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

Abstract

The application discloses a kind of multi-agent formation obstacle avoidance methods based on distributed model predictive control, in limited prediction time domain, by solving an optimization problem, the optimal control sequence of system is obtained, so as to realize the online closed-loop control of system in whole control time domain.According to the movement of the leader agent according to the predetermined trajectory, the other agents consider the consistency performance index between the leader and other agents in the neighborhood, and construct the control target, then construct the objective function based on the control target, and the position and velocity consistency performance index as the objective function.The requirements of collision avoidance and obstacle avoidance between agents are constructed into constraint conditions;The obstacle avoidance problem is converted into the optimization problem of objective function, then the optimal control sequence is obtained by using the distributed model predictive control method to solve the optimization problem, the desired formation obstacle avoidance function is realized, the system control performance is improved and the calculation complexity is reduced, and it has good practicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of formation obstacle avoidance, and particularly relates to a multi-agent formation obstacle avoidance method based on distributed model predictive control. BACKGROUND

[0002] The formation problem of multi-agent systems has been widely applied in satellite formation, deep-sea resource exploration, robot cooperative rescue and various tasks. The formation control problem has attracted much attention, which involves many constraints, such as input saturation constraints, collision avoidance constraints and the like. At present, for the constraint problem, a variety of solutions have appeared, and model predictive control (MPC) is highly praised due to its effective handling of constraints and good control performance.

[0003] The traditional centralized control method requires all agents to be able to communicate with the center agent to achieve formation control, and when the center agent fails or the communication between the agent and the center agent fails, the formation task of the agent will fail.

[0004] The centralized control method requires the center agent to be able to communicate with all other agents, which has high communication requirements. In actual applications, the communication of agents may be limited due to limited communication distance or limited bandwidth resources, etc., so that the multi-agent system can only achieve local communication, and therefore the following adjacent matrix R(k) representing the internal communication state of the group is defined:

[0005]

[0006] In the formula, Na is the number of multi-agents, r sj =1 indicates that the s th agent and the j th agent can communicate with each other, and r sj =0 indicates that the s th agent and the j th agent cannot communicate with each other. Let If , the multi-agents are fully connected, which indicates that the internal communication of the group is partially connected.

[0007] In the multi-agent system, although the distributed model predictive control is not as good as the centralized MPC in global optimality, it is widely concerned in terms of structural flexibility, computational cost and communication burden. Compared with centralized and decentralized control, the distributed model predictive control divides the system into associated subsystems, each of which is equipped with an independent local controller, and considers the influence of itself and other associated agents, that is, the distributed model predictive control has good advantages in improving system control performance and reducing computational complexity. SUMMARY

[0008] The application aims 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 constraint conditions, and then each agent performs synchronous edge calculation to obtain control quantity, thereby realizing collaborative formation obstacle avoidance function.

[0009] The application is mainly realized through the following technical solutions.

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

[0011] Step S1: constructing a target function based on a control target:

[0012]

[0013] Wherein:

[0014] N is a prediction step;

[0015] N {j} is a neighbor UAV set of the jth UAV;

[0016] s is the field UAV number of the jth UAV;

[0017] k is the current time;

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

[0019] Q2 is a weight matrix of the relative position item between UAVs;

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

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

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

[0023] u j is a control input;

[0024] Delta ij is relative position information of the ith agent and the jth agent;

[0025] g j =[g jx ,g jy ,g jvx ,g jvy ] T , wherein (g jx ,gjy represents the desired target position of the jth agent, (g jvx represents the desired target position of the jth agent, (g jvy represents the desired target position of the jth agent, (g

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

[0027]

[0028] wherein: 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 safety distance between agents and agents;

[0032] d is the safety distance between agents and obstacles;

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

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

[0035]

[0036] S.t.x j (k+i+1|k)=Ax j (k+i|k)+Bu j (k+i|k)

[0037]

[0038] x j (k+N|k)∈Ω

[0039] wherein: problem P1 is the optimal control solution of the jth agent;

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

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

[0042] Ω is a state constraint set of the agent, and includes a space position constraint and a speed constraint.

[0043] Step S4: Then, the optimization problem P1 is solved by using a distributed model prediction control method to obtain an optimal control sequence; each agent performs synchronous edge calculation to obtain a control amount, and updates the control amount of itself, thereby realizing a cooperative formation obstacle avoidance function.

[0044] To better implement the present application, further, in the step S1, the leading agent moves according to a predetermined trajectory, and other agents consider a consistency performance index between the leading agent and other agents in a 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] Wherein, the formula (1) is used to realize that the agent i and the agent j reach a desired formation formation, including a relative position relationship and a speed relationship;

[0049] The formula (2) is a desired target trajectory that the leading agent needs to track;

[0050] The formula (3) is a collision avoidance requirement between the agents;

[0051] The formula (4) is an obstacle avoidance requirement between the agent and the obstacle.

[0052] To better implement the present application, further, in the step S4, the optimal state sequence obtained at the last time is taken as a hypothetical current state to decouple and realize synchronous updating of all agents for online solving.

[0053] To better implement the present application, further, the hypothetical current state information is:

[0054]

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

[0056] The optimal state sequence calculated at k-1 moment;

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

[0058] In order to better realize the present application, further, the present application is applied to unmanned aerial vehicle formation obstacle avoidance, comprising the following steps:

[0059] Step A1: initializing current state information;

[0060] Step A2: at k moment, all unmanned aerial vehicles solve problem P1 by using neighbor's assumed state information to obtain optimal control sequence;

[0061] Step A3: the first control quantity of the control sequence is applied to the current system;

[0062] Step A4: the optimal control sequence is solved and bound into assumed state sequence and transmitted to other agents in the neighborhood, and preset state sequence from other agents is received

[0063] Step A5: whether the end condition is satisfied is judged, if yes, the process is ended, otherwise, the process returns to step A2 to continue solving.

[0064] In order to better realize the present application, further, the unmanned aerial vehicle determines A, B, Q1, Q2, R, d, g j , p o parameters in the offline stage.

[0065] The present application has the following beneficial effects:

[0066] The present application adopts the distributed model predictive control method to realize edge computing, does not depend on the central agent, and avoids the situation that the whole formation system will be paralyzed when the central agent fails. The formation obstacle avoidance problem is solved by constructing an optimization problem, the position and velocity consistency performance index is taken as the objective function, the collision avoidance requirement and obstacle avoidance requirement between agents are constructed as constraint conditions, the distributed model predictive control method is used to solve the optimization problem, the expected formation obstacle avoidance function is realized, the system control performance is effectively improved, the calculation complexity is reduced, and the present application has good practicability. BRIEF DESCRIPTION OF DRAWINGS

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

[0068] Figure 2 It is an implementation flowchart in embodiment 2;

[0069] Figure 3 It is an agent formation and obstacle avoidance trajectory in embodiment 2;

[0070] Figure 4 Distance between agents in Example 2;

[0071] Figure 5 Distance between agent and obstacle in Example 2;

[0072] Figure 6 vx velocity of agent in Example 2;

[0073] Figure 7 vy velocity of agent in Example 2;

[0074] Figure 8 Cost function in Example 2;

[0075] Figure 9 Control input in Example 2. DETAILED DESCRIPTION

[0076] Example 1:

[0077] A multi-agent formation obstacle avoidance method based on distributed model predictive control, in a limited prediction time domain, by solving an optimization problem, the optimal control sequence of the system is obtained, so as to realize the online closed loop control of the system in the whole control time domain. The specific steps are as follows:

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

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

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

[0081] Use to represent a set of vectors describing the formation shape, where g j =[g jx ,g jy ,g jvx ,g jvy ] T ,(g jx ,g jy ) represents the desired target position of the jth agent, (g jvx ,g jvy ) is the desired speed of the jth agent. The commonly used fixed geometry formation requires the speed of the multi-agent to be consistent, so g jvx =gsvx ,g jvy = svy , and the fixed position vector between multi-agent also needs to be maintained, denoted as js = 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 realize the multi-agent cooperative formation, the leader agent can be considered to move according to the predetermined trajectory, and other agents consider the consistency performance index between the leader and other agents in the neighborhood, so the following control objectives are considered:

[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 realize the desired formation between agent i and agent j, including the relative position relationship and the speed relationship, formula (2) is the desired target trajectory that the leader needs to track, formula (3) is the requirement of collision avoidance between agents, and formula (4) is the requirement of obstacle avoidance between agents and obstacles.

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

[0089]

[0090] The objective function is the formation condition of the agent, and in practical application, the obstacle avoidance problem and the collision avoidance problem in the movement process of the agent also need to be further considered. Therefore, the following constraint conditions are constructed:

[0091]

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

[0093] AsFigure 1 As shown, the rolling optimization is the core of MPC, which is to get the optimal control sequence of the system by solving an optimization problem in a limited time domain, so as to realize the online closed-loop control of the system in the whole control time domain.

[0094] The individual optimal control method is usually to solve a global optimization problem, while the model predictive control method is a local optimization in the prediction time domain, which is constantly rolling forward to solve online. Since the time and control process may be uncertain in actual application, the global optimal is generally not easy to obtain, but the local optimal in a limited time is more meaningful.

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

[0096] Through the above analysis, the multi-agent formation obstacle avoidance optimal control model can be described as follows:

[0097]

[0098] S.t.x j (k+i+1|k)=Ax j (k+i|k)+Bu j (k+i|k)

[0099]

[0100] x j (k+N|k)∈Ω

[0101] The distributed model predictive control considers the autonomy of the agent, and each UAV will perform calculation and update its own control quantity. The above problem P1 is the optimal control of the jth agent, and it can be seen that the objective function and the constraint of the optimal control of the jth agent involve the state information of other agents, which has strong coupling, so it cannot be solved directly online. Next, the optimal state sequence obtained at the last time is used as the assumed current state to decouple, so that all agents can update online synchronously.

[0102] The assumed current state information is as follows:

[0103]

[0104] By substituting the current state information assumed above into the optimization problem, an online solution can be achieved.

[0105] Example 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] During the offline phase: Determine system parameters A and B, as well as other parameters Q1, Q2, R, d, and g. j p o .

[0108] Online phase: includes the following steps:

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

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

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

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

[0113] ⑤ Determine if the simulation termination condition is met. If it is met, terminate the simulation. If the simulation duration has not ended, return to step ② to continue solving the problem.

[0114] The simulation results show that, Figure 3 As shown, the multi-agent system achieved cooperative formation while avoiding obstacles, verifying the effectiveness of the algorithm proposed in this invention. Figure 4 As shown, the spacing between the agents is greater than the safe distance of 2.5, satisfying the collision avoidance constraint. Figure 5 As shown, the distances between the agent and obstacles are all greater than the safe distance of 2. Figure 6 As shown, the agent's vx velocity change curve satisfies the upper and lower bound constraints of [-60, 50], as... Figure 7 As shown, the velocity change curve of the agent vy satisfies the upper and lower bound constraints of [-100, 110]. Figure 8 As shown, the proposed algorithm converges at approximately k=38. Figure 9 As shown, the control input variation curve satisfies the upper and lower limit constraints of [-450, 450].

[0115] The above is only the preferred embodiment of the present application, and does not limit the present application in any form. Any simple modification or equivalent change of the above embodiment according to the technical essence of the present application falls within the protection scope of the present application.

Claims

1. A multi-agent formation obstacle avoidance method based on distributed model predictive control, characterized in that, In a limited prediction horizon, the optimal control sequence of the system is obtained by solving an optimization problem, so as to realize online closed-loop control of the system in the whole control horizon, including the following steps: Step S1: constructing a target function based on a control target: Wherein: N is a prediction step; N {j} is a set of neighbor drones for the jth drone; S is the number of the jth UAV; K is a current time; Q1 is a weight matrix of a UAV tracking item; Q2 is a weight matrix of a relative position item between UAVs; R is a weight matrix of a control input item; x j is the state information of the jth agent; x s is the state information of the s-th agent; u j u for 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 ) denotes the desired target position of the jth agent, (g jvx ,g jvy ) is the desired velocity of the jth agent; Step S2: constructing a constraint condition based on requirements of collision avoidance and obstacle avoidance between intelligent agents; 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 a safe distance between intelligent agents and intelligent agents; D is a safe distance between intelligent agents and obstacles; Na is the number of multi-intelligent agents; Step S3: converting the multi-intelligent agent formation obstacle avoidance problem into an optimization problem P1: Wherein: problem P1 is an optimal control solution of the jth intelligent agent; A and B are system matrix and control matrix respectively; p s and (x s , y s ) are the position and coordinates of the agent s, respectively; Ω is a state constraint set of the intelligent agent, and includes a space position constraint and a speed constraint; Step S4: then, the optimization problem P1 is solved by using a distributed model predictive control method, so as to obtain an optimal control sequence; each intelligent agent performs synchronous edge calculation to obtain a control amount, and updates the control amount of itself, so as to realize a collaborative formation obstacle avoidance function.

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

3. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 1, wherein, In the step S4, the optimal state sequence obtained at the last time is taken as a hypothetical current state to decouple, so as to realize synchronous updating and online solving of all intelligent agents.

4. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 3, wherein, The hypothetical current state information is: wherein: is the optimal state sequence at time k; optimal state sequence calculated for time k-1; The hypothetical current state information is brought into an optimization solving problem, so as to realize online solving.

5. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 4, wherein, When applied to UAV formation obstacle avoidance, the following steps are included: Step A1: initializing current state information; Step A2: at the k time, all UAVs solve the problem P1 by using the hypothetical state information of neighbors, so as to obtain an optimal control sequence; Step A3: the first control amount of the control sequence is applied to the current system; Step A4: Obtain optimal control sequence and bind into hypothetical state sequence transmitted to other agents in the neighborhood and receive preset state sequence from other agents Step A5: judging whether an end condition is met, if yes, ending, otherwise, returning to step A2 to continue solving.

6. The multi-agent formation obstacle avoidance method based on distributed model predictive control according to claim 5, wherein, The UAV determines A, B, Q1, Q2, R, d, g in the offline phase j , p o parameters.

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