An autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots

Abstract

An autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots. First, initialize the parameters, and then use the theory of distributed convex optimization to set the cost function and optimization terms of the robots. The cost function can be divided into a total cost function and a local cost function, where the total cost function is the sum of the local cost functions, and we can obtain the minimum value of the cost function if and only if time approaches infinity. The intelligent robot α follows the leader intelligent robot to move. When approaching an obstacle, a virtual intelligent robot β is designed according to the "parallelogram law" of vectors. The virtual intelligent robot β generates a repulsive force to enable the intelligent robot α to smoothly avoid the obstacle. The present invention realizes the adaptive distributed convex optimization and autonomous obstacle avoidance flocking control of swarm robots through the optimization of the speed of swarm intelligent robots and the recognition of obstacles, combined with three sub-control protocols, while avoiding complex obstacles and following a moving target during the energy-saving optimization of swarm robots.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent robots and relates to an autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots. Technical Background

[0002] Distributed optimization problems have been a hot topic in recent years and have multiple application directions including intelligent power systems, robotics, machine learning, and data analysis. Optimization of multi-agent systems is one of them. Facing complex tasks, multi-agents cooperate in a distributed form, and the characteristic of distributed optimization is to configure resources to achieve the optimal state. Flocking is a collective behavior of multi-agents. Using limited environmental information, agents move orderly and stay together as a group. Flocking control can be used for the collective obstacle avoidance behavior of unmanned aerial vehicles or unmanned vehicles. After convex optimization, it can reduce power consumption, extend working hours, and complete more complex tasks.

[0003] Reynolds first proposed the flocking model: separation, aggregation, and velocity matching. Subsequently, Saber redefined the artificial potential function to handle situations with complex obstacles. On the basis of Saber's work, scholars such as Su introduced the concept of pinning control. By feeding back the information of virtual leaders to a small number of agents, flocking control can be performed on most agents in a multi-agent system. Scholars such as Yu proposed a flocking control with variable acceleration. Each individual agent only has partial information of the leader, and flocking control is achieved under the condition of communication connectivity. Scholars such as Pei absorbed the key features of flocking and anti-flocking to achieve local multi-swarms. Scholars such as Chen considered the inertial effect of real agents and designed a distributed control protocol that can not only ensure the local aggregation of agents but also ensure that heterogeneous agents uniformly track multiple targets. Scholars such as Lyu applied flocking control to the automotive autonomous driving network by transforming the obstacle avoidance problem into a problem of constraining the flocking control of multiple vehicles with an optimization algorithm. Scholars such as Qiu improved the multi-objective pigeon inspired optimization (MPIO) algorithm. On this basis, a distributed flocking control algorithm for unmanned aerial vehicles based on the improved MPIO was proposed to control the formation flight of unmanned aerial vehicles in a complex obstacle environment. Scholars such as Zhang studied the possible swarm behaviors of the Cucker-Smale model with distributed time delays. Scholars such as Huang addressed the flocking control problem of continuous-time multi-agent systems with non-uniform non-convex constraints. Under non-uniform and non-convex constraint control, a distributed swarm control algorithm was proposed for each agent using the local information of adjacent agents. The optimization problem of agents has attracted much attention recently, especially distributed optimization.

[0004] The research on distributed optimization algorithms can be traced back to the pioneering work of scholars such as Tsitsiklis. In recent years, a large number of scholars have conducted in-depth research on distributed optimization algorithms, especially in the proposal of optimization algorithms and the proof of convergence. Nedic proposed a distributed prediction consensus algorithm, which multi-agents can use to calibrate prediction values with special values on a time-varying network. Scholars such as Lu and Tang introduced a zero-gradient sum algorithm, and the nonlinear network dynamic system obtained by using this algorithm converges asymptotically. Varagnolo solved the distributed unconstrained convex optimization problem under the separability assumption and proposed a convex optimization algorithm in a distributed environment, which can use second-order information to accelerate the convergence speed. Scholars such as Chen solved a distributed convex optimization problem with equality constraints using a continuous-time nonlinear protocol. Scholars such as Rahili and Ren combined multi-agent flocking control with a distributed optimization convex optimization algorithm and proposed an estimation algorithm based on a sign function. On this basis, Yang proposed different cost functions, enabling agents to track the optimal speed. Scholars such as Wen introduced the discretization of the neural dynamics method, making the iterative sequence of the discrete-time method converge to the optimal solution of distributed optimization on a multi-agent system from any initial point. Scholars such as Yu constructed a directed and detailed balance network that depends on the weights of the optimization function and proposed a distributed consensus protocol with local objective gradients on the designed network, thereby asymptotically solving the global optimization problem.

[0005] However, in the face of increasingly complex tasks, simply ensuring the stability of unmanned systems has become difficult to meet the actual engineering needs. In order to save resources and control costs, energy-saving optimization must be considered. The present invention introduces distributed optimization to control the energy consumption of swarm robots. Summary of the Invention

[0006] The object of the present invention is to provide an autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots, which realizes optimal control while avoiding obstacles and tracking the leader.

[0007] The present invention is realized through the following technical solutions.

[0008] An autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots according to the present invention uses the distributed convex optimization theory to perform convex optimization on the velocity term of intelligent robot α, sets the cost function of the robot, and intelligent robot α gradually approaches the optimal velocity and is equal when time approaches infinity; during the control process of autonomous obstacle avoidance of the intelligent robot swarm, the position and velocity of the corresponding intelligent robot β (virtual intelligent robot) generated by intelligent robot α on the edge of the current obstacle are calculated according to the "parallelogram rule" of the vector. When intelligent robot α approaches the obstacle, a corresponding intelligent robot β will be generated at the edge of the obstacle. According to sub-control protocol II, intelligent robot β will generate a repulsive force on intelligent robot α, so that intelligent robot α can avoid the obstacle. At the same time, sub-control protocol I can realize the separation and aggregation of intelligent robot α and its neighboring intelligent robot α, and sub-control protocol III realizes the tracking of the leader robot.

[0009] Specifically, an autonomous obstacle avoidance flocking control method for distributed convex optimization swarm robots according to the present invention includes the following steps:

[0010] (1) Initialize parameters: the position and radius of the obstacle, the safety distance between intelligent robot α and the obstacle, the total number of intelligent robots α and the sensing radius of intelligent robot α, the initial positions and velocities of intelligent robot α and the leader intelligent robot;

[0011] (2) Use the distributed convex optimization theory to set the cost function of intelligent robot α:

[0012]

[0013] And set the velocity optimization term for intelligent robot α:

[0014]

[0015] where sgn() is the step function,

[0016]

[0017] (3) Calculate the optimal velocity p of intelligent robot α according to the convex optimization theory * : The velocity optimization term enables the velocity p of intelligent robot α to reach and maintain the optimal velocity p * ;

[0018] (4) Calculate the position and velocity of the corresponding virtual intelligent robot β of intelligent robot α on the edge of the obstacle at the current moment according to the "parallelogram rule" of the vector;

[0019] (5) Design the artificial potential function between the intelligent robot α and its neighboring intelligent robots, and design the optimization term for the intelligent robot α: sub-control protocol I, to achieve separation and aggregation among the intelligent robots α while reaching the optimal speed, so as to reduce the energy consumption of the movement of the intelligent robot α;

[0020] (6) When the intelligent robot α approaches an obstacle, design the artificial potential function between the intelligent robot α and the intelligent robot β: sub-control protocol II, to achieve the autonomous obstacle avoidance of the intelligent robot α;

[0021] (7) Design the force function between the intelligent robot α and the leader intelligent robot: sub-control protocol III, to achieve the tracking of the leader intelligent robot;

[0022] (8) Combining the three sub-control protocols of the intelligent robot α with the speed optimization term, the swarm intelligent robots reach and maintain the optimal speed, track the leader intelligent robot to complete the obstacle avoidance task.

[0023] Furthermore, the method for solving the optimal speed p * (t) of the intelligent robot α in step (3) of the present invention is as follows:

[0024] (1) Given a total cost function This is a convex function. The goal is to design the control input term u for the motion equation i , using its own cost function and the information collected from neighbors and the leader, so that all agents reach the optimal state p * (t). p * (t) is the minimum value of the time-varying convex optimization problem,

[0025]

[0026] (2) f(x) is a continuously differentiable convex function. f(x) is minimum if and only if . When p i (t) = p j (t), there is where p i ∈ R n . So the problem is simplified to the problem of finding the minimum value of a convex function. When t → ∞, the speed p(t) of the agent converges to the optimal speed p * (t), that is

[0027] (3) The cost function of a single agent is twice continuously differentiable; take the partial derivative of f i in the direction of p i (p i , t) where σ > 0, g i (t) is a differentiable function satisfying ||g i (t)|| < g, H i (p i , t) is the second-order partial derivative of f i (p i , t) in the direction of p i , so H i (p i , t) = σ;

[0028] Furthermore, the determination of the position and velocity of the virtual intelligent robot β corresponding to the intelligent robot α on the obstacle edge at the current moment in step (4) of the present invention is as follows:

[0029] (1) The safety distance between the i-th intelligent robot α and the obstacle O i -q ob,h || is determined by the norm ||q h of matrix theory, where q i represents the position of the i-th intelligent robot α, and q ob,h represents the position of the obstacle O h , h ∈ {1, 2,... m};

[0030] (2) The expected distance between the i-th intelligent robot α and the obstacle O h is d s , and furthermore

[0031] ||q i -q ob,h || < (d s +r ob,h ),

[0032] where r ob,h is the radius of the obstacle O h ;

[0033] (3) The position and velocity of the intelligent robot α are known. By the "parallelogram rule" of vectors, the position q i,k and velocity p i,k of the intelligent robot β can be obtained, where and are the position vectors of the i-th intelligent robot α and the obstacle O h to the origin of coordinates respectively, and r ob,h is the radius of the obstacle O h . In the above formulas

[0034] Furthermore, the artificial potential function and optimization terms between the intelligent robot α and its neighboring intelligent robots α in step (5) of the present invention are as follows: The design of the sub-control protocol I is as follows:

[0035] (1) The second-order dynamic equations of the leader intelligent robot and the intelligent robot α are as follows:

[0036]

[0037] where q γ , p γ , u γ are respectively the position term, velocity term, and control input term of the leader intelligent robot, and q i , p i , u i are respectively the position term, velocity term, and control input term of the intelligent robot α;

[0038] (2) The design of the sub-control protocol I for the i-th intelligent robot α:

[0039]

[0040] where is the set of the i-th intelligent robot α and its neighboring intelligent robots, φ α is the artificial potential function, and are both constants greater than zero, sgn() is the step function;

[0041] Furthermore, the design of the sub-control protocol II containing the artificial potential function between the intelligent robot α and the intelligent robot β in step (6) of the present invention is as follows:

[0042]

[0043] where represents the set of the i intelligent robots α and the virtual intelligent robot β, φ β is the force function, and are both constants greater than zero;

[0044] Furthermore, the force function between the intelligent robot α and the leader intelligent robot in step (7) of the present invention: The design of the sub-control protocol III is as follows:

[0045]

[0046] where and are both constants greater than zero;

[0047] Furthermore, for the design of the three sub-control protocols of the intelligent robot α in step (8) of the present invention, the control input quantity of the i-th intelligent robot α is as follows:

[0048]

[0049] Advantages and technical effects of the present invention:

[0050] (1) The present invention combines distributed optimization and flocking control of swarm robots, and the energy consumption of intelligent robots will decrease during processes such as aggregation and obstacle avoidance.

[0051] (2) The present invention proposes to determine the position and velocity of the virtual intelligent robot β corresponding to the intelligent robot α at the edge of the obstacle according to the "parallelogram rule" of vectors.

[0052] (3) The sub-control protocol I of the intelligent robot α designed by the present invention realizes separation and aggregation between intelligent robots α while achieving the optimal velocity, reducing the energy consumption of the movement of intelligent robots α.

[0053] (4) When the intelligent robot α approaches the obstacle, the sub-control protocol II of the intelligent robot α designed by the present invention realizes the autonomous obstacle avoidance of the intelligent robot α.

[0054] (5) At the same time, the sub-control protocol III of the intelligent robot α realizes the tracking of the leader robot by the intelligent robot α.

[0055] (6) Through the distributed optimization of the swarm behavior of swarm intelligent robots, the present invention combines the three sub-control protocols of the intelligent robot α, namely the control input quantity, and further realizes the energy-saving optimization in the processes of swarm robot aggregation and autonomous obstacle avoidance, making the swarm robots more energy-saving when collaboratively tracking moving targets in a complex obstacle environment. Description of the Drawings

[0056] Figure 1 is the flow chart of the autonomous obstacle avoidance flocking control method for convex optimization swarm robots.

[0057] Figure 2 is the schematic diagram of determining the virtual intelligent robot β at the edge of the obstacle in the present invention. In the figure, r ob,h represents the radius of the obstacle O h and r represents the sensing radius of the intelligent robot α.

[0058] Figure 3 is the initial position diagram of the swarm robots in the present invention. In the figure, the hollow circles represent the intelligent robots α, the arrows represent the movement directions of the intelligent robots α, and the solid large circles represent the obstacles.

[0059] Figure 4It is the motion state diagram of the swarm intelligent robot at t = 60s.

[0060] Figure 5 It is the motion state diagram of the swarm intelligent robot at t = 80s.

[0061] Figure 6 It is the motion state diagram of the swarm intelligent robot at t = 100s.

[0062] Figure 7 It is the motion state diagram of the intelligent robot at the final moment.

[0063] Figure 8 The scalar magnitude diagram of the speed of the swarm intelligent robot.

[0064] Figure 9 The vector direction diagram of the speed of the swarm intelligent robot. Detailed implementation manner

[0065] The present invention will be described in detail below with reference to the accompanying drawings.

[0066] According to the distributed convex optimization theory, the present invention defines a total cost function for the swarm intelligent robot This is a convex function. Our goal is to design the control input item u for the intelligent robot i , and the team cost function f(p, t) is a strictly convex function with respect to p at any time t. There exists a continuous p * (t) that minimizes the team cost function. f(x) is a continuously differentiable convex function, and f(x) is minimized if and only if When p i = p j there is where p i ∈ R n . So the problem is simplified to the problem of finding the minimum value of a convex function. When t → ∞, the speed p(t) of the agent converges to the optimal speed p * (t). The present invention sets the cost function of a single intelligent robot as follows:

[0067]

[0068] In a 2-dimensional space, there are b circular obstacles, and a swarm robot system consists of n intelligent robots and 1 leader robot. In this system, both the intelligent robots and the leader robot are regarded as mass points, ignoring their shapes and sizes. In the present invention, p i , q i ∈ R 2 respectively represent the position and speed of intelligent robot i, where i ∈ {1, 2,..., n}; p r , q rare the position and velocity of the leader robot; u i , u r respectively represent the control input quantities of the intelligent robot i and the leader robot; P ob,h represents the obstacle O h , h ∈ {1, 2, …, m} is the position; d s is the expected distance between the i-th intelligent robot α and the obstacle O h ; r ob,h represents the radius of the obstacle O h ; d is the expected distance between the intelligent robot α and its neighboring intelligent robots; r represents the sensing radius of the intelligent robot α; the set of its neighboring intelligent robots α can be defined as:

[0069]

[0070] In the swarm robot system, each intelligent robot α has its own independent input control. The motion equations are as follows:

[0071]

[0072] At the same time, the motion input equation of the leader intelligent robot is as follows:

[0073]

[0074] As Figure 2 shown, the total number of intelligent robots n = 25, the initial positions of the swarm robots are randomly generated in the range of [50, 50], and the initial velocities of the agents are randomly generated in the range of [-1, 1]. The initial position of the leader is [10, 10], and the initial velocity is [10, 10]. When the expected distance d of the agent = d s = 12, r = 11 when the agent generates a force. The force parameters in the program are a = 5, b = 5, the parameters h1 = 0.4, h2 = 0.9, s = 0.1. Four spherical obstacles are set in this section, and the parameter settings of the obstacles are stored in the matrix M ob :

[0075]

[0076] Next, the second step is introduced. According to the distributed convex optimization theory, an optimization item is designed for the sub-control protocol I of the intelligent robot α, and this optimization item includes a cost function.

[0077] Next, the third step is introduced. According to the "parallelogram law" of vectors, the position and velocity of the virtual intelligent robot β on the edge of the obstacle can be known. The following is the specific implementation process:

[0078] Based on the basis of matrix theory, the distance from the i-th intelligent robot α to the obstacle Oh The distance can be expressed as ||p i - p ob,h ||. When the intelligent robot α approaches the obstacle O h When approaching the obstacle, it satisfies ||p i - p ob,h || < (d s + r ob,h ). At this time, a virtual intelligent robot β is generated at the edge of the obstacle. It is located at the intersection of the line connecting the center of the i-th intelligent robot α and the obstacle O h and its edge, and the direction of the velocity is consistent with the positive direction of this intersection point, as shown in Figure 1 shown.

[0079] Calculate the position of the virtual intelligent robot β according to the "parallelogram law" of vectors through the position and velocity of the intelligent robot α and velocity

[0080]

[0081] Among them Among them and are the position vectors of the i-th intelligent robot α and the obstacle O h to the origin of coordinates respectively, r ob,h is the radius of the obstacle O h . In the above formula

[0082] The sub-control protocol I of the intelligent robot α is:

[0083]

[0084]

[0085]

[0086]

[0087] Among them is the set of the i-th intelligent robot α and its neighbor intelligent robots, φ α is the force function, and are both constants greater than zero, and sgn() is the step function;

[0088] φ α (x) = ρh(x / p α )φ(x - d α ), (2)

[0089]

[0090] Impulse function

[0091] φ(x) in Equation (2) is

[0092] where and

[0093] Next, introduce the sub-control protocol II:

[0094]

[0095] where is the set of the i-th intelligent robot α and its corresponding virtual intelligent robot β, and are both constants greater than zero, φ β is the force function, and its form is as follows:

[0096] φ β (x) = ρh(x / p β )φ(x - d β )

[0097] where q β = ||q|| σ , d β is the σ-norm of the global minimum value x = d β of φ s .

[0098]

[0099] Next, introduce the sub-control protocol III:

[0100]

[0101] where and are both constants greater than zero.

[0102] Combining the three sub-control protocols of the intelligent robot α, the control input of the i-th intelligent robot α is and its specific form is as follows:

[0103]

[0104] Under the action of the control input (3), the intelligent robot α can achieve distributed optimization and track the leader intelligent robot in the environment of complex obstacles.

[0105] Figure 8 andFigure 9 It is the scalar magnitude graph and direction graph of the speed of intelligent robot α. It can be seen that during the process of the group of 25 intelligent robots α distributedly optimizing obstacle avoidance and tracking the leader intelligent robot, the initial speeds of the intelligent robots α are randomly generated in a disorderly manner, and there are certain fluctuations in the speeds of the intelligent robots α during obstacle avoidance. After leaving the obstacle, the speeds of the intelligent robots α quickly reach consistency and closely follow the leader intelligent robot, and finally reach and maintain the optimal speed, indicating that the distributed optimization has achieved good results.

[0106] Figure 3 The initial position graph of intelligent robot α. The hollow circles represent intelligent robot α, and the arrows represent the directions of the speeds of intelligent robot α. It can be seen that the initial positions of the group of robots are randomly generated in the range of [50, 50], and the initial speeds of the agents are randomly generated in the range of [-1, 1].

[0107] Figures 4 to 7 It is the simulation graph of intelligent robot α following the virtual intelligent robot in a complex obstacle environment. It can be seen that intelligent robot α smoothly avoids obstacles. Based on the concept of the present invention, various replacements, changes, and modifications should not be excluded from the protection scope of the present invention.

Claims

1. An autonomous obstacle avoidance and flocking control method for a distributed convex optimization swarm robot, characterized in that It includes the following steps: (1) Initialize parameters: the position and radius of the obstacle, the safe distance between the intelligent robot α and the obstacle, the total number of intelligent robots α and the perception radius of the intelligent robot α, the initial positions and velocities of the intelligent robot α and the leader intelligent robot; (2) Using the distributed convex optimization theory, set the cost function of the intelligent robot α: And set the velocity optimization term for the intelligent robot α: where sgn() is the sign function, (3) According to convex optimization theory, find the optimal speed p of the intelligent robot α * :The speed optimization term enables the speed p of the intelligent robot α to reach and maintain the optimal speed p * ; (4) Calculate the position and velocity of the corresponding virtual intelligent robot β on the edge of the obstacle at the current moment of the intelligent robot α according to the parallelogram law of vectors; (5) Design the artificial potential energy function between the intelligent robot α and its neighbor intelligent robots, and then design the sub-control protocol I containing the velocity optimization term of the intelligent robot α to achieve separation and aggregation between the intelligent robots α while reaching the optimal velocity, so as to reduce the energy consumption of the movement of the intelligent robot α; (6) When the intelligent robot α approaches the obstacle, design the sub-control protocol II containing the artificial potential energy function between the intelligent robot α and the virtual intelligent robot β to achieve the autonomous obstacle avoidance of the intelligent robot α; (7) Design the force function between the intelligent robot α and the leader intelligent robot: the sub-control protocol III to achieve the tracking of the leader intelligent robot; (8) Combining the three sub-control protocols of the intelligent robot α with the velocity optimization term, the swarm intelligent robots reach and maintain the optimal velocity, track the leader intelligent robot to complete the obstacle avoidance task; among them, The control input quantity of the i-th intelligent robot α is as follows: The method for obtaining the optimal speed p * (t) of the intelligent robot α is as follows: (1) Given a total cost function This is a convex function; the goal is to design a control input term u for the motion equation using its own cost function and the information collected from neighbors and leaders so that all agents reach the optimal state p i , * (t); p * (t) is the minimum of a time-varying convex optimization problem: (2) f(x) is a continuously differentiable convex function if and only if f(x) is minimized; when p i (t) = p j (t), there is where p i ∈R n ; so the problem is reduced to finding the minimum value of a convex function; when t → ∞, the velocity p(t) of the agent converges to the optimal velocity p * (t), that is (3) Cost function of a single intelligent robot is twice continuously differentiable; the partial derivative of f i with respect to p i (p i , t) is where σ > 0, g i (t) is a differentiable function satisfying ||g i (t)|| < g, and H i (p i , t) is the second-order partial derivative of f i (p i , t) in the direction of p i , so H i (p i , t) = σ; The determination of the position and velocity of the corresponding virtual intelligent robot β on the edge of the obstacle at the current moment of the intelligent robot α described in step (4) is as follows: (1) Determine the safety distance between the $i$-th intelligent robot $\alpha$ and the obstacle $O$ through the norm $\|\mathbf{q} i -\mathbf{q} ob,h \|$, where $\mathbf{q} h $ represents the position of the $i$-th intelligent robot $\alpha$, and $\mathbf{q} i $ represents the position of the obstacle $O ob,h $, where $h\in\{1,2,\ldots,m\} h $; (2) The expected distance between the i-th intelligent robot α and the obstacle O h is d s , and in addition ||q i -q ob,h ||<(d s +r ob,h ), where r ob,h is the radius of the obstacle O h ; (3) The position and velocity of the intelligent robot α are known. The position q of the virtual intelligent robot β can be obtained by the parallelogram law of vectors. i,k and the velocity p i,k , where and are the position vectors of the i-th intelligent robot α and the obstacle O h to the origin of coordinates, r ob,h is the radius of the obstacle O h In the above formula The design of the sub-control protocol I containing the artificial potential energy function and the velocity optimization term between the intelligent robot α and its neighbor intelligent robots in step (5) is as follows: (1) The second-order dynamic equations of the leader intelligent robot and the intelligent robot α are as follows: i ∈ {1, 2, … n}, where q γ , p γ , u γ are respectively the position term, velocity term, and control input term of the leader intelligent robot, q i , p i , u i are respectively the position term, velocity term, and control input term of intelligent robot α; (2) The design of the sub-control protocol 1 of the i-th intelligent robot α: Among them is the set of the i-th intelligent robot α and its neighboring intelligent robots, φ α is the artificial potential function, and are both constants greater than zero, sgn() is the sign function; The design of the sub-control protocol II containing the artificial potential energy function between the intelligent robot α and the virtual intelligent robot β in step (6) is as follows: Among them, represents the set of virtual intelligent robots β of the i-th intelligent robot α, φ β is the force function, and are constants both greater than zero; The force function between the intelligent robot α and the leader intelligent robot in step (7): the design of the sub-control protocol III is as follows: wherein and are both constants greater than zero.

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