A robot body structure vibration control method based on an inertial actuator

Abstract

This invention belongs to the technical field of milling machining and discloses a method for controlling the vibration of a robot body structure based on an inertial actuator. The method includes the following steps: (1) providing an active control system for the vibration of the robot body structure, wherein the active control system includes an inertial actuator platform, and the inertial actuators of the inertial actuator platform are respectively installed on each link of the robot milling machining platform; (2) constructing a dynamic model of the robot milling system considering distributed actuation forces based on the active control system for the vibration of the robot body structure; (3) converting the mathematical expression of the dynamic model of the robot milling system into equations represented by a state-space matrix, converting the obtained equations into a discrete system without time delay based on state transformation, designing an optimal control law based on the equations corresponding to the discrete system without time delay, and using the optimal control law to suppress vibration of the robot body structure. This invention improves machining quality.

Description

Technical Field

[0001] This invention belongs to the technical field of milling machining, and more specifically, relates to a method for controlling the vibration of a robot body structure based on an inertial actuator. Background Technology

[0002] When efficiently machining large and complex components such as marine propellers, the relatively weak stiffness of the robot structure leads to poor dynamic characteristics. Under dynamic cutting forces, the structure is prone to low-frequency modal coupling chatter, causing the main chatter component to transfer from the tool tip to the robot body structure, resulting in significant chatter damage to the tool and a substantial impact on machining quality and efficiency. Therefore, research on robot body structure vibration suppression, designing distributed vibration damping devices suitable for robots, establishing attitude-dependent dynamic models, and designing control laws for active control are of positive significance for improving the efficiency of robotic milling.

[0003] To address chatter in robotic milling, traditional process optimization methods, which rely on solving milling stability lobe diagrams to guide on-site process parameters, have limitations. They cannot improve the milling stability domain, and the stability lobe diagram varies with robot posture and tool tilt angle, making the solution complex and lacking adaptability. Passive and semi-active control methods use dampers such as magnetorheological dampers, eddy current dampers, and tuned mass dampers at the spindle and tool to absorb vibration energy by adjusting their natural frequencies. However, this damping frequency range is narrow, and their installation at the spindle and tool can affect the robot's maneuverability and spatial accessibility in confined spaces. Active control, on the other hand, uses externally applied adjustable frequency excitation to apply active control force to the controlled object online, thus counteracting vibration. It offers a wide adjustable frequency range and strong adaptability. Piezoelectric actuators are widely used, overcoming bandwidth limitations, but their stroke is limited, requiring an external fixed actuator device to apply the actuation force; otherwise, it only produces a relative displacement effect at the actuator connection end. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a robot body structure vibration control method based on inertial actuator, which suppresses the vibration of the robot body structure by inhibiting joint vibration to reduce end-effector vibration in robot milling and improve machining quality.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for controlling the vibration of a robot body structure based on an inertial actuator is provided, the method mainly comprising the following steps:

[0006] (1) Provide an active control system for the vibration of the robot body structure. The active control system includes a robot milling platform, an inertial actuator platform, a Ganter four-channel controller, an actuator driver, a four-channel analog output and vibration measurement module, and an acceleration sensor. The inertial actuators of the inertial actuator platform are respectively installed on each link of the robot milling platform, and the acceleration sensor is also installed on the link.

[0007] (2) Based on the active control system for vibration of the robot body structure, a dynamic model of the robot milling system considering distributed action is constructed. The mathematical expression of the dynamic model of the robot milling system is:

[0008]

[0009] In the formula, I, C, and K are the inertia, damping, and stiffness matrices of each joint, respectively; {θ(t)} is the joint rotation angle; τ is the milling cycle; θ is the joint angle; t is the milling time; J w (θ) is the cutting force coefficient matrix related to robot posture; U(t) is the force exerted by the secondary system on the primary system;

[0010] (3) The mathematical expression of the dynamic model of the robot milling system is converted into an equation represented by a state space matrix. Based on the state transformation, the obtained equation is converted into a discrete system without time delay. Based on the equation corresponding to the discrete system without time delay, the optimal control law is designed. Based on the optimal control law, the vibration of the robot body structure is suppressed.

[0011] Furthermore, step (2) includes the following sub-steps:

[0012] (21) Construct a robot dynamics model, wherein the robot dynamics model establishes the relationship between the torque applied to the joint and the end displacement, that is, the end displacement can be obtained based on the robot dynamics model and the torque applied to the joint.

[0013] (22) The torsional vibration angle of the joint is transferred to the end displacement, thus obtaining a dynamic model of the robot milling system considering distributed action.

[0014] Furthermore, considering the robot's flexible joints as a single-degree-of-freedom system with stiffness k and damping c, the following equations can be obtained by analyzing each series joint using the d'Alembert method:

[0015]

[0016] In the formula, I, C, and K are the inertia, damping, and stiffness matrices of each joint, respectively, and {θ(t)} and {τ(t)} are the rotation angle and generalized force of each joint, respectively.

[0017] Furthermore, considering only the force and torque generated by the milling force in the x and y directions of the tool, then {P(t)} is the equivalent torque of the dynamic milling force applied by the workpiece to the robot end effector, converted to each joint, and {τ(t)} is the equivalent torque applied by the actuator to the joint:

[0018]

[0019]

[0020]

[0021] {θ(t)}=[θ1(t),θ2(t),…,θ n (t)] T , {τ(t)}=[F1(t),F2(t),…,F n (t)] T

[0022]

[0023] J T (θ) is the force Jacobian matrix at joint angle θ; where h xx (t), h xy (t), h yx (t), h yy (t) is the dynamic cutting force coefficient, w is the axial depth of cut, and r(t) is the distance from the cutting edge to the center of the tool axis.

[0024] Furthermore, the robot pose change caused by the dynamic milling force is represented as:

[0025] Δd=J(θ)(θ(t)-θ(t-τ))

[0026] In the formula, J(θ) is the robot force Jacobian matrix at joint angle θ.

[0027] Furthermore, let the force generated by the inertial actuator platform mounted on the i-th link be u, and its generalized force on the robot's first i joints be expressed as:

[0028]

[0029] U i (t) generates a generalized force on the inertial actuator platform of the i-th link, J T i (θ) is the Jacobian matrix for the 1st to the i-th joint, which is an i×6 matrix, τ i (t) represents the generalized torque applied to the i-th joint.

[0030] Furthermore, the delay-free state equation of the discrete system is:

[0031]

[0032]

[0033] In the formula, The time-varying matrix of the discrete-time system is (12+6l)×(12+6l). It is a fixed matrix of (12+6l)×6; where X(k+1)=MX(k)+NX(kl)+NX(k-l+1)+BU(k), E represents the identity matrix, and M=(E-wΔtA0) -1 (E+wΔtA0), N=wΔt(E-wΔtA0) -1 A1, Δt = τ / l, where l is the number of intervals into which the time delay is divided; w is the weight of the linear interpolation; and A0 is the state transition matrix for the non-delay term.

[0034] Furthermore, the optimal control law corresponds to a constant gain controller, and the control gain is obtained by solving the Riccati equation offline.

[0035] Furthermore, the constant gain controller comprises two sub-modules: a six-joint accelerometer sensor signal acquisition and calculation module and a control force output module.

[0036] Furthermore, the accelerometer signal acquisition and calculation module is used to acquire the torsional vibration signal measured by the accelerometer and calculate the current joint torsional vibration angle after filtering. The control force output module is used to calculate the output analog quantity of each actuator at the current moment based on the current and previous cycle joint torsional vibration signals, and output it to the inertial actuator driver, thereby driving the inertial actuator to apply control force on the link to suppress the vibration of the robot body structure and thus suppress the milling chatter at the end.

[0037] In summary, compared with the prior art, the robot body structure vibration control method based on inertial actuators provided by the present invention has the following advantages:

[0038] 1. Inertial actuators can be adapted to be installed at weak joints. Inertial actuators installed on connecting rods are simpler in design and easier to install than rotational vibration damping devices for joints.

[0039] 2. The inertial actuator is mounted on the connecting rod and is not connected to the joint end, so it does not affect the normal movement of the joint and has little impact on the end modal characteristics.

[0040] 3. The optimal control algorithm used in this invention belongs to state feedback control. It measures the torsional vibration state of each joint in real time through an accelerometer, and calculates the magnitude of the analog control force based on the designed active control law and outputs it to the driver. The inertial actuator is controlled to output the control force in real time. This method can realize real-time feedback control and adapt to real-time working conditions. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a simplified actuator-joint model according to the present invention;

[0042] Figure 2 This is a schematic diagram of the active vibration control system for the robot body structure involved in this invention;

[0043] Figure 3 This is a schematic diagram of the structure of the inertial actuator platform involved in this invention;

[0044] Figure 4 This invention relates to a flowchart of active vibration control for the robot body structure.

[0045] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1-robot milling platform, 2-inertial actuator platform, 3-Ganter four-channel controller, 4-actuator driver, 5-four-channel analog output and vibration measurement module, 6-side plate bracket, 7-fixed support, 8-voice coil motor stator, 9-voice coil motor mover, 10-flange bracket. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0047] This invention provides a method for controlling the vibration of a robot body structure based on an inertial actuator, comprising the following steps: (a) For the low-frequency vibration of the robot body structure during milling, an active control system for the vibration of the robot body structure based on an inertial actuator is designed, which includes a robot milling platform 1 composed of an industrial robot and an electric spindle, an inertial actuator platform 2, an acceleration sensor, an inertial actuator driver 4, a Ganter four-channel controller 3, a Ganter four-channel analog output module, and a Ganter four-channel vibration measurement module; (b) Considering the dynamic model of the robot milling system with distributed actuation force, specifically, the robot joints are regarded as flexible bodies and the links are regarded as rigid bodies, a robot dynamic model of flexible joints and rigid links is established, and the joints are realized by the force Jacobian matrix and Newton-Raphson formula. - Force position conversion at the end point, constructing a robot milling dynamics model considering distributed actuation force; (c) Optimal control algorithm for robot joint vibration: by state transformation, the time delay model is converted into a discrete time delay-free system, a discrete time delay optimal control model considering joint torsional vibration is constructed, and the control force related to the state quantity is input to establish a linear time-varying input-free system, and the closed-loop stability of the control system is analyzed using Flokai's theorem; (d) The vibration state of each joint is collected in real time by accelerometer and host computer software, and the output voltage is calculated based on the designed optimal control law. The control signal is transmitted to the inertial actuator driver 4 through the controller to control the output control force of the inertial actuator, thereby suppressing the vibration component of the robot body structure in the end point vibration during milling, improving milling efficiency, and ensuring the machining quality of the parts.

[0048] Please see Figure 1 , Figure 2 , Figure 3 and Figure 4 Specifically, the control method mainly includes the following steps:

[0049] Step 1: Provide an active control system for the vibration of the robot body structure. The active control system includes a robot milling platform 1, an inertial actuator platform 2, a Ganter four-channel controller 3, an actuator driver 4, a four-channel analog output and vibration measurement module 5, and an acceleration sensor. The inertial actuators of the inertial actuator platform 2 are respectively installed on each link of the robot milling platform 1, and the acceleration sensor is also installed on the link.

[0050] The robotic milling platform 1 includes an industrial robot and an electric spindle, which is used to mill workpieces. During machining, low-frequency vibrations occur due to the poor structural rigidity of the robot body. The inertial actuator platform 2 includes a side plate support 6, a fixed support 7, a voice coil motor stator 8, a voice coil motor mover 9, and a flange support 10. The two opposite ends of the side plate support 6 are respectively connected to the fixed support 7 and the flange support 10. One end of the voice coil motor stator 8 is connected to the fixed support 7, and the other end is connected to the voice coil motor mover 9. The voice coil motor mover 9 is connected to the flange support 10.

[0051] The actuation force of the inertial actuator platform 2 is generated by the high-frequency acceleration and deceleration generated by the voice coil motor stator 8 and the voice coil motor mover 9, i.e., the inertial actuator. Through the grating ruler, linear servo amplifier and motion controller, a system capable of complex position, speed and acceleration control can be generated.

[0052] The inertial actuator platform 2 is mounted on each link of the robot milling platform 1. When outputting actuation force, it generates inertial force that acts on each joint axis. When active control is applied, the joint vibration signal is collected by the accelerometer and transmitted to the four-channel analog output and vibration measurement module 5. At the same time, the Ganter four-channel controller 3 calculates the required analog control force at the current moment based on the transmitted current and previous cycle joint vibration signals, and transmits it to the inertial actuator driver 4 through the four-channel analog output and vibration measurement module 5. The inertial actuator driver 4 then outputs the required current of the actuator to the inertial actuator platform 2. The inertial actuator platform 2 outputs the corresponding control force to generate joint torsional vibration at the robot joint end, thereby suppressing end-effector vibration.

[0053] Step 2: Based on the active control system for vibration of the robot body structure, construct a dynamic model of the robot milling system considering distributed dynamic forces. The mathematical expression of the dynamic model of the robot milling system is:

[0054]

[0055] In the formula, I, C, and K are the inertia, damping, and stiffness matrices of each joint, respectively; {θ(t)} is the joint rotation angle; τ is the milling cycle; θ is the joint angle; t is the milling time; J w (θ) is the cutting force coefficient matrix related to robot posture; U(t) is the force exerted by the secondary system on the primary system.

[0056] Step two includes the following sub-steps:

[0057] (1) Construct a robot dynamics model. The robot dynamics model establishes the relationship between the torque applied to the joint and the end displacement. That is, the end displacement can be obtained based on the robot dynamics model and the torque applied to the joint.

[0058] Treating robot joints as flexible bodies and links as rigid bodies, a robot dynamics model of flexible joints and rigid links is established. The flexible joints are considered as single-degree-of-freedom systems with stiffness k and damping c. Using the d'Alembert method to analyze each series joint, the following equations can be obtained:

[0059]

[0060] In the formula, I, C, and K are the inertia, damping, and stiffness matrices of each joint, respectively, and {θ(t)} and {τ(t)} are the rotation angle and generalized force of each joint, respectively. Considering only the force and torque generated by the milling force in the x and y directions of the tool, then {P(t)} is the equivalent torque of the dynamic milling force applied by the workpiece to the robot end effector, converted to each joint, and {τ(t)} is the equivalent torque applied by the actuator to the joint:

[0061]

[0062]

[0063]

[0064] {θ(t)}=[θ1(t),θ2(t),…,θ n (t)] T , {τ(t)}=[F1(t),F2(t),…,F n (t)] T (5)

[0065]

[0066] The representation of {P(t)} is as shown in equation (6), J T (θ) is the force Jacobian matrix at joint angle θ. Where h xx (t), h xy (t), h yx (t), h yy (t) is the dynamic cutting force coefficient, w is the axial depth of cut, and r(t) is the distance from the cutting edge to the center of the tool axis.

[0067] (2) The torsional vibration angle of the joint is transferred to the end displacement, thus obtaining a dynamic model of the robot milling system considering distributed dynamics.

[0068] The dynamic milling force on the right side of equation (1) is rearranged into a form related to θ. Using the Newton-Raphson formula, a single-variable nonlinear equation is given:

[0069] f(θ=0)

[0070] Let the error between the approximate solution and the true solution of this equation be Δθ.0 Then θ = θ 0 +Δθ 0 Satisfy the equation, that is

[0071] f(θ 0 +Δθ 0 ) = 0

[0072] Expanding the function on the left side of the equation into a Taylor series yields:

[0073]

[0074] In the formula f′(θ) 0 ), f″(θ 0 ), ...f (n) (θ 0 ) are the functions f(θ) at θ 0 The first derivative, second derivative, ..., nth derivative at the point. If the difference Δθ 0 The value is very small, and the right-hand side of the above equation is Δθ. 0 Terms of second and higher orders can be neglected, that is, the above formula simplifies to:

[0075] f(θ 0 +Δθ 0 )=f(θ 0 )+f′(θ 0 )Δθ 0

[0076] Assuming that during the robot milling process, the change in robot pose caused by the end-effector feed is negligible within the milling cycle τ, then when f is the robot's kinematic formula, f′(θ) 0 )Right now For the formula f in θ 0 The Jacobian matrix J(θ)∈R at point m*n f(θ) 0 +Δθ 0 )-f(θ 0 ) for the robot in pose θ 0 The change in pose Δd when there is a small change, i.e.:

[0077]

[0078] The robot pose change caused by the dynamic milling force in formula (6) can be expressed as:

[0079] Δd=J(θ)(θ(t)-θ(t-τ)) (8)

[0080] Formula (1) can then be expressed as:

[0081]

[0082] When the inertial actuator platform 2 is subjected to an actuation force, {τ(t)} is the generalized force generated at the joint by the actuation force. The expression of {τ(t)} will be derived below.

[0083] Let u be the actuating force generated by the inertial actuator platform 2 mounted on the i-th link. The generalized force it generates on the first i joints of the robot can be expressed as:

[0084]

[0085] U i (t) generates a generalized force on the inertial actuator platform 2 of the i-th link, J T i (θ) is the Jacobian matrix for the 1st to the i-th joint, which is an i×6 matrix, τ i (t) represents the generalized torque acting on the i-th joint. Where U i The calculation method for (t) is as follows:

[0086] First, simplify the structure of the linkage with attached inertial actuator platform 2 as follows: Figure 1 The system shown.

[0087] Where m a c a k a Let m represent the mass, damping, and stiffness of the inertial actuator, respectively. p c p k p Let represent the equivalent modal mass, damping, and stiffness of the link, respectively. The link is considered as the primary system, and the inertial actuator is considered as the secondary system. The overall dynamic model of the inertial actuator and the robot can be expressed by the following formula.

[0088]

[0089]

[0090] Substituting formula (11) into formula (12), we obtain the force exerted by the secondary system on the primary system as follows:

[0091]

[0092] Therefore, the output force of the i-th inertial actuator on the i-th link is given by equation (14):

[0093]

[0094] In the formula m ai Let be the mass of the movable part of the i-th inertial actuator. The displacement acceleration of the mass is added to the i-th inertial actuator. The dynamic equation containing the control force can then be obtained as shown in equation (16).

[0095]

[0096] To simplify the formula, let:

[0097]

[0098]

[0099] Finally, the dynamic model of the robot milling system considering distributed action can be simplified to:

[0100]

[0101] Step 3: The mathematical expression of the dynamic model of the robot milling system is converted into equations represented by state space matrices. Based on the state transformation, the resulting equations are converted into a discrete system without time delay. Based on the equations corresponding to the discrete system without time delay, the optimal control law is designed. Based on the optimal control law, vibration suppression is performed on the robot body structure.

[0102] Specifically, it includes the following sub-steps:

[0103] 1) Discrete-time delay systems based on state transformation

[0104] According to formula (16), the milling system has time-varying and time-delay characteristics. For chatter control, the control system is basically represented as a time-invariant system. Therefore, it is necessary to convert the continuous system into a discrete system without time delay while retaining the time-delay characteristics of the original system.

[0105] The state-space description of formula (16) can be given in matrix form, as follows:

[0106]

[0107] in

[0108]

[0109] E 6×6 It is a 6×6 identity matrix, X(t) is a 12×1 matrix, A0(t) and A1(t) are 12×12 matrices, and B is a 12×6 matrix.

[0110] For ease of practical processing, the state variables are sampled at discrete intervals defined by the sampling frequency. Since the actual sampling period is much shorter than the time delay, it is assumed that the time delay τ is an integer multiple of the sampling time. The interval is then divided into l intervals, and the sampling rate is defined as Δt = τ / l. In the k-th interval [t... k ,t k+1 Within [the range], the equation can be discretized as:

[0111]

[0112] Using unit sampling time Δt as the interval, linear interpolation is performed on the state space equation (17) to fit the state variables that are not at the endpoints of the interval, where w is the weight of the linear interpolation and the differential term is... Discretized using the Euler method as shown below:

[0113]

[0114] Substituting equation (19) into equation (18) and rearranging, we obtain the discrete-time state equation:

[0115] X(k+1)=MX(k)+NX(kl)+NX(k-l+1)+BU(k) (20)

[0116] Where E represents the identity matrix.

[0117] M=(E-wΔtA0) -1 (E+wΔtA0) (21)

[0118] N = wΔt(E - wΔtA0) -1 A1 (22)

[0119] To remove the delayed term, variable substitution is performed, let... as follows( (It is a (12+6l)×1 matrix).

[0120]

[0121] The final state equation for the discrete system without delay is:

[0122]

[0123]

[0124] in The time-varying matrix of the discrete-time system is (12+6l)×(12+6l). The matrix is ​​(12+6l)×6. For the previously established milling system model, the output includes the torsional vibration angles of the 6 joints, which can be obtained by accelerometers.

[0125] 2) Optimal control law design

[0126] When the active control system for robot body structure vibration is converted into a discrete LTI system without state time delay, expressed by equations, an optimal control method can be used to stabilize the cutting state. If the selected design parameters are higher than the lower limit of the SLD (Stable Difference of Cutting), i.e., an unstable milling process, active control is required.

[0127] For LQR control, the discrete-time performance criterion is described as follows:

[0128]

[0129] Where Q is the symmetric positive semidefinite weight of the state, and R is the symmetric positive definite weight of the input. According to optimal control theory, when the weight matrices Q and R are fixed, the state feedback controller is uniquely determined. Since R is a weighting matrix or a constraint on the input, it is usually set as a diagonal matrix to make the closed-loop system robust. Similarly, Q is the weighting matrix of the state, also set as a diagonal matrix. The elements in matrix Q represent the importance of the corresponding state in the performance function, where the larger the value, the higher the importance.

[0130] Assume a unique optimal control law: the state feedback control gain K∈R 6×(12+6l) The optimal active control force has already been designed to be:

[0131]

[0132] Wherein the state feedback control gain matrix is:

[0133]

[0134] It is a block matrix with corresponding dimension P>0, and it is the unique symmetric positive semi-definite solution of the Licarti equation:

[0135]

[0136] According to formula (27), the optimal controller includes not only the current time term of the state feedback term, but also a linear combination of the state terms from the previous time step l, which can be obtained through the accelerometer and the Ganter four-channel controller with a 3-delay storage. The discrete-time state equation is derived by formulas (17)-(25) and the time delay term of the system is eliminated, which aims to simplify the design of the control law and obtain a constant gain controller, which is obtained by solving the Riccati equation offline.

[0137] The control gain can be calculated through the above steps. Then, by writing a controller program, vibration control of the inertial actuator can be achieved. The optimal control law corresponds to a constant gain controller. The control gain is obtained by solving the Liccati equation offline. The constant gain controller contains two sub-modules: a six-joint accelerometer signal acquisition and calculation module and a control force output module. The accelerometer signal acquisition and calculation module acquires the torsional vibration signal measured by the accelerometer and calculates the current joint torsional vibration angle after filtering. The control force output module calculates the output analog quantity of each actuator at the current moment based on the current and previous cycle joint torsional vibration signals and outputs it to the inertial actuator driver 4. This drives the inertial actuator to apply control force on the linkage to suppress the vibration of the robot body structure, thereby suppressing milling chatter at the end effector.

[0138] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the vibration of a robot body structure based on an inertial actuator, characterized in that, The method includes the following steps: (1) Provide an active control system for the vibration of the robot body structure. The active control system includes a robot milling platform, an inertial actuator platform, a Ganter four-channel controller, an actuator driver, a four-channel analog output and vibration measurement module and an acceleration sensor. The inertial actuators of the inertial actuator platform are respectively installed on each link of the robot milling platform, and the acceleration sensor is also installed on the link. (2) Based on the active control system for vibration of the robot body structure, a dynamic model of the robot milling system considering distributed action is constructed. The mathematical expression of the dynamic model of the robot milling system is: In the formula, I , C K represents the inertia, damping, and stiffness matrices of each joint, respectively. For the joint angles; For milling cycles; Joint angle; For milling time; This is the cutting force coefficient matrix related to the robot's posture; The force exerted by the secondary system on the primary system; the linkage is considered the primary system, and the inertial actuator is considered the secondary system; (3) The mathematical expression of the dynamic model of the robot milling system is converted into an equation represented by a state space matrix. Based on the state transformation, the obtained equation is converted into a discrete system without time delay. Based on the equation corresponding to the discrete system without time delay, the optimal control law is designed. Based on the optimal control law, the vibration of the robot body structure is suppressed. Step (2) includes the following sub-steps: (21) Construct a robot dynamics model, wherein the robot dynamics model establishes the relationship between the torque applied and the end displacement, that is, the end displacement can be obtained based on the robot dynamics model and the torque applied to the joint; (22) The torsional vibration angle of the joint is transferred to the end displacement, thus obtaining a dynamic model of the robot milling system considering distributed action. Treating the robot's flexible joints as a single-degree-of-freedom system with stiffness k and damping c, the following equations can be obtained by analyzing each cascaded joint using the d'Alembert method: In the formula I , C K represents the inertia, damping, and stiffness matrices of each joint, respectively. , These are the joint angles and generalized forces, respectively. The dynamic milling force applied to the robot end effector by the workpiece is converted into the equivalent torque of each joint; If we only consider the forces and moments generated by the milling force in the x and y directions of the tool, then The dynamic milling force applied to the robot end effector by the workpiece is converted into the equivalent torque of each joint. The generalized force applied to the joint by the actuator: ， Joint angle The following is the force-jacobi matrix; where , , , This is the dynamic cutting force coefficient. For axial depth of cut, This is the distance from the cutting edge to the center of the tool axis.

2. The robot body structure vibration control method based on inertial actuator as described in claim 1, characterized in that: The robot pose change caused by dynamic milling force is represented as: In the formula, Joint angle The robot's Jacobian matrix.

3. The robot body structure vibration control method based on inertial actuators as described in claim 2, characterized in that: Let the first i The inertial actuator platform mounted on each link generates the following force: u Its front of the robot i The generalized force generated by a joint is represented as: in Generate a generalized force for the inertial actuator platform on the i-th link. Let be the Jacobian matrix of the first to the i-th joints, which is an i×6 matrix. Let be the generalized force acting on the i-th joint.

4. The robot body structure vibration control method based on inertial actuator as described in claim 3, characterized in that: The state equation of a discrete system without delay is: In the formula, for Time-varying matrix of discrete-time system for Fixed matrix; where, , Represents the identity matrix. Represents the identity matrix. , , , The number of intervals into which the time delay is divided; The weights for linear interpolation; This is the state transition matrix for non-time-delay terms.

5. The robot body structure vibration control method based on inertial actuators as described in any one of claims 1-4, characterized in that: The optimal control law corresponds to a constant gain controller, and the control gain is obtained by solving the Riccati equation offline.

6. The robot body structure vibration control method based on inertial actuator as described in claim 5, characterized in that: The constant gain controller consists of two sub-modules: a six-joint accelerometer signal acquisition and calculation module and a control force output module.

7. The robot body structure vibration control method based on inertial actuator as described in claim 6, characterized in that: The accelerometer signal acquisition and calculation module is used to acquire the torsional vibration signal measured by the accelerometer and calculate the current joint torsional vibration angle after filtering. The control force output module is used to calculate the output analog quantity of each actuator at the current moment based on the joint torsional vibration signal of the current and previous cycles, and output it to the inertial actuator driver, thereby driving the inertial actuator to apply control force on the link to suppress the vibration of the robot body structure and thus suppress the milling chatter at the end.

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