Event-triggered control method with guaranteed transient performance for flexible joint robots
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- LIAOCHENG UNIV
- Filing Date
- 2024-03-13
- Publication Date
- 2026-07-21
Smart Images
Figure CN118305782B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of flexible joint robot control, specifically to a method for achieving high precision and low energy consumption in flexible joint robots by triggering intelligent control based on transient performance events. Background Technology
[0002] Event-triggered control, an advanced control strategy originating in the 1990s, has gradually emerged and improved with the development of information technology, network technology, and embedded systems. Its core idea is to determine when to perform controller actions or transmit data based on changes in system state (i.e., the occurrence of events), rather than the traditional method based on fixed time intervals. In traditional time-driven control systems, control actions and information updates are executed according to preset time cycles, which can lead to wasted resources (such as energy, computing power, and communication bandwidth), especially when system state changes are infrequent. Event-triggered control, by monitoring system state variables in real time, triggers control actions or updates information only when the system state changes significantly or specific conditions are met, thereby achieving efficient utilization of system resources and potentially improving the system's dynamic performance and stability. This control strategy is widely used in networked control systems, distributed systems, the Internet of Things, and various intelligent monitoring systems, and has significant application value, especially in energy-constrained embedded environments and large, complex systems.
[0003] Modern industry demands higher levels of precision and stringency in the performance indicators of control systems. Preset performance control, as an emerging advanced control strategy, effectively addresses these challenges. Traditional control theory often focuses on system stability and steady-state error. However, in many modern engineering applications, such as UAV flight control, robot motion control, and precision instrument operation, in addition to system stability, more precise constraints are required on the system's dynamic response process. For example, limiting the output signal to reach and remain within a predetermined error range within a specified time. Preset performance control emerged to meet this need. It pre-sets the system's dynamic performance indicators and designs corresponding control laws to ensure these indicators are met. This method not only enhances the system's robustness to uncertainties but also improves the accuracy and reliability of system control, providing a powerful tool for solving practical engineering problems. In the field of modern control, preset performance control has become an important means of achieving high-performance control.
[0004] Flexible robots possess more flexible joints, enabling them to perform more complex morphological transformations, often mimicking the free movements of a human arm. Therefore, robots have received considerable attention in recent years. For flexible joint robots, many researchers have proposed efficient control methods, such as passive control, sliding mode control, and adaptive backstepping control. However, existing outstanding results are all based on first-order state-space models using backstepping methods, requiring second-order flexible joint robot systems to be converted to first-order systems before processing. This undoubtedly increases computational complexity. To address this, a simple and direct fully actuated system approach is proposed to solve the adaptive control problem of high-order nonlinear systems, and further applied to a backstepping framework.
[0005] Inspired by the above analysis, this paper considers the adaptive dynamic event triggering problem of a flexible articulated robot system with given performance constraints based on the full-drive system approach. Unlike some recent papers, this paper proposes a low-complexity adaptive control scheme based on the full-drive system approach to handle the flexible articulated robot system. This scheme does not require reducing the system sequence, thus reducing the number of controllers and saving resources. By combining backstepping techniques with fuzzy logic systems, dynamic event triggering control can dynamically adjust threshold parameters, further optimizing the number of triggers. In addition, the proposed pre-set performance scheme eliminates the restriction on the initial value of the specified function. The effectiveness of the control scheme is verified using a laboratory second-order robotic arm platform. Summary of the Invention
[0006] The purpose of this invention is to solve the adaptive control problem of flexible joint robots, and to propose an event-triggered method that can cope with system uncertainties and achieve preset performance control. First, a flexible joint robot system model is established. Second, some nonlinear functions are constructed. Using the theory of all-drive systems and backstepping techniques, along with approximation techniques of fuzzy logic systems and the scaling method of Young's inequality, an event-triggered mechanism and controller are designed. The designed controller not only achieves preset performance control but also saves communication resources and reduces communication burden.
[0007] The specific plan is as follows:
[0008] An event-triggered control method for ensuring transient performance of a flexible joint robot includes the following steps: (a) establishing a dynamic model of an n-link flexible joint robot; for an n-link flexible joint robot system, its differential equation can be expressed as:
[0009]
[0010] Where, q, and These are the position, velocity, and acceleration vectors of the link, respectively, q m , and Let q represent the rotor angular position, rotor velocity, and acceleration vectors, respectively, and M(q) represent the symmetric positive definite inertia matrix. G(q) is the centripetal force matrix, and G(q) is the gravity vector. K is the friction force vector. m denoted as the joint flexibility coefficient, J as the rotor inertia, B as the damping coefficient, and u as the torque input.
[0011] (b) Set constraints:
[0012] Generally speaking, the reference signal q d (t) has finite energy, and some practical reference signals satisfy: q d (t), It is continuous and bounded;
[0013] (c) In the design process of the controller, unknown nonlinear functions are approximated by a fuzzy logic system, specifically expressed as follows: Let the j-th fuzzy rule be represented as follows:
[0014] Rule j: If x1 is x2 is …x n yes
[0015] Therefore: y is N j j = 1, 2, ..., L
[0016] Where x = (x1, x2, ... x n ) T ∈R n y is the output of the fuzzy logic system. and N j Let L represent the fuzzy set, and L be the total number of rules. The output of the fuzzy logic system can be represented as:
[0017]
[0018] in, and Represents fuzzy membership functions. satisfy The fuzzy basis function is defined as
[0019]
[0020] in, S=(S 1 ,S 2 …S L ) T Then the fuzzy logic system can be written as:
[0021] y = WT S(x),
[0022] If f(x) is defined as a continuous function on the compact set Ξ, then there exists a fuzzy logic system W. T S(x) can approximate any continuous nonlinear function with an ideal precision ε>0, such that...
[0023] f(x) = W T S(x)+ε(x)
[0024] Where W = [w1, w2, ... w n ] T Let S(x) be the ideal weight vector, S(x) be the basis function vector, and ε(x) be the approximation error satisfying and
[0025] (d) In the controller design process, a candidate Lyapunov function is selected at each step to construct a virtual controller until the final step of constructing the real control input. The specific control method is as follows:
[0026] First, let's explain some necessary symbols, I n Describes a positive definite matrix.
[0027]
[0028]
[0029]
[0030]
[0031]
[0032] Define the following symbols
[0033]
[0034]
[0035]
[0036] Lemma 1: If f(x) is defined as a continuous function on the compact set Ξ, then there exists a fuzzy logic system W. T S(x) can approximate any continuous nonlinear function with an ideal accuracy ε>0, such that
[0037] f(x) = W T S(x)+ε(x),
[0038] Where W = [w1, w2, ... w n ] T Let S(x) be the ideal weight vector, S(x) be the basis function vector, and ε(x) be the approximation error satisfying and
[0039] Lemma 2, (Young's inequality) for have
[0040]
[0041] Where ι>0, p>1, q>1 and (p-1)(q-1)=1;
[0042] Lemma 3, for any For σ∈R, the following inequalities hold.
[0043]
[0044] Lemma 4, when matrix A 0～n-1 Make matrix Φ(A) 0～n-1 When stable, according to Lyapunov's theorem, there exists a positive definite matrix P(A). 0～n-1 )satisfy
[0045]
[0046] Where μ i >0 (i=1,2) is a constant;
[0047] (d) Define the error variable as:
[0048] e(t)=q(t)-q d (t),
[0049] Define a time-varying smooth monotonically increasing function and a normalization function.
[0050]
[0051]
[0052] I i (t)=ζ(t)o(e i (t)),
[0053]
[0054]
[0055] Where α1 is defined as the virtual control law to be designed; according to the above notation, we can obtain
[0056]
[0057] right Differentiating, we get:
[0058]
[0059] in Furthermore, we can obtain
[0060]
[0061] in,
[0062] Constructing the virtual control law α1 and the adaptive law for:
[0063]
[0064]
[0065] It can be represented in state-space form:
[0066]
[0067] in
[0068]
[0069] right Differentiating, we get:
[0070]
[0071] Constructing the virtual control law α2 and the adaptive law for:
[0072]
[0073]
[0074] It can be represented in state-space form:
[0075]
[0076] in
[0077]
[0078] The following candidate Lyapunov functions were selected:
[0079]
[0080] Calculating the derivative of V, we get:
[0081]
[0082] By applying fuzzy logic systems and Young's inequality, we can obtain We have
[0083]
[0084] Furthermore, we have
[0085]
[0086] (e) The event triggering mechanism and adaptive event triggering controller are as follows:
[0087]
[0088]
[0089] t i,k+1 =inf{t≥0||ξ i (t)|≥η(t)|u i (t)|+d i}
[0090]
[0091] in, ξ(t)=[ξ1(t),…,ξ r (t)] T ,
[0092] d i >0, ρ>0, 0<η(0)<1, ι≥0, These are design parameters.
[0093] Considering the event triggering mechanism, we can deduce Where λ1(t)∈[-1,1], λ2(t)∈[-1,1], and thus we have
[0094]
[0095] according to It can be obtained
[0096]
[0097] Depend on We can obtain
[0098]
[0099] in, From the above formula, we can obtain
[0100]
[0101] (f) Next, prove that Zeno's behavior will not occur;
[0102] By proof Make To rule out Zeno's phenomenon; by achievable Where τ is a constant, determined by combining ξ i (t i,k ) = 0 and achievable In conclusion, the Zeno phenomenon has been ruled out.
[0103] This method addresses several real-world problems and designs a dynamic event trigger controller for nonlinear flexible joint robot models with uncertainties and tracking accuracy requirements. Compared with existing technologies, the technical solution provided by this invention has the following advantages:
[0104] (1) The modeled flexible joint robot is a second-order nonlinear system. Most existing control schemes usually transform the system into a first-order state-space form for processing. However, this deviates from the actual physical background and increases the computational complexity. Compared with existing design schemes, this invention proposes a high-order fully driven model that directly processes the second-order system, avoiding the transformation of the system into a first-order differential equation. Therefore, the control scheme proposed in this invention is simple to implement and computationally convenient.
[0105] (2) In practical applications, flexible joint robot systems all have serious uncertainties, which undoubtedly increases the difficulty of designing controllers for nonlinear systems. Unlike existing high-order full-drive system control schemes, this invention considers unknown nonlinear functions, uses fuzzy logic systems to estimate unknown nonlinear functions, and gives an adaptive adjustment law for parameters in the fuzzy system, effectively solving the design problem of complex and uncertain controllers.
[0106] (3) Traditional time control methods result in the transmission of a large amount of unnecessary information, thus wasting network resources. Therefore, this invention introduces a dynamic event triggering mechanism, which includes a fixed threshold strategy and a relative threshold strategy. Compared with other inventions, the proposed method is more flexible. Attached Figure Description
[0107] Figure 1 This is the position trajectory of the first link given in this invention.
[0108] Figure 2This is the position trajectory of the second link given in this invention.
[0109] Figure 3 These are the position trajectories of the first and second rotors given in this invention.
[0110] Figure 4 This is the trajectory of the first actual control input given by this invention.
[0111] Figure 5 This is the trajectory of the second actual control input given by the present invention.
[0112] Figure 6 These are the various components of the experimental platform provided in this invention. Detailed Implementation
[0113] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.
[0114] (a) Establish the dynamic model of the n-link flexible joint robot; for the n-link flexible joint robot system, its differential equation can be expressed as:
[0115]
[0116] Where, q, and These are the position, velocity, and acceleration vectors of the link, respectively, q m , and Let q represent the rotor angular position, rotor velocity, and acceleration vectors, respectively, and M(q) represent the symmetric positive definite inertia matrix. G(q) is the centripetal force matrix, and G(q) is the gravity vector. K is the friction force vector. m denoted as the joint flexibility coefficient, J as the rotor inertia, B as the damping coefficient, and u as the torque input.
[0117] (b) Set constraints:
[0118] Generally speaking, the reference signal q d (t) has finite energy, and some practical reference signals satisfy: q d (t), It is continuous and bounded;
[0119] (c) In the design process of the controller, unknown nonlinear functions are approximated by a fuzzy logic system, specifically expressed as follows: Let the j-th fuzzy rule be represented as follows:
[0120] Rule j: If x1 is x2 is …x n yes
[0121] Therefore: y is N j j = 1, 2, ..., L
[0122] Where x = (x1, x2, ... x n ) T ∈R n y is the output of the fuzzy logic system. and N j Let L represent the fuzzy set, and L be the total number of rules. The output of the fuzzy logic system can be represented as:
[0123]
[0124] in, and Represents fuzzy membership functions. satisfy The fuzzy basis function is defined as
[0125]
[0126] in, S=(S 1 ,S 2 …S L ) T Then the fuzzy logic system can be written as:
[0127] y = W T S(x).
[0128] If f(x) is defined as a continuous function on the compact set Ξ, then there exists a fuzzy logic system W. T S(x) can approximate any continuous nonlinear function with an ideal precision ε > 0, making
[0129] f(x) = W T S(x)+ε(x),
[0130] Where W = [w1, w2, ... w n ] T Let S(x) be the ideal weight vector, S(x) be the basis function vector, and ε(x) be the approximation error satisfying and
[0131] (d) Define coordinate transformation:
[0132]
[0133]
[0134] (e) In the adaptive control method based on backstepping technology, a virtual controller needs to be designed at each step until the final step where the actual control input is designed. Therefore, the virtual controller α i (i = 1, 2) is designed as follows:
[0135]
[0136]
[0137] Where a1, a2>0 are the parameters to be designed;
[0138] (f) Adaptive The law is constructed as
[0139]
[0140] Among them, a i >0, l i >0 represents the parameter to be designed;
[0141] (g) Construct the following dynamic event triggering mechanism and event triggering controller:
[0142]
[0143]
[0144] t i,k+1 =inf{t≥0||ξ i (t)|≥η(t)|u i (t)|+d i}
[0145]
[0146] in, ξ(t)=[ξ1(t),…,ξ r (t)] T , d i >0, ρ>0, 0<η(0)<1, ι≥0, These are design parameters.
[0147] (h) Proves that the Zeno phenomenon can be ruled out.
[0148] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the present invention. All equivalent structural changes made based on the description and drawings of the present invention are included within the scope of the present invention.
[0149] In this embodiment, the system parameters and design parameters given during simulation are set as shown in Table 1:
[0150] Table 1: System Parameters and Design Parameters
[0151]
[0152] The initial value of the system is chosen as q1(0) = 0. q2(0)=0, q m1 (0)=0, q m2 (0) = 0; In order to satisfy Lemma 4, design Select q d1 (t)=q d2 (t)=0.5sin(t); Under the action of the designed event-triggered controller, the position of the first link and the tracking trajectory are as follows: Figure 1 As shown, the position of the second link and the tracking trajectory are as follows: Figure 2 As shown, the position of the first rotor and the tracking trajectory are as follows: Figure 3 As shown, the position of the second rotor and the tracking trajectory are as follows: Figure 3 As shown, the trajectory of the first actual control input is as follows: Figure 4 As shown, the trajectory of the second actual control input is as follows: Figure 5 As shown, the various components of the experimental platform are as follows: Figure 6 As shown.
Claims
1. An event-triggered control method for ensuring the transient performance of a flexible joint robot, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the flexible joint robot system; Step 2: Introduce coordinate transformation, and with the help of backstepping technology and the theory of all-drive systems, select the Lyapunov function, and use the intelligent approximation technology of neural networks and the scaling method of Young's inequality with the properties of the tan function to design the event triggering mechanism and controller; The specific steps are as follows: (a) Establish the dynamic model of the n-link flexible joint robot; for the n-link flexible joint robot system, its differential equation is expressed as: in, , and These are the position, velocity, and acceleration vectors of the link, respectively. , and These represent the rotor angular position, rotor velocity, and acceleration vector, respectively. Represents a symmetric positive definite inertial matrix. It is the centripetal force matrix. The gravity vector Let the friction force vector be... The joint flexibility coefficient, For rotor inertia, The damping coefficient is... It is torque input; (b) Set constraints: Reference signal The energy it possesses is limited, and some practical reference signals satisfy: It is continuous and bounded; (c) In adaptive backstepping design, fuzzy logic systems are used to approximate unknown nonlinear functions, specifically as follows: Let the first... The fuzzy rule is represented as follows: rule :if yes , yes , yes , So: yes in, , It is the output of the fuzzy logic system. and Represents a fuzzy set. It is the total number of rules; the output of the fuzzy logic system is represented as: in, and Represents fuzzy membership functions. satisfy The fuzzy basis function is defined as: in, , Then the fuzzy logic system can be written as: if It is defined in compact set For continuous functions on a given surface, there exists a fuzzy logic system. It can achieve an ideal accuracy To approximate any continuous nonlinear function, such that: in It is a basis function vector, similarity error satisfy ; (d) Define coordinate transformation: (e) In adaptive control methods based on backstepping techniques, a virtual controller needs to be designed at each step until the final step where the actual control input is designed. Therefore, the virtual controller... Designed as: in, These are the parameters to be designed; (f) Adaptive The law is constructed as follows: in, , These are the parameters to be designed; (g) Construct the following dynamic event triggering mechanism and event triggering controller: in, , , , , , , , , , , These are design parameters; (h) Proves that the Zeno phenomenon can be ruled out.
2. The event-triggered control method for ensuring the transient performance of a flexible joint robot according to claim 1, characterized in that, In the controller design process, a candidate Lyapunov function is selected at each step to construct a virtual controller until the final step of constructing the actual control input. The specific control method is as follows: Symbol explanation, Describes a positive definite matrix. Define the following symbols Lemma 1, if Defined as compact set For continuous functions on a given surface, there exists a fuzzy logic system. It can achieve an ideal accuracy To approximate any continuous nonlinear function, such that: in It is an ideal-level weight vector. It is a basis function vector, and the approximation error is... satisfy and ; Lemma 2, Young's inequality, for ,have: in, , , and ; Lemma 3, for any and The following inequalities hold: Lemma 4, when matrix Make the matrix When stable, according to Lyapunov's theorem, there exists a positive definite matrix. satisfy: in It is a constant.
3. The event-triggered control method for ensuring the transient performance of a flexible joint robot according to claim 2, characterized in that, Step two specifically involves: (a) Define the error variable as: ， Define a time-varying, smooth, monotonically increasing function and a normalization function: ， in, Defined as the virtual control law to be designed; based on the notation above, we obtain... (1) right Differentiating, we get: (2) in ;get: (3) in, Constructing virtual control laws and adaptive law for: (4) (5) It can be represented in state-space form: (6) in right Differentiating, we get: Constructing virtual control laws and adaptive law for: ， Represented in state-space form: (7) in The following candidate Lyapunov functions are selected: (8) calculate The derivative is: Applying fuzzy logic systems and Young's inequality, we get .have: Furthermore, there are (b) The event triggering mechanism and the adaptive event triggering controller are as follows: in, , , , , , , , , , , These are design parameters; Considering the event triggering mechanism, we introduce... ,in Therefore: (9) according to ,get: (10) Depend on ,have to: in, From the above formula, we get: (11) (c) Next, prove that Zeno’s behavior will not occur; By proof Make To rule out Zeno's phenomenon; by ,have to in, It is a constant, through combination as well as ,have to In conclusion, the Zeno phenomenon has been ruled out.