Multi-agent formation obstacle avoidance method based on distributed model predictive control

Abstract

The invention discloses a multi-agent formation obstacle avoidance method based on distributed model predictive control, which obtains an optimal control sequence of a system by solving an optimization problem in a limited predictive time domain so as to realize online closed-loop control of the system in the whole control time domain. A leader agent moves according to a preset track, other agents consider consistency performance indexes between the leader agent and other agents in a neighborhood, a control target is constructed, then a target function is constructed based on the control target, and the position and speed consistency performance indexes serve as the target function. The collision avoidance requirements and the obstacle avoidance requirements between the intelligent agents are constructed into constraint conditions; according to the method, an obstacle avoidance problem is converted into an optimization problem of a target function, and then a distributed model prediction control method is used for solving the optimization problem to obtain an optimal control sequence, so that an expected formation obstacle avoidance function is realized, the system control performance is improved, the calculation complexity is reduced, and the method has relatively good practicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of formation obstacle avoidance, and in particular relates to a multi-agent formation obstacle avoidance method based on distributed model predictive control. Background Art

[0002] The formation problem of multi-agent systems has been widely used in various tasks such as satellite formation, deep-sea resource exploration, and robot collaborative rescue. The formation control problem has attracted much attention, which involves many constraints, such as input saturation constraints and collision avoidance constraints. At present, a variety of solution strategies have emerged for constraint problems, among which Model Predictive Control (MPC) is highly praised for its effective constraint handling and good control performance.

[0003] Traditional centralized control methods require that all intelligent agents can communicate with the central intelligent agent in order to achieve formation control. When the central intelligent agent fails or the communication between the intelligent agent and the central intelligent agent fails, the formation mission of the intelligent agent will fail.

[0004] The centralized control method requires the central agent to be able to communicate with all other agents, which places high demands on communication. In practical applications, the communication of agents may be limited due to communication distance or bandwidth resources, resulting in the multi-agent system being able to only achieve local communication. Therefore, the following adjacency matrix R(k) representing the communication state within the group is defined:

[0005]

[0006] Where Na is the number of multi-agents, r sj = 1 means that the sth agent and the jth agent can communicate with each other, r sj = 0 means that the sth agent and the jth agent cannot communicate. if Then the multiple agents are fully connected. This indicates that some communication within the group is connected.

[0007] In multi-agent systems, although distributed model predictive control is not as good as centralized MPC in terms of global optimality, it has received extensive attention in terms of structural flexibility, computational cost, and communication burden. Compared with centralized and decentralized control, distributed model predictive control divides the system into related subsystems, each of which is equipped with an independent local controller, while considering the influence of itself and other related agents. In other words, distributed model predictive control has good advantages in improving system control performance and reducing computational complexity. Summary of the invention

[0008] The purpose of the present invention is to provide a multi-agent formation obstacle avoidance method based on distributed model predictive control, construct position and speed consistency performance indicators and obstacle avoidance constraints, and then each agent performs synchronous edge calculation to obtain the control quantity to realize the collaborative formation obstacle avoidance function.

[0009] The present invention is mainly achieved through the following technical solutions:

[0010] A multi-agent formation obstacle avoidance method based on distributed model predictive control obtains the optimal control sequence of the system by solving an optimization problem within a limited prediction time domain, thereby realizing online closed-loop control of the system within the entire control time domain, including the following steps:

[0011] Step S1: Construct the objective function based on the control target:

[0012]

[0013] in:

[0014] N is the prediction step length;

[0015] N {j} is the set of neighboring drones of the jth drone;

[0016] s is the domain drone number of the jth drone;

[0017] k is the current time;

[0018] Q1 is the weight matrix of the drone tracking item;

[0019] Q2 is the weight matrix of the relative positions between UAVs;

[0020] R is the weight matrix of the control input items;

[0021] x j is the state information of the jth agent;

[0022] x s is the state information of the sth agent;

[0023] u j is the control input;

[0024] Δ ij is the relative position information of agent i and agent j;

[0025] g j =[g jx ,g jy ,g jvx ,g jvy ] T , where (g jx ,gjy ) represents the expected target position of the jth agent, (g jvx ,g jvy ) is the expected speed of the jth agent.

[0026] Step S2: constructing collision avoidance requirements and obstacle avoidance requirements between agents into constraint conditions;

[0027]

[0028] Where: p s and (x s ,y s ) are the position and coordinates of agent s respectively;

[0029] p j and (x j ,y j ) are the position and coordinates of agent j respectively;

[0030] p o and (x o ,y o ) are the position and coordinates of the obstacle respectively;

[0031] r is the safe distance between agents;

[0032] d is the safe distance between the agent and the obstacle;

[0033] Na is the number of multi-agents.

[0034] Step S3: Convert the multi-agent formation obstacle avoidance problem into the optimization problem P1:

[0035]

[0036] stx j (k+i+1|k)=Ax j (k+i|k)+Bu j (k+i|k)

[0037]

[0038] x j (k+N|k)∈\Mathbb{X}

[0039] Among them: Problem P1 is to solve the optimal control of the j-th intelligent agent;

[0040] A and B are the system matrix and control matrix respectively;

[0041] p s and (x s ,y s) are the position and coordinates of agent s respectively;

[0042] \Mathbb{X} is the state constraint set of the agent, and includes spatial position constraints and velocity constraints.

[0043] Step S4: Then, the distributed model predictive control method is used to solve the optimization problem P1 to obtain the optimal control sequence; each intelligent agent performs synchronous edge computing to obtain the control quantity, and updates its own control quantity to realize the collaborative formation obstacle avoidance function.

[0044] In order to better implement the present invention, further, in step S1, the leader agent moves according to a predetermined trajectory, and other agents consider the consistency performance index between the leader and other agents in the neighborhood to construct a control target:

[0045]

[0046] ||p i (k)-p j (k)||>r,i∈N {j} ,j=1,2,…,Na (3)

[0047] ||p o (k)-p j (k)||>d,j=1,2,…,Na (4)

[0048] Where: Formula (1) is used to achieve the desired formation between agent i and agent j, including the relative position relationship and speed relationship;

[0049] Formula (2) is the desired target trajectory that the leader needs to track;

[0050] Formula (3) is the collision avoidance requirement between agents;

[0051] Formula (4) is the obstacle avoidance requirement between the agent and the obstacle.

[0052] In order to better implement the present invention, further, in step S4, the optimal state sequence obtained at the previous moment is decoupled as the assumed current state to achieve synchronous update and online solution of all agents.

[0053] In order to better implement the present invention, further, it is assumed that the current state information is:

[0054]

[0055] in: is the optimal state sequence at time k;

[0056] is the optimal state sequence calculated at time k-1;

[0057] The assumed current state information is brought into the optimization problem to achieve online solution.

[0058] In order to better implement the present invention, further, it is applied to obstacle avoidance of drone formation, including the following steps:

[0059] Step A1: Initialize current state information;

[0060] Step A2: At time k, all drones use their neighbors’ hypothetical state information to solve problem P1 and obtain the optimal control sequence;

[0061] Step A3: Apply the first control variable of the control sequence to the current system;

[0062] Step A4: Obtain the optimal control sequence and bind it into a hypothetical state sequence to transmit to other agents in the neighborhood, and receive the preset state sequence from other agents

[0063] Step A5: Determine whether the end condition is met. If so, end the process. Otherwise, return to step A2 to continue solving the problem.

[0064] In order to better implement the present invention, further, the drone determines A, B, Q1, Q2, R, d, g in the offline stage j 、p o parameter.

[0065] The beneficial effects of the present invention are as follows:

[0066] The present invention adopts a distributed model predictive control method to realize edge computing, which is independent of the central intelligent agent, and avoids the situation where the entire formation system will be paralyzed when the central intelligent agent fails. The formation obstacle avoidance problem constructs an optimization problem, takes the position and speed consistency performance indicators as the objective function, constructs the collision avoidance requirements and obstacle avoidance requirements between intelligent agents into constraints, and uses the distributed model predictive control method to solve the optimization problem, thereby realizing the desired formation obstacle avoidance function, effectively improving the system control performance and reducing the computational complexity, and having good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is the principle block diagram of distributed model predictive control;

[0068] Figure 2 This is an implementation flow chart in Example 2;

[0069] Figure 3 The formation and obstacle avoidance trajectory of the intelligent agent in Example 2;

[0070] Figure 4 is the distance variation curve between agents in Example 2;

[0071] Figure 5 is the distance change curve between the agent and the obstacle in Example 2;

[0072] Figure 6 is the speed change curve of agent vx in Example 2;

[0073] Figure 7 is the speed change curve of agent vy in Example 2;

[0074] Figure 8 is the cost function change curve in Example 2;

[0075] Fig. 9 This is the control input variation curve in Example 2. DETAILED DESCRIPTION

[0076] Embodiment 1:

[0077] A multi-agent formation obstacle avoidance method based on distributed model predictive control obtains the optimal control sequence of the system by solving an optimization problem within a limited prediction time domain, thereby achieving online closed-loop control of the system within the entire control time domain. The specific steps are as follows:

[0078] (1) Consider a multi-agent formation system consisting of Na discrete linear systems

[0079] x j (k+1)=Ax j (k)+Bu j (k)

[0080] Among them, x j represents the state information of the jth agent, u j represents the control input, A and B are the system matrix and control matrix respectively.

[0081] use represents a set of vectors describing the formation, where g j =[g jx ,g jy ,g jvx ,g jvy ] T , (g jx ,g jy ) represents the expected target position of the jth agent, (g jvx ,g jvy ) is the expected speed of the jth agent. The commonly used fixed geometric formation requires that the speeds of multiple agents remain consistent, so there is g jvx =gsvx ,g jvy =g svy , multiple agents also need to maintain a fixed position vector, denoted by Δ js =h j -h s Represents the relative position information between agent j and agent s.

[0082] (2) Design of Distributed Formation Obstacle Avoidance Algorithm:

[0083] To achieve multi-agent collaborative formation, we can consider that the leader agent moves according to the predetermined trajectory, and other agents consider the consistency performance indicators between the leader and other agents in the neighborhood, so consider the following control objectives:

[0084]

[0085] ||p i (k)-p j (k)||>r,i∈N {j} ,j=1,2,…,Na (3)

[0086] ||p o (k)-p j (k)||>d,j=1,2,…,Na (4)

[0087] Wherein, formula (1) is used to achieve the desired formation between agent i and agent j, including the relative position relationship and speed relationship, formula (2) is the leader's need to track the desired target trajectory, formula (3) is the collision avoidance requirement between agents, and formula (4) is the obstacle avoidance requirement between agents and obstacles.

[0088] Therefore, the objective function can be constructed as follows:

[0089]

[0090] This objective function is the condition for the formation of intelligent agents. In practical applications, it is necessary to further consider the obstacle avoidance and collision avoidance problems during the movement of intelligent agents. Therefore, the following constraints are constructed:

[0091]

[0092] where p s and (x s ,y s ) are the position and coordinates of agent s, p o and (x o ,y o ) are the position and coordinates of the obstacle respectively.

[0093] like Figure 1 As shown in the figure, rolling optimization is the core of MPC. Its idea is to obtain the optimal control sequence of the system by solving an optimization problem in a limited time domain, thereby realizing online closed-loop control of the system in the entire control time domain.

[0094] Individual optimal control methods often solve the problem of global optimization. Although the model predictive control method has the optimization idea of ​​modern control theory, it is a local optimization in the prediction time domain, and it continuously rolls forward to solve the problem in real time online. In actual applications, the time and control process may be uncertain, so the global optimum is generally not easy to obtain, but the local optimum within a limited time is more meaningful.

[0095] Solving the model predictive control problem at each moment can obtain an optimal control sequence, and then the first control quantity in the optimal control sequence is applied to the current system. At the next moment, the optimization problem is solved again to update the optimal control sequence. Because the optimization process of predictive control is not performed offline once, but repeatedly online, the key steps include prediction model, error feedback correction and rolling optimization, which is more adaptable to the actual process than relying only on one-time optimization of the model, and can effectively overcome the influence of factors such as model inaccuracy and time variation, and has strong robustness.

[0096] Through the above analysis, the optimal control model of multi-agent formation obstacle avoidance can be described by the following formula:

[0097]

[0098] stx j (k+i+1|k)=Ax j (k+i|k)+Bu j (k+i|k)

[0099]

[0100] x j (k+N|k)∈\mathbb{X}

[0101] Distributed model predictive control takes into account the autonomy of the agent. Each drone will perform calculations and update its own control quantity. The above problem P1 is to solve the optimal control of the jth agent. It can be seen that the objective function and constraints of the optimal control of the jth agent involve the state information of other agents, which is strongly coupled and cannot be solved directly online. Next, using the characteristics of the model predictive control itself, the optimal state sequence obtained at the last moment is used as the assumed current state to decouple, so that all agents can be synchronized and updated online.

[0102] Present the current status information of the hypothesis:

[0103]

[0104] Take the current state information assumed above and bring it into the optimization problem to achieve online solution.

[0105] Embodiment 2:

[0106] A multi-agent formation obstacle avoidance method based on distributed model predictive control is applied to UAV formation obstacle avoidance, such as Figure 2 As shown, the specific steps are as follows:

[0107] In the offline stage: determine the system parameters A, B, and other parameters Q1, Q2, R, d, g j 、p o .

[0108] Online stage: includes the following steps:

[0109] ① Initialize the current state information and the predicted state prediction sequence;

[0110] ② At time k, all drones use their neighbors’ hypothetical state information to solve problem P1 and obtain the optimal control sequence;

[0111] ③ Apply the first control quantity of the control sequence to the current system;

[0112] ④ Obtain the optimal control sequence and bind it into a hypothetical state sequence to transmit to other agents in the neighborhood, and receive the preset state sequence from other agents

[0113] ⑤ Determine whether the simulation end conditions are met. If they are met, the simulation ends. If the simulation time has not ended, return to step ② to continue solving the problem.

[0114] From the simulation results, it can be seen that Figure 3 As shown in the figure, multiple agents have realized cooperative formation while avoiding obstacles, which verifies the effectiveness of the algorithm proposed in this invention. Figure 4 As shown in , the distance between the agents is greater than the safety distance 2.5, satisfying the collision avoidance constraint. Figure 5 As shown in , the distance between the agent and the obstacle is greater than the safe distance of 2. Figure 6 As shown, the vx speed change curve of the intelligent agent satisfies the upper and lower limit constraints of [-60,50], as shown in Figure 7 As shown in , the speed change curve of the agent vy satisfies the upper and lower limit constraints of [-100,110]. Figure 8 As shown in Figure 2, the proposed algorithm converges around k=38. Fig. 9 As shown, the control input change curve satisfies the upper and lower limit constraints of [-450, 450].

[0115] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A multi-agent formation obstacle avoidance method based on distributed model predictive control, characterized in that: In the limited prediction time domain, by solving an optimization problem, the optimal control sequence of the system is obtained, thereby realizing the online closed-loop control of the system in the entire control time domain, including the following steps: Step S1: Construct the objective function based on the control target: in: N is the prediction step length; N {j} is the set of neighboring drones of the jth drone; s is the domain drone number of the jth drone; k is the current time; Q1 is the weight matrix of the drone tracking item; Q2 is the weight matrix of the relative positions between UAVs; R is the weight matrix of the control input items; x j is the state information of the jth agent; x s is the state information of the sth agent; u j is the control input; Δ ij is the relative position information of agent i and agent j; g j =[g jx ,g jy ,g jvx ,g jvy ] T , where (g jx ,g jy ) represents the expected target position of the jth agent, (g jvx ,g jvy ) is the expected speed of the jth agent. Step S2: constructing collision avoidance requirements and obstacle avoidance requirements between agents into constraint conditions; Where: p s and (x s ,y s ) are the position and coordinates of agent s respectively; p j and (x j ,y j ) are the position and coordinates of agent j respectively; p o and (x o ,y o ) are the position and coordinates of the obstacle respectively; r is the safe distance between agents; d is the safe distance between the agent and the obstacle; Na is the number of multi-agents. Step S3: Convert the multi-agent formation obstacle avoidance problem into the optimization problem P1: s.t.x j (k+i+1|k)=Ax j (k+i|k)+Bu j (k+i|k) x j (k+N|k)∈\Mathbb{X} Among them: Problem P1 is to solve the optimal control of the j-th intelligent agent; A and B are the system matrix and control matrix respectively; p s and (x s ,y s ) are the position and coordinates of agent s respectively; \Mathbb{X} is the state constraint set of the agent, and includes spatial position constraints and velocity constraints. Step S4: Then, the distributed model predictive control method is used to solve the optimization problem P1 to obtain the optimal control sequence; each intelligent agent performs synchronous edge computing to obtain the control quantity, and updates its own control quantity to realize the collaborative formation obstacle avoidance function.

2. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 1, characterized in that: In step S1, the leader agent moves according to the predetermined trajectory, and other agents consider the consistency performance indicators between the leader and other agents in the neighborhood to construct the control target: ||p i (k)-p j (k)||>r,i∈N {j} ,j=1,2,…,By (3) ||p o (k)-p j (k)||>d,j=1,2,…,Na (4) Where: Formula (1) is used to achieve the desired formation between agent i and agent j, including the relative position relationship and speed relationship; Formula (2) is the desired target trajectory that the leader needs to track; Formula (3) is the collision avoidance requirement between agents; Formula (4) is the obstacle avoidance requirement between the agent and the obstacle.

3. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 1, characterized in that: In step S4, the optimal state sequence obtained at the last moment is decoupled as the assumed current state to achieve online solution by synchronously updating all agents.

4. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 3, characterized in that: Assume that the current status information is: in: is the optimal state sequence at time k; is the optimal state sequence calculated at time k-1; The assumed current state information is brought into the optimization problem to achieve online solution.

5. A multi-agent formation obstacle avoidance method based on distributed model predictive control according to any one of claims 1 to 4, characterized in that: Applied to UAV formation obstacle avoidance, the following steps are included: Step A1: Initialize current state information; Step A2: At time k, all drones use their neighbors’ hypothetical state information to solve problem P1 and obtain the optimal control sequence; Step A3: Apply the first control variable of the control sequence to the current system; Step A4: Obtain the optimal control sequence and bind it into a hypothetical state sequence to transmit to other agents in the neighborhood, and receive the preset state sequence from other agents Step A5: Determine whether the end condition is met. If so, end the process. Otherwise, return to step A2 to continue solving the problem.

6. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 5, characterized in that: The drone determines A, B, Q1, Q2, R, d, g in the offline stage j 、p o parameter.

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