Tension input based quantization method for tethered multi-robot formation deployment control

Abstract

The application discloses a tethered multi-robot formation deployment control method based on tension input quantization, which is composed of the following steps: step S1: a dynamics model of a tethered multi-robot formation system is established according to kinetic energy, potential energy, elastic potential energy and geometric constraint relationship of the tethered multi-robot formation system combined with an Euler-Lagrange method, step S2: an estimated value of external disturbance is obtained by estimating the external disturbance of the dynamics model by using an extended state observer, step S3: a preset time sliding mode control input value is obtained by using a sliding mode control method combined with a preset convergence time, step S4: the preset time sliding mode control input value is converted into a plurality of segmented continuous quantization input values by a quantizer, and step S5: a control method of the multi-robot formation is designed by inputting the plurality of quantization input values and the estimated value of the external disturbance into the dynamics model; the application can reduce the communication burden of the system, reduce the frequency of the actuator update, and ensure the stable deployment of the space multi-tethered robot.

Description

Technical Field

[0001] This invention belongs to the field of space tethered robot control, and particularly relates to a tethered constraint multi-robot formation deployment control method based on tension input quantization. Background Technology

[0002] As spacecraft evolve towards modularity, standardization, and lightweight designs, manufacturing costs and timelines have been significantly reduced. However, these modular spacecraft are often constrained by weight and size, leading to reduced communication resources between modules. Clearly, sparse communication data can degrade controller performance, causing system instability and mission failure. Furthermore, existing controllers, with limited communication resources, are unable to handle external disturbances and uncertainties in the system model. Summary of the Invention

[0003] The purpose of this invention is to provide a rope-constrained multi-robot formation deployment control method based on tension input quantization, in order to solve the problem that preset time-stable configurations cannot be successfully deployed under external disturbances, uncertain system models, and communication limitations.

[0004] This invention adopts the following technical solution: a rope-constrained multi-robot formation deployment control method based on tension input quantization, comprising the following steps:

[0005] Step S1: Based on the kinetic energy, potential energy, elastic potential energy, and geometric constraints of the tethered robot formation system, and using the Euler-Lagrange method, establish a dynamic model of the tethered robot formation system.

[0006] Step S2: Use the extended state observer to estimate the external disturbance of the dynamic model to obtain the estimated value of the external disturbance.

[0007] Step S3: Obtain the preset time sliding mode control input value by using the sliding mode control method in conjunction with the preset convergence time.

[0008] Step S4: Convert the preset time sliding mode control input value into multiple segmented continuous quantized input values ​​using a quantizer.

[0009] Step S5: Input multiple quantized input values ​​and estimated values ​​of external disturbances into the dynamic model to design a control method for multi-robot formation.

[0010] Furthermore, the tethered robot formation system consists of three satellites and three space tethers, and the center of mass of the tethered robot formation system rotates around the Earth's center of mass in orbit.

[0011] Furthermore, the dynamic model of the tethered robot formation system in step S1 is as follows:

[0012]

[0013] In the formula, M is the system parameter matrix, and u = Q represents the preset time sliding mode control input value. It is a non-linear summation term. For the system parameter matrix, and For system parameter vectors, It is a lumped uncertain term, and And it is a system state variable. And it is a system state variable, where t is a time variable.

[0014] Furthermore, the estimated value z of the external disturbance in step S2 v3 The calculation method is as follows:

[0015]

[0016] In the formula, and For the new state variable; and They are respectively and The derivative with respect to time; To output the observation error; K 11 K 12 K 13 K 21 K 22 K 23 , α1, α2, α3, β1, β2, β3 and γ υ All are adjustable parameters. sign(*) is a sign function, where * can take any variable, and f is a function that represents the sign function.

[0017] Furthermore, the calculation method for the preset time sliding mode control input value in step S3 is as follows:

[0018]

[0019] In the formula, u is the preset time sliding mode control input value, and c2 = diag([c 21 ,c 22 ,c 23 ,c 24 ]) is the parameter matrix; γ is the adjustment parameter; T c To preset the convergence time, For the desired acceleration, V1 is a Lyapunov candidate function. For the estimated value of the external disturbance, c1 = diag([c 11 ,c 12 ,c 13 ,c14 ]) is the parameter matrix, s represents the speed tracking error, and s represents the sliding surface.

[0020] The beneficial effects of this invention are as follows: This invention improves the stability of the controller by introducing new control terms and parameters. It reduces system communication burden and actuator update frequency while ensuring stable deployment of multi-tethered robots in space. This invention analyzes the deployment process of multi-tethered robots, equating the deployment motion to the extension motion of an "equilateral triangle," and establishes a unified Euler-Lagrange dynamics model, which can also be extended to multi-tethered systems. A fixed-time convergent state observer is designed to estimate system model uncertainties and external disturbances. The accuracy of this convergent observer is independent of initial conditions, ensuring accurate estimation of external disturbances while reducing control input chattering. This invention designs a preset-time sliding mode controller based on input quantization, ensuring system closed-loop performance while enabling the system to deploy to a stable configuration according to the desired trajectory within a preset time. Furthermore, this invention considers input quantization errors and the real-world situation of segmented sampling from the controller to the actuator, converting the control input into segmented continuous discrete values, making the control method design more consistent with real-world communication constraints. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the formation of the rope-tethered robot formation system in Embodiment 1 of the present invention;

[0022] Figure 2 This is the time response of the control input components u1 and Qu1 in Embodiment 1 of the present invention;

[0023] Figure 3 This is the time response of the control input components u2 and Qu2 in Embodiment 1 of the present invention;

[0024] Figure 4 This is the time response of the control input components u3 and Qu3 in Embodiment 1 of the present invention;

[0025] Figure 5 This is the time response of the control input components u4 and Qu4 in Embodiment 1 of the present invention;

[0026] Figure 6 This describes the unfolding process of rope length l1 in Embodiment 1 of the present invention;

[0027] Figure 7 This describes the unfolding process of rope length l2 in Embodiment 1 of the present invention;

[0028] Figure 8 This describes the unfolding process of rope length l3 in Embodiment 1 of the present invention;

[0029] Figure 9 The rate of change of rope length 1 in Embodiment 1 of the present invention;

[0030] Figure 10 The rate of change of rope length 2 in Embodiment 1 of the present invention;

[0031] Figure 11 The rate of change of angle θ1 in Embodiment 1 of the present invention;

[0032] Figure 12 The angle θ2 is the rate of change in Embodiment 1 of the present invention. Detailed Implementation

[0033] The present invention will now be described in detail with reference to specific embodiments.

[0034] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0035] This invention discloses a rope-constrained multi-robot formation deployment control method based on tension input quantization, which consists of the following steps:

[0036] Step S1: Based on the kinetic energy, potential energy, elastic potential energy, and geometric constraints of the tethered robot formation system, and using the Euler-Lagrange method, establish a dynamic model of the tethered robot formation system.

[0037] Step S2: Use the extended state observer to estimate the external disturbance of the dynamic model to obtain the estimated value of the external disturbance.

[0038] Step S3: Obtain the preset time sliding mode control input value by using the sliding mode control method in conjunction with the preset convergence time.

[0039] Step S4: Convert the preset time sliding mode control input value into multiple segmented continuous quantized input values ​​using a quantizer.

[0040] Step S5: Input multiple quantized input values ​​and estimated values ​​of external disturbances into the dynamic model to design a control method for multi-robot formation.

[0041] When the tethered robot formation system consists of three satellites and three space tethers, and the center of mass of the tethered robot formation system revolves around the Earth's center of mass in orbit, as... Figure 1As shown, the space-tethered multi-robot mainly consists of three satellites (S1, S2, and S3) and three space tethers (l1, l2, and l3). The satellites can be considered point masses and always move within their orbital planes; the three tethers are always under tension, and it is assumed that the tether deployment and retrieval mechanism can ensure stable deployment and retrieval of the tethers. The inertial coordinate system is O. I -x I y I z I And the orbital coordinate system O-xyz. The center of mass of the formation system rotates around the Earth's center of mass in orbit, and the sub-spacecraft rotates around the center of mass. At this time, step S1 consists of the following steps:

[0042] The kinetic energy of the formation system can be expressed as:

[0043]

[0044] In the formula, T v For the kinetic energy of the formation system, Let m be the total mass of the three sub-stars. i (i = 1, 2, 3) represents the mass of the child star, r i (i = 1, 2, 3) represents the position vectors from the system's center of mass to each of the sub-stars. For r i (i = 1, 2, 3) is the derivative of time, ω is the relative angular velocity of the system's center of mass revolving around the Earth, and R0 is the position vector of the Earth's center of mass pointing towards the system's center of mass.

[0045] The potential energy of the formation system can be expressed as:

[0046]

[0047] In the formula, V s1 Let R be the potential energy of the formation system, μ be the gravitational constant, and R be the gravitational constant. i =R0+r i And it is the distance between the Earth's center and the center of mass of the sub-star.

[0048] The elastic potential energy of the formation system can be expressed as:

[0049]

[0050] In the formula, V s2 Let E be the elastic potential energy of the formation system, E be Young's modulus, A be the cross-sectional area of ​​the tether, and l0 be the length of the reference rope. i (i = 1, 2, 3) represents the rope length of the spatial rope system. This is the deformation index of the rope.

[0051] From Lagrange dynamics It can be known

[0052]

[0053] In the formula, M(q) and Let G(q) be the system parameter matrix, and P(q) be the system parameter vectors. It is a dimensionless Lagrange generalized coordinate quantity. for q The derivative with respect to time, in and This is a Lagrange transformation term.

[0054] Transform it into a standard state-space equation:

[0055] make Let represent a set of four-dimensional column vectors whose components are all real numbers. Equation (4) can be expressed as the state-space equation of the formation system:

[0056]

[0057] In the formula, M represents the system parameter moments, and u = Q represents the preset time sliding mode control input value. It is a non-linear summation term. For the system parameter matrix, and For system parameter vectors, It is a lumped uncertain term, and t is a time variable.

[0058] Step S2 consists of the following steps:

[0059] In general, equation (5) The value is non-zero, requiring high gain to offset the effects of external disturbances on the system, but this can cause control input chattering. Therefore, a state observer can be designed to estimate the uncertainty term and reduce the controller gain, as shown below:

[0060]

[0061] In the formula, and For the new state variable; and They are respectively and The derivative with respect to time; To output the observation error; K 11 K 12 K 13 K 21 K 22 K 23 , α1, α2, α3, β1, β2, β3 and γ υAll are adjustment parameters sign(*) is the sign function, where * can take any variable; f is f(x) υ1 ,x υ2 ).

[0062] Substituting equation (6) into equation (5), we obtain the error state equation:

[0063]

[0064] In the formula, For velocity observation error, To prevent interference with observation errors, and They are respectively The derivative with respect to time.

[0065] Step S3 consists of the following steps:

[0066] make e υ For position tracking error, It is the speed tracking error, x 1d For the desired position, For the desired speed, To achieve the desired acceleration, the auxiliary variables are designed as follows:

[0067]

[0068] In the formula, s is the sliding surface, and c1 = diag([c 11 ,c 12 ,c 13 ,c 14 ]) is the parameter matrix, and diag(·) is the diagonal matrix generating function.

[0069] derivative of sliding surface

[0070]

[0071] Select Lyapunov candidate functions but

[0072]

[0073] To ensure stable convergence of the system, the calculation method for the preset time sliding mode control input value is designed as follows:

[0074]

[0075] In the formula, u is the preset time sliding mode control input value, and c2 = diag([c 21 ,c 22 ,c23 ,c 24 ]) is the parameter matrix; γ is the adjustment parameter; T c To preset the convergence time, For the desired acceleration, V1 is a Lyapunov candidate function. For the estimated value of the external disturbance, c1 = diag([c 11 ,c 12 ,c 13 ,c 14 ]) is the parameter matrix, f is s represents the speed tracking error, and s represents the sliding surface.

[0076] Substituting equations (9) and (11) into equation (10), then

[0077]

[0078] In the formula,

[0079] Step S4 consists of the following steps:

[0080] In actual control, the controller's control method is not continuous, but is converted into a segmented continuous constant range by a quantizer, as shown below:

[0081]

[0082] In the formula, u j (j = 1, 2, 3, 4) are control components; l is the quantization interval; Q υ (u j () represents the quantization control input, which belongs to the set.

[0083] The quantized input and the original input controller satisfy the following:

[0084] |Q υ (u j )-u j |≤δ|u j |+τ min j = 1, 2, 3, 4 (14)

[0085] In the formula, δ and τ min This is an adjustable parameter.

[0086] After introducing input quantization, the derivative of the auxiliary variable is redesigned as follows:

[0087]

[0088] Let △u=Q υSubstituting equations (15) and (11) into equation (10), we can obtain (u)-u.

[0089]

[0090] In the formula,

[0091] In step S5, the control method of the quantization controller is designed by formula (11) and formula (13), which can ensure the stable deployment of the spatial rope-constrained multi-robot.

[0092] Example 1

[0093] Considering that the generalized variables are made infinitely rigid in equation (4), the initial conditions for simulation using the method of this invention are as follows: initial generalized coordinates q0 = [0.0025, 0.0025, π / 6, 5π / 6] T The first derivative of the initial generalized coordinate position is Second derivative The simulation sampling step length is set to 0.0001; the reference trajectory for the desired configuration is selected as q. d =[1,1,θ 1d ,θ 2d ] T , τ=3, θ 10 =π / 6, θ 20 =5π / 6.

[0094] Perform the simulation using the above simulation conditions, such as Figure 2-5 As shown; Figure 2-5 These represent the four components of the control input. Solid lines represent quantized control inputs, while dashed lines represent unquantized control inputs. From... Figure 2-5 As can be seen, the control inputs of the solid and dashed lines oscillate in the initial oscillation phase, but they consistently oscillate within adjacent bounded regions. After oscillation for a period, the control inputs without input quantization and those considering input quantization show the same trend, indicating that the addition of the input quantization mechanism still ensures stable convergence of the system. The unfolding process of the three ropes is as follows... Figure 6-8 As shown, the three ropes can unfold according to the predetermined desired trajectory.

[0095] Figure 9-12 For status input The change, from Figure 9 and 10 It can be seen that the trend of the rope's unfolding speed is basically the same before and after input quantization; from Figure 11 and 12 It can be seen that before and after input quantization, the angular velocity oscillates within a bounded range at the initial moment, but eventually reaches the specified desired angular velocity.

[0096] 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, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A rope-constrained multi-robot formation deployment control method based on tension input quantization, characterized in that, It consists of the following steps: Step S1: Based on the kinetic energy, potential energy, elastic potential energy, and geometric constraints of the tethered robot formation system, and using the Euler-Lagrange method, establish a dynamic model of the tethered robot formation system. Step S2: Use the extended state observer to estimate the external disturbance of the dynamic model to obtain the estimated value of the external disturbance. Step S3: Obtain the preset time sliding mode control input value by using the sliding mode control method in conjunction with the preset convergence time. Step S4: Convert the preset time sliding mode control input value into multiple segmented continuous quantized input values ​​using a quantizer. Step S5: Input multiple quantized input values ​​and estimated values ​​of external disturbances into the dynamic model to design a control method for multi-robot formation; The dynamic model of the tethered robot formation system in step S1 is as follows: ； In the formula, For the system parameter matrix, To represent the preset time sliding mode control input value, It is a non-linear summation term. For the system parameter matrix, and For system parameter vectors, It is a lumped uncertain term, and , And it is a system state variable. And it is a system state variable. For time variables, Among them, the estimated value of the external disturbance in step S2 The calculation method is as follows: ， In the formula, , and For the new state variable; , and They are respectively , and The derivative with respect to time; To output the observation error; , , , , , , , , , , , and All are adjustable parameters. , ; For symbolic functions, Any variable can be selected. for ; The calculation method for the preset time sliding mode control input value in step S3 is as follows: ， In the formula, u is the preset time sliding mode control input value. For parameter matrices; To adjust the parameters; To preset the convergence time, For the desired acceleration, For Lyapunov candidate functions, This is an estimate of the external disturbance. For the parameter matrix, For speed tracking error, It is a sliding surface.

2. The rope-constrained multi-robot formation deployment control method based on tension input quantization according to claim 1, characterized in that, The tethered robot formation system consists of three satellites and three space tethers, and the center of mass of the tethered robot formation system rotates around the Earth's center of mass in orbit.

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