Preset-time asymmetric binary consensus control method for multi-robot hand positions

Abstract

The present invention relates to a robot control method and discloses a preset time asymmetric bipartite consistency control method for the hand position of multiple robots, comprising the following steps: calculating the state measurement error of the hand position; setting a desired convergence time and determining a time-varying scaling function; detecting an event trigger condition, and when the event trigger condition is met, updating the robot trigger moment and the trigger moment state, and transmitting the updated state to the robot itself and neighboring robot controllers; combining the trigger moment state and the time-varying scaling function of the robot itself and neighboring robots, calculating the event trigger control law, feeding it back to the robot hand, and adjusting the hand position state until the robot hand position state satisfies asymmetric bipartite consistency. The method disclosed by the present invention enables the robot to achieve asymmetric bipartite consistency of the hand position within a preset time while effectively reducing communication resource consumption.

Description

Technical Field

[0001] The present invention relates to a robot control method, and in particular to a preset time asymmetric binary consistency control method for multi-robot hand end positions. Background Art

[0002] Cooperative control technology for multi-agent systems is widely used in many engineering fields, such as drone fleets, sensor networks, intelligent power systems, and intelligent transportation. Multi-mobile robot systems, as one such application, have attracted widespread research attention. Consistency control is a key research direction in the collaborative control of multi-robot systems. It aims to drive all robots to achieve state convergence through local information exchange mechanisms. This property has important application value in engineering practice: for example, when multiple robotic arms collaborate to carry large objects, consistent control of the robot hand positions can ensure smooth and coordinated transport of the load. Specifically, the robot hand position is typically defined as any position close to the center of the wheel axle attached to the robot. Consistent control of this position can meet engineering needs. For example, if a gripper is placed at the robot hand position, coordinated control of the hand position is sufficient during the handling task.

[0003] Bipartite consistency is an important extension of the consistency problem, belonging to the collaborative control problem of multi-agent systems in cooperative and competitive networks. It means that all agents ultimately converge to a consistent state with the same value but opposite signs. For example, in a dynamic division of labor scenario, robots must autonomously split into groups and move in opposite directions to complete a region segmentation task. In addition, due to the varying magnitude of the competitive effect, each system may ultimately converge to two state values with different moduli and signs, thus achieving asymmetric bipartite consistency, which can cope with a wider range of practical application scenarios.

[0004] In practical engineering applications, multi-robot systems often operate in complex, resource-constrained environments. These resource constraints place higher demands on the system's control strategy. Traditional control methods struggle to achieve efficient resource utilization while ensuring control performance. Event-triggered control, as an efficient control strategy, has the core advantage of executing communication operations only when event trigger conditions are met. This significantly reduces unnecessary communication resource consumption while ensuring system stability, optimizes communication frequency and computational overhead, and improves the system's overall operational efficiency.

[0005] Furthermore, in traditional consistency control, the states of various systems gradually converge over time. This convergence typically occurs over an infinite timeframe, with the system states approaching consistency asymptotically. However, this infinite timeframe can result in insufficient convergence speed in practical applications, making it unsuitable for scenarios requiring rapid decision-making and real-time control. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides a preset time asymmetric binary consistency control method for the hand end positions of multiple robots, so that the robots can not only achieve asymmetric binary consistency of the hand end positions within the preset time, but also effectively reduce the consumption of communication resources.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A method for pre-setting time asymmetric binary consistency control of multi-robot hand positions includes the following steps:

[0009] S1. Collect the real-time status and triggering moment status of the robot's hand position and calculate the state measurement error of its hand position;

[0010] S2. Set the expected convergence time and determine the time-varying scaling function. Combine the state measurement error, the time-varying scaling function, and the triggering state of the robot itself and its neighboring robots to detect the event triggering condition. When the event triggering condition is met, update the robot triggering time and the triggering state at the same time, and transmit them to the robot itself and the neighboring robot controller.

[0011] S3. Combine the triggering state and time-varying scaling function of the robot itself and its neighboring robots, calculate the event triggering control law, feed it back to the robot hand, and adjust the hand position state until the robot hand position state meets the asymmetric bipartite consistency.

[0012] In the above solution, in step S1, the calculation formula of the state measurement error of the hand position is as follows:

[0013] ;

[0014] in, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and Respectively and No. The trigger moment, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, Indicates the A robot hand The state measurement error in the horizontal direction at all times, Indicates the A robot hand The state measurement error in the vertical direction at all times.

[0015] In the above solution, in step S2, the expected convergence time is set , determine the time-varying scaling function as follows:

[0016] ;

[0017] in, is the preset expected convergence time, for The time-varying scaling function of the moment, It is an adjustable constant parameter, and its value must satisfy .

[0018] In the above solution, in step S2, the event triggering conditions are as follows:

[0019] ;

[0020] in, Indicates the A robot hand The state measurement error in the horizontal direction at all times, Indicates the A robot hand The state measurement error in the vertical direction at all times, is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , For the The robot and The weight of the edge between robots, For the The neighbor set of the robot, and Respectively A robot hand The state-related thresholds in the horizontal and vertical directions at all times are in the following forms:

[0021] , ,

[0022] and is a constant whose value satisfies , , is the asymmetric proportional coefficient, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, and is a positive constant, For the A robot hand The external dynamic correlation threshold in the horizontal direction at any moment, For the A robot hand The external dynamic correlation thresholds in the vertical direction at all times are:

[0023] ;

[0024] ;

[0025] in, is a time-varying scaling function, and is a positive constant, is the preset expected convergence time.

[0026] In the above solution, in step S3, the event triggering control law is as follows:

[0027] ;

[0028] ;

[0029] in, For the A robot hand The virtual control law in the horizontal direction at all times, For the A robot hand The virtual control law in the vertical direction at all times, and is a positive constant, It is an adjustable constant parameter, and its value must satisfy , is the preset expected convergence time, is a time-varying scaling function, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, is the total number of robots, is the number of robots in subset 1, For the The robot and The weight of the edge between robots, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, is the asymmetric proportional coefficient, is a symbolic function, then The specific value of is: .

[0030] In the above scheme, in step S3, the conditions for asymmetric bisection consistency are as follows:

[0031] ;

[0032] ;

[0033] in, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and are the consistent state related constants of the robot hand in the horizontal and vertical directions, is the asymmetric proportional coefficient, is the preset expected convergence time, 、 Robot subset 1 and subset 2 are divided according to cooperative and competitive relationships.

[0034] Through the above technical solution, the preset time asymmetric binary consistency control method of the multi-robot hand end position provided by the present invention has the following beneficial effects:

[0035] 1. The present invention uses a time-varying scaling function to design a control law, ensuring that the hand position states of all robots achieve asymmetric bisection consistency within a preset time, thereby improving the convergence speed of the system;

[0036] 2. The present invention designs its own event triggering conditions for each robot, which reduces the communication frequency between robots and reduces resource consumption;

[0037] 3. In the present invention, the position coordinates of the robot hand end eventually converge to two state values with different moduli and signs, thereby being able to cope with more diverse practical application needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments or the prior art.

[0039] Figure 1 A communication topology diagram of multiple robots according to an embodiment of the present invention;

[0040] Figure 2 For the embodiment of the present invention trajectory;

[0041] Figure 3 For the embodiment of the present invention trajectory;

[0042] Figure 4 is the triggering moment of the robot in the embodiment of the present invention. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0044] The present invention provides a method for presetting the time asymmetric bisection consistency control of the position of the multi-robot hand end. The technical solution adopted is to construct a multi-robot hand end position model on a directed symbolic graph. and Treating the system as two independent first-order multi-agent systems, a time-preset asymmetric bipartite consensus control law and event triggering conditions are designed. Finally, MATLAB simulation is used to verify the effectiveness of the proposed control algorithm, which includes the following steps:

[0045] S1. Collect the real-time status and trigger moment status of the robot's hand position, and calculate the state measurement error of its hand position.

[0046] No. The kinematic model of a robot is as follows:

[0047] ;

[0048] in, , It's a robot The center of mass is The position coordinates at the moment, It is A robot in The direction of progress at all times The angle of the axis, is Linear speed control input at time, is The angular velocity control input at time t.

[0049] To handle the non-holonomic constraints of the multi-robot system, the robot hand position is defined as the distance from the robot center of mass to the robot on the robot's orientation axis. The hand position coordinates are Expressed as:

[0050] ;

[0051] in, is a small positive constant, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment.

[0052] Further, the derivative of the hand position can be obtained and , respectively, represent the virtual control law as and .because , the above control law is globally reversible, so the actual control law is and .

[0053] From the above, the dynamic model of the multi-robot hand position can be written as:

[0054] ;

[0055] Collect the real-time status of the robot's hand position and triggering state , the calculation formula of the state measurement error of the hand position is as follows:

[0056] ;

[0057] in, For the A robot, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and Respectively and No. The trigger moment, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, and That is, the trigger moment state, Indicates that the robot hand is The state measurement error in the horizontal direction at all times, Indicates that the robot hand is The state measurement error in the vertical direction at all times.

[0058] S2. Set the expected convergence time and determine the time-varying scaling function. Combine the state measurement error, the time-varying scaling function, and the triggering state of the robot itself and its neighboring robots to detect the event triggering condition. When the event triggering condition is met, update the robot triggering moment and the triggering state at the same time, and transmit them to the robot itself and the neighboring robot controller.

[0059] Directed symbolic graph for communication topology of multi-robot system Indicates that represents the set of robot nodes, represents the edge set, represents the adjacency matrix, where Represents a robot With robots For cooperative relationship, Represents a robot With robots For competitive relationship, is the set of real numbers. Neighborhood collection The present invention does not consider self-loop, that is, Assumptions and The hand positions of the robot reach two different positions respectively, and the asymmetric proportional coefficient is , according to the asymmetric bipartite consistency control goal of the multi-robot hand position, the directed symbolic graph Number set Divide into two disjoint subsets , .

[0060] Directed symbolic graph The Laplacian matrix is defined as ,in is a diagonal matrix with the following diagonal elements:

[0061] ;

[0062] Set the expected convergence time , determine the time-varying scaling function as follows:

[0063] ;

[0064] in, is the preset expected convergence time, is a time-varying scaling function, It is an adjustable constant parameter, and its value must satisfy .

[0065] Obviously, in the interval superior, ( )and . In addition, design function ,in , we can get the following formula

[0066] ;

[0067] in yes The right derivative of .

[0068] Set the event trigger conditions as follows:

[0069] ;

[0070] in, Indicates the A robot hand The state measurement error in the horizontal direction at all times, Indicates the A robot hand The state measurement error in the vertical direction at all times, is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , For the The robot and The weight of the edge between robots, For the The neighbor set of the robot, and Respectively A robot hand The state-related thresholds in the horizontal and vertical directions at all times are in the following forms:

[0071] , ,

[0072] and is a constant whose value satisfies , , is the asymmetric proportional coefficient, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, and is a positive constant, For the A robot hand The external dynamic correlation threshold in the horizontal direction at any moment, For the A robot hand The external dynamic correlation thresholds in the vertical direction at all times are:

[0073] ;

[0074] ;

[0075] in, is a time-varying scaling function, and is a positive constant, is the preset expected convergence time.

[0076] The event triggering conditions mentioned above are judged by combining the robot state measurement error, the triggering state of the robot itself and its neighboring robots, and the time-varying scaling function. If the inequality holds, the event triggering condition is satisfied, and the robot triggering moment is updated to the current moment. At the same time, the state at the triggering moment is updated to the current state, which is transmitted to the robot's own controller and then to the neighboring robot controller via the communication network, so that the subsequent robot and neighboring robots can calculate and update the event triggering control law. If the inequality does not hold, the event triggering condition is not satisfied, and the robot triggering moment and state at the triggering moment remain unchanged, and no information transmission action is performed.

[0077] S3. Combine the triggering state and time-varying scaling function of the robot itself and its neighboring robots, calculate the event triggering control law, feed it back to the robot hand, and adjust the hand position state until the robot hand position state meets the asymmetric bipartite consistency.

[0078] The event-triggered control law is as follows:

[0079] ;

[0080] ;

[0081] in, For the A robot hand The virtual control law in the horizontal direction at all times, For the A robot hand The virtual control law in the vertical direction at all times, and is a positive constant, It is an adjustable constant parameter, and its value must satisfy , is the preset expected convergence time, is a time-varying scaling function, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, is the total number of robots, is the number of robots in subset 1, For the The robot and The weight of the edge between robots, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, is the asymmetric proportional coefficient, is a symbolic function, then The specific value of is: .

[0082] It should be noted that the feedback control gain In the interval It is time-varying and plays an important role in achieving the preset time consistency control. superior, , then the feedback control gain is .therefore, The control law is similar to the common event-triggered asymptotically consistent control.

[0083] The above event-triggered control law is fed back to the robot hand to adjust its hand position and gradually achieve the asymmetric bipartite consistency control effect within the expected convergence time. The conditions for asymmetric bipartite consistency are as follows:

[0084] ;

[0085] ;

[0086] in, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and are the consistent state related constants of the robot hand in the horizontal and vertical directions, is the asymmetric proportional coefficient, is the preset expected convergence time, 、 Robot subset 1 and subset 2 are divided according to cooperative and competitive relationships.

[0087] Example

[0088] Consider a system consisting of seven robots with a communication topology such as Figure 1 As shown. Assume the asymmetric proportional coefficient , then the general Laplace matrix as follows:

[0089] ;

[0090] Set the robot's initial position state to , , , , , , .

[0091] The parameters of the control law are set as , , , , the parameters of the event trigger condition are set to , , , . Figure 2 and Figure 3 They were shown and According to the simulation results, the robot hand can achieve asymmetric bisection consensus within 5 seconds. Figure 4 The triggering moment of the robot is described, and there is no Zeno behavior in the system.

[0092] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one 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. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for pre-setting time asymmetric binary consistency control of multi-robot hand end positions, characterized in that: The steps include: S1. Collect the real-time status and triggering moment status of the robot's hand position and calculate the state measurement error of its hand position; S2. Set the expected convergence time and determine the time-varying scaling function. Combine the state measurement error, the time-varying scaling function, and the triggering state of the robot itself and its neighboring robots to detect the event triggering condition. When the event triggering condition is met, update the robot triggering time and the triggering state at the same time, and transmit them to the robot itself and the neighboring robot controller. S3: Combine the triggering state and time-varying scaling function of the robot itself and its neighboring robots, calculate the event triggering control law, feed it back to the robot hand, and adjust the hand position state until the robot hand position state meets the asymmetric bipartite consistency; In step S2, the event triggering conditions are as follows: ； in, Indicates the A robot hand The state measurement error in the horizontal direction at all times, Indicates the A robot hand The state measurement error in the vertical direction at all times, is an adjustable constant parameter, and its value is , is an adjustable constant parameter, and its value is , For the The robot and The weight of the edge between robots, For the The neighbor set of the robot, and Respectively A robot hand The state-related thresholds in the horizontal and vertical directions at the moment are in the following forms: ， ， and is a constant whose value satisfies , , is the asymmetric proportional coefficient, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, and is a positive constant, For the A robot hand The external dynamic correlation threshold in the horizontal direction at any moment, For the A robot hand The external dynamic correlation thresholds in the vertical direction at all times are: ； ； in, is a time-varying scaling function, and is a positive constant, is the preset expected convergence time.

2. The preset time asymmetric binary consistency control method for multi-robot hand end positions according to claim 1 is characterized in that: In step S1, the calculation formula of the state measurement error of the hand position is as follows: ； in, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and Respectively and No. The trigger moment, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, Indicates the A robot hand The state measurement error in the horizontal direction at all times, Indicates the A robot hand The state measurement error in the vertical direction at each moment.

3. The preset time asymmetric binary consistency control method for multi-robot hand end positions according to claim 1, characterized in that: In step S2, set the expected convergence time , determine the time-varying scaling function as follows: ； in, is the preset expected convergence time, for The time-varying scaling function of the moment, It is an adjustable constant parameter, and its value must satisfy .

4. The method for controlling the preset time asymmetric binary consistency of the multi-robot hand end positions according to claim 1, characterized in that: In step S3, the event-triggered control law is as follows: ； ； in, For the A robot hand The virtual control law in the horizontal direction at all times, For the A robot hand The virtual control law in the vertical direction at all times, and is a positive constant, It is an adjustable constant parameter, and its value must satisfy , is the preset expected convergence time, is a time-varying scaling function, 、 For robot subsets 1 and 2 divided by cooperative and competitive relationships, is the total number of robots, is the number of robots in subset 1, For the The robot and The weight of the edge between robots, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The horizontal state, For the The robot hand is triggered at the moment The vertical state, For the The robot hand is triggered at the moment The vertical state, is the asymmetric proportional coefficient, is a symbolic function, then The specific value of is: .

5. The preset time asymmetric binary consistency control method for multi-robot hand end positions according to claim 1, characterized in that: In step S3, the conditions for asymmetric bipartite consistency are as follows: ； ； in, For the A robot hand The horizontal state at the moment, For the A robot hand The vertical state at the moment, and are the consistent state related constants of the robot hand in the horizontal and vertical directions, is the asymmetric proportional coefficient, is the preset expected convergence time, 、 Robot subset 1 and subset 2 are divided according to cooperative and competitive relationships.

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