Performance constraint control method and system for multi-robot collaborative carrying of large workpieces

Abstract

The invention discloses a performance constraint control method and system for multi-robot collaborative carrying of large workpieces. The method comprises the steps that firstly, a unit quaternion is adopted to establish a coupling dynamic model containing closed-chain constraint under a task reference coordinate system; secondly, designing a completely distributed finite time observer, and performing consistency estimation on a global reference trajectory only through neighborhood communication; secondly, designing a consistency indicator function based on the estimated value, gradually activating a performance constraint function only after an observation error is converged so as to apply transient and steady-state performance boundaries, and generating an expected motion state of each robot; and finally, designing a distributed robust adaptive controller to realize trajectory tracking. According to the method, singularity is avoided through quaternion modeling, controller design of a task reference coordinate system is achieved through rigid body transformation, dependence on a centroid coordinate system is avoided, the requirement for a priori track is eliminated through a distributed observer, constraint conflicts are avoided through a strategy of'feasibility first and then constraint ', and the robustness of the system is improved. And the safety, the precision and the robustness of collaborative carrying are effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing technology, and in particular relates to a method and system for performance constraint control of multi-robot collaborative handling of large workpieces. Background Technology

[0002] Compared to traditional fixed manipulators, mobile manipulators combine the dexterity of robotic arms with the mobility of mobile chassis, thus significantly expanding the workspace. Faced with the handling and processing of large, heavy-duty, structurally diverse, and parameter-determined workpieces, the requirements for system robustness and adaptability are constantly increasing. In this context, multi-robot collaboration, with its advantages of division of labor and parallelism, spatial coverage, and redundancy tolerance, can improve efficiency and system resilience, providing a more flexible organizational approach for complex manufacturing. Therefore, collaborative operation of multiple mobile manipulators has become a promising solution. However, once multiple robots rigidly and jointly grasp the same load, the system transforms into a mechanism subject to strict kinematic and dynamic closed-loop constraints, significantly complicating the control problem.

[0003] To achieve collaborative object transport along a predetermined trajectory, existing research has proposed three control paradigms: centralized, decentralized, and distributed. Distributed control relies on local communication to improve overall performance. However, current research typically assumes that each robot knows the reference trajectory beforehand, an assumption that is often difficult to apply in real-world distributed scenarios. To compensate for this deficiency, researchers have developed control methods based on distributed observations. However, the convergence of individual observers still depends on global topological information, limiting the implementation of a fully distributed system and its scalability. Meanwhile, compared to Euler angles, the pose representation of unit quaternions avoids singularities and is more suitable for engineering applications. On the other hand, pre-defined performance controls can force the system to meet given transient and steady-state indices; however, when the reference trajectory is unknown and the observation error has not yet converged, directly applying performance constraints can easily conflict with closed-chain kinematic constraints, leading to task infeasibility or even instability. Therefore, a more prudent strategy is to first ensure that the closed-chain kinematic constraints are satisfied, and then gradually activate performance constraints after the estimation error converges, thus avoiding conflict between the two mechanisms.

[0004] Based on the above understanding, this invention proposes a performance constraint control method and system for multi-robot collaborative handling of large workpieces. Summary of the Invention

[0005] To address the above technical problems, this invention provides a method and system for performance constraint control of multi-robot collaborative handling of large workpieces.

[0006] The technical solution adopted by this invention to solve its technical problem is: A method for performance constraint control of multi-robot collaborative handling of large workpieces, the method comprising the following steps: S100. Unit quaternions are used to represent the poses of the object and the end effectors of each mobile robot. The kinematic and dynamic relationship between the robot and the object to be transported is described in the task reference coordinate system. Combined with the closed-chain kinematic constraints formed by the cooperative transport of large objects, a coupled dynamic model of cooperative transport of multiple mobile robots is obtained. S200. By utilizing the information interaction among multiple mobile robot neighbors, a fully distributed finite-time observer is designed to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. Based on the reference estimate of S200, a consistency-driven indicator function and a preset performance error transformation are designed: when the consistency indicator function indicates that the neighborhood observation error has not converged, no performance constraint is applied; when the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is gradually activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and the expected velocity and acceleration of each robot under the performance constraints are generated accordingly. Based on the expected velocity and acceleration generated by S400 and S300, a robust distributed performance constraint controller is designed for each robot to track the global reference trajectory, ensuring that the closed-loop system signal is bounded and that the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

[0007] Preferably, S100 includes: S110: Establish the first The dynamic model of the mobile robot system is as follows: ; in, It is the mass inertia matrix of the i-th mobile robot. The matrix represents the centripetal force and the Coriolis force. Represents the gravity vector. Here is the constraint matrix for the mobile robot. It is the input transformation matrix of the mobile robot. To control the input, Nonholonomic constraints on the end effector of a mobile robot and complete constraint force , Let be the generalized joint coordinates of the mobile robot, where For the pose of the mobile platform, This refers to the joint angle position of the robotic arm. Represent The first and second derivatives, Represents the total number of mobile robots. Indicates transpose; S120: Considering the... The non-holonomic constraints of each mobile platform are To obtain the reduced joint velocities , so that: ; in, yes The null space matrix satisfies , For the first Non-holonomic constraint matrices for each mobile platform For the first The generalized velocity vector of each mobile platform; therefore, multiply both sides of the dynamic model of the mobile robot in S110 by the projection matrix. Its dynamic model is rewritten as follows: ; in, The reduced Coriolis force matrix, , , , These are the block submatrices of the original inertia matrix. , , , These are the block submatrices of the original Coriolis force matrix. The input transformation matrix after order reduction. , This is a block diagonal submatrix of the original input transformation matrix. The reduced-order system inertia matrix, This is the reduced-order control input vector. This is the reduced gravity vector. , These are the block sub-vectors of the original gravity vector. The Jacobian matrix of the robot end effector after order reduction. , These are the block submatrices of the original Jacobian matrix. This is the generalized state vector after order reduction. This refers to the spinor of the external force acting on the end effector of the mobile robot.

[0008] Preferably, S100 further includes: S130: Establish the dynamic model of the object, specifically as follows: ; in, It is the mass-inertia matrix of the object. The matrix representing the centripetal and Coriolis forces of an object. It is the object's gravitational vector. The resultant force of multiple mobile robots acting on the center of mass of an object. and These are the object's pose and velocity spinor, respectively. S140: Velocity spinor based on the object's center of mass Velocity spinor with reference point Relationship: Substitute S130 and multiply on the left side of both sides of the equation. The dynamic model of the object in S130 is rewritten as follows: ; in, Here are the centripetal and Coriolis force matrices of the object in the reference coordinate system. Represents the pose of the task reference point on the object. The inertia matrix of the object in the reference coordinate system. The net force acting on an object The gravitational vector of an object. Let be the velocity mapping matrix between the reference point and the center of mass of the object. for The derivative; S150: Considering the... Load allocation coefficient matrix for each mobile robot and the The indirect force exerted by the end effector of a mobile robot on a reference point of an object. ,and Decomposed into operating force and internal strength ,Right now , No. The operational power of a mobile robot Written as: ; Wherein, the load distribution coefficient matrix satisfies The sum of internal forces satisfies ; S160: Based on kinematic relationships achievable ,in, For the robot's end effector speed, Let Jacobian be the kinematics from the object to the robot's end effector. The kinematic Jacobian of the robot from its joints to its end effector. For Jacobian matrices, for The pseudo-inverse matrix; therefore, the first... The dynamic equations of the coupling between a mobile robot and an object can be written as follows: ; in, The matrix of centripetal and Coriolis forces coupled between the robot and the object. Press the button on the robot The proportion of the Coriolis force borne by the object. This represents the coupled gravity vector between the robot and the object. Press the button on the robot The proportion of the object's weight that is borne by the proportion. For the equivalent input vector, The coupling inertia matrix between the robot and the object. Press the button on the robot The proportion of an object's inertia.

[0009] Preferably, in S200, the fully distributed finite-time observer is designed to estimate the ideal trajectory of the task reference point. Expected speed and expected acceleration , set up a robot The output of the observer is defined as , , Its specific form is: ; in, The ideal trajectory for the mission reference point, including location and attitude quaternions , The expected velocity at the mission reference point, including linear velocity. and angular velocity , The expected acceleration for the task reference point, including linear acceleration. and angular acceleration , , , For the observer pair of robot i , , The estimated value, observer gain fractional power , The consistency error of the expected location observations, The consistency error of the expected linear velocity observations, To account for the consistency error of the expected linear acceleration observations, The consistency error of the expected attitude quaternion observations, The consistency error of the expected angular velocity observations, The consistency error of the expected angular acceleration observations is specifically defined as: ; in, and These are the expected positions of robot i relative to the task reference point. and attitude quaternions The estimated value, and These are the expected linear velocities of robot i relative to the task reference point. and angular velocity The estimated value, and These are the expected linear accelerations of robot i about the task reference point. and angular acceleration The estimated value, It is the robot j's pose quaternion The estimated value The conjugate quaternion, It is the expected posture The conjugate quaternion. Furthermore, adaptive gain. and By adaptive law And adaptive law Updated to: ; in, Let i be the set of its neighbors. It is a binary indicator coefficient. It is a positive definite symmetric matrix. , Let be the estimated positions of the i-th and j-th robots in direction d, respectively. This is a reference value for the desired location. Let be the estimated pose of the i-th robot in direction d. Let be the estimated angular velocity of the i-th robot in direction d. This is the projection operator.

[0010] Preferably, the consistency indicator function in S300 Defined as: ; in, Let the consistency error function of neighbor observations be sum, and the constant satisfy... ,and It is a sufficiently small positive number.

[0011] Preferably, in S300, the preset performance error transformation is defined by the robot. Error transformation function vector To achieve, among which, For the position error transformation subvector, The attitude error transformation sub-vector, the error transformation vector The specific definition of the j-th element is: ; in, Represents robots pose tracking error The j-th element, and These represent position tracking error and attitude tracking error, respectively. Indicates a reference position. Indicates the reference posture. This represents the pose quaternion of robot i. The estimated value The conjugate quaternion, function and These are the upper and lower bounds of the consistency-driven performance constraint, respectively, and are explicitly defined as follows: ; in, The functions represent the maximum steady-state tracking errors at the upper and lower boundaries of the performance constraints, respectively. Defined as: ; in, express The exact time of its initial establishment This is the preset transition time constant.

[0012] Preferably, the design of the robust distributed performance constraint controller in S400 includes: S410: Define the augmented pose tracking error as: ; in, It is integral gain. It is half the width of the integration time window. and At time i and neighbor robot j, respectively The tracking error vector, It is a smooth window function, defined as: ; Differentiate the augmented pose tracking error and use the relation have: ; in, The velocity transformation matrix is ​​a performance constraint. , For parameters related to performance constraints, Let Jacobian matrix be the result of the error transformation. For speed error; S420: To simultaneously achieve consensus-driven performance constraints and consensus among neighbors, the robot... Reference speed Designed as follows: ; in, It is a positive definite symmetric matrix. Let i be the observer's expected velocity relative to the task reference point. The estimated value, for The inverse matrix, The value of the smooth window function at the current time. This is the time derivative of the window function; Therefore, the speed tracking error is constrained by performance. Defined as: ; And, actual reference speed The derivative is: ; in, for The derivative of for The derivative; S430: Multiply both sides of the S160 formula by the velocity transformation matrix of the performance constraint. The following error dynamics exist: ; in, The inertia matrix is ​​constrained by performance. The Coriolis force matrix is ​​a performance constraint. Coupled dynamics at the reference velocity, For the control input of robot i, where , and These represent the coupled inertia matrix between robot i and the object in the task reference coordinate system, the centripetal force and Coriolis force matrices, and the gravity vector, respectively; it is worth noting that... It can be linearly parameterized, i.e., a dynamic regression matrix exists. and dynamic parameter vector , making Therefore, the following distributed performance constraint control law is designed: ; in, The control gain matrix is ​​positive definite. It is a dynamic parameter vector The estimated value, For robust items The estimated value; right The parameter estimation error is defined as , right The parameter estimation error is defined as , Adaptive law and Adaptive law The specific expression is as follows: ; Wherein, the adaptive gain matrix It is a positive definite diagonal matrix with adaptive gain. It is a normal number.

[0013] A performance constraint control system for multi-robot collaborative handling of large workpieces includes: The coupled dynamics model building module is used to represent the pose of the object and the end effector of each mobile robot using unit quaternions. It describes the kinematic and dynamic relationship between the robot and the object to be transported in the task reference coordinate system. Combined with the closed-chain kinematic constraints formed by the cooperative transport of large objects, a coupled dynamic model of multi-mobile robot cooperative transport is obtained. The fully distributed finite-time observer design module is used to design a fully distributed finite-time observer by utilizing the information interaction between multiple mobile robot neighbors, to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. The desired state determination module under performance constraints is used to design a consistency-driven indicator function and a preset performance error transformation based on the reference estimate: when the consistency indicator function indicates that the neighborhood observation error has not converged, no performance constraint is applied; when the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is asymptotically activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and thereby generate the desired velocity and acceleration of each robot under performance constraints. The distributed control law construction module is used to design a robust distributed performance constraint controller for each robot based on the desired velocity and acceleration under performance constraints, so as to achieve tracking of the global reference trajectory and ensure that the closed-loop system signal is bounded and the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

[0014] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a performance constraint control method for multi-robot collaborative handling of large workpieces.

[0015] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a performance constraint control method for multi-robot collaborative handling of large workpieces.

[0016] The aforementioned multi-robot collaborative handling method and system for large workpieces, by employing quaternions to describe the posture and uniformly modeling it in the task reference coordinate system, avoids Euler angle singularities and eliminates dependence on the object's centroid coordinate system, thus improving engineering practicality. Through the design of a fully distributed finite-time observer, the global reference trajectory can be accurately estimated within a finite time using only neighborhood communication, enhancing adaptability to distributed scenarios and incomplete information. By introducing a two-stage strategy of "feasibility first, constraint later" and a consistency indicator function, performance constraints are dynamically activated, effectively avoiding early conflicts with closed-chain kinematic constraints. Therefore, even under model uncertainty, the system can still ensure signal boundedness and that tracking errors meet preset performance requirements, significantly improving the safety, accuracy, and robustness of collaborative handling. Attached Figure Description

[0017] Figure 1 This is a flowchart of a performance constraint control method for multi-robot collaborative handling of large workpieces according to an embodiment of the present invention; Figure 2 This is a block diagram illustrating the principle of performance constraint control for multi-robot collaborative handling of large workpieces in one embodiment of the present invention. Detailed Implementation

[0018] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0019] In one embodiment, such as Figure 1 As shown, a method for performance constraint control of multi-robot collaborative handling of large workpieces includes the following steps: S100. Unit quaternions are used to represent the poses of the object and the end effectors of each mobile robot. The kinematic and dynamic relationship between the robot and the object to be transported is described in the task reference coordinate system. Combined with the closed-chain kinematic constraints formed by the cooperative transport of large objects, a coupled dynamic model of cooperative transport of multiple mobile robots is obtained. S200. By utilizing the information interaction among multiple mobile robot neighbors, a fully distributed finite-time observer is designed to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. Based on the reference estimate of S200, a consistency-driven indicator function and a preset performance error transformation are designed: when the consistency indicator function indicates that the neighborhood observation error has not converged, no performance constraint is applied; when the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is gradually activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and the expected velocity and acceleration of each robot under the performance constraints are generated accordingly. Based on the expected velocity and acceleration generated by S400 and S300, a robust distributed performance constraint controller is designed for each robot to track the global reference trajectory, ensuring that the closed-loop system signal is bounded and that the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

[0020] This invention proposes a performance constraint control method for multi-robot collaborative handling of large workpieces. Addressing the challenges in collaborative handling by multiple mobile robot systems: (1) Existing control methods are mostly based on Euler angles or the object's centroid coordinate system, which easily introduces posture singularities and is complex to implement; (2) Existing research mainly focuses on stability or, given the prior reference trajectory, only provides semi-global performance guarantees related to initial conditions. However, in distributed scenarios, due to capability heterogeneity and incomplete information, not every robot can directly obtain the reference trajectory; (3) Collaborative handling of rigid objects creates a closed-chain kinematic constraint between end effectors. If only local information is relied upon to estimate the reference trajectory, the initial observation error is often large. If a preset performance constraint is forcibly applied at this time, it is easy to conflict with the closed-chain constraint, leading to infeasibility or instability. Each mobile robot addresses these challenges by: (1) Representing the robot and object's posture using quaternions, and... The kinematics and dynamics of the object and the end effector are described under the task reference frame, eliminating the Euler angle singularity and dependence on the object's centroid coordinate system, and realizing an engineering implementation that is singularity-free and independent of the object's centroid coordinate system; (2) For distributed scenarios, a fully distributed finite-time observer is designed for each robot, which can achieve consistent estimation of the global task reference pose and its derivatives by relying solely on neighborhood communication and ensure that the estimation error converges in finite time, thereby eliminating the dependence on the prior reference trajectory and providing a reliable reference trajectory for performance constraints; (3) In response to the problem that performance constraints and closed-chain kinematic constraints may conflict, a two-stage strategy of "feasibility first, constraint later" is proposed: during the observer convergence stage, the feasibility of the closed-chain kinematic constraints is ensured first. After the consistent neighborhood observation error converges to a sufficiently small threshold, the performance constraint function is triggered by the consistency indicator function, thereby ensuring the preset transient and steady-state performance and avoiding conflicts between early performance constraints and closed-chain constraints. Thus, even under the conditions of model uncertainty and incomplete information, the closed-loop signal can still be bounded and the tracking error can meet the consistency-driven performance constraints, significantly improving the safety and accuracy of multi-mobile robot collaborative handling of large objects.

[0021] In one embodiment, S100 includes: S110: Establish the first The dynamic model of the mobile robot system is as follows: ; in, It is the mass inertia matrix of the i-th mobile robot. The matrix represents the centripetal force and the Coriolis force. Represents the gravity vector. Here is the constraint matrix for the mobile robot. It is the input transformation matrix of the mobile robot. To control the input, Nonholonomic constraints on the end effector of a mobile robot and complete constraint force , Let be the generalized joint coordinates of the mobile robot, where For the pose of the mobile platform, This refers to the joint angle position of the robotic arm. Represent The first and second derivatives, Represents the total number of mobile robots. Indicates transpose; S120: Considering the... The non-holonomic constraints of each mobile platform are To obtain the reduced joint velocities , so that: ; in, yes The null space matrix satisfies , For the first Non-holonomic constraint matrices for each mobile platform For the first The generalized velocity vector of each mobile platform; therefore, multiply both sides of the dynamic model of the mobile robot in S110 by the projection matrix. Its dynamic model is rewritten as follows: ; in, The reduced Coriolis force matrix, , , , These are the block submatrices of the original inertia matrix. , , , These are the block submatrices of the original Coriolis force matrix. The input transformation matrix after order reduction. , This is a block diagonal submatrix of the original input transformation matrix. The reduced-order system inertia matrix, This is the reduced-order control input vector. This is the reduced gravity vector. , These are the block sub-vectors of the original gravity vector. The Jacobian matrix of the robot end effector after order reduction. , These are the block submatrices of the original Jacobian matrix. This is the generalized state vector after order reduction. This refers to the spinor of the external force acting on the end effector of the mobile robot.

[0022] In one embodiment, S100 further includes: S130: Establish the dynamic model of the object, specifically as follows: ; in, It is the mass-inertia matrix of the object. The matrix representing the centripetal and Coriolis forces of an object. It is the object's gravitational vector. The resultant force of multiple mobile robots acting on the center of mass of an object. and These are the object's pose and velocity spinor, respectively. S140: Velocity spinor based on the object's center of mass Velocity spinor with reference point Relationship: Substitute S130 and multiply on the left side of both sides of the equation. The dynamic model of the object in S130 is rewritten as follows: ; in, Here are the centripetal and Coriolis force matrices of the object in the reference coordinate system. Represents the pose of the task reference point on the object. The inertia matrix of the object in the reference coordinate system. The net force acting on an object The gravitational vector of an object. Let be the velocity mapping matrix between the reference point and the center of mass of the object. for The derivative; S150: Considering the... Load allocation coefficient matrix for each mobile robot and the The indirect force exerted by the end effector of a mobile robot on a reference point of an object. ,and Decomposed into operating force and internal strength ,Right now , No. The operational power of a mobile robot Written as: ; Wherein, the load distribution coefficient matrix satisfies The sum of internal forces satisfies ; S160: Based on kinematic relationships achievable ,in, For the robot's end effector speed, Let Jacobian be the kinematics from the object to the robot's end effector. The kinematic Jacobian of the robot from its joints to its end effector. For Jacobian matrices, for The pseudo-inverse matrix; therefore, the first... The dynamic equations of the coupling between a mobile robot and an object can be written as follows: ; in, The matrix of centripetal and Coriolis forces coupled between the robot and the object. Press the button on the robot The proportion of the Coriolis force borne by the object. This represents the coupled gravity vector between the robot and the object. Press the button on the robot The proportion of the object's weight that is borne by the proportion. For the equivalent input vector, The coupling inertia matrix between the robot and the object. Press the button on the robot The proportion of an object's inertia.

[0023] In one embodiment, S200, the fully distributed finite-time observer is designed to estimate the ideal trajectory of the task reference point. Expected speed and expected acceleration , set up a robot The output of the observer is defined as , , Its specific form is: ; in, The ideal trajectory for the mission reference point, including location and attitude quaternions , The expected velocity at the mission reference point, including linear velocity. and angular velocity , The expected acceleration for the task reference point, including linear acceleration. and angular acceleration , , , For the observer pair of robot i , , The estimated value, observer gain fractional power , The consistency error of the expected location observations, The consistency error of the expected linear velocity observations, To account for the consistency error of the expected linear acceleration observations, The consistency error of the expected attitude quaternion observations, The consistency error of the expected angular velocity observations, The consistency error of the expected angular acceleration observations is specifically defined as: ; in, and These are the expected positions of robot i relative to the task reference point. and attitude quaternions The estimated value, and These are the expected linear velocities of robot i relative to the task reference point. and angular velocity The estimated value, and These are the expected linear accelerations of robot i about the task reference point. and angular acceleration The estimated value, It is the robot j's pose quaternion The estimated value The conjugate quaternion, It is the expected posture The conjugate quaternion; in addition, adaptive gain and By adaptive law And adaptive law Updated to: ; in, Let i be the set of its neighbors. It is a binary indicator coefficient. It is a positive definite symmetric matrix. , Let be the estimated positions of the i-th and j-th robots in direction d, respectively. This is a reference value for the desired location. Let be the estimated pose of the i-th robot in direction d. Let be the estimated angular velocity of the i-th robot in direction d. This is the projection operator.

[0024] Furthermore, to prove the convergence performance of the aforementioned fully distributed finite-time observer, the observation errors in the neighborhoods of desired position, desired linear velocity, desired linear acceleration, desired attitude quaternion, desired angular velocity, and desired angular acceleration are defined as follows: and .when Time means , so when hour, It is monotonically increasing. This means that there is always a finite time interval that makes... Therefore, the neighboring observation error It converges to zero in a finite amount of time. Similarly, , , Accurate estimation within a finite time , This means that the proposed fully distributed observer can guarantee that the neighborhood observation error converges to zero within a finite amount of time.

[0025] In S200, the observer can accurately estimate the desired state under steady-state conditions, but transient estimation errors are unavoidable during convergence. If pre-set performance constraints are introduced into the cooperative operation strategy at the initial stage, the performance constraints constructed based on the estimated trajectory may conflict with the inherent kinematic constraints of the system. Therefore, a performance constraint mechanism based on consistency is introduced. In one embodiment, the consistency indicator function in S300... Defined as: ; in, Let the consistency error function of neighbor observations be sum, and the constant satisfy... ,and It is a sufficiently small positive constant. It is worth noting that if all robots can directly obtain the reference trajectory, then at the initial moment... .

[0026] Furthermore, the trajectory tracking error is defined. ,in, and Let represent the position tracking error and the attitude tracking error, respectively. The derivative of the attitude error... With angular velocity tracking error The relationship between them is: ; Among them, the velocity Jacobian matrix The expression is: ; in, and Therefore, there are ,in This is the velocity mapping matrix. This represents the velocity spinor tracking error.

[0027] In one embodiment, S300, the preset performance error transformation is defined by the robot. Error transformation function vector To achieve, among which, For the position error transformation subvector, The attitude error transformation sub-vector, the error transformation vector The specific definition of the j-th element is: ; in, Represents robots pose tracking error The j-th element, and These represent position tracking error and attitude tracking error, respectively. Indicates a reference position. Indicates the reference posture. Represents the quaternion of robot i's pose. The estimated value The conjugate quaternion, function and These are the upper and lower bounds of the consistency-driven performance constraint, respectively, and are explicitly defined as follows: ; in, The functions represent the maximum steady-state tracking errors at the upper and lower boundaries of the performance constraints, respectively. Defined as: ; in, express The exact time of its initial establishment This is the preset transition time constant.

[0028] Based on the error transformation function obtained above From the definition, we can obtain: ; in, This is a compensation term for the performance boundary. This is the error transformation gain coefficient.

[0029] Combination ,have: ; in, The error transformation gain coefficient matrix, This is the compensation vector for the performance boundary.

[0030] The consistency-driven performance function in S300 has the following properties: 1) If... In all If time remains bounded, then It is also bounded and satisfies Therefore, when At that time, the error It evolves strictly within the preset performance boundaries. When Sometimes, This means That is, no performance constraints are imposed. 2) If Keep bounded and Then there is .according to The properties of this cause the tracking error to be within Meeting the preset performance constraints is equivalent to designing a system that can maintain... Bounded controller.

[0031] In one embodiment, the design of a robust distributed performance constraint controller in S400 includes: S410: Define the augmented pose tracking error as: ; in, It is integral gain. It is half the width of the integration time window. and At time i and neighbor robot j, respectively The tracking error vector, It is a smooth window function, defined as: ; Differentiate the augmented pose tracking error and use the relation have: ; in, The velocity transformation matrix is ​​a performance constraint. , For parameters related to performance constraints, Let Jacobian matrix be the result of the error transformation. For speed error; S420: To simultaneously achieve consensus-driven performance constraints and consensus among neighbors, the robot... Reference speed Designed as follows: ; in, It is a positive definite symmetric matrix. Let i be the observer's expected velocity relative to the task reference point. The estimated value, for The inverse matrix, The value of the smooth window function at the current time. This is the time derivative of the window function; Therefore, the speed tracking error is constrained by performance. Defined as: ; And, actual reference speed The derivative is: ; in, for The derivative of for The derivative; S430: Multiply both sides of the S160 formula by the velocity transformation matrix of the performance constraint. The following error dynamics exist: ; in, The inertia matrix is ​​constrained by performance. The Coriolis force matrix is ​​a performance constraint. Coupled dynamics at the reference velocity, For the control input of robot i, where , and These represent the coupled inertia matrix between robot i and the object in the task reference coordinate system, the centripetal force and Coriolis force matrices, and the gravity vector, respectively; it is worth noting that... It can be linearly parameterized, i.e., a dynamic regression matrix exists. and dynamic parameter vector , making Therefore, the following distributed performance constraint control law is designed: ; in, The control gain matrix is ​​positive definite. It is a dynamic parameter vector The estimated value, For robust items The estimated value; right The parameter estimation error is defined as , right The parameter estimation error is defined as , Adaptive law and Adaptive law The specific expression is as follows: ; Wherein, the adaptive gain matrix It is a positive definite diagonal matrix with adaptive gain. It is a normal number.

[0032] Further stability and performance analysis is performed, considering the following Lyapunov function: ; Its time derivative is: ; Substituting the dynamic equations in S430 , can be obtained ; use and It can be deduced that: ; Combining matrices For antisymmetric matrices, i.e. Substituting the control law from S410 into the equation yields: ; Substituting the adaptive law from S430, we can derive: ; Using attributes Therefore when Sometimes: ; To analyze the stability of the entire system, the following global Lyapunov function is selected: ; Its time derivative is: ; For any ,when hour, This means that for any bounded initial conditions, and It's always bounded. Therefore... , , and It is always bounded. Therefore, a closed-loop system is always bounded. According to S200 The property, when for any ,have At that time, tracking error The preset performance constraints are met. Finally, a distributed performance constraint control program is written, and the control input is used to control the robot.

[0033] Compared with the prior art, the advantages of the present invention are as follows: (1) An innovative consensus-driven distributed performance constraint control method is proposed to explicitly coordinate kinematics and performance constraints in collaborative handling by multiple mobile robotic arms. This method can effectively cope with model uncertainty and incomplete reference information, and strictly guarantee the satisfaction of transient performance constraints after the observation error converges, thereby minimizing tracking error while ensuring safe collaboration.

[0034] (2) The designed finite-time observer is fully distributed, which can guarantee that the observation error converges to zero in finite time, and does not require global information, making it easy to apply and expand. At the same time, the object attitude is represented by a unit quaternion, which avoids the singularity problem of attitude representation and improves the applicability and robustness of the control method.

[0035] (3) By using a control strategy that is independent of the object and based on the task coordinate system, the shortcomings of relying on the object's centroid coordinate system are avoided, thereby enhancing the universality and flexibility of the control method in practical applications.

[0036] In one embodiment, a performance constraint control system for multi-robot collaborative handling of large workpieces is also provided, comprising: The coupled dynamics model building module is used to represent the pose of the object and the end effector of each mobile robot using unit quaternions. It describes the kinematic and dynamic relationship between the robot and the object to be transported in the task reference coordinate system. Combined with the closed-chain kinematic constraints formed by the cooperative transport of large objects, a coupled dynamic model of multi-mobile robot cooperative transport is obtained. The fully distributed finite-time observer design module is used to design a fully distributed finite-time observer by utilizing the information interaction between multiple mobile robot neighbors, to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. The desired state determination module under performance constraints is used to design a consistency-driven indicator function and a preset performance error transformation based on the reference estimate: when the consistency indicator function indicates that the neighborhood observation error has not converged, no performance constraint is applied; when the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is asymptotically activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and thereby generate the desired velocity and acceleration of each robot under performance constraints. The distributed control law construction module is used to design a robust distributed performance constraint controller for each robot based on the desired velocity and acceleration under performance constraints, so as to achieve tracking of the global reference trajectory and ensure that the closed-loop system signal is bounded and the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

[0037] Specific limitations regarding the performance constraint control system for multi-robot collaborative handling of large workpieces can be found in the above-described limitations of the performance constraint control method for multi-robot collaborative handling of large workpieces, and will not be repeated here. Each module in the aforementioned performance constraint control system for multi-robot collaborative handling of large workpieces can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0038] In one embodiment, a computer device is also provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a multi-robot collaborative handling performance constraint control method for large workpieces.

[0039] In one embodiment, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of a performance constraint control method for multi-robot collaborative handling of large workpieces.

[0040] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0041] The above provides a detailed description of the performance constraint control method and system for multi-robot collaborative handling of large workpieces provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for performance constraint control of multi-robot collaborative handling of large workpieces, characterized in that, The method includes the following steps: S100. Unit quaternions are used to represent the poses of the object and the end effectors of each mobile robot. The kinematic and dynamic relationship between the robot and the object to be transported is described in the task reference coordinate system. Combined with the closed-chain kinematic constraints formed by the cooperative transport of large objects, a coupled dynamic model of cooperative transport of multiple mobile robots is obtained. S200. By utilizing the information interaction among multiple mobile robot neighbors, a fully distributed finite-time observer is designed to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. Based on the reference estimate of S200, a consistency-driven indicator function and a preset performance error transformation are designed: when the consistency indicator function indicates that the neighborhood observation error has not converged, no performance constraint is applied; when the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is gradually activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and the expected velocity and acceleration of each robot under the performance constraints are generated accordingly. Based on the expected velocity and acceleration generated by S400 and S300, a robust distributed performance constraint controller is designed for each robot to track the global reference trajectory, ensuring that the closed-loop system signal is bounded and that the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

2. The method according to claim 1, characterized in that, S100 includes: S110: Establish the first The dynamic model of the mobile robot system is as follows: ； in, It is the mass inertia matrix of the i-th mobile robot. The matrix represents the centripetal force and the Coriolis force. Represents the gravity vector. Here is the constraint matrix for the mobile robot. It is the input transformation matrix of the mobile robot. To control the input, Nonholonomic constraints on the end effector of a mobile robot and complete constraint force , Let be the generalized joint coordinates of the mobile robot, where For the pose of the mobile platform, This refers to the joint angle position of the robotic arm. Represent The first and second derivatives, Represents the total number of mobile robots. Indicates transpose; S120: Considering the... The non-holonomic constraints of each mobile platform are To obtain the reduced joint velocities , so that: ； in, yes The null space matrix satisfies , For the first Non-holonomic constraint matrices for each mobile platform For the first The generalized velocity vector of each mobile platform; therefore, multiply both sides of the dynamic model of the mobile robot in S110 by the projection matrix. Its dynamic model is rewritten as follows: ； in, The reduced Coriolis force matrix, , , , These are the block submatrices of the original inertia matrix. , , , These are the block submatrices of the original Coriolis force matrix. The input transformation matrix after order reduction. , This is a block diagonal submatrix of the original input transformation matrix. The reduced-order system inertia matrix, This is the reduced-order control input vector. This is the reduced gravity vector. , These are the block sub-vectors of the original gravity vector. The Jacobian matrix of the robot end effector after order reduction. , These are the block submatrices of the original Jacobian matrix. This is the generalized state vector after order reduction. This refers to the spinor of the external force acting on the end effector of the mobile robot.

3. The method according to claim 2, characterized in that, The S100 also includes: S130: Establish the dynamic model of the object, specifically as follows: ； in, It is the mass-inertia matrix of the object. The matrix representing the centripetal and Coriolis forces of an object. It is the object's gravitational vector. The resultant force of multiple mobile robots acting on the center of mass of an object. and These are the object's pose and velocity spinor, respectively. S140: Velocity spinor based on the object's center of mass Velocity spinor with reference point Relationship: Substitute S130 and multiply on the left side of both sides of the equation. The dynamic model of the object in S130 is rewritten as follows: ； in, Here are the centripetal and Coriolis force matrices of the object in the reference coordinate system. Represents the pose of the task reference point on the object. The inertia matrix of the object in the reference coordinate system. The net force acting on an object The gravitational vector of an object. Let be the velocity mapping matrix between the reference point and the center of mass of the object. for The derivative; S150: Considering the... Load allocation coefficient matrix for each mobile robot and the The indirect force exerted by the end effector of a mobile robot on a reference point of an object. ,and Decomposed into operating force and internal strength ,Right now , No. The operational power of a mobile robot Written as: ； Wherein, the load distribution coefficient matrix satisfies The sum of internal forces satisfies ; S160: Based on kinematic relationships achievable ,in, For the robot's end effector speed, Let Jacobian be the kinematics from the object to the robot's end effector. The kinematic Jacobian of the robot from its joints to its end effector. For Jacobian matrices, for The pseudo-inverse matrix; therefore, the first... The dynamic equations of the coupling between a mobile robot and an object can be written as follows: ； in, The matrix of centripetal and Coriolis forces coupled between the robot and the object. Press the button on the robot The proportion of the Coriolis force borne by the object. This represents the coupled gravity vector between the robot and the object. Press the button on the robot The proportion of the object's weight that is borne by the proportion. For the equivalent input vector, Let be the robot-object coupling inertia matrix. Press the button on the robot The proportion of an object's inertia.

4. The method according to claim 3, characterized in that, In S200, the fully distributed finite-time observer is designed to estimate the ideal trajectory of the mission reference point. Expected speed and expected acceleration , set up a robot The output of the observer is defined as , , Its specific form is: ； in, The ideal trajectory for the mission reference point, including location and attitude quaternions , The expected velocity at the mission reference point, including linear velocity. and angular velocity , The expected acceleration for the task reference point, including linear acceleration. and angular acceleration , , , For the observer pair of robot i , , The estimated value, observer gain Fractional power , The consistency error of the expected location observations, The consistency error of the expected linear velocity observations, To account for the consistency error of the expected linear acceleration observations, The consistency error of the expected attitude quaternion observations, The consistency error of the expected angular velocity observations, The consistency error of the expected angular acceleration observations is specifically defined as: ； in, and These are the expected positions of robot i relative to the task reference point. and attitude quaternions The estimated value, and These are the expected linear velocities of robot i relative to the task reference point. and angular velocity The estimated value, and These are the expected linear accelerations of robot i about the task reference point. and angular acceleration The estimated value, It is the robot j's pose quaternion The estimated value The conjugate quaternion, It is the expected posture The conjugate quaternion; in addition, adaptive gain and By adaptive law And adaptive law Updated to: ； in, Let i be the set of its neighbors. It is a binary indicator coefficient. It is a positive definite symmetric matrix. , Let be the estimated positions of the i-th and j-th robots in direction d, respectively. This is a reference value for the desired location. Let be the estimated pose of the i-th robot in direction d. Let be the estimated angular velocity of the i-th robot in direction d. This is the projection operator.

5. The method according to claim 4, characterized in that, Consistency indicator function in S300 Defined as: ； in, Let the consistency error function of neighbor observations be sum, and the constant satisfy... ,and It is a sufficiently small positive number.

6. The method according to claim 5, characterized in that, In S300, the preset performance error transformation is defined by the robot. Error transformation function vector To achieve, among which, For the position error transformation subvector, The attitude error transformation sub-vector, the error transformation vector The specific definition of the j-th element is: ； in, Represents robots pose tracking error The j-th element, and These represent position tracking error and attitude tracking error, respectively. Indicates a reference position. Indicates the reference posture. Represents the quaternion of robot i's pose. The estimated value The conjugate quaternion, function and These are the upper and lower bounds of the consistency-driven performance constraint, respectively, and are explicitly defined as follows: ； in, The functions represent the maximum steady-state tracking errors at the upper and lower boundaries of the performance constraints, respectively. Defined as: ； in, express The exact time of its initial establishment This is the preset transition time constant.

7. The method according to claim 6, characterized in that, The design of the robust distributed performance constraint controller in S400 includes: S410: Define the augmented pose tracking error for: ； in, It is integral gain. It is half the width of the integration time window. and At time i and neighbor robot j, respectively The tracking error vector, It is a smooth window function, defined as: ； Differentiate the augmented pose tracking error and use the relation have: ； in, The velocity transformation matrix is ​​a performance constraint. , For parameters related to performance constraints, Let Jacobian matrix be the result of the error transformation. For speed error; S420: To simultaneously achieve consensus-driven performance constraints and consensus among neighbors, the robot... Reference speed Designed as follows: ； in, It is a positive definite symmetric matrix. Let i be the observer's expected velocity relative to the task reference point. The estimated value, for The inverse matrix, The value of the smooth window function at the current time. This is the time derivative of the window function; Therefore, the speed tracking error is constrained by performance. Defined as: ； And, actual reference speed The derivative is: ； in, for The derivative, for The derivative; S430: Multiply both sides of the S160 formula by the velocity transformation matrix of the performance constraint. The following error dynamics exist: ； in, The inertia matrix is ​​constrained by performance. The Coriolis force matrix is ​​a performance constraint. Coupled dynamics at the reference velocity, For the control input of robot i, where , and These represent the coupled inertia matrix between robot i and the object in the task reference coordinate system, the centripetal force and Coriolis force matrices, and the gravity vector, respectively; it is worth noting that... It can be linearly parameterized, i.e., a dynamic regression matrix exists. and dynamic parameter vector , making Therefore, the following distributed performance constraint control law is designed: ； in, The control gain matrix is ​​positive definite. It is a dynamic parameter vector The estimated value, For robust items The estimated value; right The parameter estimation error is defined as , right The parameter estimation error is defined as , Adaptive law and Adaptive law The specific expression is as follows: ； Wherein, the adaptive gain matrix It is a positive definite diagonal matrix with adaptive gain. It is a normal number.

8. A performance constraint control system for multi-robot collaborative handling of large workpieces, characterized in that, include: The coupled dynamics model building module is used to represent the pose of the object to be transported and the end effectors of each mobile robot using unit quaternions. Under the preset task reference coordinate system, it builds a coupled dynamics model of multi-robot cooperative transport that includes closed-chain kinematic constraints formed by the cooperative transport of large objects. The fully distributed finite-time observer design module is used to design a fully distributed finite-time observer by utilizing the information interaction between multiple mobile robot neighbors, to perform a consistent estimation of the reference trajectory of the task reference coordinate system and obtain the reference estimate value. The desired state determination module under performance constraints is used to design a consistency-driven indicator function and a preset performance error transformation based on the reference estimate. No performance constraints are imposed when the consistency indicator function indicates that the neighborhood observation error has not converged. Once the consistency indicator function indicates that the neighborhood observation error has converged to a set threshold, the preset performance constraint function is gradually activated to apply transient and steady-state performance boundaries to the trajectory tracking error, and thereby generate the expected velocity and acceleration of each robot under the performance constraints. The distributed control law construction module is used to design a robust distributed performance constraint controller for each robot based on the generated desired velocity and acceleration to achieve tracking of the global reference trajectory, and to ensure that the closed-loop system signal is bounded and that the tracking error meets the preset transient and steady-state boundaries after the performance constraint is triggered.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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