Preset time asymmetric dichotomy consistency control method for hand end positions of multiple robots

Abstract

The invention relates to a robot control method, and discloses a preset time asymmetric dichotomy consistency control method for hand end positions of multiple robots, which comprises the following steps of: calculating state measurement errors of the hand end positions; setting expected convergence time, and determining a time-varying scaling function; detecting an event triggering condition, when the event triggering condition is met, updating a robot triggering moment, updating a triggering moment state at the same time, and transmitting the triggering moment state to the robot and a neighbor robot controller end; and combining the triggering time state of the robot and the neighbor robot, the time-varying scale function and the calculation event triggering control law, feeding back to the hand end of the robot, and adjusting the position state of the hand end until the position state of the hand end of the robot meets the asymmetric dichotomy consistency. According to the method disclosed by the invention, the asymmetric dichotomy consistency of the hand end position of the robot can be realized within the preset time, and the consumption of communication resources can be effectively reduced.

Description

Technical Field

[0001] The present invention relates to a robot control method, and particularly to a preset-time asymmetric bipartite consensus control method for the end-effector positions of multiple robots. Background Art

[0002] The cooperative control technology of multi-agent systems is widely applied in many engineering fields, such as unmanned aerial vehicle formations, sensor networks, smart power systems, and intelligent transportation. As one of the applications, the multi-mobile robot system has attracted extensive attention in current research. Consensus control is an important research direction in the cooperative control of multi-robot systems, aiming to drive all robots to achieve state convergence through a local information interaction mechanism. This feature has important application value in engineering practice. For example, when multiple robotic arms cooperate to carry a large object, the stable and cooperative transportation of the load can be ensured by the consensus regulation of the end-effector positions of the robots. Specifically, the end-effector position of a robot is usually defined as any position close to the center of the wheel axis fixedly connected to the robot. The consensus control of this position can meet the engineering requirements. For example, a gripper is set at the end-effector position of the robot. During the execution of the handling task, only the coordinated control of the end-effector position needs to be achieved.

[0003] Bipartite consensus is an important extension of the consensus problem and belongs to the cooperative control problem of multi-agent systems under the cooperative-competitive network, meaning that all agents finally converge to a consistent state with the same numerical value but opposite signs. For example, in a dynamic division of labor operation scenario, the robots need to autonomously divide into groups and move in opposite directions to complete the area division task. In addition, due to the different magnitudes of the influence of the competitive effect, each system may finally converge to two state values with different moduli and signs, that is, achieve asymmetric bipartite consensus, so as to be able to cope with more diverse actual application scenarios.

[0004] In practical engineering applications, multi-robot systems usually operate in complex environments with resource constraints. These resource constraints pose higher requirements on the control strategies of the systems. Traditional control methods are difficult to achieve efficient utilization of resources while ensuring control performance. As an efficient control strategy, event-triggered control's core advantage lies in performing communication operations only when the event-triggering conditions are met, significantly reducing unnecessary communication resource consumption on the basis of ensuring system stability, optimizing the communication frequency and computational overhead, and improving the overall operating efficiency of the system.

[0005] In addition, during the traditional consensus control process, the states of each system gradually tend to be consistent over time. This convergence usually occurs within an infinite time, and the system states approach consensus in an asymptotic manner. However, its infinite-time convergence characteristic may lead to insufficient convergence speed in practical applications and cannot meet the scenario requirements that need quick decision-making and real-time control. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a preset-time asymmetric bipartite consensus control method for the end-effector positions of multiple robots, enabling the robots to achieve asymmetric bipartite consensus of the end-effector positions within a preset time and effectively reducing communication resource consumption.

[0007] To achieve the above object, the technical solution of the present invention is as follows: The preset-time asymmetric bipartite consensus control method for the end-effector positions of multiple robots includes the following steps: S1. Collect the real-time state and the state at the triggering moment of the end-effector position of the robot, and calculate the state measurement error of its end-effector position; S2. Set the desired convergence time and determine the time-varying scaling function; combine the state measurement error, the time-varying scaling function, the state of the robot itself and the triggering moment states of the neighbor robots to detect the event-triggering condition. When the event-triggering condition is satisfied, update the triggering moment of the robot, and at the same time update the state at the triggering moment and transmit it to the controller ends of the robot itself and the neighbor robots; S3. Combine the triggering moment states of the robot itself and the neighbor robots and the time-varying scaling function to calculate the event-triggering control law, and feedback it to the end-effector of the robot to adjust the state of the end-effector position until the state of the end-effector position of the robot satisfies the asymmetric bipartite consensus.

[0008] In the above solution, in step S1, the calculation formula for the state measurement error of the end-effector position is as follows: ; where is the horizontal direction state of the end-effector of the th robot at the moment, is the vertical direction state of the end-effector of the th robot at the moment, and respectively represent the and th triggering moments of , is the horizontal direction state of the end-effector of the th robot at the triggering moment , is the vertical direction state of the end-effector of the th robot at the triggering moment , represents the state measurement error of the th robot end-effector in the horizontal direction at the moment, represents the th robot end-effector in the The state measurement error of the moment in the vertical direction.

[0009] In the above solution, in step S2, set the desired convergence time , and determine the time-varying scale function as follows: ; where is the preset desired convergence time, is the time-varying scale function at the moment of is an adjustable constant parameter, and its value needs to satisfy .

[0010] In the above solution, in step S2, the event trigger condition is as follows: ; where represents the state measurement error of the th robot end effector in the horizontal direction at the moment of , represents the state measurement error of the th robot end effector in the vertical direction at the moment of , is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , is the weight of the edge between the th robot and the th robot, is the neighbor set of the th robot, and respectively represent the state-related thresholds of the th robot end effector in the horizontal and vertical directions at the moment of , and their specific forms are: , , and are constants, and their values satisfy , , is an asymmetric proportionality coefficient, , are subsets 1 and 2 of robots divided according to the cooperation-competition relationship, is the horizontal direction state of the th robot end effector at the trigger moment , is the The horizontal direction state of the robot hand at the trigger moment is the vertical direction state of the robot hand at the trigger moment is the vertical direction state of the robot hand at the trigger moment and are positive constants, is the external dynamic correlation threshold of the robot hand in the horizontal direction at the moment, is the external dynamic correlation threshold of the robot hand in the vertical direction at the moment, and their values are respectively: Among them, is a time-varying scaling function, and are positive constants, is a preset expected convergence time.

[0011] In the above solution, in step S3, the event-triggered control law is as follows: ; ; Among them, is the virtual control law of the robot hand in the horizontal direction at the moment, is the virtual control law of the robot hand in the vertical direction at the moment, and are positive constants, is an adjustable constant parameter, and its value needs to satisfy are robot subsets 1 and 2 divided according to the cooperation-competition relationship, is the total number of robots, is the number of robots in subset 1, is the weight of the edge between the th robot and the th robot​ is the horizontal direction state of the th robotic hand at the trigger moment . is the horizontal direction state of the th robotic hand at the trigger moment . is the vertical direction state of the th robotic hand at the trigger moment . is the vertical direction state of the th robotic hand at the trigger moment . is the asymmetric proportionality coefficient, is the sign function, then takes the following specific values: .

[0012] In the above solution, in step S3, the conditions for the asymmetric binary consensus are as follows: ; ; where is the horizontal direction state of the th robotic hand at the moment, is the vertical direction state of the th robotic hand at the moment, and are the consensus state related constants of the robotic hand in the horizontal and vertical directions respectively, is the asymmetric proportionality coefficient, is the preset expected convergence time, , are the robot subsets 1 and 2 divided according to the cooperation-competition relationship.

[0013] Through the above technical solution, the preset-time asymmetric binary consensus control method for the positions of multiple robotic hands provided by the present invention has the following beneficial effects: 1. The present invention designs the control law by using the time-varying scale function to ensure that the position states of the hands of all robots achieve asymmetric binary consensus within the preset time, improving the convergence speed of the system; 2. The present invention designs the event trigger conditions for each robot, reducing the communication frequency between robots and resource consumption; 3. In the present invention, the position coordinates of the robotic hand finally converge to two state values with different moduli and signs respectively, so as to be able to meet more diverse actual application requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art.

[0015] Figure 1 It is the communication topology diagram of multi-robots in the embodiment of the present invention; Figure 2 In the embodiment of the present invention trajectory; Figure 3 In the embodiment of the present invention trajectory; Figure 4 It is the trigger moment of the robot in the embodiment of the present invention. Specific embodiments

[0016] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention.

[0017] The present invention provides a preset-time asymmetric bipartite consensus control method for the hand-end positions of multi-robots. The technical solution adopted is to construct a multi-robot hand-end position model on a directed signed graph, regarding and as two independent first-order multi-agent systems, designing a preset-time asymmetric bipartite consensus control law and an event-triggering condition, and finally using MATLAB simulation to verify the effectiveness of the proposed control algorithm, including the following steps: S1. Collect the real-time state of the robot hand-end position and the state at the trigger moment, and calculate the state measurement error of its hand-end position.

[0018] The th robot's kinematic model is as follows: ; Among them, , is the position coordinate of the centroid of the robot at the moment, is the angle between the forward direction of the th robot and the axis at the moment, is the linear velocity control input at the moment, is the angular velocity control input at the moment.

[0019] To handle the nonholonomic constraints of the multi-robot system, the robot hand-end position is defined as being at a distance from the centroid of the robot on the direction axis of the robot The point. Then the hand - end position coordinates are expressed as: ; where, is a very small positive constant, is the horizontal - direction state of the th robot hand - end at time, is the vertical - direction state of the th robot hand - end at time.

[0020] Furthermore, by taking the derivative of the hand - end position, we can obtain and , which represent the virtual control laws as and . Since , the above - mentioned control laws are globally invertible. Therefore, the actual control laws are and .

[0021] From the above, the dynamic model of the multi - robot hand - end position can be recorded as: ;

[0022] Collect the real - time state of the robot hand - end position and the state at the trigger time . The calculation formula for the state measurement error of the hand - end position is as follows: ; where, is the th robot, is the horizontal - direction state of the th robot hand - end at time, is the vertical - direction state of the th robot hand - end at time, and respectively represent and 's th trigger time, is the horizontal - direction state of the th robot hand - end at the trigger time , is the vertical - direction state of the th robot hand - end at the trigger time , and i.e., the state at the trigger time, Denote the state measurement error of the robot end - effector at in the horizontal direction at time Denote the state measurement error of the robot end - effector at in the vertical direction at time

[0023] S2. Set the desired convergence time and determine the time - varying scaling function; combine the state measurement error, the time - varying scaling function, the states of the robot itself and its neighbor robots at the triggering moments, detect the event - triggering condition. When the event - triggering condition is satisfied, update the triggering time of the robot, and at the same time update the state at the triggering time and transmit it to the controllers of the robot itself and its neighbor robots.

[0024] The communication topology of the multi - robot system is represented by a directed signed graph where denotes the set of robot nodes, denotes the set of edges, denotes the adjacency matrix, where denotes that robot and robot are in a cooperative relationship, denotes that robot and robot are in a competitive relationship, is the set of real numbers. The neighbor set of robot is denoted by This invention does not consider self - loops, that is Assume and the end - effector positions of robots reach two different positions respectively, and the asymmetric proportionality coefficient is According to the asymmetric bipartite consensus control objective of the multi - robot end - effector positions, divide the number set of the directed signed graph into two non - overlapping subsets .

[0025] The Laplacian matrix of the directed signed graph is defined as where is a diagonal matrix, and the diagonal elements are: ;

[0026] Set the desired convergence time , and determine the time - varying scaling function as follows: ; where is the preset desired convergence time, is the time - varying scaling function, is an adjustable constant parameter, and its value needs to satisfy .

[0027] Obviously, in the interval . ( ) and . Additionally, design the function , where , and the following formula can be obtained ; where is 's right derivative.

[0028] Set the event trigger conditions as follows: ; where represents the state measurement error of the end - effector of the th robot in the horizontal direction at time , represents the state measurement error of the end - effector of the th robot in the vertical direction at time , is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , is the weight of the edge between the th robot and the th robot,[[]] is the neighbor set of the th robot, and are the state - related thresholds of the end - effector of the th robot in the horizontal and vertical directions at time respectively, and their specific forms are: , , and are constants, and their values satisfy , , is an asymmetric proportionality coefficient, , are subsets 1 and 2 of the robots divided according to the cooperation - competition relationship, is the horizontal - direction state of the end - effector of the th robot at the trigger time , is the vertical - direction state of the end - effector of the th robot at the trigger time The horizontal direction state, is the vertical direction state of the nth robot hand at the trigger moment, is the vertical direction state of the nth robot hand at the trigger moment, and are positive constants, is the external dynamic correlation threshold in the horizontal direction of the nth robot hand at the moment, is the external dynamic correlation threshold in the vertical direction of the ; ; wherein, is a time-varying scaling function, and are positive constants, is a preset desired convergence time.

[0029] Combined with the robot state measurement error, the trigger moment states of the robot itself and neighboring robots, and the time-varying scaling function, the above event-triggering conditions are judged. If the inequality holds, the event-triggering condition is satisfied, the robot trigger moment is updated to the current moment. At the same time, the trigger moment state is updated to the current state, which is transmitted to the robot's own controller side and transmitted to the neighboring robot controller side through the communication network for subsequent calculation and update of the event-triggering control law by the robot and neighboring robots; if the inequality does not hold, the event-triggering condition is not satisfied, and both the robot trigger moment and the trigger moment state remain unchanged, and no information transmission action is performed.

[0030] S3. Combine the trigger moment states of the robot itself and neighboring robots and the time-varying scaling function to calculate the event-triggering control law, feedback it to the robot hand, and adjust the hand position state until the robot hand position state satisfies the asymmetric bipartite consensus.

[0031] The event-triggering control law is as follows: ; ; wherein, is the virtual control law in the horizontal direction of the nth robot hand at the moment, The virtual control law of a robotic hand in the vertical direction at a certain moment, and are positive constants, is an adjustable constant parameter, and its value needs to satisfy , is a preset desired convergence time, is a time-varying scaling function, , are subsets 1 and 2 of robots divided according to the cooperation-competition relationship, is the total number of robots, is the number of robots in subset 1, is the th robot and the th robot, and the weight of the edge between them, is the th robot's hand state in the horizontal direction at the triggering moment , is the th robot's hand state in the horizontal direction at the triggering moment , is the th robot's hand state in the vertical direction at the triggering moment , is the th robot's hand state in the vertical direction at the triggering moment , is an asymmetric proportional coefficient, is the sign function, then takes the following specific value: .

[0032] It should be noted that the feedback control gain is time-varying in the interval , and it plays an important role in achieving the preset time consistency control. In the interval , , then the feedback control gain is . Therefore, the control law is similar to the common event-triggered asymptotic consistency control.

[0033] The above event-triggered control law is fed back to the robotic hand to adjust its hand position, gradually achieving the asymmetric bipartite consensus control effect within the desired convergence time. The conditions for asymmetric bipartite consensus are as follows: ; ; Among them, is the horizontal direction state of the th robot hand at moment, is the vertical direction state of the th robot hand at moment, and are the consistency state related constants of the robot hand in the horizontal and vertical directions respectively, is the asymmetric proportionality coefficient, is the preset desired convergence time, 、 are the robot subsets 1 and 2 divided according to the cooperation-competition relationship.

[0034] Embodiment Consider a system composed of seven robots, and the communication topology is as Figure 1 shown. Let the asymmetric proportionality coefficient , then the general Laplacian matrix is as follows: ; Set the initial position state of the robot to , , , , , , .

[0035] Set the parameters of the control law to , , , , and set the parameters of the event trigger condition to , , , . Figure 2 and Figure 3 respectively show the and trajectories. According to the simulation results, the robot hand can achieve asymmetric bipartite consensus within 5s. In addition, Figure 4 describes the trigger moments of the robots, and there is no Zeno behavior in the system.

[0036] The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. Preset-time asymmetric bipartite consensus control method for multi-robot end-effector positions, characterized in that It includes the following steps: S1. Collect the real-time state and the state at the trigger moment of the robot's end-effector position, and calculate the state measurement error of its end-effector position; S2. Set the desired convergence time and determine the time-varying scaling function; combine the state measurement error, the time-varying scaling function, the states of the robot itself and its neighbor robots at the trigger moment to detect the event trigger condition. When the event trigger condition is satisfied, update the robot's trigger moment, and at the same time update the state at the trigger moment and transmit it to the controller ends of the robot itself and its neighbor robots; S3. Combine the trigger moment states of the robot itself and its neighbor robots and the time-varying scaling function to calculate the event-triggered control law, and feedback it to the robot's end-effector to adjust the state of the end-effector position until the state of the robot's end-effector position satisfies the asymmetric bipartite consensus.

2. The preset time asymmetric bipartite consensus control method for the end - effector positions of multiple robots according to claim 1, characterized in that In step S1, the calculation formula for the state measurement error of the end-effector position is as follows: ； Among them, is the horizontal direction state of the th robotic hand at moment, is the vertical direction state of the th robotic hand at moment, and respectively represent and 's nd trigger moment, is the horizontal direction state of the th robotic hand at the trigger moment , is the vertical direction state of the th robotic hand at the trigger moment , represents the state measurement error of the th robotic hand in the horizontal direction at moment, represents the state measurement error of the th robotic hand in the vertical direction at moment.

3. The preset time asymmetric binary consensus control method for the end - effector positions of multiple robots according to claim 1, wherein In step S2, set the desired convergence time , and determine the time-varying scaling function as follows: ； Among them, is a preset expected convergence time, is the time-varying scale function at time is an adjustable constant parameter, and its value needs to satisfy .

4. The preset time asymmetric bipartite consensus control method for the end - effector positions of multiple robots according to claim 1, wherein, In step S2, the event trigger condition is as follows: ； Among them, represents the state measurement error of the th robot end effector in the horizontal direction at moment, represents the state measurement error of the th robot end effector in the vertical direction at moment, is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , is the weight of the edge between the th robot and the th robot, is the neighbor set of the th robot, and are respectively the state correlation thresholds in the horizontal and vertical directions of the th robot end effector at moment, and their specific forms are as follows: ， ， and are constants, and their values satisfy , , is an asymmetric proportionality coefficient, , are subsets 1 and 2 of robots divided according to the cooperation-competition relationship, is the horizontal direction state of the th robot end at the trigger moment , is the horizontal direction state of the th robot end at the trigger moment , is the vertical direction state of the th robot end at the trigger moment , is the vertical direction state of the th robot end at the trigger moment , and are positive constants, is the external dynamic correlation threshold in the horizontal direction of the th robot end at the moment , is the external dynamic correlation threshold in the vertical direction of the th robot end at the moment , and their values are respectively: ； ； Among them, is a time-varying scaling function, and are positive constants, is a preset desired convergence time.

5. The preset time asymmetric bipartite consensus control method for the end - effector positions of multiple robots according to claim 1, characterized in that In step S3, the event-triggered control law is as follows: ； ； Among them, is the virtual control law in the horizontal direction of the end of the th robot hand at the moment, is the virtual control law in the vertical direction of the end of the th robot hand at the moment, and are positive constants, is an adjustable constant parameter, and its value needs to satisfy , is the preset expected convergence time, is a time-varying scaling function, , are robot subsets 1 and 2 divided according to the cooperation-competition relationship, is the total number of robots, is the number of robots in subset 1, is the weight of the edge between the th robot and the th robot, is the horizontal direction state of the end of the th robot hand at the trigger moment , is the horizontal direction state of the end of the th robot hand at the trigger moment , is the vertical direction state of the end of the th robot hand at the trigger moment , is the vertical direction state of the end of the th robot hand at the trigger moment , is an asymmetric proportionality coefficient, is the sign function, then takes the specific value of: .

6. The preset-time asymmetric bipartite consensus control method for the end-effector positions of multiple robots according to claim 1, wherein In step S3, the condition for the asymmetric bipartite consensus is as follows: ； ； Among them, is the horizontal direction state of the th robot hand at moment, is the vertical direction state of the th robot hand at moment, and are the consistency state related constants of the robot hand in the horizontal direction and the vertical direction respectively, is the asymmetric proportionality coefficient, is the preset desired convergence time, , are the robot subsets 1 and 2 divided according to the cooperation-competition relationship.

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