An adaptive robust control method for snake-like robots

Abstract

This invention discloses an adaptive robust control method for a snake-like robot, comprising the following steps: establishing a dynamic model for the snake-like robot; transforming the control problem into a constrained following problem based on the desired trajectory; separating the uncertain terms in the dynamic model to obtain the nominal terms and uncertain terms of the snake-like robot system; designing an adaptive robust controller for the nominal terms and uncertain terms; and optimizing the controller by proposing an adaptive law based on a smooth region. The control method provided by this invention introduces an adaptive law based on a smooth region, which solves the problem of discontinuous adaptive parameters and improves the robustness and tracking accuracy of the snake-like robot.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical system dynamics and robot control, and in particular to an adaptive robust control method for a snake-like robot. Background Art

[0002] Soft robotics has been one of the hottest research areas in robotics in recent years. Due to their inherent flexibility, adaptability, low cost, and passive safety, soft robots hold broad application prospects in areas such as human-robot interaction and medical services. Snake-like robots, in particular, have attracted considerable attention and research due to their ability to navigate unstructured terrain without limbs and navigate through narrow openings and complex passages. Unlike rigid models, snake-like robots exhibit continuous behavior, making the development of mathematical models and control algorithms challenging.

[0003] Because snake-like robots undergo continuous deformation during motion, no suitable control algorithm currently exists. Therefore, the control problem is formulated as a constraint-following problem, and a new adaptive robust control method is proposed. Uniquely, this control method utilizes an adaptive rate based on a smooth zone. Similar to the more common dead zone method, the adaptive smooth zone method also employs a segmented adaptive rate design. However, a significant characteristic of the dead zone method is that the adaptive rate is discontinuous. This discontinuity can lead to drastic changes in the adaptive parameters and control system, severely impacting the performance of the snake-like robot. The smooth zone method, however, effectively addresses this issue. Therefore, this study investigates and improves existing structures to provide an adaptive robust control method for snake-like robots, aiming to achieve greater practical value. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0005] The present invention provides an adaptive robust control method for a snake-like robot, comprising the following steps:

[0006] Step 1: Establish a dynamic model of the snake-like robot;

[0007] Step 2: According to the desired trajectory, the control problem is transformed into a constraint following problem;

[0008] Step 3: Separate the uncertain terms in the dynamic model to obtain the nominal terms and uncertain terms of the snake robot system;

[0009] Step 4: Design an adaptive robust controller for the nominal term and the uncertain term.

[0010] Step 5: Propose an adaptive rate based on the smooth area to optimize the controller.

[0011] As a preferred technical solution of the present invention, the step 1 is specifically performed as follows:

[0012] The dynamic equation of the snake-like robot is established and expressed as:

[0013]

[0014] Where t∈R is time, q∈R n is the position vector, is the velocity vector, is the acceleration vector, represents the uncertain parameters (the set ∑ represents the possible bound of the unknown σ), u(t)∈R n is the control input vector; in addition, M(q(t),σ(t),t) represents the inertia matrix, denotes the Coriolis / centrifugal term matrix, g(q(t),σ(t),t) denotes gravity, and the functions M(·), C(·), g(·), and B(·) are continuous.

[0015] As a preferred technical solution of the present invention, the step 2 is specifically performed as follows:

[0016] Convert the desired trajectory into motion constraints, and then express the motion constraints in matrix form:

[0017]

[0018] Where A∈R (N-1)×N is the constraint matrix, (θ k is the angle of the kth rigid link, angular velocity of the kth rigid link), c∈R (N-1)×1 , taking the derivative of this equation, we get its second-order form:

[0019]

[0020] in ( angular acceleration of the kth rigid link), b∈R (N-1)×1 .

[0021] As a preferred technical solution of the present invention, the step 3 is specifically performed as follows:

[0022] For the subsequent controller design, M(·), C(·), and g(·) in the dynamic equation are decomposed into:

[0023]

[0024]

[0025]

[0026] in is called the nominal term of the snake-like robot, ΔM(q,σ,t), ΔC(q,σ,t), and Δg(q,σ,t) are called the uncertain terms of the snake-like robot, and ΔM, ΔC, and Δg are all continuous.

[0027] As a preferred technical solution of the present invention, the step 4 is specifically performed as follows:

[0028] Assume there is an unknown positive constant vector It is time-varying, construct a controller as:

[0029]

[0030] Where:

[0031]

[0032]

[0033]

[0034] here:

[0035]

[0036] Where G∈R r×r is a positive definite matrix, function Π(·): is a known function such that all ε>0 is a scalar constant;

[0037] As a preferred technical solution of the present invention, the step 5 is specifically performed as follows:

[0038] Time-varying vector Adaptive rate with dead-band method follows:

[0039]

[0040] Among them, k1, k2∈R + ,ζ∈R + ;

[0041] This adaptive rate is piecewise continuous. When the value of changes from >ζ to ≤ζ, the adaptive parameter A mutation will occur, which will cause u(t) to also mutate. Therefore, at the critical point To ensure the adaptive parameters Smooth changes, an adaptive rate based on the smooth area method is proposed:

[0042]

[0043] Substitute this adaptive rate back into the previous controller to complete the controller

[0044] design.

[0045] The beneficial effects of the present invention are:

[0046] 1. The adaptive robust control method of the snake-like robot is difficult to estimate in actual application of the snake-like robot. The adaptive robust controller proposed in this invention performs constrained following control based on the nominal term and the uncertain term respectively.

[0047] 2. This adaptive robust control method for the snake-like robot adopts an improved adaptive rate and uses the adaptive parameter α to control the uncertainty bound. Its significant feature is that the adaptation law is based on the smooth zone rather than the discontinuous dead zone. Therefore, the controller can have better control performance and higher practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0049] Figure 1 is a flow chart of an adaptive robust control method for a snake-like robot according to the present invention;

[0050] Figure 2 A structural diagram of a snake-like robot according to an adaptive robust control method of the snake-like robot of the present invention;

[0051] Figure 3 This is a comparison diagram of the control effects of controllers of different parts included in an adaptive robust control method for a snake-like robot of the present invention;

[0052] Figure 4 This is a comparison diagram of the control effects of an adaptive robust control method for a snake-like robot using different adaptive rates. DETAILED DESCRIPTION

[0053] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0054] Example: Figure 1-4 As shown in the figure, an adaptive robust control method for a snake-like robot according to the present invention includes Figure 2 As shown in the figure is a structural sketch of the snake-like robot. The snake-like robot is composed of N rigid links and N - 1 soft segments. A coordinate system is established with the midpoint of the first rigid link as the origin. The midpoint coordinates of the k-th (k < N) rigid link are (x k , y k ). l1 is the length of each rigid link, l2 is the length of each soft segment, and θ k is the angle between the k-th rigid link and the X-axis. Therefore, the curvature of each soft segment can be defined as

[0055]

[0056] Analyzing its shape, the following equations can be obtained:

[0057] Position relationship equation:

[0058]

[0059]

[0060] Dynamic balance equation:

[0061]

[0062]

[0063] Among them, m is the mass of a rigid link, are the displacement accelerations of the k-th rigid link in the X and Y axis components respectively, and f r,x , f r,y are the frictions in the X and Y axis components respectively, and h x,k , h y,k are the joint constraint forces of the k-th rigid link in the X and Y axis components respectively.

[0064] This embodiment provides an adaptive robust control method for a snake-like robot. The steps included in this method are as follows:

[0065] Step 1, establish the dynamic equation of the snake-like robot. For the convenience of simulation, we adopt a simplified model. Since l1 is much smaller than l2, the length of the rigid link can be ignored during calculation, and each rigid link can be regarded as a joint. According to the position relationship equation and the dynamic balance equation of the snake-like robot, we can obtain:

[0066]

[0067] Among them, J1, J2…J Nis the moment of inertia of each rigid link, Δs is the cross-sectional area of ​​the soft segment; C = 0; q = 0; P=[P1,P2…P N ] T ,P1,P2…P N The pressure entered for each joint.

[0068] Step 2: Based on the desired trajectory, the control problem is transformed into a constraint following problem. This step is specifically divided into the following steps:

[0069] (1) First, determine the desired motion trajectory of the snake-like robot. Its motion follows the serpentine motion, so the ideal trajectory of each soft segment is:

[0070] ρ k =vsin(ωt+Ψ k ),k=1,2····,N-1

[0071] Among them, ρ k is the curvature of the kth soft segment, v and ω are the amplitude and frequency of the curvature change rate of each soft segment, respectively, k is the phase offset.

[0072] (2) Convert the ideal motion trajectory into the following motion constraints:

[0073]

[0074] Among them, k3∈R + This constraint can make ρ k =vsin(ωt+Ψ k ), and the value of k3 is related to the convergence speed.

[0075] Substituting into the curvature formula, we get:

[0076]

[0077] (3) Motion constraints can be expressed in matrix form

[0078]

[0079] in, is the constraint matrix, (θ k is the angle of the kth rigid link, angular velocity of the kth rigid link),

[0080]

[0081] Taking the derivative of this equation, we get its second-order form:

[0082]

[0083] in ( angular acceleration of the kth rigid link),

[0084] (4) The dynamic model of the snake robot follows the constraints in (3). If there is no uncertainty (i.e., σ is completely known) and the constraints are initially satisfied, then according to the Udwadia-Kalaba theory, the explicit expression of u(t) is obtained, which can be expressed as

[0085]

[0086] The control follows the Lagrangian form of the D'Alembert principle, which enables the snake-like robot to satisfy the constraints at every moment.

[0087] Step 3: Separate the uncertain terms in the dynamic model to obtain the nominal terms and uncertain terms of the snake robot system.

[0088] Decompose M(·), C(·), and g(·) in the kinetic equation into:

[0089]

[0090]

[0091]

[0092] in is called the nominal term of the snake-like robot, ΔM(q,σ,t), ΔC(q,σ,t), and Δg(q,σ,t) are called the uncertain terms of the snake-like robot, and ΔM, ΔC, and Δg are all continuous.

[0093]

[0094]

[0095]

[0096] Where I∈R N×N is the identity matrix, then we have:

[0097] ΔD(q,σ,t)=D(q,t)E(q,σ,t)

[0098] Step 4: Design an adaptive robust controller for the nominal term and the uncertain term.

[0099] Make the following three assumptions:

[0100] (1) For each (q, t)∈R N ×R, A(q,t) is full rank. Therefore, A(q,t)A T (q,t) is reversible.

[0101] For a given positive definite matrix G∈R r×r ,let

[0102]

[0103] There is a constant ρ E >-1, satisfied

[0104]

[0105] (2) There exists an unknown positive constant vector and a known function (·): Make all

[0106] in:

[0107]

[0108]

[0109]

[0110] here

[0111]

[0112] Therefore, we design the controller as:

[0113]

[0114] Furthermore, in step 5, an adaptive rate based on the smooth region is proposed to optimize the controller.

[0115] Time-varying vector Adaptive rate with dead-band method follows:

[0116]

[0117] Among them, k1, k2∈R + ,ζ∈R + .

[0118] This adaptive rate is piecewise continuous. When the value of changes from >ζ to ≤ζ, the adaptive parameter A mutation will occur, which will cause u(t) to also mutate. Therefore, at the critical point To ensure the adaptive parameters Smooth changes, an adaptive rate based on the smooth area method is proposed:

[0119]

[0120]

[0121] Substitute this adaptive rate back into the previous controller to complete the controller design.

[0122] Step 6: Use MATLAB to perform simulation verification. Select a snake-like robot with N=5 (i.e., composed of 5 joints and 4 soft segments) for simulation verification. The joint moment of inertia of this snake-like robot is J0=8×10 -6 kg·m 2 , hose cross-sectional area Δs=7.8×10 -5 m 2 , the length of each soft segment l2 = 0.05m. Select the desired trajectory parameters: v = 20rad / s, Ψ k =0.4k(k=1,2,3,4). Initial condition parameters:

[0123]

[0124] After simulation and debugging, the following control parameters are selected: ε=100, l=1, ζ=3, k1=1000, k2=0.1, k3=10, The simulation uses the error ||β|| as the performance indicator, and the results are as follows Figure 3 、 4 shown.

[0125] Figure 3 、 4 , both use time as the horizontal axis and the value of ||β|| as the vertical axis. Figure 3 In the figure, the controllers containing p1, p1 and p2, and p1, p2 and p3 are compared. It can be seen that the controller containing p1, p2 and p3 has the best performance, followed by the controller containing p1 and p2, and the controller containing p1 has the worst performance. Figure 4In the paper, the control effects of adaptive rates based on the dead zone and the smooth zone are compared. It can be seen that the controller error using the adaptive rate based on the smooth zone is ultimately kept at a low level, and the control effect is relatively ideal, while the controller using the adaptive rate based on the dead zone has a relatively poor control effect. Therefore, the adaptive robust control method of the snake robot in this invention can enable the snake robot to exhibit the desired motion characteristics in a very short time, and the system performance is stable and has high control accuracy.

[0126] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0127] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. An adaptive robust control method for a snake-like robot, comprising the following steps: Step 1: Establish a dynamic model of the snake-like robot; Step 2: According to the desired trajectory, the control problem is transformed into a constraint following problem; Step 3: Separate the uncertain terms in the dynamic model to obtain the nominal terms and uncertain terms of the snake robot system; Step 4: Design an adaptive robust controller for the nominal term and the uncertain term. Step 5: Propose an adaptive rate based on the smooth area to optimize the controller; In the step 5, it is specifically performed as follows: Time-varying vector Adaptive rate with dead-band method follows: in, k1、k2∈R + ,ζ∈R + ; This adaptive rate is piecewise continuous. When the value of changes from >ζ to ≤ζ, the adaptive parameter A mutation will occur, which will cause u(t) to also mutate. Therefore, at the critical point At ζ, to ensure the adaptive parameters Smooth changes, an adaptive rate based on the smooth area method is proposed: Substitute this adaptive rate back into the previous controller to complete the controller design.

2. The adaptive robust control method of a snake-like robot according to claim 1, characterized in that: In the step 1, it is specifically manifested as follows: The dynamic equation of the snake-like robot is established and expressed as: Where t∈R is time, q∈R n is the position vector, is the velocity vector, is the acceleration vector, represents the uncertain parameters, the set ∑ represents the possible bound of the unknown σ, u(t)∈R n is the control input vector; in addition, M(q(t),σ(t),t) represents the inertia matrix, represents the Coriolis centrifugal term matrix, g(q(t),σ(t),t) represents gravity, and the functions M(·), C(·), g(·), and B(·) are continuous.

3. The adaptive robust control method for a snake-like robot according to claim 1, characterized in that: In the step 2, it is specifically manifested as follows: Convert the desired trajectory into motion constraints, and then express the motion constraints in matrix form: Where A∈R (N-1)×N is the constraint matrix, θ k is the angle of the kth rigid link, The angular velocity of the kth rigid link, c∈R (N-1)×1 , taking the derivative of this equation, we get its second-order form: in Angular acceleration of the kth rigid link, b∈R (N-1)×1 .

4. The adaptive robust control method for a snake-like robot according to claim 1, characterized in that: In the step 3, it is specifically manifested as follows: For the subsequent controller design, M(·), C(·), and g(·) in the dynamic equation are decomposed into: in is called the nominal term of the snake-like robot, ΔM(q,σ,t), ΔC(q,σ,t), and Δg(q,σ,t) are called the uncertain terms of the snake-like robot, and ΔM, ΔC, and Δg are all continuous.

5. The adaptive robust control method for a snake-like robot according to claim 1, characterized in that: In the step 4, it is specifically performed as follows: Assume there is an unknown positive constant vector It is time-varying, construct a controller as: Where: here: Where G∈R r×r is a positive definite matrix, function Π(·): is a known function such that all ε>0 is a scalar constant;

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