Distributed UAV dynamic formation method and system based on self-triggering coordination mechanism

Abstract

This invention discloses a distributed UAV dynamic formation method and system based on a self-triggered collaborative mechanism. Each follower UAV in a UAV formation publishes its own status information to neighboring UAVs, collects and integrates neighbor information, and calculates its expected acceleration based on that information. After communicating and acquiring neighbor information, the system estimates the global formation stability state based on that information and predicts the next communication time. Communication is repeated until the system stability variable is satisfied, completing the formation. This method eliminates the need for nearly continuous changes in the motion state of each UAV, reduces the number of communications within the formation, and does not affect the speed and results of algorithm convergence, thereby improving the robustness and practicality of the algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of automation and computer technology, and particularly relates to a distributed unmanned aerial vehicle dynamic formation method and system based on a self-triggering coordination mechanism. Background Art

[0002] Currently, multi-agent formation control schemes are categorized into centralized and distributed formation control schemes. Distributed formation control eliminates the need for a central control center; each agent simply acquires and analyzes the constraints of its neighbors. This allows for rapid system-wide information integration, enabling formation control. Distributed formation control schemes are gaining increasing attention due to their low communication costs and high practical application value.

[0003] However, the ideal formation control algorithm operates under the assumption that information is continuously exchanged between intelligent agents. However, in the real world, continuous communication may not be possible. If the communication interval increases (usually in the hundreds of milliseconds), the formation formation rate may be greatly reduced or even the formation system state may tend to diverge. The formation task will never be completed, which will have a bad impact on the stability of the formation system. Therefore, it is urgent to solve the problem of the high dependence of the UAV formation control algorithm on the continuity of UAV communication. Summary of the Invention

[0004] This invention addresses the existing problem of drone formations being unable to communicate continuously or requiring intermittent communication to reduce energy consumption. It provides a distributed drone dynamic formation method and system based on a self-triggered collaborative mechanism. Each follower drone in the drone formation publishes its own status information to neighboring drones, collects and integrates neighbor information, and calculates its own expected acceleration based on the neighbor information. After communicating and obtaining neighbor information, it estimates the global formation stability state based on the neighbor information and predicts the time for the next communication. Communication is repeated until the system stability variable is satisfied and the formation is complete. This method eliminates the need for each drone's own motion state to change continuously. The number of communications within the formation is reduced without affecting the speed and results of algorithm convergence, thereby improving the robustness and practicality of the algorithm.

[0005] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a distributed UAV dynamic formation method based on a self-triggered collaborative mechanism, in which each follower UAV in the UAV queue publishes its own status information to the neighboring UAV, collects and integrates the neighbor information, and calculates its own expected acceleration based on the neighbor information. After communicating and obtaining the neighbor information, the global formation stability state is estimated based on the neighbor information, and the time of the next communication is predicted. The communication is repeated until the system stability variable judgment is met and the formation is completed.

[0006] As an improvement of the present invention, a distributed UAV dynamic formation method based on a self-triggered coordination mechanism includes the following steps:

[0007] S1: Establish a dynamic formation model of distributed UAVs, which includes a leader UAV and a follower UAV; establish the communication topology G(V, E, Ω) of the UAVs, where V = {V1, V2...V n} represents the set of drone nodes, E={E1,E2……E n} represents the communication link between two UAVs, and Ω is the edge weight matrix of the communication link;

[0008] S2: The follower drone sends a communication request to the neighboring node, publishes its own information, and collects and integrates the neighboring drone status information; the communication request sent by the follower drone includes at least: its own position information, speed information and acceleration information;

[0009] S3: After receiving the neighboring drone status information obtained in step S2, each follower drone uses a second-order control strategy to calculate the control input, which is its own desired acceleration:

[0010]

[0011] Among them, a i To follow the desired acceleration of the drone, N i is the set of neighbor nodes of drone i, p i 、p j are the positions of drones i and j, v i 、v j are the speeds of drones i and j, k p >0,k v >0 is a constant, ω ij is the stress constant of the undirected edge formed by UAV i and UAV j in the formation;

[0012] S4: After communicating and obtaining neighbor information, the system stability variable is calculated based on the Lyapunov stability principle using the current system state, and the system stability state is predicted, and the time when the next communication event is triggered is predicted;

[0013] S5: The drone waits for the predicted event trigger time to arrive and monitors the communication channel. If the communication trigger time has not arrived, but a communication request has been received from a neighbor, it determines this time as the event trigger time, sends a communication request to the neighbor, and continues with step S2. When the predicted event trigger time arrives, the communication event is triggered and the drone's local data is updated.

[0014] S6: Determine whether the formation mission is completed based on the system stability variable. If the formation error is acceptable and the termination condition is met, the formation mission is completed.

[0015] As an improvement of the present invention, the edge weight matrix of the communication link Ω=[Ω ij Specifically:

[0016]

[0017] Among them, Ω {ij} is the element of the weight matrix, representing the communication weight between UAV i and UAV j, ω ij is the stress constant of the undirected edge formed by UAV i and UAV j in the formation, satisfying N i is the set of neighbor nodes of drone i, k is any drone in the set of neighbor drones of drone i, ω ik It is the stress constant of the undirected edge formed by UAV i and UAV k.

[0018] As another improvement of the present invention, in step S3, the expected acceleration of the following drone needs to meet the constraint conditions. A saturation velocity and saturation acceleration constraint is set for each drone. When the calculated expected acceleration is greater than the saturation acceleration constraint, the controller sets the expected velocity to the saturation acceleration and determines whether the current velocity of the drone reaches the saturation velocity constraint. If so, only the normal acceleration component is retained. The saturation acceleration constraint is as follows:

[0019]

[0020] The constraints on the saturation velocity are as follows:

[0021]

[0022] Among them, v sat ,a sat are the saturation speed and saturation acceleration that each drone needs to meet, sat a (a i ), sat v (a i ) are the execution functions for executing saturated acceleration and saturated velocity constraints respectively.

[0023] As another improvement of the present invention, the communication information content of step S4 includes the timestamp of the current moment, the current position, the current speed and the current acceleration; the neighbor information obtained by each drone is a discrete sequence with a timestamp. At the non-communication moment, the expected acceleration of the drone is calculated based on the neighbor state at the previous communication moment, and complies with the saturation acceleration constraint before the next communication moment arrives.

[0024] As another improvement of the present invention, in step S4, after the communication is completed, each UAV calculates the next communication time based on the stability variable and the current neighbor information as follows:

[0025]

[0026] in, For the next communication time, is the most recent communication time, P is the constant coefficient matrix of the formation system, I2 is the 2*2 unit matrix, δ i is the internal system error variable of UAV i, is a constant matrix, is the time derivative of the system stability variable.

[0027] As a further improvement of the present invention, in step S6, δ i Establish the system error variable for drone i, i = 1, 2, 3...n:

[0028]

[0029] Based on the Lyapunov function, the system stability variable is established for the i-th follower UAV, namely:

[0030]

[0031]

[0032] like If the global formation system is stable, then the global formation system is stable, and within each UAV,

[0033] In order to achieve the above-mentioned purpose, the present invention also adopts the following technical solution: a distributed UAV dynamic formation system based on a self-triggered collaborative mechanism, including a computer program, which implements the steps of any of the above-mentioned methods when executed by a processor.

[0034] Compared with the existing technology, the technical advantages and effects of the present invention are as follows: the present invention provides a distributed UAV dynamic formation method and system based on a self-triggering coordination mechanism, which makes up for the problem of insufficient continuity of variables in second-order linear control systems; the present invention adopts fully distributed control, and UAV communications do not need to be triggered synchronously, and there is no need to fit continuous control through high-frequency triggering of communication and control. Instead, it uses an event-triggered self-triggering mechanism to predict global state changes locally on each UAV and dynamically determine the communication time. This not only reduces the number of UAV states during the movement process, but also significantly reduces the number of communications between UAVs, and ensures that the formation system is strictly in a convergence state throughout the process. This method introduces speed and acceleration constraints into UAV motion control. In practical applications, it not only reduces the operating burden of the controller, but also realizes the estimation of the global state through constraints, so that the control algorithm can still maintain good performance in unreliable channels and is more robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the steps of the method of the present invention;

[0036] Figure 2 This is a schematic diagram of the formation effect after the formation task is completed in Example 2 of the present invention;

[0037] Figure 3 Schematic diagram of the convergence of local error variables of three following drones during the entire algorithm operation process in Example 2 of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0039] Example 1

[0040] The distributed UAV dynamic formation method based on the self-triggered coordination mechanism includes the following steps:

[0041] S1: Establish a dynamic formation model of distributed UAVs, designate three UAVs as leaders and the rest as followers; the leader perceives the environment in real time and makes its own control decisions; establish the UAV communication topology ω(V, E, Ω), where V = {V1, V2...V n} represents the set of drone nodes, E={E1,E2……E n} represents the communication link between two UAVs, and Ω is the edge weight matrix of the communication link, that is:

[0042]

[0043] where ω ijis the stress constant of the undirected edge formed by UAV i and UAV j in the formation, satisfying:

[0044]

[0045] where N i is the set of neighbor nodes of drone i, p i is the location of drone i.

[0046] S2: The follower drone sends a communication request to the neighboring node, publishes its own information, and collects and integrates the status information of neighboring drones; the communication message sent by drone i contains: its own location information p i =[x,y] T , speed information v i =[v x ,v y ] T , acceleration information a i =[a x ,a y ] T .

[0047] S3: After receiving the neighboring drone status information obtained in step S2, each follower drone uses a second-order control strategy to calculate the control input and perform the specified constraint processing on the control input. After completion, it proceeds to step S4; the control input is the desired acceleration, and the specific calculation formula is:

[0048]

[0049] Among them, N i represents the set of neighboring drones of drone i, ω ij is the stress constant of the undirected edge formed by UAV i and UAV j in the formation, k p ,k v It is a constant greater than zero, and its value will not have a significant impact on formation control. It is usually k p =k v =5.

[0050] For individuals in the formation, the expected acceleration of the following drones needs to meet the constraints. The saturation velocity and saturation acceleration constraints are set for each drone. When the calculated expected acceleration is greater than the saturation acceleration constraint, the controller sets the expected velocity to the saturation acceleration and determines whether the current velocity of the drone reaches the saturation velocity constraint. If so, only the normal acceleration component is retained. The saturation acceleration is as follows:

[0051]

[0052] The constraints on the saturation velocity are as follows:

[0053]

[0054] Among them, v sat ,a sat The saturation velocity and saturation acceleration that each drone needs to meet are determined by the actual flight environment and flight control safety of the drone. a 9a i ), sat v (a i ) are the execution functions for executing saturated acceleration and saturated velocity constraints respectively.

[0055] S4: After communicating and obtaining neighbor information, the system stability variable is calculated based on the Lyapunov stability principle using the current system state, and the system stability state is predicted, and the time when the next communication event is triggered is predicted;

[0056] The information format of the drone's internal communication is highly standardized, and the information content only includes the current timestamp t, current position p, current speed v, and current acceleration a.

[0057] Intra-drone communication is discrete, with dynamic communication intervals. Each drone receives neighbor information as a discrete sequence with a timestamp. During non-communication moments, the drone's expected acceleration is calculated based on the neighbor state at the previous communication moment, adhering to the saturation acceleration principle until the next communication moment arrives.

[0058] S5: While waiting for an event trigger, the drone monitors the communication channel. If the communication trigger moment has not yet arrived, but a communication request has been received from a neighbor, it determines this moment as the event trigger moment and initiates a communication request to the neighbor, continuing with step S2. When the predicted event trigger moment arrives, drone i initiates a communication request to the neighbor node. After communication is complete, drone i updates its local data and continues with step S3.

[0059] Based on the estimation of the formation's global information by the individual drones following it, a dynamic event self-triggering mechanism for drone communication is established, a formation error variable is established, and based on the Lyapunov stability theorem, a local Lyapunov function and its derivative value are established. The variation pattern of the Lyapunov derivative is predicted by the saturation velocity and acceleration constraints, and the time when the next communication event is triggered is predicted; drone i enters the monitoring state and proceeds to step S6. The Lyapunov function is:

[0060]

[0061]

[0062]

[0063] Among them, I2 represents the 2*2 unit matrix, P is the constant coefficient matrix, δ i is the local formation error variable of UAV i. In particular, δ i Meet the closed-loop control system The specific transformation parameters are:

[0064]

[0065] Furthermore, the triggering moment of the drone i communication event is:

[0066]

[0067] Among them, For the next communication time, The time of the most recent communication. is the constant coefficient matrix of the formation system, I2 is the 2*2 unit matrix, is the internal system error variable of UAV i, is a constant matrix, is the time derivative of the system stability variable.

[0068] S6: Determine whether the formation task is completed through the system stability variable, that is, whether the formation error is less than the acceptable range; if the error is acceptable, the formation task is completed, the termination condition is met, and the algorithm terminates and exits; if the termination condition is not met, continue to step S5.

[0069] δ i Establish the system error variable for drone i, i = 1, 2, 3...n:

[0070]

[0071] Based on the Lyapunov function, the system stability variable is established for the i-th follower UAV, namely:

[0072]

[0073]

[0074] like If it is established, the global formation system is stable, and within each UAV, it must satisfy

[0075] This approach proposes an event-triggered strategy, allowing each agent to decide whether to calculate the next control input based on existing information or to maintain the status quo. This approach allows drones to communicate only when certain events are triggered. This eliminates the need for continuous communication, making it more practical.

[0076] Example 2

[0077] The distributed UAV dynamic formation method based on the self-triggering coordination mechanism has the characteristics of asynchronous communication. For a system with 3 pilot UAVs and n follower UAVs, the specific implementation steps for i=1, 2, 3, ..., n follower UAVs are as follows: Figure 1 As shown:

[0078] S1: Establish a dynamic formation model for distributed drones, designate three drones as leaders, and the rest as followers. The leader perceives the environment in real time and makes its own control decisions. The specific steps are as follows: Establish a drone formation communication topology G(V, E, Ω), where V = {V1, V2... V n} represents a set of n drone nodes, E={E1,E2……E m} represents the communication link between two drones. At this time, the formation is defined as (G,p), where p i ∈R 2 Represents the positions of all UAVs in this formation, and defines the communication link weight matrix of this formation as Ω.

[0079] In this example, the number of drone nodes is 6, so there are 3 leaders, numbered 1, 2, and 3, and 3 followers, numbered 4, 5, and 6. The goal of the formation task in this example is to track the leader drone, whose position, velocity, and acceleration are dynamically changing, and ultimately achieve a formation shape while in motion.

[0080] Initialize the drone parameters, expressed as a two-dimensional column vector, and the position of the pilot drone is:

[0081]

[0082] The velocity and acceleration change with time respectively, and the velocity is initialized as:

[0083]

[0084] The acceleration is:

[0085]

[0086] The horizontal and vertical coordinates of the followers are both random values ​​with absolute values ​​between 0-50:

[0087]

[0088] The communication weight matrix corresponding to the target formation is:

[0089]

[0090] S2: Each drone publishes its own status information and waits for the status of neighboring drone nodes. In this embodiment, drone i publishes its location information p i =[x i ,y i ] T , speed information and acceleration information

[0091] S3: Calculate the expected acceleration a_i based on the position and velocity information of itself and its neighbors:

[0092]

[0093] Among them, k p With k v are all constants greater than zero, ω ij is the weight of the robot's internal communication topology, which can be obtained from the communication weight matrix Ω. In this embodiment, let k p =5,k v =5.

[0094] In the present invention, each drone has saturation velocity and saturation acceleration constraints. When the calculated expected acceleration is greater than the saturation acceleration constraint, the controller sets the expected velocity to the saturation acceleration. At the same time, it is determined whether the current velocity of the drone reaches the saturation velocity constraint. If so, only the normal acceleration component is retained. In this embodiment, the saturation constraint value is v sat =10,a sat = 6. Saturation constraint processing is divided into two steps:

[0095] The first step is to correct the expected acceleration to satisfy the saturation acceleration constraint. The specific formula is as follows:

[0096]

[0097] In the second step, the expected acceleration is further modified to satisfy the saturation speed constraint. The specific formula is as follows:

[0098]

[0099] Update the neighbor state cache and calculate the control input. The specific steps are as follows:

[0100] The first step is to establish a neighbor state storage sequence; in the present invention, the time sequence of the control input update is t k ,k=1,2,3..., then the continuous variable p i ,p j ,v i ,v j Treated as a sampled time series in calculations

[0101] The second step is to set the formation error variable and system stability variable, which are stored locally by each UAV and updated asynchronously. The local error variable of UAV i is:

[0102]

[0103] S4: Based on Lyapunov stability theorem, set the system stability variable when When , UAV i believes that the current system is stable.

[0104] Set a communication trigger event to monitor the status of the drone formation system. When an event occurs, send a communication request to the neighboring node and collect and integrate neighbor information. The communication event trigger function of drone i is:

[0105]

[0106] Calculate the local error variable transformation matrix

[0107] Among them, δ i is the local error variable of UAV i. When the event triggers the condition f(δ i )=0, the UAVs in the formation update their expected acceleration a i .

[0108] Therefore, when the event does not occur, the expected acceleration of the drone is i It is calculated based on the neighbor state at the previous communication moment. It generally remains unchanged and adheres to the saturation acceleration principle before the next communication moment arrives, that is:

[0109]

[0110] After the communication is completed, each drone calculates the next communication time based on the stability variable and the current neighbor information. The specific steps are as follows:

[0111]

[0112] Among them, is the most recent communication time, is the predicted event triggering time, that is, the next communication time. For the next communication time, The time of the most recent communication. is the constant coefficient matrix of the formation system, I2 is the 2*2 unit matrix, is the internal system error variable of UAV i, is a constant matrix, is the time derivative of the system stability variable.

[0113] S5: Monitor the system status and communication channel to determine whether the communication trigger conditions are met. The condition judgment will be executed cyclically. The specific cyclic steps are as follows:

[0114] The first step is to determine whether the predicted communication time t is reached k+1 , if it has been reached, return to step S2;

[0115] The second step is to monitor the internal communication channel of the system in real time. If the status information and communication request of the neighboring drone are received, it is determined that a communication event is triggered and returns to step S2.

[0116] S6: Real-time monitoring of the UAV local error variable and the number of iterations of the current algorithm. When the termination condition is met, the algorithm is terminated and the final error δ is output. i The termination condition is set as the upper limit of the maximum number of iterations or the error precision. In this embodiment, the maximum number of iterations is set to 3000. The formation task is completed. The formation is as follows Figure 2 As shown in the figure, the local error variables of the follower drones (drones No. 4, 5, and 6) during the system operation are as follows: Figure 3 shown. Figure 3 The horizontal axis is the number of algorithm iterations, from Figure 3 As can be seen, at the beginning of the formation mission, the three follower drones are far from the target position, and the error function value is large. However, as the algorithm runs, the drones get closer and closer to the target position, and the error function gradually converges to 0. At this point, the formation mission is basically completed, and the algorithm is effective.

[0117] In summary, each follower drone in this drone formation broadcasts its own state information to neighboring drones, collects and integrates neighbor information, and calculates its expected acceleration based on this information. After communicating and acquiring neighbor information, it estimates the global formation stability based on this information and predicts the next communication time. This communication repeats until the system stability variable is satisfied, completing the formation. This method eliminates the need for nearly continuous changes in the motion state of each drone, reducing the number of communications within the formation without affecting the speed and results of the algorithm's convergence, thereby improving the algorithm's robustness and practicality.

[0118] It should be noted that the above content merely illustrates the technical idea of ​​the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A distributed UAV dynamic formation method based on a self-triggered coordination mechanism, characterized by: Each follower drone in the drone formation publishes its own status information to neighboring drones, collects and integrates neighbor information, and calculates its own expected acceleration based on the neighbor information. After communicating and obtaining neighbor information, it estimates the global formation stability state based on the neighbor information and predicts the time of the next communication. The communication is repeated until the system stability variable judgment is met and the formation is completed. The specific steps include the following: S1: Establish a dynamic formation model of distributed UAVs, which includes a leader UAV and a follower UAV; establish the communication topology G(V, E, Ω) of the UAVs, where V = {V1, V2...V n } represents the set of drone nodes, E={E1,E2……E n } represents the communication link between two UAVs, Ω n×n is the edge weight matrix of the communication link; S2: The follower drone sends a communication request to the neighboring node, publishes its own information, and receives and integrates the status information of neighboring drones; The communication request sent by the follower drone includes at least: its own position information, speed information and acceleration information; S3: After receiving the neighboring drone status information obtained in step S2, each follower drone uses a second-order control strategy to calculate the control input, which is its own desired acceleration: Among them, a i To follow the desired acceleration of the drone, N i is the set of neighbor nodes of drone i, p i 、p j are the positions of drones i and j, v i 、v j are the speeds of drones i and j, k p >0,k v >0 is a constant, ω ij is the stress constant of the undirected edge formed by UAV i and UAV j in the formation; S4: After communicating and obtaining neighbor information, the system stability variable is calculated based on the Lyapunov stability principle using the current system state, and the system stability state is predicted, and the time when the next communication event is triggered is predicted; S5: The drone waits for the predicted event trigger time to arrive and monitors the communication channel. If the communication trigger time has not arrived, but a communication request has been received from a neighbor, it determines this time as the event trigger time, sends a communication request to the neighbor, and continues with step S2. When the predicted event trigger time arrives, the communication event is triggered and the drone's local data is updated. S6: Determine whether the formation mission is completed based on the system stability variable. If the formation error is acceptable and the termination condition is met, the formation mission is completed.

2. The distributed UAV dynamic formation method based on the self-triggered coordination mechanism according to claim 1, characterized in that: The edge weight matrix of the communication link Ω=[Ω ij Specifically: Among them, [Ω ij ] is the element of the weight matrix, representing the communication weight between UAV i and UAV j, ω ij is the stress constant of the undirected edge formed by UAV i and UAV j in the formation, satisfying N i is the set of neighbor nodes of drone i, k is any drone in the set of neighbor drones of drone i, ω ik It is the stress constant of the undirected edge formed by UAV i and UAV k.

3. The distributed UAV dynamic formation method based on the self-triggered coordination mechanism according to claim 2, characterized in that: In step S3, the expected acceleration of the following drone needs to meet the constraint conditions. The saturation velocity and saturation acceleration constraints are set for each drone. When the calculated expected acceleration is greater than the saturation acceleration constraint, the controller sets the expected velocity to the saturation acceleration. At the same time, it is determined whether the current velocity of the drone reaches the saturation velocity constraint. If so, only the normal acceleration component is retained. The saturation acceleration constraint is as follows: The constraints on the saturation velocity are as follows: Among them, v sat ,a sat are the saturation speed and saturation acceleration that each drone needs to meet, sat a (a i ), sat v (a i ) are the execution functions for executing saturated acceleration and saturated velocity constraints respectively.

4. The distributed UAV dynamic formation method based on the self-triggered coordination mechanism according to claim 3 is characterized by: The communication information content of step S4 includes the timestamp of the current moment, the current position, the current speed and the current acceleration; the neighbor information obtained by each drone is a discrete sequence with a timestamp. At the non-communication moment, the expected acceleration of the drone is calculated based on the neighbor state at the previous communication moment, and complies with the saturation acceleration constraint before the next communication moment arrives.

5. The distributed UAV dynamic formation method based on the self-triggered coordination mechanism according to claim 4 is characterized by: In step S4, after the communication is completed, each UAV calculates the next communication time based on the stability variable and the current neighbor information as follows: in, For the next communication time, is the most recent communication time, P is the constant coefficient matrix of the formation system, I2 is the 2*2 unit matrix, δ i is the internal system error variable of UAV i, is a constant matrix, is the time derivative of the system stability variable.

6. The distributed UAV dynamic formation method based on the self-triggered coordination mechanism according to claim 4, characterized in that: In step S6, δ i Establish the system error variable for drone i, i = 1, 2, 3...n: Based on the Lyapunov function, the system stability variable is established for the i-th follower UAV, namely: like If the global formation system is stable, then the global formation system is stable, and within each UAV, 7. A distributed UAV dynamic formation system based on a self-triggered coordination mechanism, including a computer program, characterized by: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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