Vibration suppression control method and system for large-span rope-driven flexible mechanical arm

Abstract

The invention provides a vibration suppression control method and system for a large-span rope-driven flexible mechanical arm, and the method comprises the steps: carrying out the vibration suppression control for the flexibility of an arm rod and the elasticity of a rope of a rope-driven robot, solving the problem of the flexibility of the arm rod through a hypothesis modal method, and giving a mathematical model of the rope-driven robot containing a rope mapping joint; and a terminal sliding mode control method is used for carrying out control simulation verification on the large-span flexible rope-driven robot under the on-load condition. The technical problem that in an existing rope-driven robot model, the tracking error is large due to the fact that the flexibility of an arm lever, the elasticity of a rope, the tail end load and motion interference are not fully considered and the load description is not accurate is solved.

Description

Technical Field

[0001] The 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 mechanical arm. Background Art

[0002] In recent years, with the development of robotics technology and the deepening of space exploration, space robots are increasingly used in the development of space resources. The rope-driven system has attracted extensive attention from workers in various fields due to its low mass, high load-to-weight ratio, good flexibility, and high safety performance in human-machine interaction. Rope-driven space robots are currently playing an increasingly important role in space activities and have become a hot topic in the current space on-orbit system. However, the introduction of rope-driven technology also brings new challenges and difficulties. The problems faced in the current research process include: the high complexity of dynamic parameters, the elasticity of ropes, and the flexible vibration of the arm.

[0003] To meet the high-precision control requirements of the robot, it is required to establish an accurate robot dynamics model on the one hand, and consider the influence of the flexible vibration of the robot arm and the elasticity of the rope on the robot movement on the other hand. In order to achieve this goal, the problems that need to be solved include: flexible vibration of the rope and flexible vibration control of 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 influence of the flexible vibration of the large-span rope-driven robot arm and the elasticity of the rope on the 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 "A rope-driven space manipulator modeling and testing method and system" with publication number CN117245670A, the existing method includes: making assumptions on the flexible link parameters in a global scope, 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 drive system, integrating motors, reducers, winches and other devices to drive the rope tension changes, mapped to the movement of the joint shafts of the manipulator, and controlling the target object at the end of the manipulator; according to the kinematic model, using the second-class Lagrange equation, deriving the dynamic equations of the carrier position uncontrolled, attitude controlled floating base 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 base flexible joints, and flexible arm space robot system.

[0006] In summary, the existing rope-driven robot model has technical problems such as large tracking error due to insufficient consideration of arm flexibility, rope elasticity, end load, motion disturbance, and inaccurate load description. Summary of the invention

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

[0008] The present invention adopts the following technical solutions to solve the above technical problems: A vibration suppression control method for a large-span rope-driven flexible mechanical arm includes:

[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 a Euler-Bernoulli beam;

[0010] S2. Construct kinematic equations to obtain the kinematic model of the rope-driven space manipulator system. Use the kinematic model of the rope-driven space manipulator system to obtain the coordinate transformation equation in the topological 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 rotation axis of each joint of the manipulator, so as to control the motion of the end target of the manipulator.

[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, so as 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 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 processed to obtain the terminal sliding surface according to the sliding mode control strategy, and the nonlinear control item is designed according to the flexibility influence.

[0013] The present invention performs vibration suppression control on the flexibility of the rope-driven robot arm and the elasticity of the rope, handles the arm flexibility problem by the assumed modal method, provides a mathematical model of the rope-driven robot including the rope mapping joint, and uses the terminal sliding mode control method to perform control simulation verification on the long-span flexible rope-driven robot under load. The long-span rope-driven flexible arm space manipulator model provided by the present invention has a high degree of fit with the real 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 space manipulator and ensures the controllability of flexible vibration.

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

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

[0016]

[0017] In the formula, φ ij (x i ) is the jth order mode function, δ ij (t) is the coordinate of the j-th flexible vibration mode, n is the reserved mode 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 mechanical 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] In the formula,

[0023]

[0024] c ij is the equivalent characteristic frequency of the j-order mode 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 =x 1 e x1 -ω(x 1 ,t)e y1 (4)

[0031] r δ2 = l 1 e x1 +2d 1 e s1 +x 2 e x2 -ω(x 2 ,t)e y2 (5)

[0032] r p = l 1 e x1 +2d 1 e s1 +l 2 e x2 -ω(l 2 ,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 and x2 are the distances from any point of arm 1 and 2 to the end point of the arm, respectively. 1 is the length of arm 1, d 1 is the length of the spreader;

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

[0035] e x0 =e x1 =[cos(θ 0 ) sin(θ 0 )] T

[0036] e x2 =[cos(θ 0 +θ 1 ) sin(θ 0 +θ 1 )] T

[0037]

[0038] e y1 =[-sin(θ 0 ) cos(θ 0 )] T

[0039] e y2 =[-sin(θ 0 +θ 1 ) cos(θ 0 +θ 1 )] 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, r 0 =[x 0 y 0 ] T is the position vector of the carrier mass center, l 0 is the distance from the carrier's center of mass to the arm's connection, l 1 and l 2 is the length of the arm.

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

[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 sling 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 Represents the length of the four ropes, L 1 , L 2 is the length from the root of arm 1 and arm 2 to the center of the winch, θ 1 It 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 novel 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 prior art fails to control and compensate for the vibration of the arm during the movement of the carrier position uncontrolled, attitude controlled floating base flexible joints, 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 joints, 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 influence of the arm vibration on the tracking error, and thus reduce the tracking error.

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

[0052] r s =r 0 +l 0 e x0 +l 1 e x1 +d 1 e 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 hanger, 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 to pull 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, is an 8th-order column vector including Coriolis force and centrifugal force, K 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.

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

[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 controlling the two winch drive rope systems:

[0070]

[0071] In the formula, i m =[i 1 i 2 i 3 i 4 ] 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 on the rope connected to the hanger in the rope-driven space manipulator system during the movement of the long-span rope-driven manipulator:

[0073] F=[F 11 F 12 F 13 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] In the formula, 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: 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 elastic potential energy per unit time by i Find partial derivatives:

[0085]

[0086] Then, 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)

[0089] In a more specific technical solution, S4 includes:

[0090] S41. Rewrite the dynamic equation of the rope-driven space manipulator system to obtain the following formula:

[0091]

[0092] 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 the 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 Cδa The coupled matrix representing the Coriolis and centrifugal forces of the mixed flexible and rigid parts of the system;

[0093] Using the following logic, the dynamics rewriting equation of the first rope-driven space manipulator system is obtained:

[0094]

[0095] 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 vibrating part on the rigid part of the system.

[0096] The dynamics equation of the first rope-driven space manipulator system is rewritten as:

[0097]

[0098] S42. According to the sliding mode equivalent control principle, use the following logic to design the control law:

[0099]

[0100] In the formula, i a represents the equivalent control term, i sw represents a nonlinear control term.

[0101] S43, using the following logic to determine the joint angle tracking error e, angular velocity tracking error And the angular acceleration tracking error

[0102]

[0103] Among them, θ d is the expected joint angle, θ is the actual joint angle;

[0104] S44. Design the terminal sliding surface according to the sliding mode control strategy using the following logic:

[0105]

[0106] 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;

[0107] Based on equation (32), the following equation can be obtained by taking the derivative of time t:

[0108]

[0109] S45. According to equation (33) and equation (29), without considering the influence of flexibility, the control law is expressed by the following logic:

[0110]

[0111] Among them, i a is the control current of the rigid part of the system, k 1 , k 2 are reaching law parameters, and are all greater than 0;

[0112] S46. Design nonlinear control items while considering the influence of flexibility.

[0113] Specifically, the terminal sliding mode control method of a large-span rope-driven flexible arm space manipulator designed in the present invention designs a control rate of the rigid part (Formula 34) and an adaptive compensation term of the flexible vibration part (Formula 35) compared with the prior art, wherein 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 influence of the vibration of the arm on the motion. Compared with the existing methods, the method designed in the present 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 influence of the arm vibration on the tracking error, and thus reduce the tracking error.

[0114] In a more specific technical solution, in S46, the nonlinear control item is designed using the following logic:

[0115]

[0116] Among them, i sw Compensate current for the flexible part of the system, is the estimated value of the real-time estimation parameter D of the adaptive law, where η is a positive number, representing the error coefficient, and γ is a constant, representing the adaptive factor.

[0117] In a more specific technical solution, the vibration suppression control system of the large-span rope-driven flexible manipulator includes:

[0118] 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;

[0119] The kinematic model building module is used to build 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 obtain the coordinate transformation equation in the topological 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 rotation axis of each joint of the manipulator, so as to control the motion of the end target of the manipulator and the connecting rod.

[0120] A dynamic model building module is used to derive the dynamic equation of the rope-driven space manipulator system based on the kinematic model of the rope-driven space manipulator system and use the second-class Lagrange equation to build a dynamic model of the flexible arm rope-driven space robot. The dynamic model building module is connected to the kinematic model building module;

[0121] The system control method design module is used to design the control method of 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 processed to obtain the terminal sliding surface according to the sliding mode control strategy, and the nonlinear control item is designed according to the flexibility influence. The system control method design module is connected with the dynamic model construction module.

[0122] Compared with the prior art, the present invention has the following advantages:

[0123] The present invention performs vibration suppression control on the flexibility of the rope-driven robot arm and the elasticity of the rope, handles the arm flexibility problem by the assumed modal method, provides a mathematical model of the rope-driven robot including the rope mapping joint, and uses the terminal sliding mode control method to perform control simulation verification on the long-span flexible rope-driven robot under load. The long-span rope-driven flexible arm space manipulator model provided by the present invention has a high degree of fit with the real 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 space manipulator and ensures the controllability of flexible vibration.

[0124] The present invention designs a novel 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.

[0125] The present invention solves the technical problem that in the existing rope-driven robot model, the tracking error is large due to insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 This is a 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;

[0127] Figure 2 This is a conceptual diagram of the application of a large-span rope-driven manipulator according to Embodiment 1 of the present invention;

[0128] Figure 3 This is a schematic diagram of the structure of a large-span mechanical arm model according to Embodiment 1 of the present invention;

[0129] Figure 4 This is a simplified model schematic diagram of the flexible arm of Example 1 of the present invention;

[0130] Figure 5 This is a schematic structural diagram of a rope-driven flexible mechanical arm according to Embodiment 1 of the present invention;

[0131] Figure 6 Schematic diagram of a two-rod load structure according to Embodiment 1 of the present invention;

[0132] Figure 7 This is a schematic diagram of the winch transmission of Example 1 of the present invention;

[0133] Figure 8 This is a joint angle simulation tracking trajectory diagram of Example 2 of the present invention;

[0134] Fig. 9 This is a first-order modal simulation diagram of Example 2 of the present invention;

[0135] Fig.10 This is a second-order modal simulation diagram of Example 2 of the present invention;

[0136] Fig.11 This is a first motor current simulation diagram of Embodiment 2 of the present invention;

[0137] Fig.12 This is a second motor current simulation diagram of Example 2 of the present invention. DETAILED DESCRIPTION

[0138] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0139] Example 1

[0140] like Figure 1 , Figure 2 , Figure 3 As shown, the vibration suppression control method of a large-span rope-driven flexible mechanical arm provided by the present invention includes the following basic steps:

[0141] S1. The modeling process of the flexible link in the free-floating flexible space robot is simplified by assumption;

[0142] like Figure 4 As shown, in this embodiment, in order to simplify the modeling process for the free-floating flexible space robot, the flexible link is assumed to be operated globally, wherein the assumption operation includes but is not limited to:

[0143] Only the lateral deformation of the aforementioned flexible link is considered, and the axial deformation, shear deformation and the influence of the micro-element moment of inertia of the flexible link are ignored;

[0144] Preset the lateral deformation to small deformation;

[0145] The length of the preset flexible link is much larger than its own cross-sectional dimension.

[0146] Therefore, the flexible link can be regarded as an Euler-Bernoulli beam.

[0147] like Figure 5 As shown in the example, according to the assumed modal method, the normal elastic displacement ω(x i ,t) can be described by the following truncated mode equation:

[0148]

[0149] Among them, φ ij (x i ) is the jth order mode function, δ ij (t) is the coordinate of the j-th flexible vibration mode, and n is the reserved mode order. Figure 5 , where l 11 , l 12 , l 21 , l 22 are the lengths of the four ropes, L 1 and L 2 Indicates the arm length, h 1 Indicates the length of the spreader, d 1 Indicates the shaft length, S 11 , S 12 , S 21 , S 22 Indicates the length from the end of the sling to the end of the shaft, α 11 , α 12 , α 21 , α 22 The angle between the end of the spreader and the end of the shaft and the shaft, θ 1 is the joint angle, m p The end load.

[0150] 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:

[0151] ω(x i ,t)=φ i1 (x i )δ i1 (t)+φ i2 (x i)δ i2 (t) (2)

[0152] If the robot arm is simplified as a cantilever beam, the j-th order modal function is as follows:

[0153] 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)

[0154] in, c ij is the equivalent characteristic frequency of the j-order mode function of the i-th arm.

[0155] In this embodiment, the equivalent bending stiffness matrix of the flexible arm is as follows:

[0156]

[0157] S2. Construct kinematic equations to obtain the kinematic model of the rope-driven space manipulator system;

[0158] 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:

[0159] r δ1 =x 1 e x1 -ω(x 1 ,t)e y1 (4)

[0160] r δ2 = l 1 e x1 +2d 1 e s1 +x 2 e x2 -ω(x 2 ,t)e y2 (5)

[0161] r p = l 1 e x1 +2d 1 e s1 +l 2 e x2-ω(l 2 ,t)e y2 (6)

[0162] In this embodiment, the first section of the robot arm is fixedly connected to the carrier, so:

[0163] e x0 =e x1 =[cos(θ 0 ) sin(θ 0 )] T

[0164] e x2 =[cos(θ 0 +θ 1 ) sin(θ 0 +θ 1 )] T

[0165]

[0166] e y1 =[-sin(θ 0 ) cos(θ 0 )] T

[0167] e y2 =[-sin(θ 0 +θ 1 ) cos(θ 0 +θ 1 )] T

[0168] The aforementioned x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the direction of the robot joint, r 0 =[x 0 y 0 ] T is the position vector of the carrier mass center, l 0 is the distance from the carrier's center of mass to the arm's connection, l 1 and l 2 is the length of the arm.

[0169] like Figure 6 As shown, in this embodiment, the center of mass vector of the two-bar flexible arm joint part is as follows:

[0170] r s =r 0 +l 0 e x0 +l1 e x1 +d 1 e s1 (7)

[0171] Taking the derivative of the above formula, we can get:

[0172]

[0173] in:

[0174]

[0175]

[0176] In this embodiment, in the kinematic model of the rope-driven space manipulator system, the coordinate transformation equations in the topological manipulator state space are calculated through coordinate transformation, vector operation and matrix calculation. In the rope-driven system, the integrated motor, reducer, winch and other devices drive the rope tension change and then map it to the movement of each joint shaft of the manipulator, so as to achieve high-precision motion control of the target object at the end of the manipulator. Among them, the distance between the end of the sling and the joint shaft is related to the following formula:

[0177]

[0178] In this embodiment, the rope length from the contact end of the sling rope to the contact point of the winch rope is expressed as follows:

[0179]

[0180] The above equation (13) is derived with respect to time t to obtain the relationship between the change in rope length and the angle differential θ as follows:

[0181] dl i1 =J ij dθ i (14)

[0182] Among them, the above formula (14) has the following equation relationship:

[0183]

[0184] S3, deriving the dynamic equations to construct the dynamic model of the flexible arm rope-driven space robot;

[0185] In this embodiment, according to the kinematic model of the floating-base 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-base flexible joint and flexible-arm space robot system with uncontrolled carrier position and controlled attitude.

[0186] The kinetic energy of the mechanical arm hanger is:

[0187]

[0188] The total kinetic energy of the system is:

[0189]

[0190] The elastic potential energy of the flexible rod is expressed as:

[0191]

[0192] like Figure 7 As shown, in this embodiment, the transmission mode of the large-span rope-driven space manipulator system from the motor to the winch to pull the rope to drive the manipulator arm is studied. m , the motor torque constant is K m Under this condition, the motor output torque is τ M , which is expressed as follows

[0193] τ M =K m i m (18)

[0194] 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 controlling the two winch drive rope systems can be expressed as follows:

[0195]

[0196] Among them, i m =[i 1 i 2 i 3 i 4 ] is the armature current of each motor. Affected by the rope boundary conditions, the motor drive current range is i min ≤i n ≤i max .

[0197] In this embodiment, when the large-span rope-driven manipulator completes the movement, the tension on the rope connected to the hoist in the system can be expressed as:

[0198] F=[F 11 F 12 F 13 F 14 ] T

[0199] The change in rope length is:

[0200] Δl=Δls +Δl θ

[0201] Among them, 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 virtual work principle as follows:

[0202]

[0203] 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 .

[0204] 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):

[0205] 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)

[0206] In the above formula (21), J θ ∈R n×2n The matrix is ​​expressed as follows:

[0207] J θ =[J 11 J 12 J 13 J 14 ] (twenty two)

[0208] In this embodiment, the cross-sectional area of ​​the rope is represented by S, and the elastic modulus is represented by E. According to the law of conservation of energy, the total stock of elastic potential energy loss on the rope drive can be deduced as follows:

[0209]

[0210] 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 get the following formula:

[0211]

[0212] Then the sum of the elastic potential energy of the large-span rope-driven manipulator system is:

[0213] V=V δ +W s (25)

[0214] 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:

[0215] θ rδ =[x 0 y 0 θ 0 θ 1 δ 11 δ 12 δ 21 δ 22 ] T

[0216] The dynamic equation of the flexible arm cable-driven space robot is derived from the second-kind Lagrangian equation:

[0217]

[0218] Among them, M rδ (θ rδ ) is an 8×8 positive definite symmetric matrix, is an 8th-order column vector including Coriolis force and centrifugal force, where:

[0219]

[0220] K b =diag(k 11 ,k 12 ,k 21 ,k 22 )

[0221] Q represents generalized force.

[0222] S4. Design a control method for a flexible arm rope-driven space robot;

[0223] Rewrite the kinetic equation to obtain the following formula:

[0224]

[0225] The system dynamics equation can be expressed as follows:

[0226]

[0227] in:

[0228] Can be rewritten as:

[0229]

[0230] According to the sliding mode equivalent control principle, the control law design form is:

[0231]

[0232] Among them, i a represents the equivalent control term, i sw represents a nonlinear control term.

[0233] 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:

[0234]

[0235] In this embodiment, a sliding mode control strategy is introduced, and the terminal sliding mode surface is designed to be expressed as follows:

[0236]

[0237] In this embodiment, the derivative of equation (32) with respect to time t can be obtained as follows:

[0238]

[0239] 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:

[0240]

[0241] When considering the influence of flexibility, the nonlinear control term is designed:

[0242]

[0243] Example 2

[0244] like Figures 8 to 12As 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, and stability proof is completed;

[0245] In this embodiment, the Lyapunov function of the large-span space manipulator system is designed as follows:

[0246]

[0247] By using the following formula (37) to derive the time t, we can obtain:

[0248]

[0249] Because k 1 >0,k 2 >0, Take appropriate parameter λ to satisfy:

[0250]

[0251] In summary, the present invention performs vibration suppression control on the flexibility of the rope-driven robot arm and the elasticity of the rope, handles the arm flexibility problem by the assumed modal method, provides a mathematical model of the rope-driven robot including the rope mapping joint, and uses the terminal sliding mode control method to perform control simulation verification on the large-span flexible rope-driven robot under load. The large-span rope-driven flexible arm space manipulator model provided by the present invention has a high degree of fit with the real object, and has the advantages of simple structure and strong versatility. The present invention achieves the accuracy of the rigidity control of the large-span rope-driven flexible arm space manipulator and ensures the controllability of flexible vibration.

[0252] The present invention designs a novel 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.

[0253] The present invention solves the technical problem that in the existing rope-driven robot model, the tracking error is large due to insufficient consideration of arm flexibility, rope elasticity, end load, motion interference, and inaccurate load description.

[0254] 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 the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. 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 embodiments of the present invention.

Claims

1. A vibration suppression control method and system 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 modeling process is simplified by using the assumed modal development to regard the flexible link as a Euler-Bernoulli beam; S2. Construct kinematic equations to obtain a kinematic model of a rope-driven space manipulator system. Use the kinematic model of the rope-driven space manipulator system to obtain a coordinate transformation equation in the state space of the topological manipulator 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 rotation axis of each joint of the manipulator, so as to control the motion of the end target of the manipulator. S3. According to 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, so as to construct the 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 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, and a terminal sliding surface is designed according to the sliding mode control strategy, and a nonlinear control item is designed according to the flexibility influence.

2. The vibration suppression control method and system of a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: The S1 includes: S11. According to the hypothetical modal method, the following truncated modal equation is used to describe the normal elastic displacement ω(x i ,t): In the formula, φ ij (x i ) is the jth order mode function, δ ij (t) is the coordinate of the j-th flexible vibration mode, n is the reserved mode 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. According to the following j-th order modal function, simplify the mechanical arm in the flexible link into a cantilever beam: 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) In the formula, c ij is the equivalent characteristic frequency of the j-order mode 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 ) In the formula, K b is the equivalent bending stiffness matrix of the flexible arm, 3. The vibration suppression control method and system of a large-span rope-driven flexible manipulator according to claim 1 is characterized in that: The S2 includes: S22, using the following logic, 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 +12e x2 -ω(l2,t)e y2 (6) In the formula, 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; S23. Determine the unit vector along the joint direction of the robot 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 In the formula, e x0 、e x1 、e x2 、e s1 、e y1 、e y2 is the unit vector along the joint direction of the robot arm, 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. S22, determining the center of mass position vector of the two-rod flexible arm joint part; 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 sling rope to the contact point of the winch rope using the following logic: In the formula, l 11 , l 12 , l 21 , l 22 Represent the lengths of the four ropes, L1 and L2 are the lengths from the roots of boom 1 and boom 2 to the center of the winch, and θ1 is the angle between the spreader and the boom; S25. Deriving the time t according to the formula (13), the relationship between the change in rope length and the differential of the angle θ is obtained as follows: dl i1 =J ij dθ i (14)。 4. The vibration suppression control method and system of a large-span rope-driven flexible manipulator according to claim 3 is characterized in that: In S22, the centroid position vector is determined using the following logic: r s =r0+l0e x0 +l1e x1 +d1e s1 (7) By taking the derivative of equation (7), we can get:

5. The vibration suppression control method and system of 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 hanger, the total kinetic energy of the rope-driven space 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 of 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, is an 8th-order column vector including Coriolis force and centrifugal force, K 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 and system of 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 hanger: 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:

7. The vibration suppression control method and system of a large-span rope-driven flexible manipulator according to claim 5 is characterized in that: 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 : t M =K m I m (18) The following logic is used to express the mapping relationship between the current signal controlling the two winch drive rope systems: In the formula, i m =[i1 i2 i3 i4] is the armature current of each motor, and the motor drive current range is i min ≤i n ≤i max ; The following logic is used to determine the tension on the rope connected to the hanger in the rope-driven space robot system during the movement of the long-span rope-driven robot: 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) In the formula, 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: Wherein: the tension on the rope connected to the sling in the rope-driven space manipulator system; Combining the above formula (20) and the above formula (23), the change of elastic potential energy per unit time is respectively expressed as i Find the partial derivative: Then 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 and system of 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: In the formula, 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 the 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 dynamics rewriting equation of the first rope-driven space manipulator system is obtained: In the formula, The coupled matrix representing the Coriolis force and centrifugal force in the rigid part of the system, It represents the interference term of the flexible vibrating part on the rigid part of the system. The dynamics 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: In the formula, 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 In the formula, θ d is the expected joint angle, θ is the actual joint angle; S44, using the following logic, designing the terminal sliding surface according to the sliding mode control strategy: 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. According to the formula (33) and the formula (29), without considering the influence of the flexibility, the control law is expressed using the following logic: In the formula, 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 and system of a large-span rope-driven flexible manipulator according to claim 8 is characterized in that: In S46, the nonlinear control term is designed using the following logic: In the formula, i sw Compensate current for the flexible part of the system, is the estimated value of the real-time estimation parameter D of the adaptive law, 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: 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; A kinematic model building module is used to build kinematic equations to obtain a kinematic model of a rope-driven space manipulator system. The kinematic model of the rope-driven space manipulator system is used to obtain a coordinate transformation equation in a topological 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 rotation axis of each joint of the manipulator, so as to control the motion of the end target of the manipulator, and the connecting rod; A dynamic model building module is used to derive the dynamic equation of the rope-driven space manipulator system based on the kinematic model of the rope-driven space manipulator system and use the second-kind Lagrange equation to build a dynamic model of the flexible arm rope-driven space robot, and the dynamic model building module is connected to the kinematic model building 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 processed to obtain the terminal sliding surface according to the sliding mode control strategy, and 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.

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