above description is merely 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 within the scope of protection of the present invention.

Claims

1. A method for planning the motion of a robotic arm based on an error-driven adaptive gradient dynamics model, characterized in that, The method includes the following steps: S1 Establishes the joint velocity with respect to adaptive coefficients at two adjacent time points based on the Lyapunov function. The adaptive gradient relationship is determined by setting initial values ​​for the adaptive coefficients. ; S2 uses the aforementioned adaptive gradient relationship to solve for the joint velocity at time n+1. ; The joint velocity at time n+1 was calculated using the central finite difference approximation method. ,calculate and The error between them is used to update the adaptive coefficients; S3 n=n+1; Return to step S2 until the joint velocities at all times are obtained; S4 uses the relationship between joint velocity and joint position to solve for the joint position at each moment; it uses the robotic arm motion planning model and the joint velocity at each moment to calculate the velocity of the end effector, thereby realizing the motion planning of the robotic arm. In step S1, the adaptive gradient relationship between the joint velocities at two adjacent time points with respect to the adaptive coefficients is as follows: The adaptive gradient relationship between the joint velocities at two adjacent time points with respect to the adaptive coefficients is as follows: In step S2, the joint velocity at time n is calculated using the central finite difference approximation method, and the calculation formula is as follows: in, It is the velocity information of each joint at the nth sampling time. It is the velocity information of each joint at the (n+1)th sampling time. It contains the position information of each joint at the nth sampling time. These are the adaptive coefficients at the nth sampling time. These are the first and second gain coefficients. It is the gradient of the Lyapunov function at the nth sampling time. It is the gradient of the Lyapunov function at the i-th sampling time; This is the expected velocity information of the robotic arm's end effector at the nth sampling time, indicated by the superscript. Indicates the expected value. For the desired location information at the nth sampling time, Let Jacobian matrix be the kinematic information of the robotic arm at the nth sampling time. It is a vector norm, superscript It is the vector transpose operator; It is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method. It represents the velocity of each joint at the (n-1)th sampling time. These are the adaptive coefficients at the nth sampling time. These are the first and second gain coefficients. Represents vectorized operators. It is the gradient of the Lyapunov function at the nth sampling time. It is the gradient of the Lyapunov function at the i-th sampling time.

2. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 1, characterized in that, In step S2, the error is calculated using the following formula: in, The error is calculated at the (n+1)th sampling time. It is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method. It represents the velocity of each joint at the (n+1)th sampling time, with the superscript indicating the velocity. The calculation method is the central finite difference approximation method. To correct the error at the (n+1)th sampling time, The error is calculated at the (n+1)th sampling time. It is the error calculated at the i-th sampling time. Both represent gain coefficients.

3. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 2, characterized in that, In step S2, the formula for updating the adaptive coefficients is as follows: in, These are the adaptive coefficients at the (n+1)th sampling time. The expected error is calculated using two methods. It is the gain coefficient. It is the error at the (n+1)th sampling time after correction. It is the adaptive coefficient at the nth sampling time.

4. A robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 1 or 3, characterized in that, In step S3, the formulas for calculating the joint positions at each moment are as follows: in, It contains the velocity information of each joint at the (n+1)th sampling time. Indicates the sampling interval. It contains the position information of each joint at the nth sampling time. It represents the position information of each joint at the (n+1)th sampling time.

5. A robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 1 or 3, characterized in that, In step S4, the speed of the end effector is calculated using the following formula: in, Let Jacobian matrix be the kinematic information of the robotic arm at the nth sampling time. It contains the velocity information of each joint at the nth sampling time. The speed information calculated for the end effector of the robotic arm.

6. A robotic arm motion planning system based on an error-driven adaptive gradient dynamics model, characterized in that, The system includes an actuator for executing a robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in any one of claims 1-5.

7. A computer storage medium having a computer program disposed thereon, characterized in that, When executed by the executor, the computer program is used to implement the robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in any one of claims 1-5.

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