Robot coverage control method, control system and controller based on time cost

Abstract

The present invention discloses a robot coverage control method based on time cost, which includes dividing the task area Q according to the principle of shortest time as the position of each robot i changes, updating the sub-area V corresponding to each robot i, and i ; Calculate each sub-area V i The risk centroid #imgabs0# designs a corresponding sliding surface for each robot i; controls each robot i to reach the corresponding sliding surface first and then track the risk centroid of the corresponding sub-area #imgabs1#. When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed. The robot network is controlled to cover the area in the above manner, and the robot is driven to the time-optimal coverage position. When an accident occurs in the sub-area assigned to the robot, the robot will drive to the accident site at the maximum speed, thereby realizing that the robot network performs the area coverage task at the minimum time cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot control, and more specifically, relates to a robot coverage control method, a control system and a controller based on time cost. Background Art

[0002] The collaborative task area coverage control technology of robot networks has been widely used in scenarios such as regional environmental monitoring, regional security defense, geological resource exploration, and environmental pollutant removal. The design of the collaborative task area coverage control technology of robot networks involves related theories and technologies such as graph theory, optimization theory, and multi-agent collaborative control. The collaborative task area coverage control technology of robot networks moves its position in the task area through information interaction and collaboration between robots, and achieves the optimal coverage monitoring effect of the task area through the sensor equipment or execution equipment carried by the robots. At present, the measurement of the monitoring effect of the robot network on the task area is usually considered, and the controller of the relevant robots is designed to drive the robot network to gradually converge to the desired target trajectory. However, when considering the time cost of the robot network to perform the coverage task, such as in the fire disaster prevention task, we need to carry out disaster prevention and rescue with the minimum time cost, and the existing methods cannot optimize the time cost of the robot network to perform the task. Summary of the invention

[0003] In response to the above defects or improvement needs of the prior art, the present invention provides a robot coverage control method, control system and controller based on time cost, which aims to control the robot network to optimize the coverage effect of the task area under the consideration of the time cost of performing the area coverage task.

[0004] To achieve the above object, according to one aspect of the present invention, a robot coverage control method based on time cost is provided, comprising:

[0005] As the position of each robot i changes, the task area Q is divided according to the principle of shortest time, and the sub-area V corresponding to each robot i is updated. i ;

[0006] Calculate each sub-region V i The risk centroid

[0007] Design the corresponding sliding surface for each robot i;

[0008] Control each robot i to reach the corresponding sliding surface first and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed.

[0009] In one embodiment, each sub-region satisfies

[0010]

[0011] Among them, q is any position point in the corresponding sub-area, is the robot i from the current position p i The minimum time to move to position q in the subregion, is any robot j from its current position p j The minimum time taken to move to position q in the subarea, where N is the number of robots.

[0012] In one embodiment, each sub-region V i The risk centroid Among them, q is any point in the sub-area, ψ(q,t) is the risk density function at point q at time t, and the calculation formula is:

[0013]

[0014] Where φ(q) represents the constant risk density in the sub-region when there is no important object in the sub-region, M is the number of important objects in the sub-region, and φ j (q, t) represents the contribution of the jth object to the risk density ψ(q, t) in the subregion, where φ j The contribution of (q,t) to risk density is Gaussian distributed.

[0015] In one embodiment, φ j The calculation formula for (q,t) is:

[0016]

[0017] Among them, β is a constant coefficient, s j (t)∈R 2 is the position of object j in the sub-region, and σ is the width of the Gaussian function.

[0018] In one embodiment, the calculation formula of the sliding surface s is:

[0019]

[0020] Among them, (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, (x i ,y i ) is the position coordinate of robot i, (g xi ,g yi ) are the x-axis distance component and y-axis distance component of the current position of robot i from the sliding surface coordinate, and,

[0021]

[0022] Among them, (C xi ,C yi ) is the risk centroid The position coordinates, (e xi ,e yi ) is the current position p of robot i i Distance from centroid The x-axis distance component and the y-axis distance component, k1, k2, k3, k4, α1, α2, α3, α4 are the designed constant coefficients, k1, k2, k3, k4>0, 0<α1<1, α2>1, 0<α3<1, α4>1.

[0023] In one embodiment,

[0024] The kinematic model of the first-order integral robot i is:

[0025]

[0026] Among them, u i is the speed of robot i, (u xi ,u yi ) is the control input of robot i along the x-axis and along the y-axis, ||d i ||<ρ is the bounded input disturbance, (d xi ,d yi ) is the control input disturbance component of robot i along the x-axis and along the y-axis,

[0027] The motion of robot i is controlled by designing a controller, where the speed controller of robot i is designed as:

[0028]

[0029] Among them, b1, b2, b3, b4 are the designed constant coefficients, b1, b2, b3, b4>0, β1, β2, β3, β4 are the designed controller parameters, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1.

[0030] In one embodiment, the maximum speed of each robot i needs to satisfy

[0031]

[0032] In one embodiment,

[0033] Each robot i reaches the corresponding sliding surface within a fixed time T1.

[0034]

[0035] After reaching the sliding surface, each robot i continues to track the corresponding center of mass within a fixed time T2

[0036]

[0037] According to another aspect of the present invention, a time-cost-based robot coverage control system is provided, comprising:

[0038] The division unit is used to divide the task area Q according to the principle of shortest time as the position of each robot i changes, and update the sub-area V corresponding to each robot i i ;

[0039] Risk centroid calculation unit, used to calculate each sub-area V i The risk centroid

[0040] A sliding surface design unit, used to design a corresponding sliding surface for each robot i;

[0041] The control unit is used to control each robot i to first reach the corresponding sliding surface and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed.

[0042] According to another aspect of the present invention, a robot coverage controller based on time cost is provided, wherein the controller is designed as follows:

[0043]

[0044] in,

[0045] u i is the speed of robot i, (u xi ,u yi ) is the control input of robot i along the x-axis and along the y-axis;

[0046] (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, and Among them, (x i ,y i ) is the position coordinate of robot i, (g xi ,g yi ) is the distance between the current position of robot i and the sliding surface, and Among them, (C xi ,C yi ) is the risk centroid The position coordinates, (e xi ,e yi ) is the current position p of robot i i Distance from centroid The distance between the two is , k1, k2, k3, k4, α1, α2, α3, α4 are the constant coefficients of design, k1, k2, k3, k4>0, 0<α1<1, α2>1, 0<α3<1, α4>1;

[0047] b1, b2, b3, b4 are the designed constant coefficients, b1, b2, b3, b4>0, β1, β2, β3, β4 are the designed controller parameters, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1, ρ is the limit of the input speed disturbance.

[0048] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0049] The present invention studies how to achieve the optimal time coverage of the task area, that is, considering the influence of time cost in the robot network coverage task. First, as each robot moves, the division of the entire task area is updated from time to time according to the principle of shortest time, and each robot corresponds to a sub-area. After updating the area division, the risk centroid of each sub-area is calculated. Then, the process of controlling the robot network to cover the area is divided into two processes. The first process is to control each robot to move from any position to the risk centroid position of each sub-area, and the risk centroid position is the most time-covered position. The second process is when the task requires or some triggering events occur, the robot moves from the time-optimal coverage position to the accident position at the maximum speed. Among them, the first process is divided into two steps. The first step is to control each robot to reach the corresponding sliding surface from any position, and the second step is to track the respective centroid positions after reaching the sliding surface. Research shows that by controlling the robot network to cover the area in the above manner, the robot is driven to the time-optimal coverage position. When an accident occurs in the sub-area assigned to the robot, the robot will drive to the accident scene at the maximum speed, thereby realizing the robot network to perform the area coverage task with the minimum time cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flowchart of steps of a robot coverage control method based on time cost in one embodiment;

[0051] Figure 2 This is a schematic diagram of task area division at a certain moment in an embodiment;

[0052] Figure 3is an evolution process of optimizing the coverage of a task area by a robot network in an embodiment, wherein (a), (b), (c), (d), (e), (f), (g), and (h) represent the positions of the robot network at time t=0s, t=5s, t=10s, t=15s, t=20s, t=30s, t=40, and t=50s, respectively;

[0053] Figure 4 is a graph showing the change of the sliding surface position over time in an embodiment, wherein (a) and (b) represent s xi With s yi Graph of changes over time;

[0054] Figure 5 is a graph showing the variation of the error between the robot position and the respective desired center of mass position over time in an embodiment, wherein (a) and (b) respectively represent the variation of the error of the x-axis and y-axis over time;

[0055] Figure 6 It is a curve diagram showing the change of the metric function over time in one embodiment. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0057] like Figure 1 As shown, in one embodiment, a robot coverage control method based on time cost includes the following sub-steps:

[0058] Step S100: As the position of each robot i changes, the task area Q is divided according to the principle of shortest time, and the sub-area V corresponding to each robot i is updated. i .

[0059] Analysis of area coverage tasks, including a network of N first-order integral model robots In the task region Q∈R 2 The area coverage task is performed in . The current position of each robot i can be known at any time. After the current position of robot i is known, the entire task area can be divided according to the principle of shortest time. The sub-areas divided by the principle of shortest time satisfy: the time from the current position of the robot to any point q in its assigned sub-area is less than or equal to the time for any other robot to move to the point q. It can be expressed by the formula:

[0060]

[0061] in, is the robot i from its position p i The minimum time it takes to move to position q in the task area. We consider the maximum speed v of each robot i_max is bounded, so:

[0062]

[0063] like Figure 2 The figure shows a schematic diagram of the sub-areas after the task area is divided at a certain moment, where the point '·' represents the position of the robot, and each robot is assigned to a sub-area. It can be understood that when the position of the robot moves, the division of the task area will also be updated accordingly.

[0064] Step S200: Calculate each sub-region V i The risk centroid

[0065] After assigning a sub-area to each robot, due to the different environments of the sub-areas, the importance of accidents or monitoring at different locations is different. The higher the probability of an accident or the higher the level of importance, the greater the risk density. The risk density of each location point in the sub-area can be characterized according to the environmental characteristics of the sub-area, and then the risk centroid of the corresponding sub-area can be calculated based on the risk density of each location point.

[0066] Considering that there are some important movable objects in the mission area, and each object has a Gaussian model effect on the environment of the mission area. In one embodiment, a time-varying risk density function ψ(q,t) is used to quantify the total risk of the mission area. ψ(q,t) is expressed as the total risk density function at the position point q at time t, which is different from the time-invariant risk density function φ(q) considered in most studies. The specific calculation formula is:

[0067]

[0068] Where φ(q) represents the constant risk density in the mission area when there are no important objects in the mission area, M is the number of important objects in the mission area, and φ j (q, t) represents the contribution of the jth object to the total risk density ψ(q, t), that is, the risk density caused by the jth object to the position point q at time t. j (q, t) is a Gaussian model effect. The closer to the object, the higher the corresponding risk density. Specifically, it can be expressed by the following formula:

[0069]

[0070] Among them, β is a constant coefficient, is the position of object j in the task area, l j >0 is the upper limit, σ is the width of the Gaussian function.

[0071] After determining the risk density function, the centroid calculation formula can be used to obtain the value of each sub-area V i The risk centroid of is:

[0072]

[0073] The present application has conducted research and found that when the task area is divided in the above manner and the robot is driven to the corresponding risk centroid position, the optimal coverage in time can be achieved, that is, the centroid position is the optimal coverage position in time. This can be demonstrated through the following process:

[0074] The task of the area coverage control in the present invention is to drive the robot network to track the position configuration with the minimum time cost. Here, the coverage time cost function H is used. t (P, t) is used to quantify the time cost of the robot network to cover the task area:

[0075]

[0076] It can be transformed into:

[0077]

[0078] in, is the set of neighbors of robot i in the network. We define the neighbors of robot i as the robots in the partition that have common edges with the subregion of robot i.

[0079] Metric function H t The derivative of (P, t) with respect to the position of robot i is:

[0080]

[0081] According to Leibniz's formula, we have:

[0082]

[0083] in, is the sub-region V of robot i i and its neighbor robot j’s subregion V j The common side of the vector n i (q) is the sub-region V of robot i i At the border The outward normal vector at . Vector n j(q) is the position of robot j on the boundary Virgin Region V j The outward normal vector along the boundary between adjacent robots i and j is: i (q)=-n j (q), therefore:

[0084]

[0085] in, is the sub-region V i The generalized risk quality of is the sub-region V i The generalized risk centroid of . From the above derivation, it can be seen that when the position p of robot i is located i In sub-area V i The generalized centroid of At, the metric function H t (P,t) for robot i position p i The derivative is zero, that is, the position is the function H t (P,t) is the measurement of robot i for area V i Time-optimal coverage location.

[0086] Step S300: Design a corresponding sliding surface for each robot i.

[0087] First, define the robot's current position p i The desired target location The difference e i :

[0088]

[0089] Among them, (e xi ,e yi ) is the current position p of robot i i Distance from centroid The x-axis distance component and y-axis distance component, (x i ,y i ) is the position coordinate of robot i, (C xi ,C yi ) is the risk centroid The location coordinates of .

[0090] Based on this, the sliding surface is designed:

[0091]

[0092] Among them, (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, (g xi ,gyi ) is the x-axis distance component and y-axis distance component of the current position of robot i from the sliding surface coordinate, and its calculation formula is:

[0093]

[0094]

[0095] Here k1, k2, k3, k4>0 are the constant coefficients of the design, 0<α1<1, α2>1, 0<α3<1, α4>1, is the bounded time derivative of the center of mass.

[0096] Step S400: Control each robot i to first reach the corresponding sliding surface and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed.

[0097] In one embodiment, the kinematic model of the first-order integral robot is first defined as:

[0098]

[0099] in p i =[x i ,y i ] T ∈R 2 is the position of the robot in the area, ||d i (t)||<ρ is a bounded input disturbance. We consider the maximum velocity v of each robot i_max are distinct and bounded.

[0100] Based on this kinematic model and considering the existence of input disturbance, the robot's speed controller is set as:

[0101]

[0102] Among them, b1, b2, b3, b4>0 are constant coefficients, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1 are the designed controller parameters, and ρ is the disturbance bound.

[0103] Furthermore, the maximum speed of each robot is set to satisfy:

[0104]

[0105] Under this speed constraint, it can be deduced that the controller designed for the first-order integral model robot can drive the state of robot i (i∈V) to the designed sliding surface within a fixed time T1, and the fixed time T1 is only related to the designed controller parameters and has nothing to do with the initial state of the robot. The time T1 is:

[0106]

[0107] Then we can prove that when the robot state reaches the sliding surface, the controller we designed can drive the position of each robot The state tracks its expected center of mass within a fixed time T2 The position of, where the size of time T2 is:

[0108]

[0109] Therefore, it can be concluded that the controller we designed can achieve the optimal time coverage of the robot network on the task area within the fixed time of T1+T2 when there is an input disturbance. Based on this, active control can be achieved by changing the setting parameters of the controller and adjusting the time for the robot to track the center of mass position. When an accident occurs in the sub-area assigned to the robot, the robot will drive to the accident scene at the maximum speed, thus achieving the robot network to perform the area coverage task at the minimum time cost.

[0110] Accordingly, the present application also relates to a time-cost-based robot coverage control system corresponding to the above method, which includes:

[0111] The division unit is used to divide the task area Q according to the principle of shortest time as the position of each robot i changes, and update the sub-area V corresponding to each robot i i ;

[0112] Risk centroid calculation unit, used to calculate each sub-area V i The risk centroid

[0113] A sliding surface design unit, used to design a corresponding sliding surface for each robot i;

[0114] The control unit is used to control each robot i to first reach the corresponding sliding surface and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed.

[0115] Among them, each unit is used to execute the corresponding steps in the above method. For details, please refer to the above introduction and will not be repeated here.

[0116] Accordingly, the present application also relates to a robot coverage controller based on time cost, wherein the controller is designed as follows:

[0117]

[0118] in,

[0119] u i is the speed of robot i, (u xi ,u yi ) is the control input of robot i along the x-axis and along the y-axis;

[0120] (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, and Among them, (x i ,y i ) is the position coordinate of robot i, (g xi ,g yi ) is the distance between the current position of robot i and the sliding surface, and Among them, (C xi ,C yi ) is the risk centroid The position coordinates, (e xi ,e yi ) is the current position p of robot i i Distance from centroid The distance between the two is , k1, k2, k3, k4, α1, α2, α3, α4 are the constant coefficients of design, k1, k2, k3, k4>0, 0<α1<1, α2>1, 0<α3<1, α4>1;

[0121] b1, b2, b3, b4 are constant coefficients, b1, b2, b3, b4>0, β1, β2, β3, β4 are the parameters of the designed controller, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1, ρ is the limit of the input speed disturbance.

[0122] It can be understood that the controller is used to implement the control function of the above-mentioned control unit. When the robot is equipped with the above-mentioned controller, it can track the center of mass and monitor the accident scene according to the process described above. It can optimize the coverage effect of the task area well under the measure of time cost as the area coverage effect, and achieve the optimal coverage effect of the task area within a fixed time.

[0123] Finally, a simulation experiment was conducted on a specific scenario using MATLAB. Figure 3It is the position evolution process of the robot network in a 100m×100m two-dimensional graph area and its corresponding sub-area division within 50s. At the initial moment, the position distribution of the robot network is not optimal. Through our control method, the robot approaches important objects to optimize the coverage of the area, and the robot network moves dynamically with the movement of important objects to maintain the coverage effect. Figure 4 is the sliding surface s xi With s yi From the curve of change over time, we can see that the sliding surface stabilizes to 0 in about 10 seconds. Figure 5 It is the difference between the positions of the four robots and their respective expected center of mass positions. The position error converges to 0 in about 20 seconds. Figure 6 This is the curve of the coverage effect measurement function changing with time at the cost of coverage time. At the initial moment, the measurement function value is about 8400 at the distribution position of the robot network. Then, the robot network is driven to move by the control method we proposed, and the measurement function decreases quickly. In about 20 seconds, the measurement function decreases to about 5000, and the measurement function value remains at this value for the rest of the time. This shows that through the control method we designed, the robot network can optimize the coverage effect of the task area with time cost as the regional coverage effect measurement, and achieve the optimal coverage effect of the task area within a fixed time.

[0124] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A robot coverage control method based on time cost, characterized in that: include: As the position of each robot i changes, the task area Q is divided according to the principle of shortest time, and the sub-area V corresponding to each robot i is updated. i ; Calculate each sub-region V i The risk centroid Design the corresponding sliding surface for each robot i; Control each robot i to reach the corresponding sliding surface first and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed; Each sub-region meets Among them, q is any position point in the corresponding sub-area, is the robot i from its current position p i The minimum time to move to position q in the subregion, is any robot j from its current position p j The minimum time taken to move to position q in the sub-area, N is the number of robots; Each sub-region V i The risk centroid Among them, q is any point in the sub-area, ψ(q,t) is the risk density function at point q at time t, and the calculation formula is: Where φ(q) represents the constant risk density in the sub-region when there is no important object in the sub-region, M is the number of important objects in the sub-region, and φ j (q, t) represents the contribution of the jth object to the risk density ψ(q, t) in the subregion, where φ j The contribution of (q,t) to risk density is Gaussian; φ j The calculation formula for (q,t) is: Among them, β is a constant coefficient, s j (t)∈R 2 is the position of object j in the sub-region, and s is the width of the Gaussian function.

2. The robot coverage control method based on time cost as claimed in claim 1, characterized in that: The calculation formula of sliding surface s is: Among them, (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, (x i ,y i ) is the position coordinate of robot i, (g xi ,g yi ) are the x-axis distance component and y-axis distance component of the current position of robot i from the sliding surface coordinate, and, Among them, (C xi ,C yi ) is the risk centroid The position coordinates, (e xi ,e yi ) is the current position p of robot i i Distance from centroid The x-axis distance component and the y-axis distance component, k1, k2, k3, k4, α1, α2, α3, α4 are the designed constant coefficients, k1, k2, k3, k4>0, 0<α1<1, α2>1, 0<α3<1, α4>1.

3. The robot coverage control method based on time cost as claimed in claim 2, characterized in that: The kinematic model of the first-order integral robot i is: Among them, u i is the speed of robot i, (u xi ,u yi ) is the control input of robot i along the x-axis and along the y-axis, ||d i ||<ρ is the bounded input disturbance, (d xi ,d yi ) is the control input disturbance component of robot i along the x-axis and along the y-axis, The motion of robot i is controlled by designing a controller, where the speed controller of robot i is designed as: Among them, b1, b2, b3, b4 are the designed constant coefficients, b1, b2, b3, b4>0, β1, β2, β3, β4 are the designed controller parameters, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1.

4. The robot coverage control method based on time cost as claimed in claim 3, characterized in that: The maximum speed of each robot i needs to satisfy 5. The robot coverage control method based on time cost as claimed in claim 3, characterized in that: Each robot i reaches the corresponding sliding surface within a fixed time T1. After reaching the sliding surface, each robot i continues to track the corresponding center of mass within a fixed time T2 6. A robot coverage control system based on time cost, characterized in that: include: The division unit is used to divide the task area Q according to the principle of shortest time as the position of each robot i changes, and update the sub-area V corresponding to each robot i i ; Risk centroid calculation unit, used to calculate each sub-area V i The risk centroid A sliding surface design unit, used to design a corresponding sliding surface for each robot i; The control unit is used to control each robot i to first reach the corresponding sliding surface and then track the risk centroid of the corresponding sub-area When an accident occurs in a sub-area, the robot located in the accident sub-area is controlled to drive from the risk centroid to the accident point at the maximum speed; Each sub-region meets Among them, q is any position point in the corresponding sub-area, is the robot i from its current position p i The minimum time to move to position q in the subregion, is any robot j from its current position p j The minimum time taken to move to position q in the sub-area, N is the number of robots; Each sub-region V i The risk centroid Among them, q is any point in the sub-area, ψ(q,t) is the risk density function at point q at time t, and the calculation formula is: Where φ(q) represents the constant risk density in the sub-region when there is no important object in the sub-region, M is the number of important objects in the sub-region, and φ j (q, t) represents the contribution of the jth object to the risk density ψ(q, t) in the subregion, where φ j The contribution of (q,t) to risk density is Gaussian; φ j The calculation formula for (q,t) is: Among them, β is a constant coefficient, s j (t)∈R 2 is the position of object j in the sub-region, and s is the width of the Gaussian function.

7. A robot coverage controller based on time cost, characterized in that: The controller is designed to in, u i is the speed of robot i, (u xi ,u yi ) is the control input of robot i along the x-axis and along the y-axis; (s xi ,s yi ) is the position coordinate of the sliding surface corresponding to robot i, and Among them, (x i ,y i ) is the position coordinate of robot i, (g xi ,g yi ) is the distance between the current position of robot i and the sliding surface, and Among them, (C xi ,C yi ) is the risk centroid The position coordinates, (e xi ,e yi ) is the current position p of robot i i Distance from centroid distance, k1, k2, k3, k4, α1, α2, α3, α4 are the designed constant coefficients, k1, k2, k3, k4>0, 0<α1<1, α2>1, 0<α3<1, α4>1; b1, b2, b3, b4 are the designed constant coefficients, b1, b2, b3, b4>0, β1, β2, β3, β4 are the designed controller parameters, -1<β1<0, -1<β3<0, β2, β4>1, -1<β3<0, β4>1, ρ is the limit of the input speed disturbance; Among them, the risk centroid is the sub-area V corresponding to robot i i The risk centroid of Sub-area V i satisfy Among them, q is any position point in the corresponding sub-area, is the robot i from its current position p i The minimum time to move to position q in the subregion, is any robot j from its current position p j The minimum time taken to move to position q in the sub-area, N is the number of robots; Each sub-region V i The risk centroid Among them, q is any point in the sub-area, ψ(q,t) is the risk density function at point q at time t, and the calculation formula is: Where φ(q) represents the constant risk density in the sub-region when there is no important object in the sub-region, M is the number of important objects in the sub-region, and φ j (q, t) represents the contribution of the jth object to the risk density ψ(q, t) in the subregion, where φ j The contribution of (q,t) to risk density is Gaussian; φ j The calculation formula for (q,t) is: Among them, β is a constant coefficient, s j (t)∈R 2 is the position of object j in the sub-region, and s is the width of the Gaussian function.

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