Exoskeleton decoupling control method based on fixed time expansion state observer

Abstract

The invention discloses an exoskeleton decoupling control method based on a fixed time expansion state observer, and the method comprises the following steps: 1), building a dynamic model of a multi-input-multi-output exoskeleton robot, and extracting an unknown dynamic coupling part; 2) designing a fixed time extended state observer to estimate uncertain dynamic coupling and unknown external disturbance in the system, and performing compensation by adopting a feedforward mode; and 3) in combination with the observer, designing a fixed-time nonsingular terminal sliding mode controller to quickly track the expected trajectory of the exoskeleton so as to realize decoupling control of the exoskeleton system. According to the invention, for a multi-input multi-output exoskeleton robot system with model uncertainty, a fixed-time convergence decoupling control method is designed in combination with an extended state observer and a nonsingular terminal sliding mode controller; the robustness and the stability of the system are improved, and meanwhile, the tracking error of the system can be controlled at a low level within fixed time.

Description

Technical Field

[0001] This invention relates to an exoskeleton decoupling control method based on a fixed-time extended state observer, belonging to the field of exoskeleton robot control technology. Background Technology

[0002] Exoskeleton robots, as wearable devices that assist human movement, are currently widely used in military, industrial, civilian, and medical fields. In military and industrial / civilian applications, exoskeleton robots can enhance human strength and reduce the risk of fatigue and injury. In the medical field, exoskeleton robots can provide highly repetitive rehabilitation training, promoting the functional remodeling of damaged nerves and muscles, enabling patients to return to normal life. Therefore, research on exoskeleton robots has a positive impact on social development and stability. For exoskeleton robots, different application scenarios require different control strategies to achieve better assistance. However, exoskeleton robots are multi-input multi-output systems, with severe coupling problems between joints; in addition, there are uncertain nonlinear problems such as human-machine interaction forces, parameter variations, and system model errors. These problems pose significant challenges to the design of control methods.

[0003] To address the strongly coupled nonlinearity problem in exoskeleton systems, existing methods often employ function approximators such as fuzzy logic systems and neural networks for estimation. However, the convergence process of the function approximator weights can easily affect the system's control performance. Furthermore, the parameter tuning process for these methods is cumbersome and computationally intensive. To address this, the extended state observer offers a novel approach, enabling the centralized estimation of unknown dynamic couplings between joints and external disturbances, thereby improving system robustness. However, traditional linear extended state observers have slow convergence speeds, which may lead to controller instability before observer convergence. In contrast, fixed-time extended state observers offer higher convergence speeds and stronger anti-interference capabilities, making them more suitable for practical applications in exoskeleton systems. Moreover, the controller needs to maintain tracking accuracy while rapidly responding to the user's movement intentions, thus improving user comfort at the software level. In conclusion, developing a highly disturbance-resistant, high-precision, and fast decoupling control method for exoskeleton robots has significant application value and implications. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides an exoskeleton decoupling control method based on a fixed-time extended state observer. A new fixed-time extended state observer is designed to quickly estimate unknown dynamic couplings and external disturbances in the exoskeleton system, and a feedforward method is used to compensate for them in the designed fixed-time non-singular terminal sliding mode controller, thereby realizing fast response and high-precision tracking control of the exoskeleton system.

[0005] The technical solution of this invention is:

[0006] A decoupling control method for exoskeletons based on a fixed-time extended state observer includes the following steps:

[0007] Step 1: Establish a dynamic model of a multi-input multi-output exoskeleton robot with model uncertainty, and extract the unknown dynamic coupling parts;

[0008] Step 2: Design a fixed-time extended state observer to estimate the uncertain dynamic coupling and unknown external disturbances in the system, and use a feedforward method for compensation;

[0009] Step 3: Combine the observer to design a fixed-time non-singular terminal sliding mode controller to quickly track the desired trajectory of the exoskeleton and realize the decoupled control of the exoskeleton system.

[0010] Furthermore, the process of step 1 is as follows:

[0011] The dynamic model of the exoskeleton robot is established as follows:

[0012]

[0013] In equation (1), q, These represent the exoskeleton joint angle, angular velocity, and angular acceleration vectors, respectively; M(q) and ΔM(q) represent the nominal and uncertain terms of the inertia matrix. The nominal and uncertain terms of the Coriolis force and centripetal force matrices are represented; G(q) represents the uncertain gravity vector; D represents the uncertain frictional resistance and external bounded disturbances; T represents the control input vector;

[0014] Define the state variable x1 = q. Furthermore, define M = M(q), Using equation (1), the state-space expression of the exoskeleton robot is constructed as follows:

[0015]

[0016] In equation (2), This represents the unknown and uncertain dynamic coupling term in an exoskeleton robot system. Let x1 and x2 be the first derivatives, respectively.

[0017] Furthermore, the process of step 2 is as follows:

[0018] Define a new state variable x3 = -M -1 (F+D), Equation (2) expands to:

[0019]

[0020] In equation (3), M-1 Denotes the inverse matrix of M. Let x³ represent the first derivative of x³, and w be a bounded function.

[0021] For the extended control system described by equation (3), a fixed-time extended state observer is designed as follows:

[0022]

[0023] In equation (4), Let z represent the observation error of x1. i (i = 1, 2, 3) represents state x. i The observed values, Indicate z i The first derivative; μ i (i = 1, 2, 3) represents the observer gain; Represents a switching function; α i (i = 1, 2, 3), β i (i = 1, 2, 3) represents the function exponent, satisfying the recursive relation α. i =iα-(i-1),β i =iβ-(i-1), 0<α i (i = 1, 2, 3) < 1, β i (i = 1, 2, 3) > 1, α and β are variables satisfying 1 - ε1 < α < 1, 1 < β < 1 + ε2, where ε1 and ε2 represent sufficiently small constants, 1 / 3 ≥ ε1 > 0, ε2 > 0; the symbol sig a (b) = |a| b sign(a), where a and b are arbitrary real numbers, and sign(·) denotes the sign function.

[0024] Furthermore, the switching function of the fixed-time extended state observer in equation (4) Designed as follows:

[0025]

[0026] Furthermore, the process of step 3 is as follows:

[0027] Define error variables e1 and e2 as follows:

[0028]

[0029] In equation (6), the trajectory x 1r and x 2r Let x represent the desired angle and angular velocity vectors of the exoskeleton robot system, respectively, and x... 1r first derivative

[0030] Based on equation (6), the non-singular terminal sliding surface s is designed as follows:

[0031] s = e² + k e γ1(e1)+l e γ2(e1) (7)

[0032]

[0033]

[0034] in, k e ,l e k represents the control gain. e >0, l e >0; γ1(e1) and γ2(e1) are intermediate quantities; p1 and p2 represent function exponents. m1 and m2 are positive constants, satisfying m1 > 1 and 0.5 < m2 < 1; ε is a very small positive constant; control parameters

[0035] Fixed-time approach law Designed as follows:

[0036]

[0037] In equation (10), k s ,l s k represents the control gain. s >0, l s >0; function exponent m3 and m4 are positive constants that satisfy m3 > 1 and 0.5 < m4 < 1;

[0038] Based on the above design, and combining equation (4), the decoupling controller T of equation (2) is designed as follows:

[0039]

[0040] In the formula, As an intermediate quantity, For x 2r The first derivative;

[0041] Analyze the performance of the exoskeleton robot system and construct the Lyapunov function V as follows:

[0042]

[0043] Differentiating equation (14) and substituting equations (2), (7), and (11) into it:

[0044]

[0045] In equation (15), Let r3, r4, p3, p4 be the first derivatives of V, r3 = (m3 + 1) / 2, r4 = (m4 + 1) / 2, and ρ3 = 2k. s ρ4=2l s , This represents the observation error of the expanded state x3. According to the fixed-time stability theorem, the tracking error of the exoskeleton robot system will converge to near zero within a fixed time T, where T≤1 / ρ3(r3-1)+1 / ρ4(1-r4).

[0046] The technical concept of this invention is:

[0047] For exoskeleton robot systems with model uncertainties, uncertain nonlinearities such as dynamic coupling between joints and external disturbances are extended into new system states. Then, a fixed-time extended state observer is designed to quickly estimate the state and compensate for it through a feedforward method. Next, a fixed-time nonsingular terminal sliding mode controller is designed to quickly track the desired trajectory of the exoskeleton, so as to achieve decoupled control of the exoskeleton system, improve the robustness and stability of the system, and keep the system tracking error at a low level within a fixed time.

[0048] Compared with the prior art, the beneficial effects of the present invention are:

[0049] 1. This invention solves the coupled nonlinearity problem in exoskeleton robots by using a fixed-time extended state observer. It has fast estimation speed, simple parameter adjustment, low computational cost, and is easier to apply in engineering.

[0050] 2. The switching function of the fixed-time extended state observer designed in this invention is related to the observation error, which solves the problem of discontinuous switching in the traditional fixed-time extended state observer and improves the estimation performance of the observer;

[0051] 3. Compared with traditional PID, sliding mode and other control methods, the present invention is more robust and can quickly track the desired trajectory, that is, quickly respond to the human body's movement intention, and ensure that the system tracking error converges to near zero within a fixed time. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the decoupling control principle of the present invention;

[0053] Figure 2 It is a trajectory diagram of the hip joint angle of the lower limb exoskeleton;

[0054] Figure 3 It is a trajectory diagram of the knee joint angle tracking of the lower limb exoskeleton;

[0055] Figure 4 This is a diagram showing the angle error results of the hip joint in the lower limb exoskeleton.

[0056] Figure 5 This is a diagram showing the angle error results of the knee joint in a lower limb exoskeleton.

[0057] Figure 6 It is a graph showing the observer's estimation performance in the hip joint channel for unknown couplings and disturbances;

[0058] Figure 7 This is a performance graph of the observer's estimation of unknown coupling and perturbations in the knee joint channel. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the scope of protection of the present invention.

[0060] Reference Figures 1-7 A decoupling control method for exoskeletons based on a fixed-time extended state observer includes the following steps:

[0061] Step 1: Establish a dynamic model of the multi-input multi-output exoskeleton robot with model uncertainty, and extract the unknown dynamic coupling parts. The process is as follows:

[0062] The dynamic model of the exoskeleton robot is established as follows:

[0063]

[0064] In equation (1), q, These represent the exoskeleton joint angle, angular velocity, and angular acceleration vectors, respectively; M(q) and ΔM(q) represent the nominal and uncertain terms of the inertia matrix. G(q) represents the nominal and uncertain terms of the Coriolis force and centripetal force matrices; D represents the uncertain gravity vector; T represents the uncertain frictional resistance and external bounded disturbances; and T represents the control input vector.

[0065] Define the state variable x1 = q. Furthermore, define M = M(q), Using equation (1), the state-space expression of the exoskeleton robot can be constructed as follows:

[0066]

[0067] In equation (2), This represents the unknown and uncertain dynamic coupling term in an exoskeleton robot system. Let x1 and x2 be the first derivatives, respectively.

[0068] Step 2: Design a fixed-time extended state observer to estimate the uncertain dynamic coupling and unknown external disturbances in the system, and use a feedforward method for compensation. The process is as follows:

[0069] Define a new state variable x3 = -M -1 (F+D), the state-space expression (2) can be expanded to:

[0070]

[0071] In equation (3), M -1 Denotes the inverse matrix of M. Let x3 be the first derivative of x, and w be a bounded function.

[0072] For the extended control system described by equation (3), a fixed-time extended state observer is designed as follows:

[0073]

[0074] In equation (4), Let z represent the observation error of x1. i (i = 1, 2, 3) represents state x. i The observed values, Indicate z i The first derivative; μ i (i = 1, 2, 3) represents the observer gain; Represents a switching function; α i (i = 1, 2, 3), β i (i = 1, 2, 3) represents the function exponent, satisfying the recursive relation α. i =iα-(i-1),β i =iβ-(i-1), 0<α i (i = 1, 2, 3) < 1, β i (i = 1, 2, 3) > 1, α and β are variables satisfying 1 - ε1 < α < 1, 1 < β < 1 + ε2, where ε1 and ε2 represent sufficiently small constants, 1 / 3 ≥ ε1 > 0, ε2 > 0; the symbol sig a (b) = |a| b sign(a), where a and b are arbitrary real numbers, and sign(·) denotes the sign function.

[0075] Furthermore, the switching function of the fixed-time extended state observer in equation (4) Designed as follows:

[0076]

[0077] Step 3: Combining the observer, design a fixed-time non-singular terminal sliding mode controller to quickly track the desired trajectory of the exoskeleton, thereby achieving decoupled control of the exoskeleton system. The process is as follows:

[0078] Define error variables e1 and e2 as follows:

[0079]

[0080] In equation (6), the trajectory x 1r and x 2r Let x represent the desired angle and angular velocity vectors of the exoskeleton robot system, respectively, and x... 1r first derivative

[0081] Based on equation (6), the non-singular terminal sliding surface s is designed as follows:

[0082] s = e² + k e γ1(e1)+l e γ2(e1) (7)

[0083]

[0084] in, k e ,l e k represents the control gain. e >0, l e >0; γ1(e1) and γ2(e1) are intermediate quantities; p1 and p2 represent function exponents. m1 and m2 are positive constants, satisfying m1 > 1 and 0.5 < m2 < 1; ε is a very small positive constant; control parameters

[0085] Furthermore, the fixed-time approach law Designed as follows:

[0086]

[0087] In equation (10), k s ,l s k represents the control gain. s >0, l s >0; function exponent m3 and m4 are positive constants that satisfy m3 > 1 and 0.5 < m4 < 1.

[0088] Based on the above design, and combined with the observer (4), the decoupling controller T of system (2) is designed as follows:

[0089]

[0090] In the formula, As an intermediate quantity, For x 2r The first derivative.

[0091] Analyze the performance of the exoskeleton robot system and construct the Lyapunov function V as follows:

[0092]

[0093] Differentiate equation (14) and substitute equations (2), (7), and (11) into it:

[0094]

[0095] In equation (15), Let r3, r4, p3, p4 be the first derivatives of V, r3 = (m3 + 1) / 2, r4 = (m4 + 1) / 2, and ρ3 = 2k. s ρ4=2l s , This represents the observation error of the expanded state x3. According to the fixed-time stability theorem, the tracking error of the exoskeleton robot system will converge to near zero within a fixed time T, where T≤1 / ρ3(r3-1)+1 / ρ4(1-r4).

[0096] In this embodiment, to verify the effectiveness of the proposed method, the present invention conducted simulation experiments on the observation effect of the fixed-time dilation observer shown in equation (4) and the control effect of equations (11), (12), and (13) using the MATLAB simulation platform based on the lower limb exoskeleton robot. The lower limb exoskeleton robot has two active degrees of freedom, namely the flexion and extension movements of the hip joint and the knee joint;

[0097] Figure 1 This is a schematic diagram of the decoupling control principle of the present invention. Taking a two-degree-of-freedom lower limb exoskeleton robot as an example, a fixed-time extended state observer is used to process the coupled part in the exoskeleton system, and then a feedforward method is used to compensate for it in the designed fixed-time non-singular terminal sliding mode controller to realize the decoupling control of the exoskeleton system.

[0098] The sampling time for the simulation experiment was 0.0001s, and the parameters of the exoskeleton model were selected as follows:

[0099]

[0100] Where, q h ,q kLet m and l represent the angles of the hip and knee joints, respectively; the equivalent mass of the exoskeleton thigh is taken as m1 = 0.3 kg, and the length as l1 = 0.45 m; the equivalent mass of the exoskeleton lower leg is taken as m2 = 0.2 kg, and the length as l2 = 0.35 m; the gravitational acceleration is g = 9.8 N / kg; l 1c =l1 / 2,l 2c = l2 / 2.

[0101] Select the desired trajectory q of the hip joint hr =0.2π*sin(2πt), the expected trajectory of the knee joint q kr =0.1π - 0.1π * cos(2πt), external disturbance D = [0.005 * (2 * rand - 1); 0.005 * (2 * rand - 1)], the decoupling controller parameters are determined as: m1 = 1.2, m2 = 0.8, m3 = 2, m4 = 0.8, k e =diag[10; 10], l e =diag[100; 100]; k s =diag[75; 75],l s =diag[5;5], ε=diag[0.01;0.01]; The observer parameters are determined as follows: μ1=50, μ2=1000, μ3=5000, α=0.7, β=1.1; The initial state of the system is x1=[0;0], x2=[0;0], z1=[0;0], z2=[0;0], z3=[0;0].

[0102] Figures 2-5 This is a trajectory tracking effect diagram of the hip and knee joints of the lower limb exoskeleton robot. As can be seen from the diagram, each joint can accurately track the desired trajectory, and the angle tracking error can quickly converge to a very small range. Figure 6 and Figure 7 The observation results of the fixed-time extended state observer show that the observer can quickly estimate the extended state of the system.

[0103] In summary, an exoskeleton decoupling control method based on a fixed-time extended state observer can effectively solve the coupling problem in exoskeleton systems. The controller exhibits excellent performance in terms of speed, stability, accuracy, and robustness, and has great potential for application in the control of exoskeleton robots.

[0104] The advantages of the method designed by the present invention are shown above in conjunction with the accompanying drawings and embodiments. However, the present invention is not limited to the above-described embodiments. Various modifications and implementations can be made to it without departing from the basic spirit of the present invention and without exceeding the scope of the substantive content of the present invention.

Claims

1. A fixed-time extended state observer-based exoskeleton decoupling control method, characterized in that, The method comprises the following steps: Step 1, a dynamic model of a multi-input-multi-output exoskeleton robot with model uncertainty is established, and an unknown dynamic coupling part is extracted; Step 2, a fixed-time extended state observer is designed to estimate the uncertain dynamic coupling and unknown external disturbance in the system, and a feedforward compensation is adopted; Step 3, in combination with the observer, a fixed-time non-singular terminal sliding mode controller is designed to track the desired trajectory of the exoskeleton quickly, and the decoupling control of the exoskeleton system is realized.

2. The fixed-time extended state observer-based exoskeleton decoupling control method according to claim 1, wherein, The process of step 1 is as follows: The dynamic model of the exoskeleton robot is established as follows: In formula (1), q, respectively represent the exoskeleton joint angle, angular velocity and angular acceleration vectors; M(q), AM(q) represent the nominal and uncertain terms of the inertia matrix; represent the nominal and uncertain terms of the Coriolis and centripetal force matrices; G(q) represents the uncertain gravity vector; D represents the uncertain frictional resistance and external bounded disturbance; T represents the control input vector; The state variable x1 = q is defined, Furthermore, M = M(q) is defined, By equation (1), the state space expression of the exoskeleton robot is constructed as: In formula (2), represents an unknown uncertain dynamic coupling term in the exoskeleton robot system, are first derivatives of x1, x2, respectively.

3. The fixed-time extended state observer-based exoskeleton decoupling control method according to claim 2, wherein, The process of step 2 is as follows: Define a new state variable x3 = -M -1 (F + D), equation (2) expands to: In formula (3), M -1 denotes the inverse matrix of M, denotes the first derivative of x3, and w is a bounded function. For the extended control system described in equation (3), a fixed-time extended state observer is designed as follows: in formula (4), denotes the observation error of x1, z i (i = 1, 2, 3) are state x i observations, denotes the first derivative of z i ; μ i (i = 1, 2, 3) denote observer gains; denotes a switching function; α i (i = 1, 2, 3), β i (i = 1, 2, 3) denote function exponents, satisfying the recursive relations α i = iα-(i-1), β i = iβ-(i-1), 0 < α i (i = 1, 2, 3) < 1, β i (i = 1, 2, 3) > 1, α, β are variables, satisfying 1-ε1< α < 1, 1 < β < 1+ε2, where ε1and ε2denote constants small enough, 1 / 3≥ε1> 0, ε2> 0; the symbol sig a (b) = |a| b sign(a), where a, b are arbitrary real numbers, and sign(·) denotes a sign function.

4. The fixed-time extended state observer-based exoskeleton decoupling control method according to claim 3, wherein, The switching function of the fixed time extended state observer in the formula (4) is designed as:

5. The fixed-time extended state observer-based exoskeleton decoupling control method according to claim 3, wherein, The process of step 3 is as follows: Error variables e1 and e2 are defined as follows: In formula (6), the trajectories x 1r and x 2r respectively represent the desired angle and angular velocity vectors of the exoskeleton robot system, and the first derivative of x 1r ​ Based on equation (6), a non-singular terminal sliding surface s is designed as follows: s = e2+ k e γ1(e1) + l e γ2(e1) (7) wherein, k e ,l e denotes a control gain, k e > 0, l e > 0; γ1(e1), γ2(e1) are intermediate quantities; p1, p2 denote function exponents, m1, m2 are normal numbers, satisfying m1 > 1, 0.5 < m2 < 1; ε is a very small normal number; the control parameters Fixed-time approach law Designed to: In formula (10), k s s represents a control gain, k s > 0, l s > 0; a function index m3, m4 are normal numbers, satisfying m3 > 1 and 0.5 < m4 < 1;​ Based on the above design, in combination with equation (4), the decoupling controller T of equation (2) is designed as follows: wherein is an intermediate quantity, is x 2r the first derivative; The performance of the exoskeleton robot system is analyzed, and a Lyapunov function V is constructed as follows: The derivative of equation (14) is taken, and equations (2), (7) and (11) are substituted into it as follows: In formula (15), is the first derivative of V, r3, r4, p3, p4 are function exponents, r3 = (m3 + 1) / 2, r4 = (m4 + 1) / 2, p3 = 2k s , p4 = 2l s , represents the observation error of the expansion state x3, According to the fixed time practical stability theorem, the exoskeleton robot system tracking error will converge to the vicinity of zero within a fixed time T, T ≤ 1 / p3(r3-1) + 1 / p4(1-r4).

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