A collision risk aware and highly scalable method and apparatus for motion planning of large swarms of robots

Abstract

The application belongs to the field of robots, in order to solve the problems of motion planning scalability, navigation flexibility and system safety of large-scale robot cluster, the application provides a collision risk awareness and high scalability large-scale cluster robot motion planning method and device, comprising: in the macro stage, using a Gaussian mixture model to represent the macro state of the cluster, and planning the transport trajectory of the Gaussian mixture model through model predictive control; in the micro stage, using an artificial potential field method to assign target positions to the robots, and combining a distributed model predictive control to realize the tracking and dynamic obstacle avoidance of the individual to the transport trajectory of the Gaussian mixture model. The application can effectively improve the motion planning performance of the large-scale cluster robot system in a complex environment. In the application, by adjusting the risk acceptance degree, the distance between the robot cluster and the obstacle can be flexibly adjusted, and the balance between safety and motion efficiency is realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of robots, and in particular, relates to a collision risk awareness and highly scalable large-scale swarm robot motion planning method and device. BACKGROUND

[0002] With the continuous breakthroughs in robot technology, especially in-depth research in multi-agent collaboration and autonomous decision-making, swarm robot systems will play an increasingly important role in future economic and social development, and have a profound impact on promoting industrial upgrading and improving social production efficiency. Compared with a single or a few robots, large-scale robot systems often have great advantages in efficient collaboration, task allocation and autonomous decision-making, becoming an important direction for promoting the transformation of robot technology. Relying on distributed control and self-organizing behavior, large-scale swarm robot systems can perform large-scale collaborative tasks in complex environments, such as target detection, collaborative object handling, search and rescue, and environmental monitoring.

[0003] The document "Distributed Predictive Drone Swarms in Cluttered Environments" (published in the journal "IEEE Robotics and Automation Letters", Volume 7, Issue 1, 2021, pages 73-80) proposes a distributed, real-time feasible model predictive control algorithm for multi-drone cooperative flight in cluttered environments. The algorithm does not directly search in the high-dimensional joint state space, but constructs a short-time prediction trajectory for each drone online, and only exchanges a small number of trajectory control points to indirectly couple adjacent robots, thereby significantly reducing communication and computing overhead. The algorithm introduces continuous-time collision constraints on individual prediction trajectories, uses a quadratic programming solver to quickly obtain feasible solutions that meet the requirements of dynamics, smoothness and safety distance, and continuously modifies the trajectory through local iteration to achieve global collaboration. Although the above algorithm has solid theoretical guarantees, its scalability is limited to tens of drones. When the number of drones expands to hundreds or even thousands, its adjacency graph becomes dense, communication load rises rapidly, and solving speed slows down significantly or even gives no solution. At the same time, the control prediction time domain of the algorithm is severely limited, and it performs poorly in terms of long-range global optimality.

[0004] The document "Robust and Efficient Trajectory Planning for Formation Flight in Dense Environments" (published in the journal "IEEE Transactions on Robotics", Vol. 39, No. 6, 4785-4804, 2023) uses a hierarchical motion planning framework. In the macro stage, the formation shape is measured by a symmetric normalized Laplacian matrix, and the optimal formation position sequence is precomputed, and then combined with fixed time step sampling, so that the optimization time and formation size are in a linear relationship. In the micro stage, the robot performs spatiotemporal distributed trajectory optimization within its local field of view, which can adaptively scale and rotate the formation in narrow environments, and quickly recover consistent action after formation switching or sudden disturbance. The scheme disclosed in the above document uses a complex parameterized representation of the macro state of the swarm robot, which needs to handle non-convex constraints such as obstacle avoidance and formation maintenance, resulting in high computational complexity and difficulty in guaranteeing global optimality. The scalability, flexibility and safety still need to be improved. SUMMARY

[0005] Embodiments of the present application provide a motion planning method suitable for large-scale robot swarm, which has high scalability, high flexibility and high obstacle avoidance capability. Through a hierarchical optimization framework, the problem of difficulty in balancing computational efficiency and safety when the size of the swarm is expanded is solved.

[0006] In a first aspect, embodiments of the present application provide a collision risk aware and highly scalable large-scale swarm robot motion planning method, comprising:

[0007] S101, in the macro stage, the macro state of the swarm is represented by a Gaussian mixture model, and the transport trajectory of the Gaussian mixture model is planned by model predictive control;

[0008] S103, in the micro stage, the artificial potential field method is used to assign target positions to the robots, and the distributed model predictive control is combined to realize the tracking and dynamic obstacle avoidance of the individual to the Gaussian mixture model transport trajectory.

[0009] In some embodiments, in step S101, the random variable that changes over time is used to represent the state of the robot swarm, which is subject to the distribution , wherein The covariance of describes the closeness of the robots in the robot swarm, and the position of each robot can be regarded as a sample of , that is

[0010] ~

[0011] Since Gaussian mixture models can approximate any distribution, they are used to represent the macroscopic state of a cluster, denoted as:

[0012] ,

[0013] in This indicates the number of Gaussian components in the Gaussian mixture model. For the first j There are Gaussian distribution components with a mean of 1. The covariance matrix is The weight is .

[0014] In some embodiments, in step S101, at the macroscopic stage, the initial and target distributions of the robot swarm are modeled as two Gaussian mixture models, respectively. and And establish the following optimization problem (P) to plan the transport trajectory of the Gaussian mixture model.

[0015]

[0016] (1)

[0017] (2)

[0018] in, s.t. Set symbols with underscores represent constraints. express , T f Indicates the final time step, i.e. , p This is the index variable for the time step. The optimization objective is to minimize... arrive Wasserstein distance between all Gaussian components W The weighted sum of 2, with the weight coefficient at each step. Two Gaussian distributions and The Wasserstein distance between them has an analytical expression as follows:

[0019] ,

[0020] in tr Represents the trace operation of a matrix. Constraint (1) is expressed by the expression. The collision risk between the cluster Gaussian mixture model and obstacles is quantified, and a risk cap is set to achieve obstacle avoidance between the cluster Gaussian mixture model and environmental obstacles. Constraint (2) is achieved through a linear function. and probability upper limit The maximum probability of the cluster Gaussian mixture model was constrained, thereby preventing the robot swarm from becoming too dense.

[0021] In some embodiments, in step S101, the constraints (1) of the optimization problem P established in the macroscopic stage are used to measure the collision safety performance of the Gaussian mixture model of the current robot cluster using Conditional Value of Risk (CVaR). Conditional Value of Risk (CVaR) can calculate random variables that follow a continuous distribution. Risk tolerance The conditional expected value in the worst-case scenario.

[0022]

[0023] in For Gaussian random variables Its conditional value at risk (CVaR) analytical expression is:

[0024] ,

[0025] in Let be the probability density function of the standard normal distribution. Let be the cumulative distribution function of the standard normal distribution. Also, because for the in the Gaussian mixture model... j Gaussian components and spatial obstacles The signed distance function SDF follows a Gaussian distribution, and the signed distance function SDF is denoted as . ,Right now

[0026] ,

[0027] This leads to the derivation of the Gaussian mixture model. Y The CVaR expression,

[0028] ,

[0029] in This indicates the weight of the corresponding component. yes Distribution in Value at Risk The tail probability at the quantile, i.e. Therefore, CVaR can be used to quantify the collision risk of the entire Gaussian mixture model, constraining its CVaR value to not exceed a threshold. That is, constraint (1) can be written as

[0030] (3)

[0031] in h This indicates the length of the prediction time domain.

[0032] In some embodiments, in step S101, to improve the collision risk awareness of robot swarms in obstacle environments at the macroscopic stage, a planning space discretization method for collision risk awareness is proposed. The set of discretized planning spaces is now represented as... ,in This represents the total number of Gaussian components in the Gaussian mixture model. Let... Distribute evenly throughout the planned space and optimize To minimize the collision risk between the Gaussian component and environmental obstacles, define the covariance matrix. for

[0033] ,

[0034] The optimization problem for the elements of this matrix is ​​proposed as follows:

[0035]

[0036] (4)

[0037] (5)

[0038] in , Indicates the number of obstacles. This represents the weight between different obstacles and their corresponding components. (Constraint (4)) c It should be greater than 0 to ensure The objective function is positive definite, and constraint (5) is set to avoid excessive aggregation of the robot swarm. To reduce computational complexity, the objective function is scaled using the mean inequality, and constraint (4) is introduced as a penalty term into the objective function, resulting in the following convex problem:

[0039]

[0040] ,

[0041] in Weighting coefficients are used to balance collision risk and cluster distribution divergence. The objective function design for this convex problem effectively reduces the collision risk between Gaussian components and obstacles, and also improves the spatial distribution flexibility of the robot cluster.

[0042] In some embodiments, in step S101, the transport trajectories of a series of Gaussian mixture models within a certain time domain are obtained by using the online solution method of sequential quadratic optimization of cluster motion planning. Constraint (3) is a nonlinear concave constraint, which is applied to any feasible solution. Linearize it using a first-order Taylor expansion to obtain

[0043] (6)

[0044] A strongly convex approximation is made for the objective function of the original problem P, and a subproblem P is proposed. v :

[0045]

[0046]

[0047]

[0048] in This represents the weight of the regularization term. This subproblem is a strongly convex problem; the optimal solution to the subproblem is found when... Then, the current feasible solution To find the optimal solution to the subproblem with a certain step size Moving the direction yields a new feasible solution and will replace Solve the subproblem P sequentially and iteratively. v until the solution satisfies the convergence condition, i.e. If the value is less than a certain threshold, the optimal solution to the original problem P is obtained.

[0049] In some embodiments, in step S103, after the optimal transport result is solved at the macroscopic level, i.e., the Gaussian mixture model representing the state of the robot swarm at the next moment, all robots at the microscopic level calculate their respective control inputs to track the desired macroscopic state of the swarm at the next moment; firstly, the artificial potential field method is used to centrally control the robot swarm. Assume the current and target Gaussian mixture models are respectively... and ,in and The mean of a multivariate Gaussian distribution, and Represents covariance, and The gravitational field of the robot is constructed as follows, representing the weights:

[0050]

[0051] .

[0052] The repulsive field consists of the repulsive forces exerted by the current robot on obstacles and surrounding robots. The repulsive field activates when the distance between the robot and an obstacle, or between robots, is less than a preset threshold, and the closer the distance, the stronger the repulsive force. The entire artificial potential field is composed of a combination of gravitational and repulsive fields. Each robot then specifies the coordinates of its target position based on the negative gradient direction of the artificial potential field, with a certain step size.

[0053]

[0054]

[0055] In the formula This represents the robot's step length.

[0056] Secondly, this application provides a motion planning device for large-scale swarm robots with collision risk awareness and high scalability. The device is configured to: in the macroscopic stage, use a Gaussian mixture model to represent the macroscopic state of the swarm and plan the transport trajectory of the Gaussian mixture model through model predictive control; in the microscopic stage, assign target positions to the robots through the artificial potential field method and combine distributed model predictive control to realize individual tracking and dynamic obstacle avoidance of the transport trajectory of the Gaussian mixture model.

[0057] Thirdly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described above.

[0058] Fourthly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

[0059] The collision risk awareness and highly scalable large-scale swarm robot motion planning method and apparatus of this application have the following beneficial effects:

[0060] By setting different cluster sizes, obstacle environment complexity, and risk tolerance levels... α Systematic simulations and physical experiments were conducted to fully verify the superior performance of the ROVER algorithm. Experimental results show that the proposed ROVER algorithm significantly outperforms state-of-the-art methods in key indicators such as scalability, navigation flexibility, and obstacle avoidance safety, and can efficiently generate cluster motion trajectories that balance global optimality and local safety. In particular, the proposed ROVER algorithm exhibits a unique risk awareness capability by adjusting the risk acceptance level in the CVaR constraint. α This method allows for flexible control of the swarm's approach to obstacles, achieving a dynamic balance between conservative obstacle avoidance and efficient passage, significantly improving the swarm's adaptability in complex scenarios such as narrow passages. Practical experiments further confirm that this method can achieve safe and reliable motion planning on both Ackerman wheeled robot and drone swarm platforms. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the collision risk awareness and highly scalable large-scale swarm robot motion planning method according to an embodiment of this application;

[0062] Figure 2 This is a diagram of the ROVER algorithm framework in this application. Detailed Implementation

[0063] The present application will be further described below with reference to the accompanying drawings and embodiments.

[0064] In the following description, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. The following description provides multiple embodiments of the invention, which can be substituted or combined with each other. Therefore, this application can also be considered to include all possible combinations of the same and / or different embodiments described. Thus, if one embodiment includes features A, B, and C, and another embodiment includes features B and D, then this application should also be considered to include embodiments containing one or more other possible combinations of features A, B, C, and D, even if such embodiments are not explicitly described in the following text.

[0065] like Figure 1 , Figure 2 As shown, to enable large-scale robot swarms to achieve safe and efficient movement from the initial area to the target area in complex obstacle environments, this invention proposes the ROVER algorithm, which combines a Gaussian mixture model and a risk-aware hierarchical motion planning framework, divided into two stages: macro-planning and micro-control. In the macro-stage (step S101), a Gaussian mixture model is used to represent the macro-state of the swarm, and model predictive control is used to plan a Gaussian mixture model transport trajectory that satisfies CVaR obstacle avoidance constraints. In the micro-stage (step S103), a collision-free target position is generated using the artificial potential field method, and distributed model predictive control is used to achieve accurate tracking of the Gaussian mixture model transport trajectory by individual robots. The ROVER algorithm will be described in detail below from the aspects of macro-planning and micro-control:

[0066] (I) Macro Planning

[0067] Using random variables that change over time The state of the robot swarm is represented by a distribution. ,in The covariance roughly describes the density of robots in a robot swarm, while the position of each robot... Can be regarded as middle A sample, namely

[0068] ~

[0069] The macroscopic state of the cluster is represented using a Gaussian mixture model, i.e.:

[0070] ,

[0071] in This indicates the number of Gaussian components in the Gaussian mixture model. For the first j There are Gaussian distribution components with a mean of 1. The covariance matrix is The weight is .

[0072] The initial and target distributions of the robot swarm are modeled as two Gaussian mixture models. and And establish the following optimization problem (P) to plan the transport trajectory of the Gaussian mixture model.

[0073]

[0074] (1)

[0075] (2)

[0076] in, s.t. Set symbols with underscores represent constraints. express , T f Indicates the final time step, i.e. , p This is the index variable for the time step. The optimization objective is to minimize... arrive Wasserstein distance between all Gaussian components W The weighted sum of 2, with the weight coefficient at each step. Two Gaussian distributions and The Wasserstein distance between them has an analytical expression as follows:

[0077] ,

[0078] in tr Represents the trace operation of a matrix. Constraint (1) is expressed by the expression. The collision risk between the cluster Gaussian mixture model and obstacles is quantified, and a risk cap is set to achieve obstacle avoidance between the cluster Gaussian mixture model and environmental obstacles. Constraint (2) is achieved through a linear function. and probability upper limit The maximum probability of the cluster Gaussian mixture model was constrained, thereby preventing the robot swarm from becoming too dense.

[0079] The ROVER algorithm proposed in this application establishes the following constraints for the optimization problem P at the macroscopic stage: (1) The Conditional Value at Risk (CVaR) is used to measure the collision safety performance of the Gaussian mixture model of the current robot swarm. CVaR can calculate random variables that follow a continuous distribution. Risk tolerance The conditional expected value in the worst-case scenario.

[0080]

[0081] in For Gaussian random variables Its conditional value at risk (CVaR) analytical expression is:

[0082] ,

[0083] in Let be the probability density function of the standard normal distribution. Let be the cumulative distribution function of the standard normal distribution. Also, because for the in the Gaussian mixture model... j Gaussian components and spatial obstacles The signed distance function SDF (denoted as It follows a Gaussian distribution, that is

[0084] ,

[0085] This leads to the derivation of the Gaussian mixture model. Y The CVaR expression,

[0086] ,

[0087] in This indicates the weight of the corresponding component. yes Distribution in Value at Risk The tail probability at the quantile, i.e. Therefore, CVaR can be used to quantify the collision risk of the entire Gaussian mixture model, constraining its CVaR value to not exceed a threshold. That is, constraint (1) can be written as

[0088] (3)

[0089] in h This indicates the length of the prediction time domain.

[0090] To enhance the collision risk awareness of robot swarms in obstacle-filled environments at the macroscopic level, the ROVER algorithm employs a planning space discretization method for collision risk awareness. The discretized planning space is now represented as... ,in This represents the total number of Gaussian components in the Gaussian mixture model. Let... Distribute evenly throughout the planned space and optimize To minimize the collision risk between the Gaussian component and environmental obstacles, define the covariance matrix. for

[0091] ,

[0092] The optimization problem for the elements of this matrix is ​​proposed as follows:

[0093]

[0094] (4)

[0095] (5)

[0096] in , Indicates the number of obstacles. This represents the weight between different obstacles and their corresponding components. (Constraint (4)) c It should be greater than 0 to ensure The objective function is positive definite, and constraint (5) is set to avoid excessive aggregation of the robot swarm. To reduce computational complexity, the objective function is scaled using the mean inequality, and constraint (4) is introduced as a penalty term into the objective function, resulting in the following convex problem:

[0097]

[0098] ,

[0099] in Weighting coefficients are used to balance collision risk and cluster distribution divergence. The objective function design for this convex problem effectively reduces the collision risk between Gaussian components and obstacles, and also improves the spatial distribution flexibility of the robot cluster.

[0100] Finally, the ROVER algorithm solves the problem online using a sequential quadratic optimization method, generating a series of Gaussian mixture model transport trajectories that satisfy the constraints within the planning time domain. Since constraint (3) is a nonlinear concave constraint, it is applicable to any feasible solution. Linearize it using a first-order Taylor expansion to obtain

[0101] (6)

[0102] A strongly convex approximation is made for the objective function of the original problem P, and a subproblem P is proposed. v :

[0103]

[0104]

[0105]

[0106] in This represents the weight of the regularization term. This subproblem is a strongly convex problem; the optimal solution to the subproblem is found when... Then, the current feasible solution To find the optimal solution to the subproblem with a certain step size Moving the direction yields a new feasible solution and will replace Solve the subproblem P sequentially and iteratively. v until the solution satisfies the convergence condition, i.e. If the value is less than a certain threshold, the optimal solution to the original problem P is obtained.

[0107] (ii) Micro-control

[0108] Once the optimal transport result is obtained at the macroscopic level, i.e., the Gaussian mixture model representing the state of the robot swarm at the next moment, each robot at the microscopic level calculates its own control input to track the desired macroscopic state of the swarm at the next moment. First, the artificial potential field method is used for centralized control of the robot swarm. Assume the current and target Gaussian mixture models are respectively... and ,in and The mean of a multivariate Gaussian distribution, and Represents covariance, and The gravitational field of the robot is constructed as follows, representing the weights:

[0109]

[0110] .

[0111] The repulsive field consists of the repulsive forces exerted by the current robot on obstacles and surrounding robots. The repulsive field activates when the distance between the robot and an obstacle, or between robots, is less than a preset threshold, and the closer the distance, the stronger the repulsive force. The entire artificial potential field is composed of a combination of gravitational and repulsive fields. Each robot then specifies the coordinates of its target position based on the negative gradient direction of the artificial potential field, with a certain step size.

[0112]

[0113]

[0114] In the formula This represents the robot's step length.

[0115] This invention proposes a hierarchical motion planning method and apparatus for risk-aware large-scale robot swarms, which consists of two stages: macroscopic and microscopic. The macroscopic stage uses a Gaussian mixture model to describe the overall state of the robot swarm and plans the transport trajectory of each component in the Gaussian mixture model based on finite-time model predictive control. The microscopic stage uses an artificial potential field method to assign a collision-free target position to each robot and combines it with distributed model predictive control to achieve trajectory tracking and dynamic obstacle avoidance for individual robots. The innovations of this application's hierarchical motion planning method for risk-aware large-scale robot swarms are mainly reflected in three aspects:

[0116] (1) A cluster state representation method based on Gaussian mixture model is proposed. A set of Gaussian components is constructed by discretizing the workspace, and the optimal transport path between Gaussian components is calculated based on optimal transport theory and Wasserstein metric. Each Gaussian component node contains an optimized covariance matrix to adapt to collision risk constraints in complex environments.

[0117] (2) An innovative collision risk quantification system at the Gaussian mixture model level was established, the probability distribution of the signed distance function between the Gaussian mixture model and obstacles was derived, and an explicit expression of the CVaR of the Gaussian mixture model was proposed as a risk constraint index. This method is the first to achieve accurate modeling of collision risk for the overall distribution of the cluster rather than for a single Gaussian component.

[0118] (3) An efficient solution algorithm based on sequential quadratic optimization was designed, which transforms the non-convex optimization problem with CVaR constraints into a series of linear programming subproblems, and realizes real-time motion planning for large-scale clusters through iterative solution. The algorithm has convergence guarantee and its computational complexity is independent of the cluster size.

[0119] By setting different cluster sizes, obstacle environment complexity, and risk tolerance levels... α Systematic simulations and physical experiments were conducted to fully verify the superior performance of the ROVER algorithm. Experimental results show that the proposed ROVER algorithm significantly outperforms state-of-the-art methods in key indicators such as scalability, navigation flexibility, and obstacle avoidance safety, and can efficiently generate cluster motion trajectories that balance global optimality and local safety. In particular, the proposed ROVER algorithm exhibits a unique risk awareness capability by adjusting the risk acceptance level in the CVaR constraint. α This method allows for flexible control of the swarm's approach to obstacles, achieving a dynamic balance between conservative obstacle avoidance and efficient passage, significantly improving the swarm's adaptability in complex scenarios such as narrow passages. Practical experiments further confirm that this method can achieve safe and reliable motion planning on both Ackerman wheeled robot and drone swarm platforms.

[0120] This application also provides a hierarchical motion planning device for a large-scale robot swarm with risk awareness. The device is configured as follows: in the macroscopic stage, a Gaussian mixture model is used to describe the overall state of the robot swarm, and the transport trajectory of each component in the Gaussian mixture model is planned based on finite-time model predictive control; in the microscopic stage, an artificial potential field method is used to assign a collision-free target position to each robot, and distributed model predictive control is combined to realize trajectory tracking and dynamic obstacle avoidance of individual robots.

[0121] In this application, the embodiments of the hierarchical motion planning device for risk-aware large-scale robot swarms are basically similar to the embodiments of the hierarchical motion planning method for risk-aware large-scale robot swarms. For relevant details, please refer to the description of the embodiments of the hierarchical motion planning method for risk-aware large-scale robot swarms.

[0122] This application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

[0123] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the hierarchical motion planning method steps for a large-scale robot swarm with risk awareness described above. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A collision risk-aware and highly scalable method for motion planning of large swarms of robots, characterized in that, Comprising: S101, in the macro stage, the macro state of the cluster is represented by a Gaussian mixture model, and the transport trajectory of the Gaussian mixture model is planned through model predictive control; the constraint (1) of the optimization problem P established in the macro stage measures the collision safety performance of the current robot cluster using the conditional value at risk CVaR, which can calculate the conditional expectation value of the worst case of the risk acceptance degree α of the random variable subject to continuous distribution the conditional expectation value in the worst case of the risk acceptance degree α wherein For Gaussian random variables The conditional value at risk CVaR analytical expression is ， wherein is the probability density function of the standard normal distribution, is the cumulative distribution function of the standard normal distribution, and since the signed distance function SDF of the j ith Gaussian component in the Gaussian mixture model and the spatial obstacle satisfies a Gaussian distribution, the signed distance function SDF is denoted as i.e. ， Further, the CVaR expression of the Gaussian mixture model is derived Y Y ， where denotes the weight of the corresponding component, is the tail probability of the distribution of quantile, i.e. Thus, the collision risk of the entire Gaussian mixture model is quantified using CVaR, constraining its CVaR value to be less than a threshold i.e. constraint (1) is written as ，（3） wherein h denotes the prediction temporal length; S103, in the micro phase, the target position of the robot is allocated by the artificial potential field method, and the tracking and dynamic obstacle avoidance of the individual to the Gaussian mixture model transport trajectory are realized by combining the distributed model predictive control.

2. The method of claim 1, wherein, In step S101, a random variable that varies over time is used to represent the state of the robot swarm, which is subject to a distribution where The covariance of the robot swarm roughly describes the closeness of the robots in the robot swarm, while the position of each robot is regarded as a sample in the distribution, that is ~ Since the Gaussian mixture model can be fitted to any distribution, the macro state of the cluster is represented by the Gaussian mixture model, denoted as: ， in This indicates the number of Gaussian components in the Gaussian mixture model. For the first j Gaussian components with a mean of The covariance matrix is The weight is .

3. The method of claim 2, wherein, In step S101, in the macroscopic phase, the initial and target distributions of the robot swarm are modeled as two Gaussian Mixture Models and respectively, and an optimization problem P is established to plan the transport trajectory of the Gaussian Mixture Models, （1） （2） where s.t. denotes the constraint, the underlined set symbol denotes , T f denotes the final time step, i.e. , p is the index variable for the time steps, the optimization objective is to minimize the weighted sum of the Wasserstein distances between all Gaussian components in W 2, the weight coefficients for each step , the Wasserstein distance between two Gaussian distributions and has an analytical expression​ ， where, tr denotes the trace operation of a matrix, constraint (1) is expressed by quantifies the collision risk between the cluster Gaussian mixture model and the obstacle, and sets a risk upper limit, which realizes the obstacle avoidance between the cluster Gaussian mixture model and the environmental obstacle, constraint (2) is expressed by a linear function and the probability upper limit constrains the maximum probability of the cluster Gaussian mixture model.

4. The method of claim 1 or 2, wherein, In step S101, the set of discretized representations of the planning space is denoted as where denotes the total number of Gaussian components in the Gaussian mixture model, and let be uniformly distributed throughout the planning space, and optimize to minimize the collision risk between the Gaussian components and the environmental obstacles, define the covariance matrix as ， The optimization problem of the matrix element is proposed as （4） （5） where , denotes the number of obstacles, denotes the weights between different obstacles and corresponding components, the constraint (4) in c should be greater than 0 to ensure positive definite, the constraint (5) is set to avoid the over-concentration of the robot swarm; by scaling the objective function through the mean inequality and introducing the constraint (4) as a penalty term into the objective function, the following convex problem is obtained: ， wherein Weighting factors for balancing collision risk and cluster distribution spread.

5. The method of claim 1 or 2, wherein, In step S101, a sequence quadratic optimization online solution method of cluster motion planning is used to obtain a series of Gaussian mixture model transport trajectories in a certain time domain. The constraint (3) is a nonlinear concave constraint, which is linearized by first-order Taylor expansion at any feasible solution to obtain （6） The objective function of the original problem P is strongly convexly approximated, and a subproblem P v is proposed where denotes the regular term weight, the subproblem is a strongly convex problem, and the optimal solution of the subproblem is denoted by The current feasible solution is moved in the direction of the subproblem optimal solution with a certain step size to obtain a new feasible solution and replace The subproblem P v is solved in sequence until the solution satisfies the convergence condition, i.e. is less than a certain threshold value, and the optimal solution of the original problem P is obtained.

6. The method of claim 1 or 2, wherein, In step S103, when the macro layer solves the optimal transport result, i.e., the Gaussian mixture model representing the state of the robot swarm at the next moment, all robots at the micro layer calculate their respective control inputs to track the expected macro state of the swarm at the next moment; first, the artificial potential field method is used for centralized control of the robot swarm, assuming that the current and target Gaussian mixture models are and where and represent the mean of the multivariate Gaussian distribution, and represent the covariance, and represent the weight, and the gravitational field of the robot is constructed as follows: . repulsive field U rep (k) is composed of the repulsive force of the current robot to the obstacle and the surrounding robots, when the distance between the robot and the obstacle or between the robots is less than the preset threshold, the repulsive field starts to take effect, and the closer the distance, the greater the repulsive force generated. The whole artificial potential field is composed of the attractive field and the repulsive field, then each robot specifies the coordinates of its target position according to the negative gradient direction of the artificial potential field with a certain step size, In the formulae is the step length of the robot.

7. A collision risk aware and highly scalable large-scale swarm robot motion planning apparatus, comprising: The device is configured to: in the macro stage, use a Gaussian mixture model to represent the macro state of the cluster, and plan a transport trajectory of the Gaussian mixture model through model predictive control; the constraint (1) of the optimization problem P established in the macro stage uses the conditional value at risk CVaR to measure the collision safety performance of the Gaussian mixture model of the current robot cluster, and the conditional value at risk CVaR can calculate the conditional expectation value in the worst case of the risk acceptance degree alpha of a random variable subject to a continuous distribution the conditional expectation value in the worst case of the risk acceptance degree alpha wherein For Gaussian random variables The conditional value at risk CVaR analytical expression is ， where is the probability density function of the standard normal distribution, is the cumulative distribution function of the standard normal distribution, and since the signed distance function SDF of the j th Gaussian component in the Gaussian mixture model and the spatial obstacle satisfies a Gaussian distribution, the signed distance function SDF is denoted as i.e. ， Further, the CVaR expression of the Gaussian mixture model is derived Y Y Y Y Y Y Y ， where denotes the weight of the corresponding component, is the tail probability of the distribution of quantile, i.e. Thus, the collision risk of the whole Gaussian mixture model is quantified using CVaR, constraining its CVaR value to be less than a threshold i.e. constraint (1) is written as （3） wherein h denotes the prediction temporal length; In the micro phase, the target position of the robot is allocated by the artificial potential field method, and the tracking and dynamic obstacle avoidance of the individual to the Gaussian mixture model transport trajectory are realized by combining the distributed model predictive control.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to realize the steps of the method in any one of claims 1-6.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to realize the steps of the method in any one of claims 1-6.

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