Coupling output limited robot motion control method based on event triggering, medium and equipment
By decoupling and transforming coupled output constraints using event-triggered mechanisms and fuzzy logic, the method addresses uncertainty in robot systems, enhancing control stability and efficiency, ensuring precise end-effector tracking.
Patent Information
- Application Number
- CN202510594288.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-09
- Publication Date
- 2025-07-15
AI Technical Summary
The prior art is difficult to effectively solve the problem of limited coupling output of robots in uncertain environments, affecting the stability and tracking performance of the robot system.
Using fuzzy logic system and event triggering mechanism, we design controllers in known and unknown situations of robot dynamics models, and convert them into uncoupled restricted outputs through decoupling, introduce event triggering strategies to reduce the frequency of control updates, and optimize the use of computing resources.
It improves the design feasibility and applicability of the robot controller, enhances the stability and real-time nature of the system, reduces the consumption of computing resources, and improves the robot's adaptability in complex environments.
Smart Images
Figure CN120307294A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of control, and particularly relates to a motion control method, medium and device for a robot with coupled output constraints based on event triggering. Background Technique
[0002] With the continuous development of robot technology, robots play an important role in human society. Robots have important functions in the fields of health, agriculture, manufacturing, etc., and can replace humans to engage in complex tasks, such as rescue and exploration in dangerous and extreme environments.
[0003] Coupled output constraints are of relatively important significance for robots, which can limit the response of the system, ensure that the system operates within the specified range and prevent abnormal output of the system. At the same time, uncertainty affects the tracking performance of the robot. Uncertainty may come from the system model parameters of the robot itself, such as inaccurate estimation of friction or mass distribution, or from the external environment, such as changes in ground conditions or sensor noise. How to design a controller with output constraints and how to reduce the impact of uncertainty on the robot system are the core problems that need to be solved by the current robot motion control methods. Summary of the Invention
[0004] Aiming at the deficiencies in the prior art, the present invention provides a motion control method, medium and device for a robot with coupled output constraints based on event triggering. By designing a fuzzy logic system and an event triggering mechanism, the system is made stable.
[0005] To achieve the above object, the present invention adopts the following technical solutions:
[0006] In the first aspect, the present invention provides a motion control method for a robot with coupled output constraints based on event triggering, including the following steps:
[0007] S1: Establish the dynamic model of the robot;
[0008] S2: Decouple the coupled output constraints of the robot, transform them into time-varying uncoupled constraints, and incorporate the time-varying uncoupled constraints into the controller of the robot;
[0009] S3: Design the controller for the time-varying uncoupled constrained robot when the dynamic model parameters are known;
[0010] S4: Based on the controller in step S3, design the controller for the time-varying uncoupled constrained robot when the dynamic model parameters are unknown;
[0011] S5: Based on the controller in step S4, design the controller for the time-varying uncoupled constrained robot when the dynamic model parameters are unknown under the event triggering mechanism, for the motion control of the robot.
[0012] Optionally, in step S1, the dynamic model of the robot is a mathematical model when the end effector of the robot moves, specifically:
[0013]
[0014]
[0015] where q is the position coordinate in the joint space of the robotic arm; s is the coordinate in the Cartesian space of the end effector of the robotic arm; is the velocity in the Cartesian space of the end effector of the robotic arm; is the acceleration in the Cartesian space of the end effector of the robotic arm; the dot on top of the character represents the first derivative with respect to time t, and the two dots on top of the character represent the second derivative with respect to time t; M(q) is the inertia matrix of the robotic arm; is the Coriolis and centrifugal force matrix of the robotic arm; G(q) is the gravity vector of the robotic arm; F s is the input torque in the Cartesian space; τ is the input torque in the joint space; is the Jacobian matrix.
[0016] Optionally, in step S2, the coupled output constraint form of the robot is a rhombus constraint on the end effector of the robot, specifically:
[0017] |s3| ≤ π;
[0018] |s1| + |s2| ≤ π - |s3|;
[0019] where s = (s1, s2, s3) is the coordinate in the Cartesian space of the end effector of the robotic arm;
[0020] Design the following rotation matrix T(φ) to simplify the coupled output constraint:
[0021]
[0022] where φ represents the rotation angle;
[0023] Use to transform s, and obtain:
[0024]
[0025] Calculate the transformed robot tracking error s d is the ideal trajectory of the end effector of the robotic arm;
[0026] Finally, the time-varying uncoupled constraint is obtained as:
[0027] δ u= [ω - r d1 , ω - r d2 , π - r d3 T ;
[0028] δ l = [-ω - r d1 , -ω - r d2 , -π - r d3 T ;
[0029]
[0030] where δ u and δ l are the upper and lower bounds of the time - varying constraint respectively, and r d1 , r d2 , r d3 are the three components of r d respectively.
[0031] Optionally, in step S3, when the parameters of the dynamic model are unknown, the controller of the time - varying non - coupled constrained robot is:
[0032]
[0033] where M is M(q) in the dynamic model, C is in the dynamic model, and G is G(q) in the dynamic model;
[0034]
[0035] ε = T -1 α;
[0036]
[0037] where p1 and p2 are gain constants, is the derivative of , i = 1, 2, 3, represents 's three components, δ ui is the three components of δ u , δ li is the three components of δ l and T represents the rotation matrix.
[0038] Optionally, in step S4, when the parameters of the dynamic model are unknown, the controller of the time - varying non - coupled constrained robot is:
[0039]
[0040] where the adaptive system to approximate ∈(Z) is the approximation error, used to replace the unknown parameters in the dynamic model; let gradually approach Ξ * , Ξ * is the weight of the ideal fuzzy logic system FLS, represents the estimated parameter, Θ(Z) is the fuzzy basis function, is the input parameter of the fuzzy basis function, virtual control quantity
[0041] Optionally, in step S5, when the dynamic model parameters of the time-varying non-coupled constrained robot are unknown under the event-triggering mechanism, the controller is:
[0042]
[0043] where τ1 is the input torque obtained by the controller, is the variable obtained by H based on the event-triggering mechanism, is the variable obtained by based on the event-triggering mechanism.
[0044] In a second aspect, the present invention provides a computer-readable storage medium storing a computer program, and the computer program causes a computer to execute the event-triggered coupled output constrained robot motion control method as described in the first aspect.
[0045] In a third aspect, the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the event-triggered coupled output constrained robot motion control method as described in the first aspect is implemented.
[0046] The beneficial effects of the present invention are as follows: The present invention solves the motion control problem of a robot with coupled output constraints under uncertainty. By gradually decoupling the coupled constraints of the robot output, it is transformed into a more easily handled non-coupled constraint problem, improving the feasibility and applicability of the controller design. The present invention separately designs controllers for the cases where the robot dynamic model is known and unknown, making the method have a wide range of applications and not being limited to a specific robot system. An event-triggering strategy is introduced in the controller design, reducing the frequency of control updates, optimizing the use of computing resources, and improving the real-time performance and energy efficiency of the system. Through strict mathematical derivations and stability analyses, the present invention ensures the stability of the designed controller and improves the adaptability of the robot system in complex environments. Description of the Drawings
[0047] Figure 1 is the model of the robotic arm.
[0048] Figure 2 is the tracking error of the robotic arm.
[0049] Figure 3 is the output performance with limited output coupling of the robotic arm.
[0050] Figure 4 is the triggering moment of the event-triggering mechanism of the robotic arm.
[0051] Figure 5 is the motion trajectory of the end effector of the robotic arm in the Cartesian space. Specific implementation manners
[0052] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application.
[0053] By decoupling the output limitation problem, the present invention separately designs controllers under known and unknown models, and introduces an event-triggering mechanism, improving the applicability, stability and energy efficiency of robot control, and realizing the path tracking of the end effector of the robot.
[0054] In one embodiment, the present invention proposes an event-triggering based motion control method for a coupled output-limited robot, including the following steps:
[0055] S1: Establish the dynamic model of the robot.
[0056] In this embodiment, the mathematical model during the motion of the end effector of the robot is:
[0057]
[0058] where q is the position coordinate in the joint space of the robotic arm; s is the coordinate in the Cartesian space of the end effector of the robotic arm; is the velocity in the Cartesian space of the end effector of the robotic arm; is the acceleration in the Cartesian space of the end effector of the robotic arm; the dot on the top of the character represents the first derivative with respect to time t, and the two dots on the top of the character represent the second derivative with respect to time t; M(q) is the inertia matrix of the robotic arm; is the Coriolis and centrifugal force matrix of the robotic arm; G(q) is the gravity vector of the robotic arm; F s is the input torque in the Cartesian space; τ is the input torque in the joint space; is the Jacobian matrix.
[0059] The spatial limitation of the end effector of the robotic arm is expressed as:
[0060] |s1| + |s2| + |s3| ≤ π
[0061] Among them, π is a known constant, and |s1| represents the absolute value of s1.
[0062] S2: Decouple the restricted output coupling of the robot and transform it into a time-varying non-coupled restriction.
[0063] In this embodiment, decouple the restricted output coupling of the robot end effector into a time-varying output non-coupled restriction:
[0064] |s3| ≤ π
[0065] |s1| + |s2| ≤ ω ′
[0066] Among them, ω ′ = π - |s3| is a time-varying variable.
[0067] The rhombus constraint can be transformed into the upper and lower bounds of a square using a rotation matrix. The corresponding rotation matrix is:
[0068]
[0069] Among them, is the rotation angle.
[0070] Let r1 = [r 11 , r 12 , r 13 T represent the state of s after rotation:
[0071]
[0072] r2 = [r 21 , r 22 , r 23 T is the state after rotation and
[0073] Therefore, the transformed end effector limit is:
[0074]
[0075] Among them,
[0076] This decoupling method is not limited to the rhombus constraint and can be applied to various spatial constraints in life. Different decoupling methods can be used to decouple different output coupling constraints. For example, represent the spherical constraint as:
[0077]
[0078] The corresponding time-varying constraint formula is:
[0079]
[0080] Among them, Under spherical constraint The upper and lower bounds of the time-varying constraint are respectively:
[0081]
[0082] For cylindrical constraint:
[0083]
[0084] |s3| ≤ π2
[0085] The upper and lower bounds of the time-varying constraint are respectively:
[0086]
[0087] S3: Design the controller of the robot with output coupling constraint under the known robot model according to the robot system state.
[0088] In this embodiment, let s d represent the ideal trajectory in the Cartesian space, and the position tracking error in the Cartesian space is expressed as ∈ = s - s d . The transformed tracking error is defined as where r d = Ts d .
[0089] The coupled output constraint can be transformed into:
[0090]
[0091] And The upper and lower bounds of are defined as:
[0092] δ u = [ω - r d1 , ω - r d2 , π - r d3 T
[0093] δ l = [-ω - r d1 , -ω - r d2 , -π - r d3 T
[0094] Consider the following Lyapunov function:
[0095]
[0096] Among them,
[0097]
[0098] For taking the derivative with respect to time, we get:
[0099]
[0100] where,
[0101]
[0102] Then we get
[0103]
[0104] where, Define and the virtual control quantity Then we can get:
[0105]
[0106] where, (p1I - Υ)>0, Υ = diag[v1, v2, v3], Consider the Lyapunov function:
[0107]
[0108] Taking the derivative with respect to time, we get:
[0109]
[0110] where, ε = T -1 α.
[0111] Design the robot controller based on the dynamics:
[0112]
[0113] We can get
[0114]
[0115] where, λ max represents the maximum value among the matrix eigenvalues; λ min represents the minimum value among the matrix eigenvalues. Thus, the stability of the controller can be proved.
[0116] S4: According to the robot system state, design the controller of the output-coupled limited robot with an unknown robot model.
[0117] In this embodiment, due to the uncertainties of M(q), G(q), the model-based control design may not be feasible. Therefore, the above model-based control is not applicable to robots with uncertainties. To solve this problem, a fuzzy logic system is adopted to approximate the uncertainties.
[0118] denotes the weights of the FLS (fuzzy logic system), and Θ(Z) denotes the fuzzy basis function. The fuzzy logic approximation is defined as follows:
[0119]
[0120] where is the input variable of the fuzzy logic system, ∈(Z) ∈ R n denotes the approximation error and are fixed constants. The adaptation rate of the fuzzy logic system is Γ i is the gain matrix, κ is a small positive constant greater than 0, and the introduction of the κ correction term is to enhance the robustness of the closed-loop system to bounded disturbances.
[0121] The controller designed based on the fuzzy logic system is:
[0122]
[0123] Consider the Lyapunov function:
[0124]
[0125] where
[0126] For taking the derivative gives:
[0127]
[0128] Substituting into the above formula gives:
[0129]
[0130] where
[0131]
[0132] S5: According to the robot system state, design the controller of the robot model unknown output coupling limited robot under the event-triggered mechanism.
[0133] In this embodiment, in order to minimize the computational burden as much as possible, the following state update strategy is adopted.
[0134] Let \(t\) 1,j+1 , \(t\) 2,j+1 , \(t\) 3,j+1 , \(t\) 4,j+1 , \(t\) 5,j+1 represent the triggering moment of event - triggered control, \(j\in\mathbb{Z}_{\geq0}\). The ETM (Event - Triggering Mechanism) used is as follows:
[0135]
[0136] Select At \(t\) n \(\in[t\) n,k , \(t\) n,k+1 as the input of the controller, and to reduce the computational load of the controller.
[0137] The corresponding controller incorporating the ETM is designed as:
[0138]
[0139] Among them, and are the variables of \(H\) and after being processed by the ETM.
[0140] \(\tau\) is a continuous function of all parameters, and all parameters must be bounded. According to the Lipschitz theorem, we can obtain:
[0141]
[0142] Among them, \(\|\tau_1 - \tau\|\leq e\) τ .
[0143] The derivative of the corresponding Lyapunov function with respect to time is:
[0144]
[0145] Analyze the key part:
[0146]
[0147] Among them, \(|\Theta(Z)|\) 2 \(\leq N\), and further we can obtain:
[0148]
[0149] Among them,
[0150]
[0151] To ensure that Ω2 > 0, control the gains p1, p2, and β Ξ The selection of min must satisfy the following conditions λ
[0152] S6: Verify the stability of the designed output-coupling limited robot controller in the system.
[0153] Next, combine specific experiments to prove the effectiveness of the method proposed in this embodiment, including the following steps:
[0154] Step A: Establish the mathematical model of the robot's motion:
[0155]
[0156] Step B: Set the parameters of the robot as:
[0157]
[0158] G(q) = [0 0 (m2 + m3)g] T
[0159]
[0160] where
[0161]
[0162] Step C: Design the robot's controller according to the output-limited conditions.
[0163] The controller designed based on the fuzzy logic system is:
[0164]
[0165] Consider the Lyapunov function:
[0166]
[0167] Derive the Lyapunov function to obtain:
[0168]
[0169] where
[0170]
[0171] The specific parameter settings are g = 9.81 m / s 2 , I1 = 1.3 kg·m 2 , m2 = 0.78 kg, m3 = 0.34 kg.
[0172] The numerical simulation results show that the control method proposed in this embodiment has good feasibility. The simulation platform is based on Matlab R2022a under the Windows 11 64-bit operating system, and the simulation object is the robot as shown in Figure 1 the figure. The figure shows the model of the robotic arm. According to the geometric relationship of the robot joints, the angle of the robot in the initial state is The initial position is s(0) = [0.3, 0.3, 0.4] T . The following reference trajectory of the robot is: s d = [0.5sin(2t), 0.6cos(2t), 0.2 + 0.1sin(2t)] T .
[0173] In this embodiment, the parameters of the selected robot are shown in Table 1:
[0174] Table 1 Robot parameters
[0175]
[0176]
[0177] Figure 2 is the tracking error of the robotic arm. Figure 3 is the output performance with restricted output coupling of the robotic arm. Figure 4 is the computer computing power reduced by the time-triggered mechanism of the robotic arm. The length of the vertical line represents the time interval since the last update, and the position of the vertical line indicates the update time. Figure 5 is the motion trajectory of the end effector of the robotic arm in the Cartesian space. As shown in the figure, it does not exceed the coupling-restricted area, demonstrating good control performance.
[0178] In another embodiment, the present invention proposes a computer-readable storage medium storing a computer program, and the computer program causes a computer to execute the event-triggered coupled output restricted robot motion control method of the foregoing embodiment.
[0179] In another embodiment, the present invention proposes an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the event-triggered coupled output restricted robot motion control method of the foregoing embodiment is implemented.
[0180] In the embodiments disclosed in the present application, the computer storage medium may be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of the computer storage medium would include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CDROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.
[0181] Those of ordinary skill in the art will appreciate that the units and algorithm steps of the examples described in connection with the embodiments disclosed in the present application can be implemented in electronic hardware or in a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present application.
[0182] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art in the technical field, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.
Claims
1. An event-triggered coupled output-constrained robot motion control method, characterized in that, It includes the following steps: S1: Establish the dynamic model of the robot; S2: Decouple the coupled output limitation of the robot, transform it into time-varying non-coupled limitation, and incorporate the time-varying non-coupled limitation into the controller of the robot; S3: Design the controller of the time-varying non-coupled limited robot with known dynamic model parameters; S4: Based on the controller in step S3, design the controller of the time-varying non-coupled limited robot with unknown dynamic model parameters; S5: Based on the controller in step S4, design the controller of the time-varying non-coupled limited robot with unknown dynamic model parameters under the event-triggering mechanism for the motion control of the robot.
2. The method for controlling the motion of a robot with limited coupled output based on event triggering according to claim 1, wherein: In step S1, the dynamic model of the robot is the mathematical model when the end effector of the robot moves, specifically: Among them, q is the position coordinate in the joint space of the robotic arm; s is the coordinate in the Cartesian space of the end effector of the robotic arm; is the velocity in the Cartesian space of the end effector of the robotic arm; is the acceleration in the Cartesian space of the end effector of the robotic arm; The dot on top of the character represents the first derivative with respect to time t, and the two dots on top of the character represent the second derivative with respect to time t; M(q) is the inertia matrix of the robotic arm; is the Coriolis and centrifugal force matrix of the robotic arm; G(q) is the gravity vector of the robotic arm; F s is the input torque in the Cartesian space; τ is the input torque in the joint space; is the Jacobian matrix.
3. The event-triggered coupled output-constrained robot motion control method according to claim 2, wherein: In step S2, the form of the coupled output limitation of the robot is the diamond constraint on the end effector of the robot, specifically: |s3|≤π； |s1| + |s2| ≤ π - |s3|; where s = (s1, s2, s3) is the coordinate in the Cartesian space of the end effector of the robotic arm; Design the following rotation matrix T(φ) to simplify the coupled output limitation: where φ represents the rotation angle; Use to convert s, obtaining: The robot tracking error after the transformation of the computer robot s d is the ideal trajectory of the end effector of the robotic arm; Finally, the time-varying non-coupled limitation is obtained as: δ u = [ω - r d1 , ω - r d2 , π - r d3 T ; δ l = [-ω - r d1 , -ω - r d2 , -π - r d3 T ; where, δ u and δ l are the upper and lower bounds of the time-varying constraint respectively, and r d1 , r d2 , r d3 are the three components of r d respectively.
4. The method for controlling the motion of a robot with coupled output limitations based on event triggering according to claim 3, characterized in that: In step S3, the controller of the time-varying non-coupled limited robot with unknown dynamic model parameters is: Among them, M is M(q) in the kinetic model, and C is G is G(q) in the kinetic model; ε = T -1 α; where p1 and p2 are gain constants, is the derivative of , i = 1, 2, 3, represents the three components of , δ ui are the three components of δ u , δ li are the three components of δ l , and T represents the rotation matrix.
5. The method for controlling the motion of a robot with limited coupled output based on event triggering according to claim 4, characterized in that: In step S4, the controller of the time-varying non-coupled limited robot with unknown dynamic model parameters is: Among them, an adaptive system is used to approximate ∈(Z) is the approximation error, which is used to replace the unknown parameters in the dynamic model; let gradually approach Ξ * , Ξ * is the ideal fuzzy logic system FLS weight, represents the estimated parameter, Θ(Z) is the fuzzy basis function, is the input parameter of the fuzzy basis function, virtual control quantity 6. The method for controlling the motion of a robot with limited coupled output based on event triggering according to claim 5, wherein: In step S5, the controller of the time-varying non-coupled limited robot with unknown dynamic model parameters under the event-triggering mechanism is: Among them, τ1 is the input torque obtained by the controller, is a variable obtained by H based on the event-triggering mechanism, is a variable obtained based on the event-triggering mechanism.
7. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to execute the event-triggered coupled output limited robot motion control method according to any one of claims 1-6.
8. An electronic device, characterized in that, It includes: A memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the event-triggered coupled output limited robot motion control method according to any one of claims 1-6.