Real-time grasping and trajectory tracking method and system for mobile redundant robot arm

Abstract

The application discloses a mobile redundant manipulator real-time grabbing and trajectory tracking method and system based on optimization theory. In the method, the mobile redundant manipulator platform carries out real-time distance measurement on a target object based on a camera, and when the distance is less than a set threshold, a grabbing operation is performed. The application constructs a mobile redundant manipulator platform dynamics model based on robot forward kinematics, establishes a mobile redundant manipulator platform optimization model based on kinetic energy loss, designs a corresponding objective function, and sets constraint conditions of the corresponding optimization model in combination with physical limit conditions of the mobile redundant manipulator platform. By sampling time, inputting a current state of the mobile redundant manipulator platform, solving joint angular velocity and mobile platform speed at a next time, real-time trajectory tracking of the mobile redundant manipulator platform is realized. The application greatly increases the working range of the manipulator, the model is simple and easy to solve, accurate trajectory tracking can be realized, and the application prospect is wide.

Description

Technical Field

[0001] This invention belongs to the field of real-time optimal control of intelligent agents, and relates to a method and system for real-time grasping and trajectory tracking of a mobile redundant robotic arm based on optimization theory. Background Technology

[0002] With the continuous development of sensing and artificial intelligence technologies, autonomous mobile robots with perception, cognition, and self-decision-making capabilities have been widely used in military, civilian, and scientific research. Among these, robotic arms, as the most common and important actuators in human-robot collaboration, can not only perform a series of activities such as welding, handling, and throwing, but also assist humans in completing many tasks in complex industrial and daily life environments. As production demands evolve and service targets change, the requirements for the sensitivity and operability of robotic arms are becoming increasingly stringent. This presents new challenges to both the mathematical theory and engineering practice of robotic arm research. To overcome the limitations inherent in typical robotic arms and achieve rapid trajectory tracking and collaborative work, it is necessary to explore new mathematical theories and technical methods.

[0003] Currently, with the development of industrial production and the changing needs of people's lives and service targets, traditional rigid automated production lines, producing only a single type of product, can no longer meet the demands of diversified production. The flexibility and intelligence of industrial production lines have become the mainstream development trend. Therefore, our requirements for the sensitivity and operability of robotic arms are also increasing. Currently, the industry mainly requires robotic arms to have the following characteristics: good flexibility, easy-to-operate mechanical properties, effective operability, and rapid obstacle avoidance capabilities. Robotic arms are redundant robots; their joint space dimension is greater than the task space dimension, and their pluralistic nature allows for wide applications in industry and daily life.

[0004] A common approach in robotic arm research is to perform mechanism dynamics modeling and analysis. Commonly used mechanism dynamics modeling methods include the Newton-Euler method, the Lagrange method, the Kane equation method, and the virtual work principle method. These methods typically require calculating a large number of mechanical equations to solve for joint internal forces, and the dynamic model format is complex, making the calculation process cumbersome. Furthermore, based on mechanism dynamics modeling, kinematic analysis is also required. Kinematic problems refer to solving the functional mapping relationship between joint inputs and end effector outputs, mainly including forward and inverse kinematics analysis. Kinematic analysis is one of the most fundamental and important problems in mechanism research, mainly including position analysis, velocity analysis, and acceleration analysis. Position analysis is the most fundamental problem in mechanism kinematic analysis, and it forms the basis for solving problems related to velocity analysis, acceleration analysis, dynamics modeling, workspace analysis, and motion control. Position analysis is divided into forward position analysis and inverse position analysis. When the inputs of the mechanism are known, solving for the pose of the end effector is called forward position analysis; otherwise, it is called inverse position analysis. Generally, the forward position solution of a series mechanism is relatively easy, while the inverse position solution is more complex and has multiple solutions. The main methods for solving the position solution include analytical methods, numerical methods, and screw methods. The purpose of velocity and acceleration analysis is to solve the mapping relationship between the velocities and accelerations of the input joints and the velocities and accelerations of the end effectors. Common methods for analyzing the kinematic velocities and accelerations of a mechanism include the influence coefficient method, vector method, and screw method. The key is to establish the Jacobian matrix and Hessian matrix of the mechanism.

[0005] Currently, due to the inherent limitations of robotic arms, the operability of a single fixed robotic arm is very limited, confined to its arm length range, thus restricting its application scenarios, such as transporting goods and collaborative handling. To overcome this difficulty, adding a movable base to the robotic arm is an effective solution. This solution can greatly increase the robotic arm's working range and flexibility, enabling it to be used more widely.

[0006] Therefore, in order to enable the robotic arm to be controlled in real time based on its current state and to have a wide working range, it is essential to design a real-time trajectory tracking algorithm for a mobile redundant robotic arm platform. Summary of the Invention

[0007] Purpose of the invention: In view of the current requirements for real-time control of robotic arms, the purpose of this invention is to propose a method and system for real-time grasping and trajectory tracking of a mobile redundant robotic arm based on optimization theory, which can increase the working range of the robotic arm while achieving accurate trajectory tracking.

[0008] Technical Solution: To achieve the above-mentioned objectives, this invention provides a real-time grasping and trajectory tracking method for a mobile redundant robotic arm based on optimization theory. After camera recognition and object grasping, real-time trajectory planning of the mobile robotic arm is performed. First, a dynamic model of the mobile redundant robotic arm platform is established based on the robot's forward kinematics. Then, an optimization model of the mobile redundant robotic arm platform is established using kinetic energy loss as an indicator, and a corresponding objective function is designed. After setting relevant constraints on the mobile redundant robotic arm platform based on physical limitations, the model is solved, ultimately obtaining the real-time speed of the mobile platform and the robotic arm, achieving real-time trajectory tracking and completing accurate trajectory tracking. The method includes the following steps:

[0009] (1) A mobile redundant robotic arm platform is formed by combining a wheeled robot, a redundant robotic arm and a camera.

[0010] (2) Using the camera's image detection and recognition function, the distance between the platform and the object is detected in real time. When the distance between the two is less than a certain threshold, the platform stops moving and the robotic arm grabs the object.

[0011] (3) Based on the forward kinematics theory of redundant robotic arms and the kinematics theory of bottom moving platform, a dynamic model of mobile redundant robotic arm platform based on robot forward kinematics is established.

[0012] (4) Establish an optimization model for the mobile redundant robotic arm platform. The optimization model takes the energy loss of the robotic arm joints and the mobile platform as the optimization index, the angular velocity of the robotic arm joints and the movement speed of the bottom mobile platform as the decision variables, and the physical limitations of the robotic arm and the mobile platform as the constraints. For the robotic arm, the maximum allowable rotation angle and the maximum angular velocity of its joints are used as constraints. For the bottom mobile platform, its position and speed relative to the end of the robotic arm are used as constraints.

[0013] (5) The objective function and corresponding constraints proposed in the mobile redundant robotic arm platform optimization model are transformed into a corresponding quadratic optimization problem. The global position of the robotic arm end, each joint of the robotic arm and the target trajectory at the current moment are used as inputs to solve the angular velocity of each joint of the robotic arm and the component velocities in each direction of the bottom moving platform at the next moment, so as to realize the real-time tracking of the target trajectory by the robotic arm end.

[0014] Preferably, in step (2), the object grasping method based on image recognition is as follows: first, a distance threshold dist0 is set, then the image captured by the camera is recognized, and the distance dist between the grasped object and the mobile redundant robotic arm platform at the current moment is measured based on the obtained image. t When dist0 ≤ dist t When the bottom moving platform continues to move forward at the set speed; when dist0 ≥ dist tAt that moment, the bottom moving platform immediately stops moving, and the robotic arm begins to grasp the object.

[0015] Preferably, in step (3), the dynamic model of the mobile redundant robotic arm platform based on the robot's forward kinematics is described mathematically as follows:

[0016]

[0017] in Let be the velocity of the robotic arm's end effector in the global Cartesian coordinate system at time t. Let be the velocity of the bottom moving platform in the global Cartesian coordinate system at time t. Let f(θ) be the Jacobian matrix of the angular velocities of the robotic arm joints, f(θ) be the given forward transformation function of the robotic arm, which is related to the physical structure of the robotic arm, and θ be the angles of each joint of the robotic arm. Let t be the angular velocity of each joint of the robotic arm.

[0018] Preferably, in step (4), the objective function of the mobile redundant robotic arm platform optimization model is defined as:

[0019]

[0020] Where ||·|| represents the Euclidean norm, and α∈[0,1] is a weighting coefficient used to adjust the ratio between the kinetic energy of the robotic arm joints and the kinetic energy of the moving platform. Let be the angular velocities of each joint of the robotic arm. Let θ represent the speed of the bottom moving platform, and Ω represent the feasible region of the optimization variables, which is determined by their corresponding constraints.

[0021] Preferably, in step (4), the constraints of the mobile redundant robotic arm platform optimization model are expressed as follows:

[0022]

[0023]

[0024] Among them, θ, θ min θ max These represent the angles and angular velocities of each joint of the robotic arm, and the minimum and maximum allowable angles of rotation for each joint of the robotic arm, respectively. p min p max Representing the mobile platform's position, speed, minimum and maximum allowed positions, respectively, r, σ and γ represent the position and velocity of the robotic arm's end effector in the global coordinate system, respectively; σ and γ are the corresponding scaling factors, used to dynamically update the feasible domain of the corresponding variables.

[0025] Preferably, the quadratic optimization problem of the transformation in step (5) is expressed as follows:

[0026]

[0027] subject to Ax=b,

[0028] l≤x≤h,

[0029] Where Q = diag{(1-α)I} m ,αI n}, The vector represents the composite vector of joint angular velocity and mobile platform velocity. l and h represent the lower and upper bounds of variable x, respectively. A and b are determined by the dynamic model of the mobile redundant manipulator platform. I is the identity matrix, m is the number of manipulator joints, and n is the dimension of the task space.

[0030] Preferably, in step (5), a fixed-step-size optimization algorithm is used for solving the problem, and its iterative format is as follows:

[0031]

[0032] Where Proj(·) is the projection operator, and its upper and lower bounds are h, l, y. t Let λ be the iteration step size and k be the number of iterations, which are the dual variables. Here, denoted by 'gradient', and eig represents the eigenvalues ​​of the matrix.

[0033] Based on the same inventive concept, this invention provides a real-time grasping and trajectory tracking system for a mobile redundant robotic arm based on optimization theory. The system employs a wheeled robot, a redundant robotic arm, and a camera to form a mobile redundant robotic arm platform. It includes a grasping module and a trajectory tracking module. The grasping module utilizes the camera's image detection and recognition capabilities to detect the distance between the platform and the object in real time. When the distance is less than a certain threshold, the platform stops moving, and the robotic arm grasps the object. The trajectory tracking module is used to construct a dynamic model of the mobile redundant robotic arm platform based on the forward kinematics theory of the redundant robotic arm and the kinematics theory of the bottom moving platform. It also constructs an optimization model of the mobile redundant robotic arm platform, which is based on the robotic arm's... The optimization index is the kinetic energy loss of the joints and the mobile platform. The decision variables are the angular velocity of the robotic arm joints and the motion speed of the bottom mobile platform. The physical limitations of the robotic arm and the mobile platform are the constraints. For the robotic arm, the maximum allowable rotation angle and maximum angular velocity of its joints are the constraints. For the bottom mobile platform, the position and velocity relative to the end effector of the robotic arm are the constraints. The objective function and corresponding constraints proposed in the mobile redundant robotic arm platform optimization model are transformed into a corresponding quadratic optimization problem. The global position of the end effector of the robotic arm, each joint of the robotic arm, and the target trajectory at the current moment are used as inputs to solve for the angular velocities of each joint of the robotic arm and the component velocities of the bottom mobile platform in each direction at the next moment, so as to realize the real-time tracking of the target trajectory by the end effector of the robotic arm.

[0034] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:

[0035] 1) Compared to most robotic arm trajectory control methods that are only applicable to independent robotic arms and whose operable range is limited to their arm length, the mobile redundant robotic arm trajectory control method based on optimization theory proposed in this invention overcomes this deficiency. Introducing a movable base to the robotic arm significantly increases its working range, enabling the system to better perform industrial activities such as transporting goods and collaborative handling, thus allowing for wider application.

[0036] 2) Compared with most robotic arm trajectory control methods that use mechanical equations to solve the joint internal forces, such as the Newton-Euler method, Lagrange method, Kane's equation method and virtual work principle method, which have the disadvantages of complex dynamic model format and cumbersome calculation process, the mobile redundant robotic arm trajectory control method based on optimization theory proposed in this invention directly models the positive kinematics of the robotic arm. The model has the characteristics of being simple and easy to solve, which greatly reduces the space and time resources consumed in the solution process.

[0037] 3) This invention takes kinetic energy loss as the optimization objective and uses a fixed step-size constraint optimization algorithm to solve the joint angular velocity of the robotic arm and the speed of the moving platform. While achieving accurate trajectory tracking, the algorithm's low time complexity ensures its real-time performance, enabling it to calculate the optimal speed for the next moment based on its current real-time state. Attached Figure Description

[0038] Figure 1 This is a detailed flowchart of the present invention;

[0039] Figure 2 This is a schematic diagram of the equipment used in this invention;

[0040] Figure 3 This is a schematic diagram of the device position before the grasping operation of this invention;

[0041] Figure 4 This is a schematic diagram illustrating the object-grabbing operation achieved by using AR codes in this invention.

[0042] Figure 5 This is a time-error graph of executing a single algorithm in the physical experiment of this invention;

[0043] Figure 6 This is a graph showing the speed variation of the moving platform in the physical experiment of this invention;

[0044] Figure 7 This is a graph showing the change in the joint angular velocity of the robotic arm during the physical experiment of this invention;

[0045] Figure 8 This is a diagram of the actual trajectory of the robotic arm's end effector in the physical experiment of this invention. Detailed Implementation

[0046] The invention's objectives, technical solutions, and advantages will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Most robotic arm trajectory control methods are only applicable to standalone robotic arms, with their operable range limited to the arm's length. Furthermore, the modeling of most methods is complex, hindering rapid algorithm development. This clearly does not meet the real-time control requirements of robotic arm trajectory control. Figure 1 As shown, the present invention utilizes as follows Figure 2 The device shown provides a real-time grasping and trajectory tracking method for a mobile redundant robotic arm based on optimization theory. It employs a wheeled robot, a redundant robotic arm, and a camera to form a mobile redundant robotic arm platform, specifically including the following steps:

[0048] I. Object Grabbing Based on AR Image Recognition

[0049] First, a distance threshold dist0 is set. Then, the AR images captured by the camera are identified, and the distance dist from the grasped object to the mobile redundant robotic arm platform at each time step is measured based on the obtained images. t :

[0050] When dist0≤dist t At that time, the mobile platform continues to move forward at a certain speed, such as... Figure 3 As shown;

[0051] When dist0≥dist t At that moment, the mobile platform immediately stops moving, and the robotic arm begins to grasp the object, such as... Figure 4 As shown.

[0052] II. Establishing a dynamic model of a mobile redundant robotic arm platform based on robot forward kinematics

[0053] This model is based on the forward kinematics theory of redundant robotic arms. It describes the change in the position of the robotic arm's end effector in the global Cartesian coordinate system, considering the relative motion between the robotic arm and the underlying mobile platform. Subsequently, it describes the change in the velocity of the mobile platform in the global Cartesian coordinate system by combining the kinematic relationship between displacement and time. The combination of these two models constitutes the dynamic model of a mobile redundant robotic arm platform based on the robot's forward kinematics, enabling the robotic arm's end effector to track specific trajectories. The specific process is as follows:

[0054] Based on the robot arm's parameters and forward kinematics, the mapping relationship f(·):θ→p' from the robot arm's joint space to its task space is determined.

[0055] p'(t)=f(θ(t))

[0056] Where p'(t)∈R n Let θ(t) represent the three-dimensional coordinates of the robotic arm's end effector based on its own base. m Let represent the angles of each joint of the robotic arm at time t, f represent the coordinate transformation matrix of the robotic arm, m represent the number of joints of the robotic arm, and n represent the dimension of the task space.

[0057] Based on the motion law of the mobile platform, its real-time position p(t) is obtained, and finally, the three-dimensional coordinates r(t) of the robotic arm end effector in the global coordinate system are obtained:

[0058] r(t) = p(t) + f(θ(t))

[0059] Differentiating the equation yields the velocity relationship among the three components, which is the dynamic model of the mobile redundant robotic arm platform:

[0060]

[0061] in Let be the velocity of the robotic arm's end effector in the global coordinate system at time t. Let be the velocity of the bottom moving platform in the global coordinate system at time t. Here is the Jacobian matrix for the angular velocities of the robotic arm joints. Let t be the angular velocity of each joint of the robotic arm.

[0062] III. Establishing an optimization model for a mobile redundant robotic arm platform based on kinetic energy loss.

[0063] This model uses the energy loss of the robotic arm joints and the moving platform as the optimization index, and establishes a corresponding optimization model with the angular velocity of the robotic arm joints and the movement speed of the bottom moving platform as decision variables. Based on this model, the optimal angular velocity of the robotic arm joints and the optimal movement speed of the bottom moving platform at each moment are solved to minimize the system's energy loss. The specific description is as follows:

[0064] Using the system's energy loss as the optimization index, an objective function for the kinetic energy loss of the robotic arm joints and the moving platform is established, defined as:

[0065]

[0066] Where ||·|| represents the Euclidean norm, and α∈[0,1] is a weighting coefficient used to adjust the ratio between the kinetic energy of the robotic arm joints and the kinetic energy of the mobile platform.

[0067] IV. Propose constraints for constructing a mobile redundant robotic arm platform based on physical limitations.

[0068] The constraints take into account the physical limitations imposed on the robotic arm and the mobile platform by the hardware. For the robotic arm, the maximum allowable angle of joint rotation and the maximum angular velocity of the joint are used as constraints. For the bottom mobile platform, the position and velocity relative to the end of the robotic arm are used as constraints.

[0069] First, the relationship between the end effector velocity of the robotic arm and the angular velocity of its joints must be satisfied:

[0070]

[0071] in Let t be the preset velocity of the robotic arm's end effector in the global coordinate system at time t.

[0072] The relevant constraints caused by physical hardware are:

[0073] θ min ≤θ≤θ max ,

[0074]

[0075] p min ≤pr≤p max ,

[0076]

[0077] Where θ min ,θ max p represents the minimum and maximum allowable rotation angles of each joint of the robotic arm, respectively. min ,p max These represent the minimum and maximum positions that the mobile platform is allowed to reach, respectively. Specifically, based on the specific physical meaning of the variables, the last four constraints can be updated as follows:

[0078]

[0079]

[0080] Where σ and γ are the corresponding scaling factors, used to dynamically update the feasible region of the corresponding variables.

[0081] Furthermore, the above formula can be transformed into:

[0082]

[0083]

[0084] Where, θ - The i-th element is represented as θ + The i-th element is represented as p - The j-th element is represented as The j-th element is represented as

[0085] Furthermore, considering that the mobile platform has 2 degrees of freedom, it has no velocity component in the z-direction, and this constraint is expressed as follows:

[0086]

[0087] Where the matrix As a constraint matrix in the z-direction.

[0088] V. Solving the model using a constraint optimization algorithm based on a fixed step size.

[0089] Combining the objective function and constraints proposed in steps three and four, the optimization problem can be written as a quadratic programming problem as follows:

[0090]

[0091] subject to Ax=b,

[0092] l≤x≤h,

[0093] Where Q = diag{(1-α)I} m ,αI n}, This represents the composite vector of joint angular velocity and moving platform velocity. l=((p - ) T ,(θ - ) T ) T , h=((p + ) T ,(θ + ) T ) T .

[0094] Finally, a constrained optimization algorithm with a fixed step size is used to solve the problem, and its iterative format is as follows:

[0095]

[0096] Where Proj(·) is the projection operation, and its upper and lower bounds are h, l, y. t Let λ be the dual variable and λ be the iteration step size.

[0097] After solving the problem using a constrained optimization algorithm with a fixed step size, the angular velocities of the robotic arm joints and the velocity of the moving platform at time t+1 are obtained. t+1 Then, the speed value is input into the mobile robotic arm system and executed. After the execution is completed, the real-time position r(t+1) of the robotic arm end is read.

[0098] Once all time points have been sampled, the mobile redundant robotic arm platform reaches the designated position, and the system stops moving.

[0099] The following is a physical experiment demonstrating the real-time trajectory tracking method for a mobile redundant robotic arm platform based on optimization theory designed in this invention. This experiment uses a TurtleBot3 Waffle_Pi nonholonomically constrained wheeled robot, an OpenManipulator-X redundant robotic arm, and a Raspberry Camera V2 to form a mobile redundant robotic arm platform. The dimensions m of the robotic arm joint velocity vector and n of the end-effector position vector are n=3 and m=4, respectively. The weighting coefficient α=0.8, and the maximum and minimum velocities of the mobile platform are... The maximum and minimum angular velocities of the robotic arm joints are The preset trajectory equation is:

[0100]

[0101]

[0102]

[0103] Experimental results are as follows Figure 5-8 As shown. Figure 5 This shows the change in error convergence during one execution of the algorithm, as seen at t=10. -4 The error converged to the preset value of 1×10 in approximately s. -3 The figure shows that the fixed-step-size constraint optimization algorithm is accurate and real-time in real-time trajectory planning. Figure 6 This displays the changes in the mobile platform's speed throughout the entire real-time trajectory planning process. Figure 7 This displays the changes in the angular velocity of the robotic arm joints throughout the entire real-time trajectory planning process. Figure 6 and Figure 7 It was verified that the speed of the robotic arm joints and the speed of the moving platform are continuous and meet the set constraints, and can respond quickly according to the real-time status of the system. Figure 8 This displays the real-time position of the robotic arm's end effector, and its trajectory matches the preset trajectory, verifying the accuracy of the method.

[0104] The above experimental results show that the real-time trajectory tracking method for the mobile redundant robotic arm platform based on optimization theory designed in this invention is accurate and fast, and can effectively achieve real-time accurate tracking of the preset trajectory, with satisfactory results in actual object handling application scenarios.

[0105] Based on the same inventive concept, this invention provides a real-time grasping and trajectory tracking system for a mobile redundant robotic arm based on optimization theory. The system employs a wheeled robot, a redundant robotic arm, and a camera to form a mobile redundant robotic arm platform. It includes a grasping module and a trajectory tracking module. The grasping module utilizes the camera's image detection and recognition capabilities to detect the distance between the platform and the object in real time. When the distance is less than a certain threshold, the platform stops moving, and the robotic arm grasps the object. The trajectory tracking module is used to construct a dynamic model of the mobile redundant robotic arm platform based on the forward kinematics theory of the redundant robotic arm and the kinematics theory of the bottom moving platform. It also constructs an optimization model of the mobile redundant robotic arm platform, which is based on the robotic arm joints. The optimization index is the kinetic energy loss of the mobile platform. The decision variables are the angular velocity of the robotic arm joints and the motion speed of the bottom mobile platform. The physical limitations of the robotic arm and mobile platform are the constraints. For the robotic arm, the constraints are its maximum allowable joint rotation angle and maximum joint angular velocity. For the bottom mobile platform, the constraints are its position and velocity relative to the robotic arm's end effector. The objective function and corresponding constraints proposed in the mobile redundant robotic arm platform optimization model are transformed into a corresponding quadratic optimization problem. Using the global position of the robotic arm's end effector, the joints of the robotic arm, and the target trajectory at the current moment as input, the problem solves for the angular velocities of the robotic arm's joints and the component velocities of the bottom mobile platform in each direction at the next moment, thereby achieving real-time tracking of the target trajectory by the robotic arm's end effector. Specific implementation details are detailed in the above method embodiments and will not be repeated here.

Claims

1. A method for real-time grasping and trajectory tracking with a mobile redundant robotic arm, characterized in that, Includes the following steps: (1) A mobile redundant robotic arm platform is formed by combining a wheeled robot, a redundant robotic arm and a camera. (2) Using the camera's image detection and recognition function, the distance between the platform and the object is detected in real time. When the distance between the two is less than a certain threshold, the platform stops moving and the robotic arm grabs the object. (3) Based on the forward kinematics theory of redundant robotic arms and the kinematics theory of bottom moving platform, a dynamic model of mobile redundant robotic arm platform based on robot forward kinematics is established. (4) Establish an optimization model for the mobile redundant robotic arm platform. The optimization model takes the energy loss of the robotic arm joints and the mobile platform as the optimization index, the angular velocity of the robotic arm joints and the movement speed of the bottom mobile platform as the decision variables, and the physical limitations of the robotic arm and the mobile platform as the constraints. For the robotic arm, the maximum allowable rotation angle and the maximum angular velocity of its joints are used as constraints. For the bottom mobile platform, its position and speed relative to the end of the robotic arm are used as constraints. (5) The objective function and corresponding constraints proposed in the mobile redundant robotic arm platform optimization model are transformed into a corresponding quadratic optimization problem. The global position of the robotic arm end, each joint of the robotic arm and the target trajectory at the current moment are used as inputs to solve the angular velocity of each joint of the robotic arm and the component velocities in each direction of the bottom moving platform at the next moment, so as to realize the real-time tracking of the target trajectory by the robotic arm end.

2. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 1, characterized in that, In step (2), the object grasping method based on image recognition is as follows: First, a distance threshold dist0 is set, then the image captured by the camera is recognized, and the distance dist between the grasped object and the mobile redundant robotic arm platform at the current moment is measured based on the obtained image. t When dist0 ≤ dist t When the bottom moving platform continues to move forward at the set speed; when dist0 ≥ dist t At that moment, the bottom moving platform immediately stops moving, and the robotic arm begins to grasp the object.

3. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 1, characterized in that, In step (3), the dynamic model of the mobile redundant robotic arm platform based on the robot's forward kinematics is described mathematically as follows: in Let be the velocity of the robotic arm's end effector in the global Cartesian coordinate system at time t. Let be the velocity of the bottom moving platform in the global Cartesian coordinate system at time t. Let f(θ) be the Jacobian matrix of the angular velocities of the robotic arm joints, f(θ) be the given forward transformation function of the robotic arm, which is related to the physical structure of the robotic arm, and θ be the angles of each joint of the robotic arm. Let t be the angular velocity of each joint of the robotic arm.

4. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 1, characterized in that, In step (4), the objective function of the mobile redundant robotic arm platform optimization model is defined as: Where ||·|| represents the Euclidean norm, and α∈[0,1] is a weighting coefficient used to adjust the ratio between the kinetic energy of the robotic arm joints and the kinetic energy of the moving platform. Let be the angular velocities of each joint of the robotic arm. Let θ represent the speed of the bottom moving platform, and Ω represent the feasible region of the optimization variables.

5. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 1, characterized in that, In step (4), the constraints of the mobile redundant robotic arm platform optimization model are expressed as follows: Among them, θ, θ min θ max These represent the angle and angular velocity of each joint of the robotic arm, and the minimum and maximum allowable angles of rotation for each joint of the robotic arm, respectively; p, p min p max Representing the mobile platform's position, speed, minimum and maximum allowed positions, respectively, r, σ and γ represent the position and velocity of the robotic arm's end effector in the global coordinate system, respectively; σ and γ are the corresponding scaling factors, used to dynamically update the feasible domain of the corresponding variables.

6. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 1, characterized in that, In step (5), the secondary optimization problem of the transformation is expressed as follows: subject to Ax=b, l≤x≤h, Where Q = diag{(1-α)I} m ,αI n }, Represents joint angular velocity and mobile platform speed The composite vector, l and h represent the lower and upper bounds of variable x, respectively, A and b are determined by the dynamic model of the mobile redundant manipulator platform, I is the identity matrix, m is the number of manipulator joints, n is the dimension of the task space, and α∈[0,1] is the weight coefficient.

7. The method for real-time grasping and trajectory tracking of a mobile redundant robotic arm according to claim 6, characterized in that, In step (5), a fixed-step-size optimization algorithm is used to solve the problem, and its iterative format is as follows: Where Proj(·) is the projection operator, and its upper and lower bounds are h, l, y. t Let λ be the iteration step size and k be the number of iterations, which are the dual variables. Here, denoted by 'gradient', and eig represents the eigenvalues ​​of the matrix.

8. A mobile redundant robotic arm real-time grasping and trajectory tracking system, characterized in that, The system uses a wheeled robot, a redundant robotic arm, and a camera to form a mobile redundant robotic arm platform; it is equipped with a grasping module and a trajectory tracking module. The grasping module uses the camera's image detection and recognition function to detect the distance between the platform and the object in real time. When the distance between the two is less than a certain threshold, the platform stops moving and the robotic arm grasps the object. The trajectory tracking module is used to establish a dynamic model of the mobile redundant manipulator platform based on the forward kinematics theory of the redundant manipulator and the kinematics theory of the bottom moving platform. A mobile redundant robotic arm platform optimization model was established. This model uses the energy loss of the robotic arm joints and the mobile platform as the optimization index, the angular velocity of the robotic arm joints and the motion speed of the bottom mobile platform as decision variables, and the physical limitations of the robotic arm and the mobile platform as constraints. For the robotic arm, the maximum allowable rotation angle and maximum angular velocity of its joints are used as constraints. For the bottom mobile platform, its position and velocity relative to the end effector of the robotic arm are used as constraints. The model also transforms the objective function and corresponding constraints proposed in the mobile redundant robotic arm platform optimization model into a corresponding quadratic optimization problem. Using the global position of the end effector of the robotic arm, the joints of the robotic arm, and the target trajectory at the current moment as input, the model solves for the angular velocities of the joints of the robotic arm and the component velocities of the bottom mobile platform in each direction at the next moment, so as to achieve real-time tracking of the target trajectory by the end effector of the robotic arm.

9. The real-time grasping and trajectory tracking system for a mobile redundant robotic arm according to claim 8, characterized in that, In the trajectory tracking module, the dynamic model of the mobile redundant robotic arm platform based on the robot's forward kinematics is mathematically described as follows: in Let be the velocity of the robotic arm's end effector in the global Cartesian coordinate system at time t. Let be the velocity of the bottom moving platform in the global Cartesian coordinate system at time t. Let f(θ) be the Jacobian matrix of the angular velocities of the robotic arm joints, f(θ) be the given forward transformation function of the robotic arm, which is related to the physical structure of the robotic arm, and θ be the angles of each joint of the robotic arm. Let t be the angular velocity of each joint of the robotic arm.

10. The real-time grasping and trajectory tracking system for a mobile redundant robotic arm according to claim 8, characterized in that, In the trajectory tracking module, the objective function of the mobile redundant robotic arm platform optimization model is defined as: Where ||·|| represents the Euclidean norm, and α∈[0,1] is a weighting coefficient used to adjust the ratio between the kinetic energy of the robotic arm joints and the kinetic energy of the moving platform. Let be the angular velocities of each joint of the robotic arm. Let θ represent the speed of the bottom moving platform, and Ω represent the feasible region of the optimization variables. The constraints of the optimization model for the mobile redundant robotic arm platform are expressed as follows: Among them, θ, θ min θ max These represent the angles and angular velocities of each joint of the robotic arm, and the minimum and maximum allowable angles of rotation for each joint of the robotic arm, respectively. p min p max Representing the mobile platform's position, speed, minimum and maximum allowed positions, respectively, r, σ and γ represent the position and velocity of the robotic arm's end effector in the global coordinate system, respectively; σ and γ are the corresponding scaling factors, used to dynamically update the feasible domain of the corresponding variables.

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