Distributed control method and system for maintaining global connectivity of teleoperation open multi-robot

Abstract

The invention provides a distributed control method and system for maintaining global connectivity of teleoperation open type multiple robots, and belongs to the field of teleoperation multiple robot control. In order to solve the problems that a distributed control method is difficult to carry out rapid and simple estimation on a Fischer eigenvalue, and the control of the movement range of a single robot is limited under the dual connectivity of a multi-robot system. According to the method, the teleoperation multi-robot system with quantity fluctuation is used as an application object, calculation of a Fischer eigenvalue is improved and optimized on the basis of a traditional distributed control strategy, and distributed control during quantity fluctuation of the teleoperation multi-robot system is achieved by combining a distance-dependent control strategy and an energy tank mechanism. While the stability and connectivity of the system are maintained, the influence on the energy fluctuation of the system is also considered, and the method has relatively high engineering application potential.

Description

Technical Field

[0001] The present invention relates to the technical field of teleoperation multi-robot control, and more particularly, to a distributed control method and system for maintaining global connectivity of a teleoperated open multi-robot system. Background Art

[0002] When multi-robot systems execute complex tasks, through the cooperation between robots, the flexibility, efficiency and robustness of the system operation are significantly enhanced, and they are widely used in many key fields such as manufacturing. Open multi-robot systems allow individual robots to leave the system and execute tasks independently, and can return at any time to cooperate with other robots to achieve common goals. Bilateral teleoperation multi-robot systems make full use of the decision-making ability of operators and can respond more safely and effectively to sudden changes in the face of unknown and complex dynamic environments. Whether it is a traditional, open, autonomous or remotely controlled multi-robot system, effective control mechanisms must be designed to address the challenges faced in coordination and communication.

[0003] Distributed control strategies support mutual communication between adjacent robots and make autonomous control decisions, which are widely used in multi-robot systems. Connectivity is a key factor to ensure effective communication between robots. Global connectivity can dynamically adjust the topological structure to flexibly cope with uncertain factors in complex environments on the basis of ensuring system connectivity, so it has received extensive attention and research. Existing research shows that the connectivity of the system is closely related to the Fiedler eigenvalue (i.e., the second smallest eigenvalue of the Laplacian matrix related to the system connectivity graph). As long as the Fiedler eigenvalue is positive, the connectivity of the system can be ensured. By constructing a weighted Laplacian matrix, the Fiedler eigenvalue can be continuously adjusted according to the distance change between robots. Since calculating the Fiedler eigenvalue requires knowledge of the distance information between all adjacent robots in the system, the current acquisition methods are divided into two types: centralized and decentralized. Although the centralized calculation method is simple, it highly depends on the central processor, has poor robustness and high calculation cost. For the decentralized estimation method, the estimated Fiedler eigenvalue takes some time to converge to the actual value, and over time, the estimation error will gradually increase. Therefore, there is an urgent need for a new estimation method to ensure that the estimated Fiedler eigenvalue quickly converges to the actual value.

[0004] In an open multi-robot system, when a certain robot is assigned to perform other tasks and leaves the system, it may cause the remaining robots to be divided into multiple unconnected subsystems. To address this issue, the concept of a k-node connected graph is introduced to maintain the connectivity of the system when fewer than k nodes are removed. However, as the value of k increases, the robustness of the system is enhanced, but this also results in a restricted activity range for each node. Therefore, biconnectivity (k = 2) has been widely applied in open multi-robot systems. Nevertheless, current research on the biconnectivity of multi-robot systems mainly focuses on ensuring the biconnectivity of the entire system, that is, the connectivity of the remaining system is not affected when any one robot leaves. Although this approach helps to maintain the stability of the system, it also limits the movement range of individual robots. Summary of the Invention

[0005] The technical problem to be solved by the present invention is:

[0006] To solve the problem that it is difficult to quickly and simply estimate the Fiedler eigenvalue by the distributed control method, and under the biconnectivity of the multi-robot system, it restricts the movement range control of individual robots.

[0007] The technical solution adopted by the present invention to solve the above technical problem:

[0008] The present invention provides a distributed control method for maintaining the global connectivity of a teleoperated open multi-robot system, including the following steps:

[0009] S100. Establish a dynamic model and weight matrix of the teleoperated multi-robot system. During the interaction between the teleoperated control signal and the remote robot system, the remote robots include leaders and followers, and adjust their speeds and positions according to the control signals input by local robot users; ensure the connectivity between robots through a distance-dependent weight matrix;

[0010] S200. Establish a control strategy for the teleoperated multi-robot system. According to the dynamic model of the teleoperated multi-robot system established in step S100, determine the control strategy for synchronization between local robot users and remote leaders, and then introduce an energy tank to dynamically adjust the energy exchange to ensure the stability and passivity of the system when the number of robots changes;

[0011] S300. Estimate the Fiedler eigenvalue by distributed control. According to the communication model established in step S100, utilize the communication capabilities of robots in the distributed framework to estimate the Fiedler eigenvalue according to the changes in the system topology structure;

[0012] S400. Connectivity Maintenance Control of Multi-Robot System during Departure or Return to Task. When a robot leaves the system after being assigned a task or returns to the system after completing a specified task, the global connectivity of the system is maintained by adjusting the relative distance and control parameters between robots, and potential collision risks are avoided.

[0013] Further, in step S100, it includes

[0014] The dynamic model of the remote robot is:

[0015]

[0016] where the subscript 1 represents the remote leader, and the rest are remote followers; and are the velocities and accelerations of all remote robots; M i and B i are the mass and local damping matrix of remote robot i; the control input is where is to maintain the connectivity of the multi-robot system while ensuring that the distance between remote robot i and its adjacent robots approaches the desired value; is the control input to make all remote machines i move at the same speed, is the teleoperation control input of the remote leader;

[0017] In the remote robot system, define the graph G=(V, E, A, L) as the connectivity graph of the remote robots; where the vertex set V={1,…, N} is the set of all remote robots; the edge set is the set of all adjacent remote robots; N i ={j∈V|(i, j)∈E} is the set of all adjacent robots j of remote robot i; if (i, j)∈E, then the adjacency weighted matrix associated with graph G is A=[a ij ∈R N×N , a ij is the weight of the edge (V j , V i ); if nodes V i and V j are adjacent, the element a ij >0 in the matrix; the Laplacian matrix L=[l ij =diag{ζ i}-A∈R N×N , where and is a positive semi-definite matrix;

[0018] Using the method of graph theory, a weighted adjacency matrix A and a Laplacian matrix L are constructed to describe the connection and communication strength between robots; the second smallest eigenvalue λ of the dynamically adjusted Laplacian is introduced 2 , and λ 2 changes continuously with the relative distance between adjacent remote robots and the distance from surrounding obstacles; for this purpose, the following adjacency weighted matrix A = [a ij is designed:

[0019]

[0020] where the adjustment parameter α ij is the distance between robot i and robot j, the adjustment parameter α is is the distance between robot i and obstacle s, d ij (t) is the relative distance between robot i and robot j that changes with time, is the relative distance between robot i and obstacle s that changes with time, is the set of all obstacles detected by robot i; β i (t) is the velocity damping term matrix of robot i;

[0021] The factor α ij (d ij ) in formula (3) is:

[0022]

[0023] where, d ij = ||x ij || = ||x i - x j ||; The expected distance between robot i and j; d max is the maximum sensing range between remote robots; d min The minimum safe distance between remote robots;

[0024]

[0025] where, is the position of the s-th obstacle detected by the i-th robot; is the maximum distance for a remote robot to detect an obstacle; is the minimum safe distance between a robot and an obstacle;

[0026]

[0027] The weight a ijFor maintaining the connection of multiple remote robots and by adjusting the parameter α ij Drive the distance between adjacent remote robots to the desired distance By adjusting the parameter α is Prevent collisions with obstacles.

[0028] Furthermore, in step S200, it includes determining the control strategy for synchronization between the user's local robot and the remote leader:

[0029]

[0030] where f lc is the teleoperation control force that connects the local robot to the remote leader robot, k l (t) is the gain function, and by adjusting its value, the synchronization effect between the local robot and the remote leader is controlled. The pseudo-velocity r of the remote leader l depends on the position and velocity of the local robot;

[0031] During the teleoperation process, the dynamic model of the remote robot is:

[0032]

[0033] For the remote robot system, design respectively Synchronize the motion of the leader and the local robot, and by Ensure the consistency of the speed between robots and the global connectivity of the system;

[0034] In is the common potential form to ensure where P i is the common potential energy function, is the estimated Federer eigenvalue of robot i, ε is the design parameter and ensures represents the control strength in the communication link of robot i;

[0035] To ensure the passivity of the system, each remote robot is interconnected with a dynamically adjusted energy tank:

[0036]

[0037] where x t1 is the state of the energy tank of the robot leader; x ti is the state of the energy tank of the i-th robot and the energy function of the energy tank T max > 0 represents the upper limit of the energy tank; 0 < T min < T max For the energy tank T irepresents the lowest energy level;

[0038] and the control parameter limits the energy T of robot i i within the range of [T min , T max ; when T i ≥ T max , the energy is limited by selecting ; when T min ≥ T i , select When T i ≥ T max and ∑(T j - T i ) > 0 or T min ≥ T i and ∑(T j - T i ) < 0, select When the number of robots fluctuates, the energy can be dissipated through dynamic damping to partially compensate for the change in energy in the system.

[0039] Furthermore, in step S300, it includes that, under the distributed framework, robot i sends its position x i (k), speed parameter α is (k) and β i (k) data to adjacent robots together; each robot stores the current adjacency matrix A i (k) with the adjacency matrices from the previous two time steps and ; for any robot, the adjacency matrix at the initial moment is known and the weights in A i (k) are calculated by formula (4); the corresponding weights received from its adjacency matrix in A (k - 1) s replace the weights j (k - 1) s

[0040] Furthermore, in step S400, it includes

[0041] Suppose where d d represents the ideal communication distance between robots under normal operation, and is the ideal communication distance set for the additional communication link;

[0042] Set the parameter De ∈ {0, V} to identify the robot ready to leave the system, which is stored in each robot. Here, V is the label of the robot. In the initial state, De = 0. When robot i is assigned a task and leaves the system, De = i. dim = N indicates that there are N remote robots in the current system. The Fiedler eigenvalue is obtained by removing the i-th row and the i-th column of A i and then calculating the eigenvalue of the Laplacian matrix. When , robot i and its adjacent robot j are within the normal working communication distance and the connectivity is maintained. The parameter μ > 1 is an adjustable factor, which helps to modify and values more quickly. Continuously adjust the value to ensure that When , robot i will start to decelerate and get ready to leave the system. At this time, the system adjusts the action command according to the control strategy, recalculates and updates the Fiedler eigenvalue. When robot i is in a stationary state waiting to return to the system, once the return command of robot i is received, the main control remote robot starts to move towards robot i and decelerates to ensure the safe return of robot i.

[0043] Furthermore, perform passivity analysis on the multi-robot system during the leaving or returning tasks. According to the energy tank designed in step S200, it can cope with the sudden fluctuation of the system energy when the number of robots fluctuates, and introduce the Lyapunov function to prove whether the multi-robot system has passivity under remote operation control.

[0044] Furthermore, when the number of robots changes, and will experience instantaneous changes, resulting in a sudden fluctuation of the energy stored in the energy tank. If the system is passive, there exists a time-varying Lyapunov function V(t) and the initial Lyapunov function V(0), satisfying the following conditions:

[0045]

[0046] where the scalar ψ ≤ 0; f h is the external input force, is the transpose of the external input force vector; r l is the external input response; η is the independent variable in the integrand;

[0047] Construct the Lyapunov function of the teleoperation system as:

[0048]

[0049] where, V l (t) = K lLet \(V(t)\) be the Lyapunov function of the leader robot. i \(V(t)=K\) i (t)+T i Let \(V_i(t)\) be the Lyapunov function of each follower robot.

[0050] Let \(t_{out}\) l be the time when a robot leaves the system, and \(t_{in}\) r be the time when it returns to the system. During the interval \([t_{out}\) r , \(t_{in})\), the time derivative of the Lyapunov function \(V_i(t)\) of each follower robot is: i After derivation, we get:

[0051]

[0052] It is derived that:

[0053]

[0054] Satisfying where

[0055] Integrating and summing over the intervals and \([t_{out}\) r , \(t_{in})\) respectively, and combining the known prior conditions, the energy change of the system at any time is:

[0056]

[0057] where is the total energy upper limit of all robots in the system, proving the passivity of the system under the fluctuation of the number of robots and the estimated value of \(\lambda\). 2

[0058] A distributed control system for maintaining global connectivity of a teleoperated open multi-robot, the system having program modules corresponding to the above steps, and executing the steps in the distributed control method for maintaining global connectivity of a teleoperated open multi-robot when running.

[0059] A computer-readable storage medium storing a computer program configured to implement the steps of the distributed control method for maintaining global connectivity of a teleoperated open multi-robot when called by a processor.

[0060] Compared with the prior art, the beneficial effects of the present invention are:

[0061] In view of the situation of robot number fluctuations in a teleoperated multi-robot system, the present invention proposes a distance-dependent distributed control strategy. A distributed controller related to the Fiedler eigenvalue is used to ensure that the robots maintain connectivity and collision avoidance among themselves during task execution, and ensure their safe departure. At the same time, the passivity of the system is analyzed. Specifically, the beneficial effects of the present invention are as follows:

[0062] ① Compared with traditional centralized and decentralized control methods, the present invention uses a distance-related control algorithm to specifically design a distributed controller based on λ 2 under the change of the number of robots, and dynamically adjusts the relative positions and control parameters of the robots to ensure the efficiency and robustness of the multi-robot system during formation control and obstacle avoidance tasks.

[0063] ② Compared with traditional fixed robot number and energy consumption control schemes, the present invention fully considers the impact of robot number changes on system energy fluctuations by designing an energy tank with exchangeable energy for each robot, and can achieve passivity under the λ 2 estimation situation through an energy exchange mechanism when the number changes. This not only ensures the passivity of the system during operation, but also guarantees the stability and connectivity of the system, effectively coping with the energy fluctuations caused by the departure and return of robots.

[0064] In summary, taking the teleoperated multi-robot system with number fluctuations as the application object, the present invention improves and optimizes the calculation of the Fiedler eigenvalue on the basis of traditional distributed control strategies, combines a distance-dependent control strategy and an energy tank mechanism, for the distributed control of a teleoperated multi-robot system with number fluctuations. While maintaining the stability and connectivity of the system, it also considers the impact on system energy fluctuations, and has high engineering application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flowchart of a distributed control method for maintaining global connectivity of a teleoperated open multi-robot in an embodiment of the present invention;

[0066] Figure 2 is a path diagram of a remote robot in an embodiment of the present invention;

[0067] Figure 3 is a curve graph of the value of λ 2 of robots in a teleoperated multi-robot system with number fluctuations changing with time in an embodiment of the present invention;

[0068] Figure 4 is a curve graph of the error between the estimated value λ 2 and the actual value in a teleoperated multi-robot system with number fluctuations in an embodiment of the present invention;

[0069] Figure 5 This is a comparison chart of the energy change of the robot energy tank in the teleoperated multi-robot system under quantity fluctuation in the embodiment of the present invention;

[0070] Figure 6 This is a flowchart of estimating the Federer eigenvalue by distributed control in the embodiment of the present invention;

[0071] Figure 7 This is a flowchart of the control strategy algorithm for managing the departure of a specific robot in the embodiment of the present invention;

[0072] Figure 8 This is a flowchart of the control strategy algorithm for managing the return of a specific robot in the embodiment of the present invention. Detailed implementation manners

[0073] To make the above objects, features and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings.

[0074] Specific implementation manner one: Combining Figure 1 、 Figures 6 to 8 As shown, the present invention provides a distributed control method for maintaining global connectivity of a teleoperated open multi-robot, including the following steps:

[0075] S100. Establish the dynamic model and weight matrix of the teleoperated multi-robot system. During the interaction between the teleoperation control signal and the remote robot system, the remote robots (leaders and followers) adjust their speeds and positions according to the control signals input by the local robot users to ensure the synchronization between the remote leader and the local robot; and ensure the connectivity between the robots through the distance-dependent weight matrix to achieve collision avoidance and maintain effective communication;

[0076] The dynamic model of the remote robot is:

[0077]

[0078] Among them, the subscript 1 represents the remote leader, and the rest are remote followers; for all remote robots i = 1, 2,..., N; and are the speed and acceleration of robot i; M i and B i are the mass and local damping matrix of robot i; the control input is where is to maintain the connectivity of the multi-robot system while ensuring that the distance between the remote robot i and its adjacent robots approaches the expected value; makes the remote machine i move at the same speed, is the teleoperation control input of the remote leader;

[0079] In a remote robot system, the connected graph of the remote robot is defined as G=(V, E, A, L); where the vertex set V={1,…,N} is the set of all remote robots; the edge set is the set of all adjacent remote robots; N i ={j∈V|(i,j)∈E} is the set of all adjacent robots j of remote robot i; if (i,j)∈E, the adjacent weighted matrix associated with graph G is A=[a ij ∈R N×N , a ij is the weight of the edge (V j ,V i ); if nodes V i and V j are adjacent, then the element a ij in the matrix is greater than 0; the Laplacian matrix L=[l ij =diag{ζ i}-A∈R N×N , where and is a positive semi - definite matrix; using the method of graph theory, the adjacent weighted matrix A and the Laplacian matrix L are constructed to describe the connection and communication strength between robots; the present invention introduces a dynamically adjusted second smallest eigenvalue λ 2 (λ 2 >0, indicating that graph G is connected), λ 2 changes continuously with the relative distance between adjacent remote robots and the distance from surrounding obstacles; for this reason, the following adjacent weighted matrix A=[a ij is designed:

[0080]

[0081] where the adjustment parameter α ij reflects the distance between robot i and robot j, the adjustment parameter α is reflects the distance between robot i and obstacle s, d ij (t) is the relative distance between robot i and robot j changing with time, is the relative distance between robot i and obstacle s changing with time, is the set of all obstacles detected by robot i; β i (t) is the speed damping term matrix of robot i;

[0082] The factors in formula (3) are provided in the following equations:

[0083]

[0084] where, d ij = ||x ij || = ||x i -x j ||; is the expected distance between robots i and j; d max is the maximum sensing range between remote robots; d min The minimum safe distance between robots;

[0085]

[0086] where is the position where the i-th robot detects the s-th obstacle; is the maximum distance at which a remote robot can detect an obstacle; is the minimum safe distance between a robot and an obstacle;

[0087]

[0088] The weight a mentioned in formula (4) ij is to maintain the connection of the multi-robot system and, by adjusting the parameter α ij drive the distance between adjacent remote robots to the expected distance By adjusting the parameter α is prevent collisions with obstacles;

[0089] S200. Establish the control strategy for the teleoperated multi-robot system. According to the dynamic model of the teleoperated multi-robot system established in step S100, determine the control strategy for synchronization between the user's local robot and the remote leader, and then introduce an energy tank to ensure the stability and passivity of the system when the number of robots changes by dynamically adjusting the energy exchange:

[0090]

[0091] where, f lc is the teleoperation control force that connects the local robot to the remote leader robot, k l (t) is the gain function, and by adjusting its value, the synchronization effect between the local robot and the remote leader is controlled. The pseudo-velocity r l of the remote leader depends on the position and velocity of the local robot; during teleoperation, the dynamic model of the remote robot is:

[0092]

[0093] For the remote robot system, where For remote operation control force, connect the remote leader to the user's local robot and through Distributed control ensures the consistency of the final speeds among robots; is the common potential form used to ensure P i is the common potential energy function, is the estimated Fiedler eigenvalue of i, and ε is the design parameter to ensure represents the control strength in the communication link of robot i. A larger k P enhances the break resistance of the communication link, while a smaller k P promotes the change of system connectivity;

[0094] To ensure the passivity of the system, the present invention interconnects each remote robot with a dynamically regulated energy tank:

[0095]

[0096] where, x t1 is the state of the energy tank of the robot leader; x ti is the state of the energy tank of the i-th robot and the energy function of the energy tank T max >0 represents a suitable upper limit of an energy tank; 0 < T min < T max For the energy tank T i represents the lowest energy level; and the control parameter limits the energy T of robot i within the set range [T i , T min , T max and adjusts the control parameter as needed to maintain the stability of the system; specifically, when T i ≥ T max , limit the energy by selecting ; if T min ≥ T i select When T i ≥ T max and ∑(T j - T i ) > 0 or T min ≥ T i and ∑(T j - T i ) < 0, select When the number of robots fluctuates, the energy can be dissipated through dynamic damping to partially compensate for the change in energy in the system;

[0097] S300. Distributed control estimates the Fiedler eigenvalue. According to the communication model established in step S100, using the communication capabilities of the robots in the distributed framework, the Fiedler eigenvalue is estimated according to the changes in the system topology structure;

[0098] In the distributed framework, at each sampling time k, robot i sends its position x i (k), speed parameter α is (k) and β i (k) data to the robots adjacent to i together; the received data is based on Figure 6 shown to calculate λ 2 , where robot i is used as a representative example to illustrate the process of calculating the adjacency matrix A i (k); each robot should store the current adjacency matrix A i (k) and the adjacency matrices from the previous two time steps and ; for any robot, the adjacency matrix at the initial moment is known and the weights in A i (k) are calculated by formula (4); the corresponding weights received from its adjacency matrix in A (k - 1)s replace the weights j

[0099] S400. Connectivity maintenance control of the multi-robot system during the process of leaving or returning to the task. When a certain robot is assigned a task and leaves the system, or when it completes the specified task and returns to the system, the global connectivity of the system is maintained by adjusting the relative distances and control parameters between the robots, and potential collision risks are avoided; using the Fiedler eigenvalue calculated in step S300, it is ensured that the multi-robot system maintains the global connectivity under the condition of quantity fluctuations, so as to ensure the cooperative cooperation between the multi-robots;

[0100] In this step, a control strategy is designed to ensure that the remaining robot system can continue to operate normally when a certain robot leaves the system; make the following reasonable assumptions: where d d represents the ideal communication distance between robots under normal operation, and is the ideal communication distance set for the additional communication link;

[0101] Taking robot i as an example, the execution process of the algorithm is as Figure 7 shown; the parameter De ∈ {0, V} is used to identify the robot ready to leave the system, stored in each robot, V is the label of the robot; initially De = 0, and when robot i is assigned a task and leaves the system, De = i; dim = N means that there are N remote robots in the current system; the Fiedler eigenvalue is the eigenvalue of the Laplacian matrix calculated after removing the \(i\)-th row and \(i\)-th column of \(A\); when i is the case, robot \(i\) and its adjacent robot \(j\) are within the normal working communication distance and the connectivity is maintained. The parameter \(\mu>1\) is an adjustable factor, which helps to modify and and values more quickly; continuously adjust the value to ensure that when the condition is met, robot \(i\) will start to decelerate and prepare to leave the system to avoid collision with other robots; at this time, other robots regard it as an obstacle and the system will adjust the action instructions according to the control strategy and recalculate and assign this value to to maintain the global connectivity of the remaining system. The other robots do not need to be processed and only consider the adjacent robots of robot \(i\); taking robot \(i\) mentioned in Figure 7 as an example, Figure 8 gives the control strategy for this robot to rejoin the system after completing the specified task; robot \(i\) is in a stationary state waiting to return to the system. Once the return command of robot \(i\) is received, the master control remote robot starts to move towards robot \(i\) and decelerates to make it within the maximum sensing range, and updates the position of robot \(i\) through formulas (9) and (10) to ensure the safe return of robot \(i\) and the global connectivity and passivity of the system;

[0102] S500. Passivity analysis of the multi-robot system during the process of leaving or returning. According to the energy tank designed in step S200, it can cope with the sudden fluctuation of the system energy when the number of robots fluctuates, and introduce the Lyapunov function to prove the passivity of the multi-robot system under remote operation control;

[0103] When the number of robots changes, and will experience instantaneous changes, resulting in a sudden fluctuation of the energy stored in the energy tank; if the system is passive, there exists a time-varying Lyapunov function \(V(t)\) and the initial Lyapunov function \(V(0)\) that satisfy the following conditions:

[0104]

[0105] where the scalar \(\psi\leq0\); \(f\) h is the external input force, is the transpose of its vector; \(r\) l is the external input response; \(\eta\) is the independent variable in the integrand;

[0106] To analyze the passivity of the system, a Lyapunov function of a teleoperation system is constructed as:

[0107]

[0108] Among them, V l (t) = K l (t) is the Lyapunov function of the leader robot, and V i (t) = K i (t) + T i (t) is the Lyapunov function of each follower robot;

[0109] Time t l is the moment when the robot leaves the system, and time t r is the moment when it returns to the system; within the time interval [t r , t), the derivative of the Lyapunov function V i (t) with respect to time is:

[0110]

[0111] Further derivation gives:

[0112]

[0113] Satisfying Among them is the teleoperation control input of robot i;

[0114] For the interval and [t r , t) are respectively integrated and summed over , combined with the known prior conditions, the energy change of the system at any time:

[0115]

[0116] Among them, is the total energy upper limit of all robots in the system, so it is proved that the system is passive under the condition of robot number fluctuation and the λ 2 estimation value.

[0117] Specific implementation plan two: The present invention provides a distributed control system for maintaining global connectivity of teleoperated open multi-robots. This system has program modules corresponding to the above steps and executes the steps in the distributed control method for maintaining global connectivity of teleoperated open multi-robots when running.

[0118] Other combinations and connection relationships in this implementation plan are the same as those in specific implementation plan one.

[0119] Specific Embodiment 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement the steps of a distributed control method for maintaining global connectivity in teleoperated open multi-robot systems when called by a processor.

[0120] The other combinations and connection relationships in this embodiment are the same as those in Specific Embodiment 1.

[0121] To verify the effectiveness of the proposed distributed control method for maintaining global connectivity in a multi-robot system with fluctuating numbers under remote operation, system simulation was used for testing and verification:

[0122] The simulated multi-robot system consists of a leader and four followers and operates in a two-dimensional environment. During the task execution, the five simulated robots are initially stationary, and their coordinates are x 1 (0) = [20, 10] m, x 2 (0) = [10, 5] m, x 3 (0) = [30, 5] m, x 4 (0) = [0, 0] m, x 5 (0) = [0, 40] m; and the obstacles existing in the simulation environment are located at The path of the remote robot can be seen in Figure 2 . The parameters of the remote robot are set as mass m = 2 kg, damping b = 3 Ns / m, maximum transmission range d max = 18 m, The desired distance d between robots d = 13 m Minimum safety distance The control force parameters are set as k = 0.01, ζ = 1, ρ 1 = 5, ρ 2 = 100, k v = 20, k p = 1, ε = 0.01. In Algorithm 2, μ = 10. The upper and lower limits of the energy in the energy tank are T max = 40 J, T min = 1 J, the initial energy is set as T ini = 32 J, and the sampling time is set as 0.01 s.

[0123] Suppose the system receives the command for Robot 3 to leave at t = 100 s, as shown in Figure 2 . Since the distance between Robot 5 and other robots is greater than 18 m, Robot 5 only communicates with Robot 3. To ensure the global connectivity of the remaining system after Robot 3 leaves, Algorithm 2 is used to establish communication between Robot 1 and Robot 5 at t = 100 s. As shown in Figure 4 λ 2The surface suddenly decreases at t = 420 s At this time, the robot 3 starts to decelerate and leave the system (see Figure 2 ), in addition, to avoid collisions, other robots regard robot 3 as an obstacle. At the moment when robot 3 leaves and robot 6 joins, see Figure 5 , adjust the energy in the energy tank to compensate for the change in the system energy caused by the sudden change in the robot speed and the eigenvalue λ 2 . As long as there is enough energy in the energy tank, the energy will always exceed the set lower limit, thus ensuring the normal operation of the system. In Figure 4 , it is clearly shown that the estimation error only fluctuates greatly during the period when the robot leaves or joins the system. However, after a short sampling time interval, the estimated λ 2 is closely synchronized with the actual value. Applying the designed scheme realizes the rapid matching of the estimated value of λ 2 with the true value, and at the same time ensures the passivity and global connectivity of the system.

[0124] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art of the present invention can make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A distributed control method for maintaining global connectivity of teleoperated open multi-robots, characterized in that: The following steps are involved: S100, establishing a dynamic model and weight matrix of a teleoperated multi-robot system, wherein during the interaction between the teleoperated control signal and the remote robot system, the remote robots including the leader and the follower adjust their speed and position according to the control signal input by the local robot user; and ensuring the connectivity between the robots through the distance-dependent weight matrix; S200, establishing a control strategy for the teleoperated multi-robot system, determining a control strategy for synchronization between the local robot user and the remote leader according to the teleoperated multi-robot system dynamics model established in step S100, and then introducing an energy tank to dynamically adjust energy exchange to ensure the stability and passivity of the system when the number of robots changes; S300, estimating Federer eigenvalues ​​through distributed control, using the communication model established in step S100, utilizing the communication capability of the robot in a distributed framework, and estimating Federer eigenvalues ​​according to changes in the system topology; S400, the connectivity of the multi-robot system is maintained and controlled during the process of leaving or returning to a task. When a robot is assigned a task and leaves the system, or returns to the system after completing a designated task, the relative distance and control parameters between the robots are adjusted to maintain the global connectivity of the system and avoid potential collision risks.

2. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 1, characterized in that: In step S100, it includes: The dynamic model of the telerobot is: Among them, subscript 1 indicates the remote leader, and the rest are remote followers; and are the speed and acceleration of all remote robots; M i and B i is the mass and local damping matrix of the remote robot i; the control input is in, To maintain the connectivity of the multi-robot system while ensuring that the distance between the remote robot i and the adjacent robots approaches the expected value; To control all remote machines i to move at the same speed, Provide teleoperation control input for remote leaders; In the telerobot system, the graph G = (V, E, A, L) is defined as the connected graph of the telerobot; where the vertex set V = {1, ..., N} is the set of all telerobots; the edge set is the set of all adjacent remote robots; N i = {j∈V|(i,j)∈E} is the set of all robots j adjacent to remote robot i; if (i,j)∈E, then the adjacency weight matrix associated with graph G is A=[a ij ]∈R N×N , a ij For the edge (V j ,V i ) if the weight of the node V i and V j is adjacent, the element a in the matrix ij > 0; the Laplacian matrix L associated with the graph G = [l ij ] = diag{ζ i }-A∈R N×N ,in and is a positive semidefinite matrix; Using graph theory, we construct a weighted adjacency matrix A and a Laplace matrix L to describe the connection and communication strength between robots. We introduce a dynamically adjusted second smallest Laplace eigenvalue λ2, which changes continuously with the relative distance between adjacent remote robots and the distance to surrounding obstacles. To this end, we design the following adjacency weighted matrix A=[a ij ]: Among them, the adjustment parameter α ij is the distance between robot i and robot j, and the adjustment parameter α is is the distance between robot i and obstacle s, d ij (t) is the relative distance between robot i and robot j that changes with time, is the relative distance between robot i and obstacle s that changes over time, is the set of all obstacles detected by robot i; β i (t) is the velocity damping matrix of robot i; The factor α in formula (3) ij (d ij )for: in, d ij =||x ij ||=||x i -x j ||; The expected distance between robots i and j; d max is the maximum sensing range between remote robots; d min Minimum safe distance between remote robots; in, The position of the sth obstacle detected by the i-th robot; The maximum distance at which the remote robot can detect obstacles; is the minimum safe distance between the robot and obstacles; The weight a in formula (4) ij It is used to maintain the connection between multiple remote robots and adjust the parameter α ij Drive the distance between adjacent remote robots to the desired distance By adjusting the parameter α is Prevent collisions with obstacles.

3. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 2, characterized in that: In step S200, it includes determining a control strategy for synchronization between the user's local robot and the remote leader: Among them, f lc is the teleoperation control force that connects the local robot to the remote leader robot, k l (t) is the gain function, which controls the synchronization effect between the local robot and the remote leader by adjusting its value. The pseudo speed r of the remote leader l Depends on the local robot's position and velocity; During teleoperation, the dynamic model of the remote robot is: Designed for remote robot systems Synchronize the movement of the leader and the local robot and pass Ensure the consistency of speed between robots and the global connectivity of the system; exist middle Yes to ensure The commonly used potential form, where P i is a commonly used potential energy function, is the estimated Federer eigenvalue of robot i, ε is the design parameter and ensures represents the control strength in the communication link of robot i; To ensure the passivity of the system, each telerobot is connected to a dynamically regulated energy tank: Among them, x t1 The status of the robot leader's energy tank; x ti is the energy tank state of the i-th robot and the energy function of the energy tank T max >0 represents the upper limit of the energy tank; 0 <T min <T max For Energy Tank T i Represents the lowest energy level; And control parameters Set the energy of robot i to T i Restricted to [T min ,T max ]; when T i ≥T max When selecting To limit the energy; when T min ≥T i When When T i ≥T max And∑(T j -T i )>0 or T min ≥T i And∑(T j -T i )<0, select When the number of robots fluctuates, the energy dissipated can be dynamically damped to partially compensate for the changes in energy in the system.

4. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 3, characterized in that: In step S300, in a distributed framework, robot i changes its position x to i (k), speed Parameter α is (k) and β i (k) The data is sent to the adjacent robots; each robot sends the current adjacency matrix A i (k) and the adjacency matrix from the first two times and Storage; For any robot at the initial moment, the adjacency matrix is ​​known and A i (k) Weight Calculated by formula (4); A j (k-1)s replace the weights with the corresponding weights received from its adjacency matrix 5. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 4, characterized in that: In step S400, it includes: Assumptions Among them, d d represents the ideal communication distance between robots under normal working conditions, and The ideal communication distance for the additional communication links; The parameter De∈{0,V} is used to identify the robot that is about to leave the system and is stored in each robot. V is the robot number. In the initial state, De=0. When robot i is assigned a task and leaves the system, De=i. Dim=N indicates that there are N remote robots in the current system. The Federer eigenvalue By removing A i After calculating the eigenvalues ​​of the Laplace matrix, we can get the eigenvalues ​​of the Laplace matrix. When , robot i and its neighboring robot j are in normal working communication distance and connectivity is maintained. The parameter μ>1 is an adjustable factor, which helps to modify faster. and The value of The value of when , robot i will start to decelerate and prepare to leave the system; at this time, the system adjusts the action instructions according to the control strategy, recalculates and updates the Federer eigenvalue; when robot i is in a stationary state waiting to return to the system, once the return command of robot i is received, the main control remote robot starts to move towards robot i and decelerates to ensure the safe return of robot i.

6. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 5, characterized in that: The passivity of the multi-robot system during the leaving or returning task is analyzed. The energy tank designed according to step S200 is used to cope with the sudden fluctuation of system energy when the number of robots fluctuates. The Lyapunov function is introduced to prove whether the multi-robot system is passive under remote operation control.

7. A distributed control method for maintaining global connectivity of teleoperated open multi-robots according to claim 6, characterized in that: When the number of robots changes, and It will experience instantaneous changes, causing sudden fluctuations in the energy stored in the energy tank; if the system is passive, there is a time-varying Lyapunov function V(t) and an initial Lyapunov function V(0), satisfying the following conditions: Among them, the scalar ψ≤0; f h is the external input force, is the transpose of the external input force vector; r l is the external input response; η is the independent variable in the integrand; The Lyapunov function for constructing the teleoperation system is: Among them, V l (t) = K l (t) is the Lyapunov function of the leader robot, V i (t) = K i (t)+T i (t) Lyapunov function for each follower robot; t l is the moment when the robot leaves the system, t r is the time of returning to the system; r ,t), the Lyapunov function V of each follower robot i Differentiating (t) with respect to time yields: It is deduced that: satisfy in For interval and [t r ,t) respectively in Integrate and sum, combined with known prior conditions, the energy change of the system at any time: in, is the upper limit of the total energy of all robots in the system, and the passivity of the system is proved when the number of robots fluctuates and the estimated value of λ2.

8. A distributed control system for teleoperated open multi-robots with global connectivity maintained, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 7, and executes the steps of the distributed control method for maintaining global connectivity of teleoperated open multi-robots when running.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which is configured to implement the steps of the distributed control method for maintaining global connectivity of teleoperated open multi-robots according to any one of claims 1 to 7 when called by a processor.

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