Azimuth-angle-based distributed attitude estimation method for mobile multi-agent system

Abstract

The invention provides a distributed attitude estimation method for a mobile multi-agent system based on azimuth angles, which comprises the following steps that: a leader-follower multi-agent network is constructed, and a follower agent only acquires azimuth angle measurement information and self angular velocity information between the follower agent and a neighbor agent; designing a distributed preset time attitude observer; the follower agent attitude estimation error is converged to a preset boundary within preset convergence time through the distributed preset time attitude observer, the singular point problem in an existing method is avoided through the design of the Lyapunov inequality and the observer, and the numerical stability is improved; according to the method, the attitude estimation error can be converged to the preset boundary within the preset time defined by the user, the convergence time is irrelevant to the initial condition, and the strict requirement of the task on the time is met; the method has the advantages of rapid convergence, low calculation burden and high robustness, the observer convergence speed is higher, the time-varying gain form is simpler, and the calculation burden is lower.

Description

Technical Field

[0001] This invention relates to the field of intelligent agent control technology, and in particular to a distributed attitude estimation method for a mobile multi-agent system based on azimuth angle. Background Technology

[0002] Multi-agent systems, through collaboration, can significantly improve the efficiency, safety, and scalability of complex tasks, and are therefore widely used in numerous fields. Accurate attitude information (including position and orientation) is fundamental to the efficient operation of multi-agent systems; however, due to sensor limitations and cost constraints, configuring high-precision attitude measurement equipment for each agent is often prohibitively expensive. Therefore, utilizing relative measurements and communication between agents to achieve distributed attitude estimation has become a research hotspot.

[0003] Existing localization algorithms can solve the azimuth-based distributed localization problem when the global orientation is known or can be estimated. However, in multi-agent systems, follower agents often lack accurate self-attitude information, posing a challenge to attitude estimation. In attitude estimation, the Gram-Schmidt process represents the agent's attitude by constructing an orthogonal basis to form a rotation matrix, but this method is computationally intensive and suffers from numerical instability related to singularities.

[0004] To overcome the above problems, related studies have proposed a variety of improved methods: for example, consensus methods based on Euler angles; distributed SO(3) attitude estimation strategies based on absolute angular velocity and linear velocity measurements; and SO(3) attitude estimation based on only azimuth angles, which achieves almost global asymptotic convergence. However, these methods are sensitive to initial azimuth errors. Subsequent work has achieved global stability through hybrid switching, but the problems of pre-set time convergence and singularity have not yet been solved.

[0005] Therefore, there is an urgent need for a distributed attitude estimation method that is computationally simple, has no singularities, and allows for preset convergence time, in order to meet the real-time and stability requirements of multi-agent systems. Summary of the Invention

[0006] This invention addresses the problems of heavy computational burden, singularity, uncontrollable convergence time, and sensitivity to initial errors in distributed attitude estimation of multi-agent systems in existing technologies. This invention provides a distributed attitude estimation method for mobile multi-agent systems based on azimuth angle, which achieves attitude estimation error convergence within a preset time and ensures numerical stability.

[0007] The technical solution of this invention is: a distributed attitude estimation method for a mobile multi-agent system based on azimuth angle, comprising the following steps:

[0008] S1) Construct a leader-follower multi-agent network, where follower agents only obtain azimuth measurement information with neighboring agents and their own angular velocity information;

[0009] S2) Design a distributed preset time attitude observer (DPTAO);

[0010] S3) The distributed preset time-attitude observer (DPTAO) is used to ensure that the follower agent's attitude estimation error is within a preset convergence time T. a Converging to the preset boundary ε a V0, and in t>T a It then asymptotically converges to zero, where V0 is the initial value of the Lyapunov function, and ε... a These are design parameters.

[0011] Preferably, in step S1), the interaction relationship of the multi-agent network is modeled through a directed graph, and the follower agent only interacts with the neighboring agents, without needing global position or direction information.

[0012] Preferably, in step S2), the expression for the distributed preset time attitude observer is:

[0013]

[0014] In the formula, The first derivative of attitude estimation is represented by the first derivative. Indicates attitude estimation; ω i k represents the angular velocity of agent i. ai N represents the time-varying gain; i Represents the set of neighbors of agent i; Let i and j represent the relative azimuth vectors measured by agents i and j, respectively; T represents the transpose operation.

[0015] Preferably, in step S2), the time-varying gain k ai Represented as:

[0016]

[0017] In the formula, k i t is a positive control parameter; t is time; T a The preset convergence time; ε a For design parameters; k 0a To control the gain.

[0018] Preferably, the method achieves convergence within a predetermined time based on Lyapunov's inequality, which satisfies:

[0019]

[0020] In the formula, V is the Lyapunov function. It is the first derivative of the Lyapunov function.

[0021] Preferably, the Lyapunov function V(t) converges within a preset time T. a The inner condition satisfies V(t)≤ε a V0, and converges asymptotically to zero as t→∞, where V0=V(0).

[0022] The beneficial effects of this invention are as follows:

[0023] 1. The singularity-free and numerically stable nature of this invention: The Lyapunov inequality and observer design of this invention avoid the singularity problem in existing methods, improve numerical stability, and are suitable for real-time systems;

[0024] 2. The present invention can converge the attitude estimation error to a preset boundary within a user-defined preset time, and the convergence time is independent of the initial conditions, thus meeting the strict time requirements of the task.

[0025] 3. The present invention has the advantages of fast convergence and low computational burden. Compared with existing observers (DPTAO1, DPTAO2), the observer of the present invention has a faster convergence speed, a simpler time-varying gain form, and a lower computational burden.

[0026] 4. This invention has the advantage of strong robustness. It only relies on azimuth and angular velocity measurements and does not require global information. It is suitable for distributed multi-agent systems with limited communication and is not sensitive to initial errors. Attached Figure Description

[0027] Figure 1 This is a schematic flowchart of the method of the present invention;

[0028] Figure 2 This is a network diagram of five intelligent agents in Embodiment 2 of the present invention;

[0029] Figure 3 In Embodiment 2 of the present invention, the observer DPTAO and the comparison observer from Embodiment 1 are used.

[0030] DPTAO1 and DPTAO2 are schematic diagrams showing the change of the average attitude estimation error norm of the comparison objects over time.

[0031] Figure 4 In this embodiment 2 of the invention, the observer DPTAO and the comparison observer from embodiment 1 are used.

[0032] DPTAO1 and DPTAO2 are schematic diagrams illustrating the time-varying gain of the comparison objects over time. Detailed Implementation

[0033] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0034] Example 1

[0035] like Figure 1 As shown in the figure, this embodiment provides a distributed attitude estimation method for a mobile multi-agent system based on azimuth angle, including the following steps:

[0036] S1) Construct a leader-follower multi-agent network, where follower agents only obtain azimuth measurement information with neighboring agents and their own angular velocity information;

[0037] The interaction relationships of the multi-agent network are modeled through a directed graph. Follower agents only interact with neighboring agents and do not require global position or orientation information.

[0038] S2) Design a distributed preset time-attitude observer; the expression of the distributed preset time-attitude observer is:

[0039]

[0040] In the formula, The first derivative of attitude estimation is represented by the first derivative. Indicates attitude estimation; ω i k represents the angular velocity of agent i. ai N represents the time-varying gain; i Represents the set of neighbors of agent i; Let i and j represent the relative azimuth vectors measured by agents i and j, respectively; T represents the transpose operation.

[0041] Preferably, in step S2), the time-varying gain k ai Represented as:

[0042]

[0043] In the formula, k i t is a positive control parameter; t is time; T a The preset convergence time; ε a For design parameters; k 0a To control the gain.

[0044] The method described above achieves convergence within a predetermined time based on Lyapunov's inequality, which satisfies the following:

[0045]

[0046] In the formula, V is the Lyapunov function. It is the first derivative of the Lyapunov function.

[0047] Furthermore, the Lyapunov function V(t) converges within a preset time T. aThe inner condition satisfies V(t)≤ε a V0, and converges asymptotically to zero as t→∞, where V0=V(0).

[0048] S3) The distributed preset time-attitude observer is used to ensure that the attitude estimation error of the follower agent is within a preset convergence time T. a Converging to the preset boundary ε a V0, and in t>T a It then asymptotically converges to zero, where V0 is the initial value of the Lyapunov function, and ε... a These are design parameters.

[0049] Furthermore, the distributed preset time attitude observer in this embodiment converges to the preset boundary within a preset convergence time, regardless of the initial conditions.

[0050] Example 2

[0051] This embodiment considers a network consisting of five agents, whose interactions are modeled by a directed graph, such as... Figure 2 As shown, the neighbor set definition N3={1,2}, N4={2,3}, N5={3,4};

[0052] The initial conditions for the five agents are specified as follows:

[0053] The initial position is:

[0054] p1(0) = [4, -4, 4] T p2(0) = [2,2,6] T p3(0) = [0,0,0] T p4(0) = [2, 2, -4] T p5(0) = [4, -4, -2] T ;

[0055] All initial orientations are set to: R i (0) = I3, i = 1, 2, 3, 4, 5, where I3 is a 3x3 identity matrix;

[0056] The speed of the agent evolves as follows:

[0057] v i (t)=-[0.5σ i sin(σ i t), 0.5σ i cos(σ i t), 0.1σ i ] T ;

[0058] Where, when i = 1, 2, σ i=-1; when i=3,4,5, σ i =1;

[0059] Rotational kinematics is driven by angular velocity, as follows:

[0060] ω1(t)=[1,-2,1] T ,ω2(t)=[-cos(3t),1,sin(2t] T ω3(t)=

[0061] [-cos(t),1,sin(2t)] T ,ω4(t)=[-cos(2t),1,sin(5t] T ω5(t)=

[0062] [-cos(t),1,sin(9t)] T ;

[0063] For follower agent i∈{3,4,5}, the initial position estimation settings are as follows:

[0064] The initial observer rotation matrix estimate is given by the following equation:

[0065]

[0066] The observer parameters are configured as follows:

[0067] Preset convergence time T a =1,ε a =0.01, control gain k 0a =5, k3=10, k4=5, k5=3;

[0068] This embodiment compares the performance of the proposed attitude observer with two other distributed preset time attitude observers, DPTAO1 and DPTAO2, through numerical simulation. The dynamics of the comparison observer DPTAO1 are given by the following equation:

[0069]

[0070] Wherein, the control gain k a1i Defined as:

[0071]

[0072] In the formula, T a1 To preset the convergence time, k i For agent i, there is a constant baseline gain, which ensures that the attitude estimation error is within T. a1 The neighborhood that converges to zero.

[0073] The dynamic design of the distributed preset time attitude observer DPTAO2 is as follows:

[0074]

[0075] Wherein, the control gain k a2i Defined as:

[0076]

[0077] Time scaling function Defined as:

[0078]

[0079] In 0 <t<T a2 The derivative at time is:

[0080]

[0081] In the formula, T a2 The preset convergence time is denoted by k, and ∈2 represents the control residual boundary. 02 As the baseline gain, the attitude estimation error is in T a2 It converges to the preset boundary.

[0082] To ensure a fair comparison among the proposed attitude observers, DPTAO1, and DPTAO2, all observers are configured with the same parameters: T a1 =T a2 =T a =1s;∈2=ε a =0.01; k 02 =k 0a =5; Compare the simulation results as follows Figure 3 As shown. Figure 3 This indicates that all three observers successfully drove the attitude estimation error to a zero neighborhood within the preset time. Notably, the observer proposed in Example 1 exhibited the fastest convergence speed. The DPTAO1 observer at t=T a1 Previously, gain switching was required to avoid singularities. Therefore, although theoretically, from t→T... a1 While it can achieve near-zero error, DPTAO1 exhibits the largest error in actual simulations.

[0083] Figure 4 The time-varying gain k is shown. ai (11) k a1i (14) k a2i (16) Evolution over time; with the gain k of DPTAO2 a2i In comparison, the gain k of the observer proposed in Example 1 aiThe form is significantly simpler. Furthermore, with the same parameter settings, k ai Maintain the minimum amplitude. In contrast, the gain k of DPTAO... a1i At t→T a1 The time increased significantly.

[0084] The embodiments and descriptions above are merely illustrative of the principles and preferred embodiments of the present invention. Various changes and modifications may be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A distributed attitude estimation method for a mobile multi-agent system based on azimuth angle, characterized in that, Includes the following steps: S1) Construct a leader-follower multi-agent network, where follower agents only obtain azimuth measurement information with neighboring agents and their own angular velocity information; S2) Design a distributed preset time attitude observer (DPTAO); S3) The distributed preset time-attitude observer (DPTAO) is used to ensure that the follower agent's attitude estimation error is within a preset convergence time T. a Converging inward to the preset boundary ε a V0, and in t>T a It then asymptotically converges to zero, where V0 is the initial value of the Lyapunov function, and ε... a These are design parameters.

2. The distributed attitude estimation method for a mobile multi-agent system based on azimuth angle according to claim 1, characterized in that: In step S1), the interaction relationship of the multi-agent network is modeled through a directed graph. The follower agent only interacts with the neighboring agents and does not require global position or direction information.

3. The distributed attitude estimation method for a mobile multi-agent system based on azimuth angle according to claim 1, characterized in that: In step S2), the expression for the distributed preset time attitude observer is: In the formula, The first derivative of attitude estimation is represented by the first derivative. Indicates attitude estimation; ω i k represents the angular velocity of agent i. ai N represents the time-varying gain; i Represents the set of neighbors of agent i; Let i and j represent the relative azimuth vectors measured by agents i and j, respectively; T represents the transpose operation.

4. The distributed attitude estimation method for a mobile multi-agent system based on azimuth angle according to claim 3, characterized in that: In step S2), the time-varying gain k ai Represented as: In the formula, k i t is a positive control parameter; t is time; T a The preset convergence time; ε a For design parameters; k 0a To control the gain.

5. The distributed attitude estimation method for a mobile multi-agent system based on azimuth angle according to claim 1, characterized in that: The method described above achieves convergence within a predetermined time based on Lyapunov's inequality, which satisfies the following: In the formula, V is the Lyapunov function. It is the first derivative of the Lyapunov function.

6. The distributed attitude estimation method for a mobile multi-agent system based on azimuth angle according to claim 5, characterized in that: The Lyapunov function V(t) converges within a preset time T. a The inner condition satisfies V(t)≤ε a V0, and converges asymptotically to zero as t→∞, where V0=V(0).

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