Vibration suppression control method and system for long-span rope-driven flexible manipulator

Abstract

The application provides a large-span rope-driven flexible mechanical arm vibration suppression control method and system, and the method comprises the following steps: vibration suppression control is carried out for the flexibility of a rope-driven robot arm rod and the elasticity of a rope, the arm rod flexibility problem is processed through a hypothesis modal method, a mathematical model of a rope-driven robot containing a rope mapping joint is given, and a terminal sliding mode control method is used to control and simulate a large-span flexible rope-driven robot under a load condition. The application solves the technical problem that a large tracking error is caused by the fact that the flexibility of an arm rod, the elasticity of a rope, end load and motion disturbance are not fully considered, and load description is not accurate in the existing rope-driven robot model.

Description

Technical Field

[0001] The present invention relates to the field of robots and flexible vibration control, and in particular to a vibration suppression control method and system for a large-span rope-driven flexible robotic arm. Background Art

[0002] In recent years, with the advancement of robotics and the deepening of space exploration, the application of space robots in space resource development has become increasingly frequent. Tether-driven systems, due to their low mass-to-load ratio, high flexibility, and safety, along with their human-robot interaction features, have attracted widespread attention from researchers across various fields. Tether-driven space robots are playing an increasingly important role in space activities and have become a hot topic in current on-orbit space systems. However, the introduction of tether-driven technology also presents new challenges and difficulties. Current research challenges include the high complexity of dynamic parameters, the elasticity of the tether, and the flexible vibration of the arm.

[0003] Meeting the demands of high-precision robot control requires, on the one hand, establishing an accurate robot dynamics model, and, on the other hand, considering the effects of the flexible vibration of the manipulator arm and the elasticity of the cable on the robot's motion. To achieve this goal, the challenges that need to be addressed include controlling the flexible vibration of the cable and the arm.

[0004] Existing control methods for rope-driven space robots only consider the movement of the rigid arm in the unloaded state, without considering the impact of the flexible vibration of the large-span rope-driven robot arm and the elasticity of the rope on motion control, nor the interference between the end load and the movement of the large-span rope-driven robot. The existing rope-driven robot model is difficult to accurately describe when dealing with the load problem of the large-span flexible rope-driven robot arm, resulting in large tracking errors.

[0005] The existing invention patent application document with publication number CN117245670A is "A rope-driven space manipulator modeling and testing method and system". The existing method includes: making assumptions on the flexible link parameters on a global scale, and in the kinematic model of the rope-driven space manipulator system, calculating the coordinate transformation equations in the topological manipulator state space through coordinate transformation, vector operation and matrix processing to establish the kinematic equations. In the rope-driven system, integrated motors, reducers, winches and other devices drive the rope tension changes, which are mapped to the movement of the joint shafts of the manipulator to control the target object at the end of the manipulator; based on the kinematic model, the second-order Lagrange equation is used to derive the dynamic equations of the carrier position uncontrolled, attitude-controlled floating-based flexible joints, and flexible arm space robot system. However, the existing solution application document fails to control and compensate for the arm vibration phenomenon during the movement of the carrier position uncontrolled, attitude-controlled floating-based flexible joints, and flexible arm space robot system.

[0006] In summary, the existing rope-driven robot model has technical problems such as insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description, which leads to large tracking errors. Summary of the Invention

[0007] The technical problem to be solved by the present invention is: how to solve the technical problem in the existing rope-driven robot model, which is caused by insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description, resulting in large tracking errors.

[0008] The present invention solves the above technical problems by adopting the following technical solutions: A vibration suppression control method for a large-span rope-driven flexible manipulator comprises:

[0009] S1. For the flexible link in the flexible arm space robot system, the modeling process is simplified by using the assumed modal development to regard the flexible link as an Euler-Bernoulli beam;

[0010] S2. Construct kinematic equations to obtain a kinematic model of the rope-driven space manipulator system. Using this kinematic model, coordinate transformation equations in the manipulator state space are topologically derived through coordinate transformation, vector operations, and matrix calculations. In the rope-driven system, the driving rope tension change data is integrated and mapped to the motion of the manipulator's joint axes to control the motion of the manipulator's end target.

[0011] S3. Based on the kinematic model of the rope-driven space manipulator system, the second-kind Lagrange equation is used to derive the dynamic equation of the rope-driven space manipulator system to construct the dynamic model of the flexible-arm rope-driven space robot.

[0012] S4. Design a control method for a rope-driven space manipulator system, wherein the control law is designed based on the derivation of the dynamic equations of the rope-driven space manipulator system in accordance with the sliding mode equivalent control principle, and the joint angle tracking error, angular velocity tracking error, and angular acceleration tracking error of the rope-driven space manipulator system are obtained by processing. Based on this, the terminal sliding surface is designed according to the sliding mode control strategy, and the nonlinear control term is designed according to the flexibility influence.

[0013] This invention addresses vibration suppression control for a rope-driven robot's arm flexibility and rope elasticity. By addressing arm flexibility through a hypothetical modal approach, a mathematical model of the rope-driven robot, including rope-mapped joints, is proposed. Terminal sliding mode control is then used to simulate and verify the control of a large-span, flexible rope-driven robot under load. The proposed large-span, rope-driven, flexible-arm spatial manipulator model closely matches the actual model and boasts a simple structure and strong versatility. This invention achieves precise rigidity control of the large-span, rope-driven, flexible-arm spatial manipulator and ensures controllable flexible vibration.

[0014] In a more specific technical solution, S1 includes:

[0015] S11. According to the hypothetical modal method, the following truncated modal equation is used to describe the normal elastic displacement ω(x i ,t):

[0016]

[0017] Where, φ ij (x i ) is the j-th order mode function, δ ij (t) is the coordinate of the j-th order flexible vibration mode, n is the mode retention order, x i is the length from a certain point of the arm to the root;

[0018] S12. According to the following logic, the first two modal vibration modes are used to reflect the deformation of the flexible beam:

[0019] ω(x i ,t)=φ i1 (x i )δ i1 (t)+φ i2 (x i )δ i2 (t) (2)

[0020] S13. According to the following j-th order modal function, the robotic arm in the flexible link is simplified to a cantilever beam:

[0021] φ ij (x i )=[cos(c ij x i )-cosh(c ij x i )]+A ij [sin(c ij x i )-sinh(c ij x i )] (3)

[0022] Where,

[0023]

[0024] c ij is the equivalent characteristic frequency of the j-order modal function of the i-th arm, l i is the length of arm i;

[0025] S14. Use the following logic to express the equivalent bending stiffness matrix of the flexible arm:

[0026] K b =diag(k 11 ,k 12 ,k 21 ,k 22 ),

[0027] Among them, K b is the equivalent bending stiffness matrix of the flexible arm,

[0028] In a more specific technical solution, S2 includes:

[0029] S21. Use the following logic to determine the position vector of any point on each flexible arm relative to the origin O of the inertial coordinate system (O-XY), r δi (i=1, 2) is as follows:

[0030] r δ1 =x1e x1 -ω(x1,t)e y1 (4)

[0031] r δ2 =l1e x1 +2d1e s1 +x2e x2 -ω(x2,t)e y2 (5)

[0032] r p =l1e x1 +2d1e s1 +l2e x2 -ω(l2,t)e y2 (6)

[0033] Among them, r δ1 、r δ2 、r p are the center of mass vectors of arm 1, arm 2 and end load, e x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the joint direction of the robot arm; x1, x2 are the distances from any point of arm 1 and 2 to the end point of the arm, l1 is the length of arm 1, and d1 is the length of the sling;

[0034] S22. Determine the unit vector along the joint direction of the robotic arm using the following logic:

[0035] e x0 =e x1 =[cos(θ0) sin(θ0)] T

[0036] e x2 =[cos(θ0+θ1) sin(θ0+θ1)] T

[0037]

[0038] e y1 =[-sin(θ0) cos(θ0)] T

[0039] e y2 =[-sin(θ0+θ1) cos(θ0+θ1)] T

[0040] Among them, e x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the direction of the robot joint, r0=[x0 y0] T is the position vector of the carrier's center of mass, l0 is the distance from the carrier's center of mass to the arm connection, and l1 and l2 are the lengths of the arm.

[0041] S23, determining the center of mass position vector of the two-rod flexible arm joint;

[0042] S24. Use the following logic to express the distance relationship between the end of the spreader and the joint axis:

[0043]

[0044] S25. Determine the rope length from the contact end of the spreader rope to the contact point of the winch rope using the following logic:

[0045]

[0046] Among them, l 11 、l 12 、l 21 、l 22 They represent the lengths of the four ropes respectively, L1 and L2 are the lengths from the roots of arm 1 and arm 2 to the center of the winch, and θ1 is the angle between the spreader and the arm.

[0047] S26. According to formula (13), the relationship between the change in rope length and the differential of the angle θ is obtained as follows:

[0048] dl i1 =J ij dθ i (14).

[0049] The present invention designs a new rigid-flexible hybrid dynamics model and performs decoupling, which provides a basis for further realizing stable control of a large-span rope-driven flexible arm space manipulator.

[0050] Specifically, in response to the phenomenon that the existing technology fails to control and compensate for the arm vibration phenomenon during the movement of the carrier position uncontrolled, attitude controlled floating base flexible joint, and flexible arm space robot system, the present invention designs a sliding mode controller to control the position accuracy of the carrier position uncontrolled, attitude controlled floating base flexible joint, and flexible arm space robot system, and designs a nonlinear compensator to suppress the flexible vibration during the movement. This method has the advantages of simple structure, excellent vibration compensation effect, and fast fitting speed. This patent decouples the dynamic model into a fast-changing subsystem and a slow-changing subsystem, and decouples the flexible vibration part of the arm. Compared with traditional control methods, it can better suppress the vibration of the arm, reduce the impact of the arm vibration on the tracking error, and thus reduce the tracking error.

[0051] In a more specific technical solution, in S21, the center of mass position vector is determined using the following logic:

[0052] r s =r0+l0e x0 +l1e x1 +d1e s1 (7)

[0053] By taking the derivative of formula (7), we can get:

[0054]

[0055] In more specific technical solutions, S3 includes:

[0056] S31. Express the kinetic energy of the manipulator spreader, the total kinetic energy of the rope-driven space manipulator system, and the elastic potential energy of the flexible rod;

[0057] S32. For the rope-driven space manipulator system, obtaining transmission mode information from the motor to the winch pulling the rope to drive the manipulator arm;

[0058] S33. Using the following logic and the second-kind Lagrange equation, the dynamic equation of the rope-driven space manipulator system is derived:

[0059]

[0060] Among them, M rδ (θ rδ ) is an 8×8 positive definite symmetric matrix, representing the generalized mass matrix of the system, K is an 8th-order column vector including Coriolis force and centrifugal force. δrepresents the arm stiffness coefficient, K b =diag(k 11 ,k 12 ,k 21 ,k 22 ), Q represents generalized force, J θ is the motor current torque coefficient, i m Input current for each motor.

[0061] In a more specific technical solution, in S31, the following logic is used to express the kinetic energy of the robotic arm spreader:

[0062]

[0063] The total kinetic energy of the rope-driven space manipulator system is expressed using the following logic:

[0064]

[0065] The elastic potential energy of the flexible rod is expressed using the following logic:

[0066]

[0067] In a more specific technical solution, in S32, according to the given motor current control signal i m , motor torque constant K m , use the following logic to determine the winch output torque with radius r as τ M :

[0068] τ M =K m i m (18)

[0069] The following logic is used to express the mapping relationship between the current signal control of the two winch drive rope systems:

[0070]

[0071] Where i m =[i1 i2 i3 i4] is the armature current of each motor, and the motor drive current has a value range of i min ≤i n ≤i max ;

[0072] The following logic is used to determine the tension in the rope connected to the spreader in a rope-driven spatial manipulator system during the movement of a long-span rope-driven manipulator:

[0073] F=[F 11 F 12 F13 F 14 ] T

[0074] Using the principle of virtual work, we can deduce:

[0075]

[0076] Where δθ is the differential vector of each shaft angle change, and the differential vector of each rope length change is expressed as: δl=[δl 11 δl 12 δl 13 δl 14 ] T ;

[0077] According to the tension on the rope connected to the sling in the rope-driven space manipulator system, it is deduced that:

[0078] J θ F θ =[τ s ]+[τ θ ]=[J 11 F 11 +J 12 F 12 +J 13 F 13 +J 14 F 14 ] (twenty one)

[0079] Where, J θ ∈R n×2n The matrix is ​​expressed as follows:

[0080] J θ =[J 11 J 12 J 13 J 14 ] (twenty two)

[0081] Based on the law of energy conservation, the total stock of elastic potential energy loss on the rope drive is derived as:

[0082]

[0083] Where: is the tension on the rope connected to the sling in the rope-driven space manipulator system;

[0084] Combining equations (20) and (23), we can calculate the change of θ using the change of elastic potential energy per unit time. i Find the partial derivative:

[0085]

[0086] The following logic is used to determine the sum of the elastic potential energy of the rope-driven space manipulator system:

[0087] V=V δ +W s (25)

[0088] In a more specific technical solution, S4 includes:

[0089] S41. Based on the dynamic equation of the rope-driven space manipulator system, the following equation is rewritten:

[0090]

[0091] Among them, θ r represents the generalized coordinates of the rigid part of the system, θ δ is the generalized coordinate of the flexible part of the system, represents the generalized velocity of the rigid part of the system, represents the generalized velocity of the flexible part of the system, represents the generalized acceleration of the rigid part of the system, represents the generalized acceleration of the flexible part of the system, C a The coupling matrix of the Coriolis force and centrifugal force in the rigid part of the system, C δ The coupling matrix of the Coriolis force and centrifugal force in the flexible part of the system, C aδ and C δa The coupled matrix representing the Coriolis and centrifugal forces of the mixed flexible and rigid parts of the system;

[0092] Using the following logic, the dynamic rewriting equation of the first rope-driven space manipulator system is obtained:

[0093]

[0094] in, The coupled matrix representing the Coriolis force and centrifugal force of the rigid part of the system, It represents the interference term of the flexible vibration part on the rigid part in the system.

[0095] The dynamic equation of the first rope-driven space manipulator system is rewritten as:

[0096]

[0097] S42. Based on the sliding mode equivalent control principle, use the following logic to design the control law:

[0098]

[0099] Where i a represents the equivalent control term, i sw represents a nonlinear control term.

[0100] S43, using the following logic to determine the joint angle tracking error e, angular velocity tracking error and angular acceleration tracking error

[0101]

[0102] Among them, θ d is the desired joint angle, θ is the actual joint angle;

[0103] S44. Design the terminal sliding surface according to the sliding mode control strategy using the following logic:

[0104]

[0105] Among them, β, p, and q are all control parameters, satisfying β>0, p and q are both positive odd numbers and p>q>0;

[0106] Based on formula (32), the following formula can be obtained by taking the derivative of time t:

[0107]

[0108] S45. According to equations (33) and (29), without considering the influence of flexibility, the control law is expressed using the following logic:

[0109]

[0110] Among them, i a is the control current of the rigid part of the system, k1 and k2 are reaching law parameters, and both are greater than 0;

[0111] S46. Design nonlinear control items while considering the influence of flexibility.

[0112] Specifically, the sliding mode control method for the terminal of a large-span rope-driven flexible arm spatial manipulator designed in the present invention designs a control rate of the rigid part (Equation 34) and an adaptive compensation term of the flexible vibration part (Equation 35) compared with the prior art. The control rate of the rigid part ensures the motion accuracy of the manipulator system, and the control rate of the flexible vibration part reduces the impact of the vibration of the arm on the motion. Compared with the existing methods, the method designed in this application has the advantages of simple structure, excellent vibration compensation effect, and fast fitting speed. The patent decouples the dynamic model into a fast-changing subsystem and a slow-changing subsystem, and decouples the flexible vibration part of the arm. Compared with the traditional control method, it can better suppress the vibration of the arm, reduce the impact of the arm vibration on the tracking error, and thus reduce the tracking error.

[0113] In a more specific technical solution, in S46, the nonlinear control term is designed using the following logic:

[0114]

[0115] Among them, i sw Compensate current for the flexible part of the system, is the estimated value of the parameter D of the adaptive law in real time, where η is a positive number, representing the error coefficient, and γ is a constant, representing the adaptive factor.

[0116] In a more specific technical solution, the vibration suppression control system for a large-span rope-driven flexible manipulator includes:

[0117] The modeling simplification module is used to simplify the modeling process of the flexible link in the flexible arm space robot system by using the assumed modal development to treat the flexible link as an Euler-Bernoulli beam;

[0118] The kinematic model construction module is used to construct the kinematic equations and obtain the kinematic model of the rope-driven space manipulator system. The kinematic model of the rope-driven space manipulator system is used to topologically transform the coordinate transformation equation in the manipulator state space through coordinate transformation, vector operation and matrix calculation. In the rope-driven system, the driving rope tension change data is integrated to map to the motion of the joint axis of the manipulator, so as to control the motion of the end target of the manipulator and the connecting rod.

[0119] A dynamic model construction module is used to derive the dynamic equations of the rope-driven space manipulator system based on the kinematic model of the rope-driven space manipulator system and the second-kind Lagrange equation, so as to construct a dynamic model of the flexible-arm rope-driven space robot. The dynamic model construction module is connected to the kinematic model construction module;

[0120] The system control method design module is used to design the control method of the rope-driven space manipulator system. The control law is designed based on the dynamic equation of the rope-driven space manipulator system according to the sliding mode equivalent control principle. The joint angle tracking error, angular velocity tracking error and angular acceleration tracking error of the rope-driven space manipulator system are processed and the terminal sliding surface is designed according to the sliding mode control strategy. The nonlinear control item is designed according to the flexibility influence. The system control method design module is connected to the dynamic model construction module.

[0121] Compared with the prior art, the present invention has the following advantages:

[0122] This invention addresses vibration suppression control for a rope-driven robot's arm flexibility and rope elasticity. By addressing arm flexibility through a hypothetical modal approach, a mathematical model of the rope-driven robot, including rope-mapped joints, is proposed. Terminal sliding mode control is then used to simulate and verify the control of a large-span, flexible rope-driven robot under load. The proposed large-span, rope-driven, flexible-arm spatial manipulator model closely matches the actual model and boasts a simple structure and strong versatility. This invention achieves precise rigidity control of the large-span, rope-driven, flexible-arm spatial manipulator and ensures controllable flexible vibration.

[0123] The present invention designs a new rigid-flexible hybrid dynamics model and performs decoupling, which provides a basis for further realizing stable control of a large-span rope-driven flexible arm space manipulator.

[0124] The present invention solves the technical problem in existing rope-driven robot models that large tracking errors are caused by insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 Schematic diagram of the basic steps of the vibration suppression control method for a large-span rope-driven flexible manipulator according to Example 1 of the present invention;

[0126] Figure 2 This is a conceptual diagram of the application of a large-span rope-driven manipulator according to Example 1 of the present invention;

[0127] Figure 3 This is a schematic structural diagram of a large-span robotic arm model according to Example 1 of the present invention;

[0128] Figure 4 Schematic diagram of a simplified model of the flexible arm of Example 1 of the present invention;

[0129] Figure 5 This is a schematic structural diagram of a rope-driven flexible robotic arm according to Example 1 of the present invention;

[0130] Figure 6 Schematic diagram of a two-rod load structure according to embodiment 1 of the present invention;

[0131] Figure 7 This is a schematic diagram of the winch transmission of Example 1 of the present invention;

[0132] Figure 8 This is a joint angle simulation tracking trajectory diagram of Example 2 of the present invention;

[0133] Figure 9 This is a first-order modal simulation diagram of Example 2 of the present invention;

[0134] Figure 10 This is a second-order modal simulation diagram of Example 2 of the present invention;

[0135] Figure 11 This is a first motor current simulation diagram of Example 2 of the present invention;

[0136] Figure 12 This is a second motor current simulation diagram of Example 2 of the present invention. DETAILED DESCRIPTION

[0137] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0138] Example 1

[0139] like Figure 1 、 Figure 2 、 Figure 3 As shown, the vibration suppression control method for a large-span rope-driven flexible manipulator provided by the present invention includes the following basic steps:

[0140] S1. The modeling process of the flexible link in the free-floating flexible space robot is simplified by making assumptions;

[0141] like Figure 4 As shown, in this embodiment, in order to simplify the modeling process for the free-floating flexible space robot, an assumption operation is performed on the flexible link in a global scope, wherein the assumption operation includes but is not limited to:

[0142] Only the lateral deformation of the flexible link is considered, and the axial deformation, shear deformation and the influence of the infinitesimal moment of inertia of the flexible link are ignored.

[0143] Preset the lateral deformation to be small;

[0144] The length of the preset flexible link is much larger than its own cross-sectional size.

[0145] Therefore, the flexible link can be regarded as an Euler-Bernoulli beam.

[0146] like Figure 5 As shown in this embodiment, according to the assumed modal method, the normal elastic displacement ω(x i ,t) can be described by the following truncated modal equation:

[0147]

[0148] Among them, φ ij (xi ) is the j-th order mode function, δ ij (t) is the coordinate of the j-th flexible vibration mode, and n is the number of modes retained. Figure 5 , where l 11 、l 12 、l 21 、l 22 are the lengths of the four ropes, L1 and L2 represent the arm lengths, h1 represents the sling length, d1 represents the shaft length, and S 11 、S 12 、S 21 、S 22 Indicates the length from the end of the spreader to the end of the shaft, α 11 , α 12 , α 21 , α 22 represents the angle between the line connecting the end of the spreader to the end of the shaft and the shaft, θ1 is the joint angle, m p For the end load.

[0149] In this embodiment, since the deformation of the flexible beam is mainly reflected by the first two modal vibration modes, the value that can be taken in this embodiment is, for example, n=2, as shown in the following formula:

[0150] ω(x i ,t)=φ i1 (x i )δ i1 (t)+φ i2 (x i )δ i2 (t) (2)

[0151] If the robot arm is simplified as a cantilever beam, the j-th order modal function is as follows:

[0152] φ ij (x i )=[cos(c ij x i )-cosh(c ij x i )]+A ij [sin(c ij x i )-sinh(c ij x i )] (3)

[0153] in, c ij is the equivalent characteristic frequency of the j-order mode function of the i-th arm.

[0154] In this embodiment, the equivalent bending stiffness matrix of the flexible arm is as follows:

[0155]

[0156] S2. Construct kinematic equations to obtain the kinematic model of the rope-driven space manipulator system;

[0157] In this embodiment, the position vector r of any point on each flexible arm relative to the origin O of the inertial coordinate system (O-XY) is δi (i=1, 2) is as follows:

[0158] r δ1 =x1e x1 -ω(x1,t)e y1 (4)

[0159] r δ2 =l1e x1 +2d1e s1 +x2e x2 -ω(x2,t)e y2 (5)

[0160] r p =l1e x1 +2d1e s1 +l2e x2 -ω(l2,t)e y2 (6)

[0161] In this embodiment, the first section of the robotic arm is fixedly connected to the carrier, so:

[0162] e x0 =e x1 =[cos(θ0) sin(θ0)] T

[0163] e x2 =[cos(θ0+θ1) sin(θ0+θ1)] T

[0164]

[0165] e y1 =[-sin(θ0) cos(θ0)] T

[0166] e y2 =[-sin(θ0+θ1) cos(θ0+θ1)] T

[0167] The aforementioned e x0 、e x1 、e x2 、e s1 、e y1 、e y2is the unit vector along the direction of the robot joint, r0=[x0 y0] T is the position vector of the carrier's center of mass, l0 is the distance from the carrier's center of mass to the arm connection, and l1 and l2 are the lengths of the arm.

[0168] like Figure 6 As shown, in this embodiment, the center of mass vector of the two-bar flexible arm joint part is as follows:

[0169] r s =r0+l0e x0 +l1e x1 +d1e s1 (7)

[0170] Taking the derivative of the above formula, we can get:

[0171]

[0172] in:

[0173]

[0174]

[0175] In this embodiment, the kinematic model of the rope-driven spatial manipulator system uses coordinate transformation, vector operations, and matrix calculations to calculate the coordinate transformation equations in the topological manipulator state space. In the rope-driven system, integrated motors, reducers, winches, and other devices drive the rope tension changes, which are then mapped to the motion of the manipulator's joint shafts, achieving high-precision motion control of the target object at the end of the manipulator. The distance between the end of the spreader and the joint shaft is related to the following equation:

[0176]

[0177] In this embodiment, the rope length from the contact end of the spreader rope to the contact point of the winch rope is expressed as follows:

[0178]

[0179] The relationship between the change in rope length and the angle differential θ can be obtained by differentiating the above formula (13) with respect to time t as follows:

[0180] dl i1 =J ij dθ i (14)

[0181] Among them, the above formula (14) has the following equality relationship:

[0182]

[0183] S3. Derive the dynamic equations to construct the dynamic model of the flexible arm cable-driven space robot;

[0184] In this embodiment, based on the kinematic model of the floating-based flexible joint and flexible-arm space robot system analyzed in the previous section, the second-kind Lagrange equation is used to derive the dynamic equations of the floating-based flexible joint and flexible-arm space robot system with uncontrolled carrier position and controlled attitude.

[0185] The kinetic energy of the robotic arm spreader is:

[0186]

[0187] The total kinetic energy of the system is:

[0188]

[0189] The elastic potential energy of the flexible rod is expressed as:

[0190]

[0191] like Figure 7 As shown in this embodiment, the transmission mode of the large-span rope-driven space manipulator system is studied, in which the motor drives the winch to pull the rope to drive the manipulator arm. m , the motor torque constant is K m Under this condition, the motor output torque is τ M , which is expressed as follows

[0192] τ M =K m i m (18)

[0193] In this embodiment, see Figure 7 , the output torque of the winch with radius r is τ M , the mapping relationship between the current signal control of the two winch drive rope systems can be expressed as follows:

[0194]

[0195] Among them, i m =[i1 i2 i3 i4] is the armature current of each motor. Affected by the rope boundary conditions, the motor drive current has a value range of i min ≤i n ≤i max .

[0196] In this embodiment, when the large-span rope-driven manipulator completes its movement, the tension on the rope connected to the spreader in the system can be expressed as:

[0197] F=[F11 F 12 F 13 F 14 ] T

[0198] The change in rope length is:

[0199] Δl=Δl s +Δl θ

[0200] Where, Δl s is the elastic deformation of the rope, and the loss moment is τ s , Δl θ is the change in the rope when the joint changes, and the torque is τ θ The overall system can be deduced from the principle of virtual work as follows:

[0201]

[0202] The differential vector of each shaft angle change is expressed as: δθ, and the differential vector of each rope length change is expressed as: δl=[δl 11 δl 12 δl 13 δl 14 ] T .

[0203] In this embodiment, there is a rope tension F θ =[F 11 F 12 F 21 F 22 ] T ∈R 4×1 The matrix is ​​derived as follows based on formula (20):

[0204] J θ F θ =[τ s ]+[τ θ ]=[J 11 F 11 +J 12 F 12 +J 13 F 13 +J 14 F 14 ] (twenty one)

[0205] In the above formula (21), J θ ∈R n×2n The matrix is ​​expressed as follows:

[0206] J θ =[J 11 J 12J 13 J 14 ] (twenty two)

[0207] In this embodiment, the cross-sectional area of ​​the rope is represented as S, and the elastic modulus is represented as E. According to the law of conservation of energy, the total elastic potential energy loss on the rope drive can be expressed as follows:

[0208]

[0209] In this embodiment, combined with the above formula (9) and formula (12), the change of elastic potential energy per unit time is respectively i Taking partial derivatives we can get the following formula:

[0210]

[0211] Then the sum of the elastic potential energy of the large-span rope-driven manipulator system is:

[0212] V=V δ +W s (25)

[0213] In this embodiment, considering the microgravity environment of outer space, the large-span rope-driven manipulator system satisfies the kinetic energy theorem without external force, and the generalized coordinates of the system are taken as:

[0214] θ rδ =[x0 y0 θ0 θ1 δ 11 δ 12 δ 21 δ 22 ] T

[0215] The dynamic equations of the flexible-arm cable-driven space robot are derived from the second-kind Lagrange equation:

[0216]

[0217] Among them, M rδ (θ rδ ) is an 8×8 positive definite symmetric matrix, is an 8th-order column vector containing the Coriolis force and centrifugal force, where:

[0218]

[0219] K b =diag(k 11 ,k 12 ,k 21 ,k 22 )

[0220] Q represents generalized force.

[0221] S4. Design a control method for a flexible-arm rope-driven space robot;

[0222] Rewrite the kinetic equation to obtain the following formula:

[0223]

[0224] Then the system dynamics equation can be expressed as follows:

[0225]

[0226] in:

[0227] Can be rewritten as:

[0228]

[0229] According to the sliding mode equivalent control principle, the control law design form is:

[0230]

[0231] Among them, i a represents the equivalent control term, i sw represents a nonlinear control term.

[0232] In this embodiment, the tracking errors of each joint angle, angular velocity, and angular acceleration can be expressed as: e, It is expressed as follows:

[0233]

[0234] In this embodiment, a sliding mode control strategy is introduced, and the terminal sliding mode surface is designed to be expressed as follows:

[0235]

[0236] In this embodiment, the derivative of equation (32) with respect to time t yields:

[0237]

[0238] In order to keep the controller design stable and convergent, based on the above equations (33) and (29), without considering the influence of flexibility, the control law of the large-span space manipulator system can be expressed as follows:

[0239]

[0240] When considering the influence of flexibility, the nonlinear control term is designed:

[0241]

[0242] Example 2

[0243] like Figures 8 to 12 As shown, in this embodiment, S5, a terminal sliding mode control method is used to perform control simulation verification on a large-span flexible rope-driven robot under load, completing the stability proof;

[0244] In this embodiment, the Lyapunov function of the large-span space manipulator system is designed as follows:

[0245]

[0246] By taking the derivative of the time t using the following formula (37), we can obtain:

[0247]

[0248] And because k1>0, k2>0, Take appropriate parameter λ to satisfy:

[0249]

[0250] In summary, the present invention performs vibration suppression control on the flexibility of the rope-driven robot arm and the elasticity of the rope. The arm flexibility problem is handled by the assumed modal method, a mathematical model of the rope-driven robot including a rope-mapped joint is given, and the control simulation verification of the long-span flexible rope-driven robot under load is performed using the terminal sliding mode control method. The long-span rope-driven flexible arm spatial manipulator model provided by the present invention has a high degree of fit with the actual object and has the advantages of simple structure and strong versatility. The present invention achieves the accuracy of the rigidity control of the long-span rope-driven flexible arm spatial manipulator and ensures the controllability of flexible vibration.

[0251] The present invention designs a new rigid-flexible hybrid dynamics model and performs decoupling, which provides a basis for further realizing stable control of a large-span rope-driven flexible arm space manipulator.

[0252] The present invention solves the technical problem in existing rope-driven robot models that large tracking errors are caused by insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description.

[0253] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A vibration suppression control method for a large-span rope-driven flexible manipulator, characterized in that: The method comprises: S1. For the flexible link in the flexible arm space robot system, the assumed modal method is used to simplify the modeling process so that the flexible link can be regarded as an Euler-Bernoulli beam. S2. Constructing kinematic equations to obtain a kinematic model of the rope-driven space manipulator system. Using the kinematic model of the rope-driven space manipulator system, coordinate transformation equations in the topological manipulator state space are obtained through coordinate transformation, vector operations, and matrix calculations. In the rope-driven system, the driving rope tension change data is integrated to map to the motion of the rotation axes of each joint of the manipulator, thereby controlling the motion of the end target of the manipulator. S3. Based on the kinematic model of the rope-driven space manipulator system, the second-kind Lagrange equation is used to derive the dynamic equation of the rope-driven space manipulator system to construct a dynamic model of the flexible-arm rope-driven space robot; S4. Design a control method for the rope-driven space manipulator system, wherein a control law is designed based on the dynamic equations of the rope-driven space manipulator system and the sliding mode equivalent control principle, and the joint angle tracking errors, angular velocity tracking errors, and angular acceleration tracking errors of the rope-driven space manipulator system are obtained by processing. Based on these errors, a terminal sliding surface is designed according to the sliding mode control strategy, and a nonlinear control term is designed according to the flexibility influence.

2. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: Said S1 comprises: S11. According to the hypothetical modal method, the following truncated modal equation is used to describe the normal elastic displacement ω(x i ,t): Where, φ ij (x i ) is the j-th order mode function, δ ij (t) is the coordinate of the j-th order flexible vibration mode, n is the mode retention order, x i is the length from a certain point of the arm to the root; S12. According to the following logic, the first two modal vibration modes are used to reflect the deformation of the flexible beam: ω(x i ,t)=φ i1 (x i )d i1 (t)+φ i2 (x i )d i2 (t) (2) S13. Simplify the robotic arm in the flexible link into a cantilever beam according to the following j-th order modal function: φ ij (x i )=[cos(c ij x i )-cosh(c ij x i )]+A ij [sin(c ij x i )-sinh(c ij x i )] (3) Where, c ij is the equivalent characteristic frequency of the j-order modal function of the i-th arm, l i is the length of arm i; S14. Use the following logic to express the equivalent bending stiffness matrix of the flexible arm: K b =diag(k 11 ,k 12 ,k 21 ,k 22 ) Where K b is the equivalent bending stiffness matrix of the flexible arm, 3. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: The S2 includes: S22. Use the following logic to determine the position vector of any point on each flexible arm relative to the origin O of the inertial coordinate system (O-XY), r δi (i=1, 2) is as follows: r δ1 =r0+l0e x0 +x1e x1 -ω(x1,t)e y1 (4) r δ2 n0+l0e x0 +l1e x1 +2d1e s1 +x2e x2 -ω(x2,t)e y2 (5) r p =r0+l0e x0 +l1e x1 +2d1e s1 +l2e x2 -ω(l2,t)e y2 (6) Where r δ1 、r δ2 、r p are the center of mass vectors of arm 1, arm 2 and end load, e x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the direction of the robot arm joint; x1, x2 are the distances from any point of arm 1, 2 to the end point of the arm, l1 is the length of arm 1, d1 is the length of the sling, ω(x i ,t) is the normal elastic displacement of the flexible arm i; S23. Determine the unit vector along the joint direction of the robotic arm using the following logic: it is x0 =e x1 =[cos(θ0) sin(θ0)] T e x2 =[cos(θ0+θ1) sin(θ0+θ1)] T e y1 =[-sin(θ0) cos(θ0)] T e y2 =[-sin(θ0+θ1) cos(θ0+θ1)] T Where, e x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the direction of the robot joint, r0=[x0 y0] T is the position vector of the carrier's center of mass, l0 is the distance from the carrier's center of mass to the arm's connection, l1 and l2 are the lengths of the arm; S22, determining the center of mass position vector of the two-rod flexible arm joint; S23. Use the following logic to express the distance relationship between the end of the spreader and the joint axis: S24. Determine the rope length from the contact end of the spreader rope to the contact point of the winch rope using the following logic: Where, l 11 、l 12 、l 21 、l 22 They represent the lengths of the four ropes respectively, L1 and L2 are the lengths from the roots of arm 1 and arm 2 to the center of the winch, θ1 is the angle between the spreader and the arm, α 11 , α 12 , α 13 , α 14 Indicates the angle between the line connecting the end of the spreader to the end of the shaft and the shaft; S25. Derivative the time t according to the formula (13) to obtain the relationship between the change in rope length and the differential of the angle θ as follows: dl i1 =J ij dθ i (14)。 4. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 3 is characterized in that: In S22, the center of mass position vector is determined using the following logic: r s =r0+l0e x0 +l1e x1 +d1e s1 (7) By taking the derivative of formula (7), we can get:

5. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: The S3 includes: S31. Expressing the kinetic energy of the manipulator hoist, the total kinetic energy of the rope-driven spatial manipulator system, and the elastic potential energy of the flexible rod; S32. For the rope-driven space manipulator system, obtaining transmission mode information from the motor to the winch to pull the rope to drive the manipulator arm; S33. Using the following logic and the second-type Lagrange equation, derive the dynamic equation of the rope-driven space manipulator system: Where M rδ (θ rδ ) is an 8×8 positive definite symmetric matrix, representing the generalized mass matrix of the system, K is an 8th-order column vector including Coriolis force and centrifugal force. δ represents the arm stiffness coefficient, K b =diag(k 11 ,k 12 ,k 21 ,k 22 ), Q represents generalized force, J θ is the motor current torque coefficient, i m Input current for each motor.

6. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 5 is characterized in that: In S31, the following logic is used to express the kinetic energy of the robotic arm spreader: The total kinetic energy of the rope-driven space manipulator system is expressed using the following logic: The elastic potential energy of the flexible rod is expressed using the following logic: In the formula, ω(x i ,t) represents the normal elastic displacement of the flexible arm i.

7. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 5 is characterized in that: In the step S32, the motor current control signal i is given. m , motor torque constant K m , use the following logic to determine the winch output torque with radius r as τ M : t M =K m I m (18) The following logic is used to express the mapping relationship between the current signal control of the two winch drive rope systems: Where i m =[i1 i2 i3 i4] is the armature current of each motor, and the motor drive current has a value range of i min ≤i n ≤i max ; The following logic is used to determine the tension on the rope connected to the spreader in the rope-driven spatial manipulator system during the movement of the long-span rope-driven manipulator: F=[F 11 F 12 F 13 F 14 ] T Using the principle of virtual work, we can deduce: Where δθ is the differential vector of each shaft angle change, and the differential vector of each rope length change is expressed as: δl=[δl 11 δl 12 δl 13 δl 14 ] T ; According to the tension on the rope connected to the sling in the rope-driven space manipulator system, it is deduced that: J θ F θ =[τ s ]+[τ θ ]=[J 11 F 11 +J 12 F 12 +J 13 F 13 +J 14 F 14 ] (21) Where, J θ ∈R n×2n The matrix is ​​expressed as follows: I θ =[J 11 I 12 I 13 I 14 ] (22) Based on the law of energy conservation, the total stock of elastic potential energy loss on the rope drive is derived as: Where, the tension on the rope connected to the sling in the rope-driven space manipulator system, l 11 、l 12 、l 21 、l 22 are the lengths of the four ropes respectively; Combining the above formula (20) and the above formula (23), the change of elastic potential energy per unit time is used to calculate θ i Find the partial derivative: The following logic is used to determine the sum of the elastic potential energy of the rope-driven space manipulator system: V=V δ +W s (25)。 8. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: The S4 includes: S41. Rewrite the dynamic equation of the rope-driven space manipulator system to obtain the following equation: Where θ r represents the generalized coordinates of the rigid part of the system, θ δ is the generalized coordinate of the flexible part of the system, represents the generalized velocity of the rigid part of the system, represents the generalized velocity of the flexible part of the system, represents the generalized acceleration of the rigid part of the system, represents the generalized acceleration of the flexible part of the system, C a The coupling matrix of the Coriolis force and centrifugal force in the rigid part of the system, C δ The coupling matrix of the Coriolis force and centrifugal force in the flexible part of the system, C aδ and C δa The coupled matrix representing the Coriolis and centrifugal forces of the mixed flexible and rigid parts of the system; Using the following logic, the dynamic rewriting equation of the first rope-driven space manipulator system is obtained: Where, The coupled matrix representing the Coriolis force and centrifugal force of the rigid part of the system, Represents the interference term of the flexible vibration part on the rigid part of the system; The dynamic equation of the first rope-driven space manipulator system is rewritten as: S42. According to the sliding mode equivalent control principle, the control law is designed using the following logic: Where i a represents the equivalent control term, i sw represents a nonlinear control term; S43, using the following logic to determine the joint angle tracking error e, the angular velocity tracking error And the angular acceleration tracking error Where θ d is the desired joint angle, θ is the actual joint angle; S44. Design the terminal sliding surface according to the sliding mode control strategy using the following logic: Where β, p, and q are control parameters, satisfying β>0, p and q are both positive odd numbers, and p>q>0; Based on the above formula (32), the following formula can be obtained by taking the derivative of time t: S45. Based on the equation (33) and the equation (29), without considering the influence of the flexibility, the control law is expressed using the following logic: Where i a is the control current of the rigid part of the system, k1 and k2 are reaching law parameters, and both are greater than 0; S46. Design the nonlinear control item while taking the flexibility influence into consideration.

9. The vibration suppression control method for a large-span rope-driven flexible manipulator according to claim 8, characterized in that: In S46, the nonlinear control term is designed using the following logic: Where i sw Compensate current for the flexible part of the system, is the estimated value of the parameter D of the adaptive law in real time, where η is a positive number, representing the error coefficient, and γ is a constant, representing the adaptive factor.

10. A vibration suppression control system for a large-span rope-driven flexible manipulator, characterized in that: The system comprises: A modeling simplification module is used to simplify the modeling process of the flexible link in the flexible arm space robot system by using the assumed modal method to regard the flexible link as an Euler-Bernoulli beam; A kinematic model construction module is used to construct kinematic equations to obtain a kinematic model of a rope-driven space manipulator system. Using this kinematic model, coordinate transformation equations in the topological manipulator state space are generated through coordinate transformation, vector operations, and matrix calculations. In the rope-driven system, the driving rope tension change data is integrated and mapped to the motion of the rotation axes of each joint of the manipulator, thereby controlling the motion of the target object at the end of the manipulator. a dynamic model construction module, configured to derive the dynamic equations of the rope-driven space manipulator system based on the kinematic model of the rope-driven space manipulator system and using the second-kind Lagrange equation to construct a dynamic model of the flexible-arm rope-driven space robot, wherein the dynamic model construction module is connected to the kinematic model construction module; A system control method design module is used to design a control method for the rope-driven space manipulator system, wherein the control law is designed based on the dynamic equation of the rope-driven space manipulator system according to the sliding mode equivalent control principle, and the joint angle tracking error, angular velocity tracking error and angular acceleration tracking error of the rope-driven space manipulator system are obtained by processing. Based on this, the terminal sliding surface is designed according to the sliding mode control strategy, and the nonlinear control term is designed according to the flexibility influence. The system control method design module is connected to the dynamic model construction module.

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