Mechanical arm motion planning method and system based on error-driven adaptive gradient kinetic model

Abstract

The invention belongs to the related technical field of mechanical arm motion planning, and discloses a mechanical arm motion planning method and system based on an error-driven adaptive gradient model. The method comprises the following steps: S1, establishing a gradient relationship between joint velocities at two adjacent moments and an adaptive coefficient lambda n based on a Lyapunov function; s2, solving the joint velocity at the moment (n + 1) by utilizing the gradient relationship, calculating the joint velocity at the moment (n + 1) by adopting a central finite difference method, calculating an error between the joint velocity and the error, and updating a self-adaptive coefficient; s3n = n + 1; returning to the step S2 until the joint speeds at all moments are obtained; s4, solving the joint position by using the relation between the joint speed and the joint position; and the speed of an end effector is calculated through the mechanical arm motion planning model and the joint speeds at all moments, and therefore motion planning of the mechanical arm is achieved. According to the invention, the problem of low calculation efficiency of mechanical arm motion planning is solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mechanical arm motion planning, and more particularly relates to a mechanical arm motion planning method and system based on an error-driven adaptive gradient dynamics model. BACKGROUND

[0002] Mechanical arm motion planning has always been the focus of modern industrial society. With the rapid development of robot technology, computer technology and servo control technology, mechanical arm motion planning has become the focus of attention of scholars in various fields. The research and application of this field covers many important fields such as industrial production, medical surgery, transportation and assembly. In today's highly automated production environment, mechanical arm motion planning is not only a necessary means to improve production efficiency, but also one of the key technologies to achieve complex tasks and precise operations. By accurately planning the motion trajectory of the mechanical arm, complex operations can be completed in a small space, improving the flexibility and adaptability of the production line. In the medical field, the application of mechanical arm motion planning provides support for precise surgical operations, reduces the invasiveness to patients, and improves the safety and success rate of surgery. In addition, the widespread application of mechanical arms in transportation and assembly fields also brings higher benefits and quality assurance to logistics and manufacturing industries. Overall, the continuous innovation and application of mechanical arm motion planning drive the technological development of modern society and bring more intelligent, efficient and safe solutions to various fields.

[0003] Neural dynamic model has strong fitting ability and parallel processing ability, and has been widely used in the field of manipulator motion planning and control technology. It is worth pointing out that in the solution of manipulator motion planning, the calculation of the derivative and pseudo-inverse of the relationship matrix between the actual space and the joint space of the manipulator (Jacobian matrix) cannot be avoided. In addition, improving the solution efficiency of the neural dynamic model applied to the manipulator motion planning has been one of the frontiers in this field. In other words, how to develop a manipulator motion planning acceleration method suitable for neural dynamic model is particularly important. At present, the acceleration methods of manipulator motion planning based on neural dynamic model mainly include the following two kinds: 1) using activation function; 2) introducing time-varying coefficient. Although the above two kinds of methods have made constructive and forward-looking achievements in theory, they still have their own shortcomings. For example, the acceleration method of activation function has specific requirements for discretization and step length, otherwise it is easy to produce deviation, and 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 time-varying coefficient types mainly include exponential type and error type. The disadvantage of the exponential time-varying coefficient is that its corresponding value will increase with time, so when the time is large, the calculation will overflow. The error type time-varying coefficient is only determined by the error norm of the current time, and does not contain the related dynamic information of high-order error or Lyapunov function, which leads to that its acceleration performance is not further evaluated by these potential dynamics. The acceleration methods of the above two kinds of time-varying coefficients do not consider the influence of high-order error and historical error sum on the solution speed, which undoubtedly wastes these two parameters with potential acceleration properties.

[0004] Through the above description and analysis, it is necessary to develop a method for manipulator motion planning and utilizing the potential parameter information and dynamic characteristics of adaptive gradient model. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a manipulator motion planning method and system based on error-driven adaptive gradient dynamic model, which solves the problem of long calculation time of manipulator motion planning.

[0006] To achieve the above purpose, according to one aspect of the present application, a manipulator motion planning method based on error-driven adaptive gradient dynamic model is provided, which comprises the following steps:

[0007] S1, an adaptive gradient relationship of joint velocity about adaptive coefficient λ n between two adjacent time points is established based on Lyapunov function, and the initial value λ n of adaptive coefficient is set.

[0008] S2, the joint velocity at n+1 time is solved by using the adaptive gradient relationship. 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] wherein, is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method, is the velocity of each joint at the nth sampling time, λ n is the adaptive coefficient at the nth sampling time, ω1, ω2 are the first and second gain coefficients, vec(·) represents the vectorization operator, is the gradient of the Lyapunov function at the nth sampling time, V i is the gradient of the Lyapunov function at the ith sampling time.

[0020] Further preferably, in step S2, the calculation formula of the error is as follows:

[0021]

[0022] wherein, δ n+1 is the error calculated at the (n+1)th sampling time, is the joint velocity at the (n+1)th sampling time calculated using the central finite difference approximation method, is the velocity of each joint at the (n+1)th sampling time, superscript (·) C is the calculation method, which is the central finite difference approximation method, E n+1 is the error at the (n+1)th sampling time after correction, δ n+1 is the error calculated at the (n+1)th sampling time, δ i is the error calculated at the ith sampling time, η2, η3 both represent gain coefficients.

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

[0024]

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

[0026] Further preferably, in step S3, the calculation formula of the joint position at each time is as follows:

[0027]

[0028] wherein, is the velocity information of each joint at the n+1 sampling moment, τ represents a sampling interval, and θ n is the position information of each joint at the n sampling moment, θ n+1 is the position information of each joint at the n+1 sampling moment.

[0029] Further preferably, in step S4, the calculation formula of the velocity of the end effector is as follows:

[0030]

[0031] wherein J(θ n ) is a Jacobian matrix corresponding to the kinematics information of the robot arm at the n sampling moment, is the velocity information of each joint at the n sampling moment, is the velocity information of the end effector of the robot arm calculated.

[0032] According to another aspect of the present application, there is provided a robot arm motion planning system based on an error-driven adaptive gradient dynamic model, which comprises an executor configured to execute the robot arm motion planning method based on the error-driven adaptive gradient dynamic model.

[0033] According to another aspect of the present application, there is provided a computer storage medium, which is provided with a computer program configured to implement the robot arm motion planning method based on the error-driven adaptive gradient dynamic model when executed by an executor.

[0034] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0035] 1. The present application proposes a robot arm motion planning acceleration method based on an error-driven adaptive gradient dynamic model, which not only avoids the time-consuming processes of deriving and pseudo-inverting the Jacobian matrix, but also realizes the acceleration of the adaptive gradient dynamic model for solving the robot arm motion planning, which has extremely important practical significance for real-time industrial production operations and military applications.

[0036] 2. The adaptive update formula of the present application is constructed based on a proportional controller (P controller), which realizes the precise adaptation of the joint motion characteristics by fusing the core control ideas of proportional and integral elements: the proportional term dynamically responds to real-time errors to ensure fast tracking, the integral term adaptively adjusts to eliminate steady-state errors, 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 the application constructs a new high-order error compensation term by differentiating the high-order error and the low-order error, which has the following advantages: 1) the gradual convergence of the error is realized by the order promotion of the error term; 2) the introduction of the compensation term effectively suppresses the low-order error component; and 3) the adaptive mechanism can dynamically adjust the compensation strength according to the system state.

[0038] 4. The mechanical arm motion planning acceleration method based on the error-driven adaptive gradient dynamics model proposed in the application uses the error-driven method to design and analyze the adaptive gradient dynamics model, uses the potential acceleration properties of the high-order error and the historical error sum in the adaptive gradient dynamics model through the adaptive error-driven scheme, determines the coefficients in the adaptive gradient neural network through the adaptive error-driven scheme, and greatly improves the timeliness and convergence of the adaptive gradient neural network for mechanical arm motion planning.

[0039] 5. The application combines the actual application requirements of the current adaptive gradient dynamics model for mechanical arm motion planning, constructs a mechanical arm motion planning acceleration method based on the error-driven adaptive gradient dynamics model, realizes the mechanical arm motion planning based on the adaptive gradient dynamics model, and has the advantages of fast convergence speed, short calculation time, and high solution accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is a flowchart of a mechanical arm motion planning acceleration method based on the error-driven adaptive gradient dynamics model constructed according to the preferred embodiment of the application.

[0041] Figure 2 is the motion state of each joint of the motion trajectory of the mechanical arm end effector generated according to the preferred embodiment of the application.

[0042] Figure 3 is the error component state of the motion trajectory of the mechanical arm end effector generated according to the preferred embodiment of the application and the ideal trajectory in two-dimensional space.

[0043] Figure 4 is the joint angle position state of the mechanical arm constructed according to the preferred embodiment of the application. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below with reference to the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

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

[0046] S1, an adaptive gradient dynamics model is constructed to solve the Lyapunov function of the mechanical arm motion planning model, the adaptive gradient dynamics model is determined and its parameters are initialized.

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

[0048]

[0049] wherein the subscript (·) n represents the nth sampling time, V n is the Lyapunov function at the nth sampling time, the superscript (·) d represents the expected value, is the expected velocity information of the mechanical arm end effector at the nth sampling time, is the velocity information of each joint at the nth sampling time, θ n is the position information of each joint at the nth sampling time, J(θ n ) is the Jacobian matrix corresponding to the kinematics information of the mechanical arm at the nth sampling time, vec(·) represents the vectorization operator, and ||·||2 represents the vector L2 norm.

[0050] The adaptive coefficients λ0 and λ1, the gain coefficients ω1 and ω2 are obtained, for the above-mentioned Lyapunov function, the adaptive gradient dynamics model used to solve it is determined, as shown below

[0051]

[0052] wherein the subscript (·) n represents the nth sampling time, the superscript (·) d represents the expected value, is the expected velocity information of the mechanical arm end effector at the nth sampling time, is the expected position information at the nth sampling time, is the velocity information of each joint at the nth sampling time, θ n is the position information of each joint at the nth sampling time, J(θ n ) is the Jacobian matrix corresponding to the kinematics information of the mechanical arm at the nth sampling time, vec(·) represents the vectorization operator, and ||·||2 represents the vector L2 norm, V n is the Lyapunov function at the nth sampling time, represents the gradient of the Lyapunov function at the nth sampling time, the superscript denotes the transpose operator of a vector, ω1, ω2 denote gain coefficients, λ n denotes the adaptive coefficient at the n-th sampling time.

[0053] Initialize the determined adaptive gradient dynamics model related variables and hyperparameters, including the initial Jacobian matrix J(θ0) of the robot arm, the initial velocity 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 velocity information of each joint of the robot arm is calculated using the Euler method and the central finite difference approximation method respectively.

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

[0056]

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

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

[0059] Compare the calculation errors of the Euler method and the central finite difference approximation method, and sum the historical error information, as shown below:

[0060]

[0061] wherein subscript (·) n denotes the n th sampling moment, is the joint velocity at the n+1 th sampling moment calculated using the central finite difference approximation method, superscript (·) C denotes the calculation method is the central finite difference approximation method, δ n is the error calculated at the n th sampling moment, δ i is the error calculated at the i th sampling moment, δ n+1 is the error calculated at the n+1 th sampling moment, E n is the error at the n th sampling moment after correction, E n+1 is the error at the n+1 th sampling moment after correction, η 2, η 3 both denote gain coefficients, and vec(·) represents a vectorization operator.

[0062] An adaptive coefficient updating scheme is executed;

[0063] An adaptive updating scheme is executed as follows:

[0064]

[0065] wherein subscript (·) n denotes the n th sampling moment, γ denotes the expected error calculated using two methods, and η 1 denotes a gain coefficient, E n+1 is the error at the n+1 th sampling moment after correction, λ n is the adaptive coefficient at the n th sampling moment, λ n+1 is the adaptive coefficient at the n+1 th sampling moment.

[0066] S3 n = n+1; return to step S2 until the joint velocities at all moments are obtained.

[0067] If t n ≥ t f , stop the calculation and output the sequence information of the joint velocities of the robot arm { θ 0, θ 1, …, θ f}; according to the relationship between the joint velocities of each robot arm and the end effector velocity of the robot arm in the robot arm motion planning model in step 1, the sequence information of the end effector velocity of the robot arm can be obtained; performing integration on the sequence information of the end effector velocity of the robot arm can obtain the sequence information of the end effector position of the robot arm { r 0, r 1, …, r f}; otherwise, jump to S2);

[0068] S4 solves the joint position at each time by using the relationship between the joint velocity and the joint position, and calculates the velocity of the end effector by using the motion planning model of the robot arm and the joint velocity at each time, so as to realize the motion planning of the robot arm.

[0069]

[0070] wherein subscript (·) n represents the n-th sampling time, and τ represents a sampling interval, is the velocity information of each joint at the n+1-th sampling time, and θ n is the position information of each joint at the n-th sampling time, and θ n+1 is the position information of each joint at the n+1-th sampling time.

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

[0072] Obtain the relevant information of the robot arm, and construct a motion planning model of the robot arm.

[0073] Obtain the desired velocity information of the end effector of the robot arm desired position information r d (t), and superscript (·) d represents a desired value, and each joint velocity information position information θ(t), kinematics information f(θ(t)) of the robot arm, calculate the corresponding Jacobian matrix J(θ(t)), and construct a motion planning model of the robot arm, which is specifically as follows:

[0074]

[0075] Discretize the constructed motion planning model of the robot arm to obtain

[0076]

[0077] wherein subscript (·) n represents the n-th sampling time, and J(θ n ) is the Jacobian matrix corresponding to the kinematics information of the robot arm at the n-th sampling time, is the velocity information of each joint at the n-th sampling time, is the desired velocity information of the end effector of the robot arm at the n-th sampling time, and superscript (·) d represents a desired value.

[0078] According to the solving result, a control signal of the motion planning of the robot arm is converted and transmitted to a lower computer controller, so as to realize the motion planning task of the robot arm.

[0079] The application will be further described in combination with specific embodiments.

[0080] 1. Test process

[0081] The operation process of the application will be described as follows in combination with a specific simulation operation and in combination with the attached Figure 1 flowchart.

[0082] The method of the application is simulated by experiment by taking the operation of repeating the path generation by using MATLAB software and a five-degree-of-freedom mechanical arm as an example.

[0083] Step 1, obtaining the desired initial velocity of the end effector of the mechanical arm desired initial position initial velocity of each joint initial position θ0, initial Jacobian matrix J(θ0)

[0084]

[0085] Then, according to the above parameter information, the initial time mechanical arm motion planning model can be constructed:

[0086]

[0087] wherein J(θ0) is the initial Jacobian matrix, θ0 is the initial position of each joint of the mechanical arm, is the initial velocity of each joint of the mechanical arm, the superscript (·) d represents the desired value, is the desired initial velocity information of the end effector of the mechanical arm.

[0088] Step 1, facing the above mechanical arm motion planning model, constructing an adaptive gradient dynamics model to solve the Lyapunov function of the mechanical arm motion planning, as shown below

[0089]

[0090] wherein the subscript (·) n represents the nth sampling time, V n is the Lyapunov function at the nth sampling time, the superscript (·) d represents the desired value, is the desired velocity information of the end effector of the mechanical arm at the nth sampling time, is the velocity information of each joint at the nth sampling time, θ n is the position information of each joint at the nth sampling time, J(θ n ) is the Jacobian matrix corresponding to the kinematics information of the mechanical arm at the nth sampling time, vec(·) represents the vectorization operator, and ||·||2 represents the vector L2 norm.

[0091] Based on the above Lyapunov function, an adaptive gradient dynamic model for solving it is determined as follows:

[0092]

[0093] wherein subscript (·) n represents the n th sampling time, superscript (·) d represents the expected value, is the velocity information expected by the end effector of the manipulator at the n th sampling time, is the position information expected at the n th sampling time, is the velocity information of each joint at the n th sampling time, θ n is the position information of each joint at the n th sampling time, J(θ n ) is the Jacobian matrix corresponding to the kinematics information of the manipulator at the n th sampling time, vec(·) represents the vectorization operator, ||·|| 2 represents the L 2 norm of the vector, V n is the Lyapunov function at the n th sampling time, represents the gradient of the Lyapunov function at the n th sampling time, superscript represents the transposition operator of the vector, ω 1, ω 2 both represent gain coefficients, λ n represents the adaptive coefficient at the n th sampling time; initialize the variables and hyperparameters related to the adaptive gradient dynamic model determined, including the initial iteration number n = 0, the initial time t 0 = 0 s (seconds), the gain coefficients ω 1 = ω 2 = η 1 = 0.1, η 2 = η 3 = 1, the expected error γ = 0.1, the initial adaptive coefficient λ 0 = λ 1 = 1, the sampling interval τ = 0.001 s (seconds), and the termination time t f = 7 s (seconds);

[0094] Step 2, respectively using Euler method and central finite difference approximation method to calculate the velocity information of each joint of the manipulator, as shown below

[0095]

[0096] wherein subscript (·) n represents the n th sampling time, represents the velocity information of each joint calculated using Euler method at the n-1 th sampling time, represents the velocity information of each joint calculated using Euler method at the n th sampling time, represents the velocity information of each joint calculated using Euler method at the n+1 th sampling time, superscript (·) C represents the calculation method is central finite difference approximation method, represents the velocity information of each joint calculated using central finite difference approximation method at the n th sampling time, λn is the adaptive coefficient at the n-th sampling time, vec(·) represents the vectorization operator, ω1, ω2 are the first and second gain coefficients, is the gradient of Lyapunov function at the n-th sampling time, is the gradient of Lyapunov function at the i-th sampling time.

[0097] The calculation errors of Euler method and central finite difference approximation method are compared, and the historical error information is summed up as follows

[0098]

[0099] wherein the subscript (·) n represents the n-th sampling time, is the joint velocity at the n+1-th sampling time calculated using the central finite difference approximation method, the superscript (·) C represents that the calculation method is the central finite difference approximation method, δ n is the error calculated at the n-th sampling time, δ i is the error calculated at the i-th sampling time, δ n+1 is the error calculated at the n+1-th sampling time, E n is the error at the n-th sampling time after correction, E n+1 is the error at the n+1-th sampling time after correction, η2, η3 both represent gain coefficients, and vec(·) represents the vectorization operator.

[0100] An adaptive updating scheme is performed as follows:

[0101]

[0102] wherein the subscript (·) n represents the n-th sampling time, γ represents the expected error calculated using the two methods, and η1 represents the gain coefficient, E n+1 is the error at the n+1-th sampling time after correction, λ n is the adaptive coefficient at the n-th sampling time, λ n+1 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 joint velocity sequence information of the robot arm position sequence information {θ0, θ1, …, θ fAccording to the relationship between the joint speed and the end effector speed of each robot arm in the robot arm motion planning model, the end effector speed sequence information of the robot arm can be obtained The end effector position sequence information of the robot arm can be obtained by integrating the end effector speed sequence information of the robot arm f Otherwise, jump to step 2).

[0105] Step 4, solve the joint position at each time by using the relationship between the joint speed and the joint position, and calculate the end effector speed by using the robot arm motion planning model and the joint speed at each time, so as to realize the motion planning of the robot arm.

[0106]

[0107] Wherein, the subscript (·) n n represents the nth sampling time, τ represents the sampling interval, is the speed information of each joint at the n+1th sampling time, θ n is the position information of each joint at the nth sampling time, θ n+1 is the position information of each joint at the n+1th sampling time.

[0108] Obtain the initial speed of the end effector of the robot arm the initial position r0, the initial speed of each joint the initial position θ0, the initial Jacobian matrix J(θ0)

[0109]

[0110] Then, according to the above existing parameter information, the initial time robot arm motion planning model can be constructed:

[0111]

[0112] Wherein, the subscript (·)1 represents the 1st sampling time, is the speed information of the end effector of the robot arm at the 1st sampling time, the superscript (·) c represents the calculated value, J(θ1) is the Jacobian matrix corresponding to the kinematics information of the robot arm at the 1st sampling time, is the speed information of each joint at the 1st sampling time.

[0113] According to the solving result, the control signal of the robot arm motion planning is converted and transmitted to the lower computer controller, so as to realize the robot 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 present invention applies a method for accelerating the motion planning of a robotic arm based on an error-driven adaptive gradient dynamics model. 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 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 ; 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.

2. The robotic arm motion planning method based on a differential-driven adaptive gradient dynamics model as described in claim 1, characterized in that, 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: 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.

3. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 2, characterized in that, The gradient of the Lyapunov function at the nth sampling time The calculation formula is as follows: in, This represents the expected velocity information of the robotic arm's end effector at the nth sampling time, indicated by the superscript (·). d Indicates the expected value. For the desired location information at the nth sampling time, J(θ) n Let be the Jacobian matrix corresponding to the kinematic information of the robotic arm at the nth sampling time, and ||·||2 be the L2 norm of the vector. It is the vector transpose operator.

4. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 3, characterized in that, 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 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. It is the gradient of the Lyapunov function at the i-th sampling time.

5. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 4, characterized in that, In step S2, the error is calculated using the following formula: 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 η2 and η3 are the errors calculated at the i-th sampling time, and both represent the gain coefficients.

6. The robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 5, characterized in that, In step S2, the formula for updating the adaptive coefficients is as follows: 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.

7. A robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 1 or 6, characterized in that, In step S3, the formulas for calculating the joint positions at each moment are as follows: 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.

8. A robotic arm motion planning method based on an error-driven adaptive gradient dynamics model as described in claim 1 or 6, characterized in that, In step S4, the speed of the end effector is calculated using the following formula: 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.

9. 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 1-8.

10. 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 1-8.

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