Motion planning method for six-degree-of-freedom redundant manipulator based on dme-ntznn

Abstract

The application discloses a kind of six degree of freedom redundant mechanical arm motion planning methods based on DME-NTZNN, belong to robot control and motion planning technical field.The application first establishes the kinematic model of mechanical arm and defines desired trajectory;Second, construct discrete momentum enhanced noise suppression zeroization neural network model, the model is introduced by integral term based on history error accumulation to suppress measurement noise, and by introducing momentum feedforward term based on last cycle joint speed to accelerate convergence;Then, in each control cycle, based on the model real-time solving joint speed instruction that meets tracking requirements;Finally, according to the speed instruction updates joint state and drives mechanical arm motion.The application has significant effect in improving trajectory tracking convergence speed, enhancing system anti-interference ability and guaranteeing high-precision motion control.

Description

Technical Field

[0001] This invention relates to the field of robot control and motion planning technology, specifically to a motion planning method for a six-degree-of-freedom redundant robotic arm based on DME-NTZNN. Background Technology

[0002] Motion planning for redundant robotic arms requires not only high-precision trajectory tracking but also consideration of joint limit constraints, obstacle avoidance, and anti-interference capabilities. Motion planning is essentially a constrained time-varying nonlinear optimization problem. With the digitization of computer control systems, discretizing continuous-time solution algorithms and deploying them in digital controllers has become an inevitable trend. However, traditional discretization methods often suffer from truncation errors and are sensitive to measurement noise.

[0003] Currently, solutions to this type of problem can be mainly divided into the following three categories:

[0004] Existing technical solution 1: A pseudo-inverse control scheme based on gradient projection. This scheme uses the pseudo-inverse of the Jacobian matrix to solve the inverse kinematics and handles redundancy through null space projection to optimize secondary tasks, such as avoiding limits. Its drawback is the need for frequent calculations of the matrix inverse, resulting in high computational complexity. Furthermore, it is extremely unstable near singular points, prone to sudden changes in joint velocity, and lacks the ability to actively suppress measurement noise.

[0005] Existing technical solution two: the traditional continuous-time nullification neural network scheme. This scheme constructs continuous differential equations. This can be solved using analog circuits or high-precision numerical integration. Its drawback is that discretization is necessary when implementing it on a digital computer, for example, by using the Euler method, which introduces... The discretization error of the first order causes it to fail to converge precisely to zero in steady state, i.e., there is a steady-state residual, and its convergence speed is limited by the gain coefficient. Excessive gain will lead to rigidity problems.

[0006] Existing technical solution three: the standard discrete-time scheme. This scheme is directly based on linear difference equations. The design is as follows. Its drawbacks are that while it solves some discretization problems, its convergence speed is typically linear, and its ability to track rapidly changing time-varying signals is weak. Most importantly, this scheme usually does not consider noise interference in industrial environments; when the input data contains constant or time-varying noise, the accuracy of the solution will significantly decrease. Summary of the Invention

[0007] To address the aforementioned shortcomings in the existing technology, this invention provides a motion planning method for a six-degree-of-freedom redundant robotic arm based on DME-NTZNN.

[0008] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0009] A motion planning method for a six-DOF redundant robotic arm based on DME-NTZNN includes the following steps:

[0010] S1. Perform kinematic modeling on the six-degree-of-freedom redundant manipulator, obtain the mapping relationship between its end position and joint angles, and set the time-varying expected trajectory that the end effector needs to track.

[0011] S2. Construct a discrete momentum-enhanced noise suppression nullification neural network model. This model actively suppresses measurement noise by defining an error evolution law that includes integral feedback, and accelerates network convergence by introducing a momentum term based on historical velocity.

[0012] S3. In each sampling control cycle, based on the model constructed in S2, combined with the current state of the robotic arm, the desired trajectory information and the speed command of the previous cycle, the joint speed command that meets the trajectory tracking requirements is calculated in real time.

[0013] S4. Using the joint speed commands calculated by S3, drive the movement of each joint of the robotic arm and update the joint angle state of the robotic arm to achieve closed-loop control.

[0014] Furthermore, S1 specifically includes:

[0015] S11. Establish the forward kinematics equations of the robotic arm, obtain the function of the end position with respect to the joint angles, and derive the Jacobian matrix relationship of its velocity level.

[0016] S12. Set a desired motion trajectory for the end effector of the robotic arm that varies over time, the trajectory including position and velocity information.

[0017] Furthermore, the discrete momentum enhancement noise suppression nullification neural network model constructed in S2 is expressed as follows:

[0018]

[0019] In the formula, To track errors, Its first-order differential; and For design parameters, This is the time integral term.

[0020] Furthermore, the specific process by which S3 solves for the joint velocity command in each control cycle is as follows:

[0021] S31: Calculate the basic term used to drive the system, which consists of the sum of three parts: the velocity feedforward of the desired trajectory, the proportional negative feedback of the current end position error, and the integral negative feedback of the historical cumulative error.

[0022] S32. Multiply the joint velocity command calculated in the previous control cycle by a momentum factor to form a momentum enhancement feedforward term.

[0023] S33: Add the basic term to the momentum enhancement feedforward term to form the correction target for the desired velocity at the end of the current cycle;

[0024] S34. Using the corrected target as the right-hand side of the equation and the Jacobian matrix under the current robotic arm configuration as the coefficient matrix, construct and solve a system of linear equations about the current joint speed to obtain a joint speed command that combines noise reduction and acceleration effects.

[0025] Furthermore, the momentum enhancement feedforward term specifically comprises:

[0026] Based on the principle of inertia in physics, the joint velocity command calculated in the previous control cycle is multiplied by a momentum factor between 0 and 1. The product is then introduced into the solution process of the current cycle as a momentum feedforward term to simulate the inertial effect using historical motion information and accelerate network convergence.

[0027] Furthermore, the integral negative feedback of the historical cumulative error is obtained by summing the end position tracking error in each control cycle since the start of the motion.

[0028] Furthermore, the specific method for updating the state of the robotic arm in S4 is as follows: multiply the joint speed command solved in the current control cycle by the sampling time interval to obtain the joint angle increment within the cycle, and then add this increment to the joint angle at the previous moment to update the joint angle command to be executed at the next moment.

[0029] The present invention has the following beneficial effects:

[0030] 1. Acceleration characteristics: DT-ZNN only utilizes the error gradient descent at the current moment, and the convergence path is zigzag or gradual. In contrast, the DME-NTZNN of this invention uses the momentum term to simulate the inertia of physical entities, which can overcome local flat regions and converge with a steeper slope. Experiments show that the convergence speed is improved by 30%-50% under the same computing resources.

[0031] 2. Anti-interference characteristics: DT-ZNN lacks memory for noise, and instantaneous noise is directly reflected in the output. This invention, by memorizing historical errors through the integral term, can average out zero-mean noise and cancel constant deviations, thereby improving the final steady-state accuracy by 1-2 orders of magnitude. Attached Figure Description

[0032] Figure 1 This is a flowchart of the technical solution of the present invention.

[0033] Figure 2 This is a graph showing the change of joint angles of a six-degree-of-freedom robotic arm over time under the control of the DME-NTZNN algorithm in an embodiment of the present invention.

[0034] Figure 3 This is a convergence curve of the position error norm of the end effector of the robotic arm in a circular trajectory tracking task according to an embodiment of the present invention.

[0035] Figure 4 This is a three-dimensional spatial comparison diagram of the actual output trajectory of the robotic arm end effector and the expected circular trajectory in an embodiment of the present invention.

[0036] Figure 5 This is a schematic diagram of the evolution of the link spatial posture during the trajectory planning process of the robotic arm in an embodiment of the present invention.

[0037] Figure 6 This is a snapshot of an experiment demonstrating the robotic arm's circular drawing of the DME-NTZNN algorithm in the CoppeliaSim simulation platform, as part of an embodiment of the present invention.

[0038] Figure 7 This is another snapshot of the robotic arm's circular drawing experiment verifying the DME-NTZNN algorithm in the CoppeliaSim simulation platform, as an embodiment of the present invention. Detailed Implementation

[0039] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0040] The explanation in this invention is as follows:

[0041] 1. UR5 Robotic Arm: A lightweight collaborative robot with 6 rotary joints, widely used in industrial automation.

[0042] 2. Kinematic Redundancy: This refers to the fact that the number of joint degrees of freedom of a robotic arm is greater than the task space dimension required for the end effector to complete the task. For example, if there are 6 joints but only 3 dimensions are needed for position control, the robotic arm can have countless joint configurations to achieve the same end pose.

[0043] 3. Zeroing Neural Network (ZNN): A recurrent neural network used to solve time-varying problems. It solves time-varying nonlinear equations in real time by defining an error function and making it converge to zero exponentially.

[0044] 4. DME-NTZNN (Discrete Momentum-Enhanced Noise-Tolerant ZNN): Discrete Momentum-Enhanced Noise-Tolerant ZNN, the core algorithm proposed in this invention, combines a discrete solution model with a momentum acceleration term and a noise-resistant integral mechanism.

[0045] A motion planning method for a six-DOF redundant robotic arm based on DME-NTZNN, such as Figure 1 As shown, it includes the following steps:

[0046] S1. Perform kinematic modeling on the six-degree-of-freedom redundant manipulator, obtain the mapping relationship between its end position and joint angles, and set the time-varying expected trajectory that the end effector needs to track.

[0047] In this embodiment, for the UR5 robotic arm, we need to solve a system of time-varying nonlinear equations:

[0048]

[0049] in For joint angle, The desired trajectory is given. To handle redundancy and constraints, we construct an augmented state vector containing Lagrange multipliers. .

[0050] S2. Construct a discrete momentum-enhanced noise suppression nullification neural network model. This model actively suppresses measurement noise by defining an error evolution law that includes integral feedback, and accelerates network convergence by introducing a momentum term based on historical velocity.

[0051] In this embodiment, in order to suppress noise, the traditional ZNN evolution... This is no longer sufficient. This invention defines a novel noise-resistant differential-integral error evolution equation:

[0052]

[0053] in and These are the design parameters. This equation introduces an integral term; according to control theory, the integral action can eliminate steady-state error and suppress constant noise.

[0054] S3. In each sampling control cycle, based on the model constructed in S2, combined with the current state of the robotic arm, the desired trajectory information and the speed command of the previous cycle, the joint speed command that meets the trajectory tracking requirements is calculated in real time.

[0055] In this embodiment, in order to implement it in a digital system, we use a time interval of... The discretization scheme is as follows: The derivative is approximated using the backward difference formula:

[0056]

[0057] Using approximate integration through summation:

[0058]

[0059] Substituting the above approximation into the evolution equation of step two and rearranging, we can obtain the following about... Discrete error dynamics:

[0060]

[0061] make The above equation defines the next-time expected error pattern with noise resistance.

[0062] S4. Using the joint speed commands calculated by S3, drive the movement of each joint of the robotic arm and update the joint angle state of the robotic arm to achieve closed-loop control.

[0063] This embodiment defines a basic error driving term. First, based on the derivation in step S3, in order for the system to satisfy the noise-resistant error dynamics, the basic control input required by the system should include the feedforward of the desired trajectory, the proportional feedback of the current error, and the integral feedback of the historical error. The basic error driving term is defined as:

[0064]

[0065] in For trajectory feedforward, For the proportion term, This is the noise resistance integral term.

[0066] Define the momentum feedforward term Based on the principle of inertia in physics, the joint velocity from the previous control cycle is utilized. Constructing the momentum term:

[0067]

[0068] in This is the momentum factor.

[0069] Construct the overall objective function. Include the momentum term. As additional feedforward compensation, it is added to the basic error driving term. The above forms the modified dynamic constraint equations:

[0070]

[0071] This equation achieves a mathematical connection between historical motion information (momentum) and current task requirements (error-driven).

[0072] The equations defined above and Specifically, by expanding upon the equations and substituting them into the overall objective equation, we obtain the final result used to calculate the current joint velocity. The system of linear equations:

[0073]

[0074] This formula clearly shows the four components of the right-hand side of the equation and their physical origin: trajectory feedforward. Ensures rapid tracking of time-varying desired trajectories; proportional feedback. Eliminate current position error; noise immunity integral Used to eliminate steady-state errors and filter noise; momentum feedforward Accelerate convergence by utilizing inertia.

[0075] In each control cycle The optimal joint velocity is obtained by solving this system of linear equations, and the joint angles are updated. .

[0076] To verify the effectiveness of the above algorithm, numerical simulation and physical experiments were conducted, and the results are analyzed as follows:

[0077] Figure 2 The graphs show the time-varying angles of each joint of the six-DOF UR5 robotic arm under the control of the DME-NTZNN algorithm. It is clearly observed from the graph that the angle changes of the six joints are smooth and continuous, without any abrupt changes or high-frequency jitter, and all joint angles remain within the safe range of the robotic arm's physical limitations. This indicates that the momentum enhancement mechanism proposed in this invention does not introduce additional instabilities, and the generated inverse kinematic solution has good smoothness, which is beneficial for protecting the robotic arm's drive motor and reduction mechanism.

[0078] Figure 3 This demonstrates the convergence of the position error norm over time when the end effector tracks a circular trajectory. The curves show that the position error decreases exponentially rapidly within a very short time after system startup, eventually stabilizing at a constant value. The magnitude is even lower. Compared with conventional algorithms that do not introduce momentum terms, this scheme significantly shortens the transition time by utilizing momentum acceleration, proving the effectiveness of momentum terms in accelerating convergence, while the integral term ensures that the steady-state error is almost zero.

[0079] Figure 4 The comparison between the actual trajectory (red solid line) of the robotic arm's end effector in three-dimensional space and the desired circular trajectory (blue solid line) is shown. The two trajectories highly overlap in space, making the deviation almost indistinguishable to the naked eye. This intuitively verifies the high accuracy of the DME-NTZNN algorithm in handling complex spatial curve tracking tasks, demonstrating that the algorithm successfully overcomes discretization errors and achieves accurate reproduction of the desired path.

[0080] Figure 5 This image presents snapshots of the spatial attitude of the links at different moments during the robotic arm's circular trajectory tracking task. The figure visually reflects the configuration changes of the robotic arm within the workspace. Throughout the movement, the robotic arm maintains a relaxed posture without any singular configurations or self-collisions between links. This further validates the algorithm's effectiveness in handling redundant degrees of freedom, demonstrating its ability to automatically select optimized joint configurations to complete the end-effector task.

[0081] Figure 6 , Figure 7 This is a real-time snapshot of the DME-NTZNN algorithm running in the CoppeliaSim simulation environment. Simulation results show that the virtual UR5 robotic arm can accurately draw a preset standard circle on the drawing board. This verifies that the control scheme proposed in this invention remains effective in physical simulation engines that include rigid body dynamics, and the algorithm possesses good model adaptability and numerical stability.

[0082] In actual operation, despite interference from non-ideal factors such as sensor measurement noise and friction, the robotic arm was still able to smoothly draw a smooth and closed circular trajectory on the whiteboard. The success of the practical experiment strongly demonstrates the effectiveness of the noise suppression integral term in the algorithm and showcases the robustness and engineering application value of this technical solution in real industrial environments.

[0083] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0084] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0085] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0086] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0087] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A motion planning method for a six-degree-of-freedom redundant robotic arm based on DME-NTZNN, characterized in that, Includes the following steps: S1. Perform kinematic modeling on the six-degree-of-freedom redundant manipulator, obtain the mapping relationship between its end position and joint angles, and set the time-varying expected trajectory that the end effector needs to track. S2. Construct a discrete momentum-enhanced noise suppression nullification neural network model. This model actively suppresses measurement noise by defining an error evolution law that includes integral feedback, and accelerates network convergence by introducing a momentum term based on historical velocity. The discrete momentum-enhanced noise suppression nullification neural network model is expressed as follows: In the formula, To track errors, Its first-order differential; and For design parameters, For time integration; S3. In each sampling control cycle, based on the model constructed in S2, combined with the current state of the robotic arm, the desired trajectory information, and the speed command of the previous cycle, the joint speed command that meets the trajectory tracking requirements is calculated in real time. The specific process of solving the joint speed command in each control cycle is as follows: S31: Calculate the basic term used for the drive system. This basic term consists of three parts: the velocity feedforward of the desired trajectory, the proportional negative feedback of the current end position error, and the integral negative feedback of the historical cumulative error. The integral negative feedback of the historical cumulative error is obtained by summing the end position tracking error in each control cycle since the start of motion. S32. Multiply the joint velocity command calculated in the previous control cycle by a momentum factor to form a momentum enhancement feedforward term. The momentum enhancement feedforward term is as follows: Based on the principle of inertia in physics, the joint velocity command calculated in the previous control cycle is multiplied by a momentum factor between 0 and 1. The product is then introduced into the solution process of the current cycle as a momentum feedforward term to simulate the inertial effect using historical motion information and accelerate network convergence. S33: Add the basic term to the momentum enhancement feedforward term to form the correction target for the desired velocity at the end of the current cycle; S34. Using the corrected target as the right side of the equation and the Jacobian matrix under the current robotic arm configuration as the coefficient matrix, construct and solve a system of linear equations about the current joint speed to obtain a joint speed command that combines noise reduction and acceleration effects. S4. Using the joint speed commands calculated by S3, drive the movement of each joint of the robotic arm and update the joint angle state of the robotic arm to achieve closed-loop control.

2. The motion planning method for a six-degree-of-freedom redundant robotic arm based on DME-NTZNN according to claim 1, characterized in that, S1 specifically includes: S11. Establish the forward kinematics equations of the robotic arm, obtain the function of the end position with respect to the joint angles, and derive the Jacobian matrix relationship of its velocity level. S12. Set a desired motion trajectory for the end effector of the robotic arm that varies over time, the trajectory including position and velocity information.

3. The motion planning method for a six-degree-of-freedom redundant robotic arm based on DME-NTZNN according to claim 1, characterized in that, The specific method for updating the state of the robotic arm in S4 is as follows: multiply the joint speed command solved in the current control cycle by the sampling time interval to obtain the joint angle increment within the cycle, and then add this increment to the joint angle at the previous moment to update the joint angle command to be executed at the next moment.

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