A terminal control method for modular rope-driven flexible manipulator

Abstract

The present application provides a method for controlling the end of a modular rope-driven flexible manipulator, and relates to the field of mechanical control technology. A method for controlling the end of a modular rope-driven flexible manipulator comprises: constructing a first data-driven model to establish a mapping relationship between variables of the joint space of the manipulator and the task space; based on the first data-driven model, setting the end posture controller of the manipulator and obtaining the expected joint angular velocity of the joint space; constructing a second data-driven model to establish a mapping relationship between variables of the driving space of the manipulator and the joint space; based on the second data-driven model, setting the joint angle controller of the manipulator and obtaining the joint driving torque of the manipulator according to the expected joint angular velocity; and controlling the end of the manipulator through the joint driving torque. According to an embodiment of the present application, accurate and robust trajectory tracking control of the end of the flexible manipulator can be achieved.

Description

Technical Field

[0001] The present application relates to the field of mechanical control technology, and in particular to an end control method of a modular rope-driven flexible robotic arm. Background Art

[0002] The rope-driven flexible manipulator is a new type of manipulator system that uses ropes for remote drive. It has the advantages of large aspect ratio, light weight and high redundant degrees of freedom. This design gives the rope-driven flexible manipulator a unique advantage in small and unstructured environments, while ensuring the safety of its interaction with equipment and personnel. Compared with traditional manipulators, the rope-driven flexible manipulator shows higher flexibility and adaptability when performing delicate tasks, effectively solving the shortcomings of traditional manipulators in terms of volume, inertia and buffering and shock absorption performance.

[0003] The end control of a manipulator refers to the precise adjustment of the end position and posture of the manipulator according to the predetermined desired target by applying torque to each joint of the manipulator, which is crucial for the execution of manipulator tasks. However, due to factors such as elastic deformation of the rope, friction, unknown loads and uncertainty of the external environment, the end control of a rope-driven flexible manipulator faces the challenges of high precision and strong robustness.

[0004] At present, the control research of rope-driven flexible manipulators is mainly divided into two categories: model-based and model-free control schemes. The model-based control scheme relies on the accurate modeling of the rope-driven flexible manipulator, including kinematic and dynamic models. However, the computational cost of the Jacobian matrix in this method is high, which is difficult to meet the requirements of real-time control. Moreover, in a complex and changing external environment, it is very difficult to accurately identify the model parameters. In addition, the rope-driven flexible manipulator faces problems such as elastic deformation of the rope, nonlinear friction, hysteresis, and unknown loads, which make it particularly difficult to establish an accurate model.

[0005] The model-free control scheme does not rely on an accurate mechanism model, but instead compensates for the uncertainty and nonlinearity of the rope-driven flexible manipulator through offline learning or online state estimation. However, the offline learning method requires re-collecting data for training when the scene changes, and has poor transferability and environmental adaptability. Moreover, the algorithm has high computational complexity and is difficult to guarantee real-time performance. In addition, there may be risks of convergence to local optimality, difficulty in adjusting parameters, and difficulty in proving system stability.

[0006] The main difficulties faced in the current field of rope-driven flexible manipulator control can be summarized as follows:

[0007] (1) It is difficult to establish an accurate mechanism model: Due to the nonlinear elastic deformation, complex friction characteristics, hysteresis behavior of the rope, and the flexibility of the rope-driven manipulator itself, the construction of the kinematic and dynamic mechanism models and the accurate identification of the model parameters are extremely challenging, making it difficult for traditional control methods to achieve precise motion control.

[0008] (2) Model complexity increases the difficulty of controller design: Factors such as rope deformation, tension change, and friction make the rope-driven flexible manipulator exhibit highly coupled, nonlinear, and uncertain dynamic characteristics. This complex motion characteristic increases the difficulty of controller design based on the mechanism model.

[0009] (3) Parameter perturbation, external interference and system vibration: The parameter perturbation of the rope-driven flexible manipulator itself, the uncertain external interference in the environment and the vibration problem of the system itself will all affect the control performance of the end of the manipulator. The control accuracy will be further reduced, which puts higher requirements on the robustness of the control strategy.

[0010] (4) High computational cost and difficulty in ensuring real-time control: Model-based control strategies, whether they rely on precise and complex dynamic models or control algorithms based on the inversion of the Jacobian matrix of a super-redundant manipulator, usually have high computational complexity and are difficult to meet the requirements of real-time control. In addition, some model-free control methods may also face high computational costs during implementation, affecting their real-time control capabilities. Therefore, how to reduce the amount of computation and ensure the real-time performance of the control strategy remains a challenge to be solved.

[0011] Therefore, how to develop a high-precision modular rope-driven flexible robotic arm end control strategy that is independent of the precise mechanism model, ensures robustness in time-varying environments and unknown external disturbances, and meets the requirements of low computing cost and real-time performance has become an important issue that needs to be solved urgently. Summary of the invention

[0012] According to one aspect of the present application, a method for controlling the end of a modular rope-driven flexible robotic arm is provided, comprising: constructing a first data-driven model to establish a mapping relationship between variables of the joint space of the robotic arm and the task space; based on the first data-driven model, setting the end posture controller of the robotic arm and obtaining the desired joint angular velocity of the joint space; constructing a second data-driven model to establish a mapping relationship between variables of the driving space of the robotic arm and the joint space; based on the second data-driven model, setting the joint angle controller of the robotic arm and obtaining the joint driving torque of the robotic arm according to the desired joint angular velocity; and performing end control of the robotic arm through the joint driving torque.

[0013] According to some embodiments, a first data-driven model is constructed to establish a mapping relationship between variables from the joint space of the robotic arm to the task space, including: constructing a kinematic mechanism model from the joint space to the task space; transforming the kinematic mechanism model to obtain the first data-driven model; and updating the first data-driven model in real time.

[0014] According to some embodiments, the first data-driven model is updated in real time, including: setting a first estimation criterion function; obtaining a first pseudo-Jacobian matrix item corresponding to the first data-driven model and calculating a real-time estimation value of the first pseudo-Jacobian matrix item according to the first estimation criterion function; and updating the first data-driven model in real time according to the real-time estimation value of the first pseudo-Jacobian matrix item.

[0015] According to some embodiments, real-time updating of the first data-driven model also includes: setting a first state-space expression of the robotic arm based on the first pseudo-Jacobian matrix term and the first total disturbance term corresponding to the first data-driven model; obtaining a first variable structure expanded state observation expression through the first state-space expression; and obtaining a real-time estimated value of the first total disturbance term based on the first variable structure expanded state observation expression to update the first data-driven model in real time.

[0016] According to some embodiments, based on a first data-driven model, an end posture controller of a robotic arm is set and the expected joint angular velocity in the joint space is obtained, including: setting a first control input criterion function; transforming the first control input criterion function according to a first pseudo-Jacobian matrix item and a first total disturbance item corresponding to the first data-driven model, and completing an optimization solution to obtain an expression corresponding to the end posture controller; and calculating the expected joint angular velocity through the expression corresponding to the end posture controller.

[0017] According to some embodiments, a second data-driven model is constructed to establish a mapping relationship between variables from the drive space to the joint space of the robotic arm, including: constructing a dynamic mechanism model from the drive space to the joint space; transforming the dynamic mechanism model to obtain a second data-driven model; and updating the second data-driven model in real time.

[0018] According to some embodiments, the second data-driven model is updated in real time, including: setting a second estimation criterion function; obtaining the second pseudo-Jacobian matrix item corresponding to the second data-driven model and calculating the real-time estimation value of the second pseudo-Jacobian matrix item according to the second estimation criterion function; and updating the second data-driven model in real time according to the real-time estimation value of the second pseudo-Jacobian matrix item.

[0019] According to some embodiments, real-time updating of the second data-driven model also includes: setting a second state space expression of the robotic arm based on the second pseudo-Jacobian matrix term and the second total disturbance term corresponding to the second data-driven model; obtaining a second variable structure expanded state observation expression through the second state space expression; and obtaining a real-time estimated value of the second total disturbance term based on the second variable structure expanded state observation expression to update the second data-driven model in real time.

[0020] According to some embodiments, based on a second data-driven model, a joint angle controller of the robotic arm is set and the joint driving torque of the robotic arm is obtained according to the expected joint angular velocity, including: setting a second control input criterion function; transforming the second control input criterion function according to the second pseudo-Jacobian matrix item and the second total disturbance item corresponding to the second data-driven model, and completing the optimization solution to obtain an expression corresponding to the joint angle controller; calculating the joint driving torque according to the expected joint angular velocity through the expression corresponding to the joint angle controller.

[0021] According to one aspect of the present application, there is provided a modular rope-driven flexible robotic arm, comprising: a base; a movable mechanism, comprising a plurality of modular arm segments, the plurality of modular arm segments being connected end to end in sequence, and the head end of a modular arm segment at the head end among the plurality of modular arm segments being connected to the base; and an end effector, connected to the tail end of a modular arm segment at the tail end among the plurality of modular arm segments.

[0022] According to some embodiments, each modular arm segment includes a rigid arm, a joint, a rope-linked transmission, and a drive control.

[0023] According to the embodiments of the present application, only the real-time input and output data of the system is relied on, and there is no need to build a complex mechanism model, thereby reducing the difficulty and complexity of model establishment. Through the online real-time construction of the dynamic data-driven model, it is possible to maintain robustness under time-varying environments and unknown external disturbances, effectively respond to parameter perturbations and external interference, and enhance the system's adaptability to various uncertainties. In addition, while ensuring high-precision control, it ensures low computing costs and real-time requirements, providing an efficient and reliable solution for the motion control of modular rope-driven flexible manipulators.

[0024] It should be understood that the foregoing general description and the following detailed description are exemplary only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application.

[0026] Figure 1A schematic diagram of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application is shown.

[0027] Figure 2 A schematic diagram showing modular arm segments of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application.

[0028] Figure 3 A flow chart of a method for controlling an end of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application is shown.

[0029] Figure 4 A block diagram showing the architecture of the end control of a modular rope-driven flexible robot arm according to an exemplary embodiment of the present application.

[0030] Figure 5 A schematic diagram showing a reference trajectory and a trajectory tracking curve of the end position of a modular rope-driven flexible manipulator according to an exemplary embodiment of the present application.

[0031] Figure 6 A schematic diagram of a trajectory tracking error curve showing the end position of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application.

[0032] Figure 7 A schematic diagram showing a reference trajectory and a trajectory tracking curve of the end posture of a modular rope-driven flexible manipulator according to an exemplary embodiment of the present application.

[0033] Figure 8 A schematic diagram of a trajectory tracking error curve showing the end posture of a modular rope-driven flexible manipulator according to an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0034] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this application will be comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The same reference numerals in the figures represent the same or similar parts, and thus their repeated description will be omitted.

[0035] The described features, structures or characteristics may be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present application. However, those skilled in the art will appreciate that the technical scheme of the present application may be put into practice without one or more of these specific details, or other modes, components, materials, devices or operations may be adopted. In these cases, known structures, methods, devices, realizations, materials or operations will not be shown or described in detail.

[0036] The flowcharts shown in the accompanying drawings are only exemplary and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps can be decomposed, and some operations / steps can be combined or partially combined, so the actual execution order may change according to actual conditions.

[0037] The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0038] The present application provides an end control method of a modular rope-driven flexible robotic arm, which can achieve high-precision control of the modular rope-driven flexible robotic arm system.

[0039] A method for controlling the end of a modular rope-driven flexible robotic arm according to an embodiment of the present application will be described in detail below with reference to the accompanying drawings.

[0040] Figure 1 A schematic diagram of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application is shown.

[0041] Figure 2 A schematic diagram showing a modular arm segment according to an exemplary embodiment of the present application.

[0042] like Figure 1 As shown, the modular cable-driven flexible robotic arm includes a base 100 , a movable mechanism 200 and an end effector 300 .

[0043] The movable mechanism 200 adopts a segmented linkage design without a driving rope, which includes a plurality of modular arm segments. Figure 1 As shown, the plurality of modular arm segments include modular arm segment 210 , modular arm segment 220 , and modular arm segment 230 .

[0044] The multiple modular arm segments are connected head to tail in sequence. Among them, the head end of a modular arm segment at the head end of the multiple modular arm segments is connected to the base 100, and the tail end of a modular arm segment at the tail end of the multiple modular arm segments is connected to the end effector 300.

[0045] For example, Figure 1As shown, the modular arm segment 210 , the modular arm segment 220 and the modular arm segment 230 are connected end to end in sequence. The head end of the modular arm segment 210 is connected to the base 100 , and the tail end of the modular arm segment 230 is connected to the end effector 300 .

[0046] like Figure 2 As shown, one of the modular arm segments 210 of the movable mechanism 200 includes a rigid arm rod 211 , a joint 212 , a rope-linked transmission device 213 and a drive control device 214 .

[0047] According to some embodiments, the movable mechanism 200 further includes a driving motor 215 .

[0048] The drive control device 214 receives the calculated joint drive torque and drives the rigid arm 211 around the cross axis ( Figure 2 The movable mechanism 200 and the end effector 300 are rotated (not shown) and the motion is transmitted to other joints 212 and the rigid arm 211 through a rope-linked transmission device, thereby realizing the motion of the movable mechanism 200 and the end effector 300 to control the motion trajectory of the end effector 300.

[0049] According to the embodiment of the present application, the modular arm segment 210 has two degrees of freedom: yaw and pitch. The uniformly distributed rigid arm rods 211 inside the modular arm segment 210 achieve synchronous movement through the rope-linked transmission device 213, thereby ensuring that the movement angles of the linked joints 212 remain consistent, and the modular arm segment 210 achieves an effect of equal curvature bending.

[0050] Figure 3 A flow chart of a method for controlling an end of a modular rope-driven flexible robotic arm according to an exemplary embodiment of the present application is shown.

[0051] The technical solution of this application adopts a cascade control architecture, and its control block diagram is as follows: Figure 4 shown.

[0052] The control architecture of the present application includes two control closed loops, namely, a control loop from joint space to task space and a control loop from drive space to joint space. The control loop from joint space to task space provides the desired trajectory of joint angular velocity for the control loop from drive space to joint space.

[0053] like Figure 4 As shown, the control loop design from joint space to task space includes:

[0054] Firstly, the kinematic mechanism model from joint space to task space is transformed to obtain the first data-driven model from joint space to task space of modular rope-driven flexible manipulator.

[0055] Then, based on the improved projection algorithm, the estimated first pseudo-Jacobian matrix item is obtained in real time At the same time, a variable structure extended state observer is designed to calculate the estimated value of the first total disturbance term in real time .

[0056] Based on historical input and output data ( and ), and update the first data-driven model in real time during each sampling period.

[0057] Then, based on the improved model-free adaptive control algorithm, the terminal posture controller is designed to obtain the terminal real-time posture and angular velocity and linear velocity measurement data ( and ), completing the closed-loop feedback, achieving real-time tracking control of the desired position and posture of the end of the robot arm, and obtaining the desired joint angular velocity in the robot arm joint space ( ), which is used to design controllers from drive space to joint space.

[0058] like Figure 4 As shown, the control loop design from the drive space to the joint space includes:

[0059] Firstly, the dynamic mechanism model from the driving space to the joint space is transformed to obtain the second data-driven model from the driving space to the joint space of the modular rope-driven flexible manipulator.

[0060] Furthermore, based on the improved projection algorithm, the second pseudo-Jacobian matrix term is estimated in real time At the same time, a variable structure extended state observer is designed to calculate the estimated value of the second total disturbance term in real time .

[0061] Based on historical input and output data (τ and ), and update the second data-driven model in real time during each sampling period.

[0062] Then, based on the improved model-free adaptive control algorithm, the joint angle controller is designed to obtain the real-time joint angular velocity measurement data of the robot arm ( ), completes the closed-loop feedback, realizes the real-time tracking control of the angular velocity of the robot arm joint space, and obtains the joint driving torque τ to input into the robot arm, thus completing the entire control loop.

[0063] In order to simplify the model and improve calculation efficiency, the technical solution of the present application ignores factors such as rope deformation, friction, and slippage in the rope-driven flexible robotic arm (hereinafter referred to as the robotic arm), and assumes that the angles of the linkage joints in each modular arm segment of the robotic arm are completely equal, that is, the state of a modular arm segment is determined by only two joint angles.

[0064] Based on this assumption, the technical solution of the present application only uses the two joint angular velocities close to the root of each modular arm segment of the robotic arm as input variables when constructing the model, and designs a total disturbance term to compensate for the model error caused by this assumption in real time, so as to reduce the calculation complexity and improve the real-time and response speed of the robotic arm system.

[0065] Furthermore, based on Figure 1 The rope-driven flexible robotic arm (hereinafter referred to as the robotic arm) shown in the figure, the variables in the technical solution of this application are defined as follows:

[0066] Indicates i Segment The yaw angle of the joint near the root of the modular arm segment, Indicates i The pitch angle of the joint near the root of the segment modular arm. i =1,2,3. The joint angle vector of the robot arm is defined as , Represents the joint angular velocity, and the end pose vector of the robot arm in the Cartesian coordinate system is defined as , Indicates the end pose velocity of the robot arm.

[0067] like Figure 3 As shown, in step S100, a first data-driven model is constructed to establish a mapping relationship between variables of the joint space of the robot arm and the task space.

[0068] For example, in step S100, a first data-driven model is constructed through a kinematic mechanism model from the joint space to the task space of the robot arm to achieve an accurate estimation of the mapping relationship of variables from the joint space to the task space.

[0069] First, a kinematic mechanism model of the velocity layer from the joint space to the task space of the robot is constructed, which can be expressed by the following formula.

[0070] , (1)

[0071] in, Represents the velocity level Jacobian matrix of the robot arm. It is a partial derivative matrix whose elements are closely related to the geometric relationship between the various parts of the robot arm and are about the joint angles of the robot arm. During the movement of the robot, the Jacobian matrix will continue to change with the movement of each component. No. i Line j The elements of a column are represented as:

[0072] , (2)

[0073] in, The position of the end of the robot arm i coordinates, Indicates the first j joint angles.

[0074] According to some embodiments, the robot arm may experience elastic deformation, friction, slippage, etc. of the rope, and the linkage joints in the modular arm segments of the robot arm cannot actually change completely at equal angles. Therefore, the possible errors in the kinematic mechanism model are modified and can be expressed by the following formula.

[0075] , (3)

[0076] in, Represents the error term of the kinematic mechanism model.

[0077] Furthermore, the kinematic mechanism model including the error term is discretized to obtain a first data-driven model. The first data-driven model can be expressed by the following formula.

[0078] , (4)

[0079] in, k Indicates k Sampling period, , represents the first pseudo-Jacobian matrix term of the manipulator system, , represents the error term including the kinematic mechanism model and the first total disturbance term of the robotic arm system due to parameter estimation error.

[0080] According to some embodiments, the first data-driven model may be updated in real time by acquiring real-time estimated values ​​of the first pseudo-Jacobian matrix term and the first total disturbance term in the first data-driven model.

[0081] First, a first estimation criterion function is set to reduce the error between the actual output and the estimated output of the manipulator system and increase the robustness of the estimation algorithm. The first estimation criterion function can be expressed by the following formula.

[0082] , (5)

[0083] in, μ >0 is a weight factor, which is used to suppress drastic changes in parameter estimates. express k -1 moment The first pseudo-Jacobian matrix of .

[0084] Furthermore, the first estimation criterion function After transformation, we get the following formula.

[0085] , (6)

[0086] According to the obtained formula (6), the first estimation criterion function is minimized by a preset algorithm to obtain the following formula.

[0087] , (7)

[0088] in, express k time The first pseudo-Jacobian matrix of Represents the identity matrix.

[0089] According to some embodiments, the preset algorithm may adopt an improved projection algorithm.

[0090] By further simplifying formula (7), the calculation formula for the first pseudo-Jacobian matrix item corresponding to the first data-driven model can be obtained as follows.

[0091] , (8)

[0092] in, η (0,2] is the step size factor. μ >0 is a weight factor, which is used to suppress drastic changes in parameter estimates. is the first total disturbance term Real-time estimates of .

[0093] According to some embodiments, a reset mechanism for the first pseudo-Jacobian matrix item may be set to reset the estimated value of the first pseudo-Jacobian matrix item to the initial value, thereby reducing the performance degradation caused by the accumulation of estimation errors and enhancing the tracking capability of time-varying parameters to ensure the stability and reliability of the control performance during the operation of the manipulator system. For example,

[0094] ,if or ,

[0095] ,if , i ≠ j , i , j =1,2,3,4,5,6.

[0096] in, yes The initial value of yes The initial value of represents the first pseudo-Jacobian matrix term The diagonal elements of represents the first pseudo-Jacobian matrix term The off-diagonal elements of . α , b 1, b 2 are design parameters, used to limit range, satisfying α ≥1, b 2>2 b 1(2 α +1).

[0097] According to formula (8), the real-time estimated value of the first pseudo-Jacobian matrix item corresponding to the first data-driven model can be obtained, and the first data-driven model can be updated in real time based on this.

[0098] Real-time estimated value of the first pseudo-Jacobian matrix item corresponding to the first data-driven model and the first total disturbance term , the first state space expression of the robotic arm system is constructed as follows:

[0099] , (9)

[0100] in, , , are all state variables.

[0101] Then, the first variable structure extended state observation expression is obtained through the first state space expression, wherein, through express The estimated value of , represents the observation error, i =1,2. The first variable structure expansion state observation expression can be expressed by the following formula.

[0102] , (10)

[0103] in, , T Represents the sampling time, the real-time estimate of the first total disturbance term , ( i =1,2) is the observation error gain, which can be expressed as follows:

[0104]

[0105]

[0106] in, is the observation bandwidth, and >0.

[0107] According to the first variable structure expanded state observation expression, a real-time estimated value of the first total disturbance term corresponding to the first data driven model can be obtained and the first data driven model can be updated in real time.

[0108] In step S200, based on the first data-driven model, the end posture controller of the robot arm is set and the expected joint angular velocity in the joint space is obtained.

[0109] For example, in step S200, based on the first data-driven model, an optimization problem is solved for the set first control input criterion function to obtain an expression corresponding to the end posture controller and calculate the expected joint angular velocity.

[0110] According to some embodiments, a first control input criterion function may be set according to a model-free adaptive control algorithm, which is expressed as follows.

[0111] , (11)

[0112] in, λ >0 is the weight factor, which is used to prevent the control input from changing too much.

[0113] Real-time estimated value of the first pseudo-Jacobian matrix item corresponding to the first data-driven model and the real-time estimate of the first total disturbance term , minimize the first control input criterion function and obtain the following formula.

[0114] , (12)

[0115] Formula (12) is simplified to obtain the following formula without matrix inversion operation.

[0116] , (13)

[0117] in, ρ (0,1] is the step size factor.

[0118] According to some embodiments, formula (13) may be further optimized by a PID control algorithm to obtain an expression corresponding to the end posture controller. The expression corresponding to the end posture controller may be expressed by the following formula.

[0119] , (14)

[0120] in, λ >0, ρ (0,1], represents the desired joint angular velocity in joint space, is the expected velocity (linear velocity, angular velocity) of the end position of the robot arm, is the real-time estimated value of the first total disturbance term of the robotic arm system observed and estimated, , , is the proportional gain, is the integral gain, is the differential gain.

[0121] The end posture controller of the robot arm is set according to the derived expression corresponding to the end posture controller, and the expected joint angular velocity of the joint space of the robot arm is calculated by the expression corresponding to the end posture controller.

[0122] In step S300, a second data-driven model is constructed to establish a mapping relationship between variables of the driving space of the robot arm and the joint space.

[0123] For example, in step S300, a second data-driven model is constructed through a dynamic mechanism model from the drive space to the joint space of the robot arm to achieve accurate estimation of the mapping relationship of variables from the drive space to the joint space.

[0124] First, a dynamic mechanism model from the driving space to the joint space of the robot is constructed, which can be expressed by the following formula.

[0125] , (15)

[0126] in, represents the joint driving torque, represents the inertia matrix, represents the Coriolis force and centrifugal force matrix, Represents the gravity matrix. When the robotic arm works in a microgravity environment, , Represents the model error term, which includes modeling errors caused by unmodeled items, external disturbances, parameter uncertainties, etc.

[0127] According to some embodiments, the dynamic mechanism model including the error term is discretized to obtain a second data-driven model. The second data-driven model can be expressed by the following formula.

[0128] , (16)

[0129] in, k Indicates k Sampling period, , represents the second pseudo-Jacobian matrix term of the robotic arm system, , represents the error term including the kinetic mechanism model and the second total disturbance term of the robotic arm system due to parameter estimation error.

[0130] According to some embodiments, the second data-driven model may be updated in real time by acquiring real-time estimated values ​​of the second pseudo-Jacobian matrix term and the second total disturbance term in the second data-driven model.

[0131] First, set the second estimation criterion function, which can be expressed as the following formula.

[0132] , (17)

[0133] in, >0 is a weight factor, which is used to suppress drastic changes in parameter estimates. express k -1 moment The second pseudo-Jacobian matrix of .

[0134] Furthermore, the second estimation criterion function After transformation, we get the following formula.

[0135] , (18)

[0136] According to the obtained formula (18), the second estimation criterion function is minimized by a preset algorithm to obtain the following formula.

[0137] , (19)

[0138] in, express k time The second pseudo-Jacobian matrix of , I represents the identity matrix.

[0139] According to some embodiments, the preset algorithm may adopt an improved projection algorithm.

[0140] By further simplifying formula (19), the calculation formula for the second pseudo-Jacobian matrix item corresponding to the second data-driven model can be obtained as follows.

[0141] , (20)

[0142] in, (0,2] is the step size factor. >0 is a weight factor, which is used to suppress drastic changes in parameter estimates. is the second total disturbance term Real-time estimates of .

[0143] According to some embodiments, a reset mechanism for the second pseudo-Jacobian matrix item may be set to reset the estimated value of the second pseudo-Jacobian matrix item to the initial value, thereby reducing the performance degradation caused by the accumulation of estimation errors and enhancing the tracking capability of time-varying parameters to ensure the stability and reliability of the control performance during the operation of the manipulator system. For example,

[0144] ,if or ,

[0145] ,if , i ≠ j , i , j =1,2,3,4,5,6.

[0146] in, yes The initial value of yes The initial value of Represents the second pseudo-Jacobian matrix term The diagonal elements of Represents the second pseudo-Jacobian matrix term The off-diagonal elements of . , , These are design parameters used to limit range, satisfying ≥1, >2 (2 +1).

[0147] According to formula (20), the real-time estimated value of the second pseudo-Jacobian matrix item corresponding to the second data-driven model can be obtained, and the second data-driven model can be updated in real time based on this.

[0148] Real-time estimated value of the second pseudo-Jacobian matrix item corresponding to the second data-driven model and the second total disturbance term , the second state space expression of the robotic arm system is constructed as follows:

[0149] ,(twenty one)

[0150] in, , , are all state variables.

[0151] Then, the second variable structure extended state observation expression is obtained through the second state space expression, where express The estimated value of , represents the observation error, i =1,2. The second variable structure expansion state observation expression can be expressed by the following formula.

[0152] ,(twenty two)

[0153] in, , T Represents the sampling time, the real-time estimate of the second total disturbance term , ( i =1,2) is the observation error gain, which can be expressed as follows:

[0154]

[0155] in, is the observation bandwidth, and >0.

[0156] According to the second variable structure expanded state observation expression, a real-time estimated value of the second total disturbance term corresponding to the second data driven model can be obtained and the second data driven model can be updated in real time.

[0157] In step S400, based on the second data-driven model, a joint angle controller of the robotic arm is set and the joint driving torque of the robotic arm is obtained according to the expected joint angular velocity.

[0158] For example, in step S400, based on the second data-driven model, the set second control input criterion function is optimized and solved to obtain an expression corresponding to the joint angle controller and calculate the joint driving torque according to the expected joint angular velocity.

[0159] According to some embodiments, the second control input criterion function may be set according to a model-free adaptive control algorithm, and its formula is expressed as follows.

[0160] ,(twenty three)

[0161] in, >0 is the weight factor, which is used to prevent the control input from changing too much.

[0162] Real-time estimated value of the second pseudo-Jacobian matrix item corresponding to the second data-driven model and the real-time estimate of the second total disturbance term , minimize the second control input criterion function and obtain the following formula.

[0163] ,(twenty four)

[0164] Formula (24) is simplified to obtain the following formula without matrix inversion operation.

[0165] , (25)

[0166] in, (0,1] is the step size factor.

[0167] According to some embodiments, formula (25) may be further optimized by a PI control algorithm to obtain an expression corresponding to the joint angle controller. The expression corresponding to the joint angle controller may be expressed by the following formula.

[0168] , (26)

[0169] in, >0, (0,1], represents the joint driving torque, represents the desired joint angular velocity in joint space, is the real-time estimated value of the second total disturbance term of the robotic arm system observed and estimated, , is the proportional gain, is the integral gain.

[0170] The joint angle controller of the robot arm is set according to the derived expression corresponding to the joint angle controller, and the joint driving torque of the robot arm is calculated by the expression corresponding to the joint angle controller and the expected joint angular velocity in the joint space.

[0171] In step S500, the end of the robot arm is controlled by the joint driving torque.

[0172] For example, in step S500, the calculated joint driving torque of the robot arm is input into the robot arm system to drive the robot arm to move and realize the end control of the robot arm.

[0173] The calculated joint driving torque is input into the driving control device in the robot system, so that the driving control device drives the joints in the robot system to rotate, and drives the arm rod to rotate through the rope linkage transmission device, thereby realizing the movement and end control of the robot.

[0174] The simulation effect of controlling the movement of the robot arm through the joint driving torque and realizing the end control of the robot arm is as follows:

[0175] like Figure 5As shown, assuming that the initial actual position of the end of the robotic arm is (0,0,0) meters and the initial expected position is (0.5,0,0) meters, there is a large initial error in the x-axis direction of the three-dimensional coordinate system.

[0176] The joint driving torque is calculated through the technical solution of the present application to control the tracking effect and tracking error of the end position and end posture of the robot arm.

[0177] in, Figure 6 The figure shows the trajectory tracking error curve of the end of the robot arm changing with time in the process of controlling the movement of the robot arm through the joint driving torque. Figure 7 The figure shows the angle variation curves of the three posture angles at the end of the robot arm changing with time in the process of controlling the movement of the robot arm through the joint driving torque. Figure 8 The trajectory tracking error curves of the three posture angles at the end of the robot arm changing with time in the process of controlling the movement of the robot arm through the joint driving torque are shown.

[0178] like Figure 5-Figure 8 As shown, the technical solution of the present application has a faster convergence speed and higher tracking accuracy.

[0179] The embodiments of the present application are described in detail above, and the description of the above embodiments is only used to help understand the method and core idea of ​​the present application. At the same time, changes or deformations made by those skilled in the art based on the idea of ​​the present application, the specific implementation method and the scope of application of the present application, all belong to the scope of protection of the present application. In summary, the content of this specification should not be construed as limiting the present application.

Claims

1. A method for controlling the end of a modular rope-driven flexible manipulator, characterized in that: include: Construct a first data-driven model to establish a mapping relationship between variables of the joint space of the robot arm and the task space, and update the first data-driven model in real time. The first data-driven model is expressed as follows: , in, represents the end position velocity of the robot arm, k Indicates k Sampling period, , represents the first pseudo-Jacobian matrix term, represents the joint angular velocity, , represents the first total disturbance term; Based on the first data-driven model, setting the end posture controller of the robotic arm and obtaining the expected joint angular velocity of the joint space; A second data-driven model is constructed to establish a mapping relationship between the driving space of the robot arm and the variables of the joint space, and the second data-driven model is updated in real time. The second data-driven model is expressed as follows: ， in, , represents the second pseudo-Jacobian matrix term, represents the joint driving torque, , represents the second total disturbance term; Based on the second data-driven model, setting a joint angle controller of the robotic arm and obtaining a joint driving torque of the robotic arm according to the expected joint angular velocity; Performing end control of the robotic arm through the joint driving torque; Wherein, updating the first data-driven model in real time includes: A first estimation criterion function is set, wherein the first estimation criterion function is expressed as follows: in, μ >0 is the weight factor, express k -1 time first pseudo-Jacobian matrix entry Real-time estimates of According to the first estimation criterion function, a first pseudo-Jacobian matrix item corresponding to the first data-driven model is obtained and a real-time estimated value of the first pseudo-Jacobian matrix item is calculated. The calculation formula of the first pseudo-Jacobian matrix item is expressed as follows: ， in, η (0,2] is the step size factor, for k The first total disturbance term at time -1 Real-time estimates of Based on the first pseudo-Jacobian matrix term and the first total disturbance term corresponding to the first data-driven model, a first state space expression of the robotic arm is set, and the first state space expression is expressed as follows: ， in, , , are all state variables; The first variable structure extended state observation expression is obtained through the first state space expression. The first variable structure extended state observation expression is expressed as follows: ， in, , T represents the sampling time, the real-time estimated value of the first total disturbance term , ( i =1,2) is the observation error gain; Based on the first variable structure extended state observation expression, obtaining a real-time estimated value of the first total disturbance term; updating the first data-driven model in real time according to the real-time estimated value of the first pseudo-Jacobian matrix item and the real-time estimated value of the first total disturbance item; Wherein, updating the second data-driven model in real time includes: A second estimation criterion function is set, and the second estimation criterion function is expressed as follows: in, >0 is the weight factor, express k -1 second pseudo-Jacobian matrix entry Real-time estimates of According to the second estimation criterion function, the second pseudo-Jacobian matrix item corresponding to the second data-driven model is obtained and the real-time estimated value of the second pseudo-Jacobian matrix item is calculated. The calculation formula of the second pseudo-Jacobian matrix item is expressed as follows: , in, (0,2] is the step size factor, for k The second total disturbance term at time -1 Real-time estimates of Based on the second pseudo-Jacobian matrix term and the second total disturbance term corresponding to the second data-driven model, a second state space expression of the robotic arm is set, and the second state space expression is expressed as follows: ， in, , , are all state variables; The second variable structure extended state observation expression is obtained by the second state space expression. The second variable structure extended state observation expression is expressed as follows: ， in, , the real-time estimated value of the second total disturbance term , ( i =1,2) is the observation error gain; Based on the second variable structure extended state observation expression, obtaining a real-time estimated value of the second total disturbance term; The second data-driven model is updated in real time according to the real-time estimated value of the second pseudo-Jacobian matrix term and the real-time estimated value of the second total disturbance term.

2. The method according to claim 1, characterized in that Constructing the first data-driven model to establish a mapping relationship between the variables of the joint space of the robot arm and the task space, including: Constructing a kinematic mechanism model from the joint space to the task space; The kinematic mechanism model is transformed to obtain the first data-driven model.

3. The method according to claim 1, characterized in that Based on the first data-driven model, setting the end pose controller of the robotic arm and obtaining the expected joint angular velocity of the joint space includes: Setting a first control input criterion function; According to the first pseudo-Jacobian matrix term and the first total disturbance term corresponding to the first data-driven model, the first control input criterion function is transformed, and an optimization solution is performed to obtain an expression corresponding to the terminal posture controller; The desired joint angular velocity is calculated using an expression corresponding to the end posture controller.

4. The method according to claim 1, characterized in that: Constructing a second data-driven model to establish a mapping relationship between the drive space of the robot arm and the variables of the joint space, including: Constructing a dynamic mechanism model from the drive space to the joint space; The kinetic mechanism model is transformed to obtain the second data-driven model.

5. The method according to claim 1, characterized in that Based on the second data-driven model, setting a joint angle controller of the robotic arm and obtaining a joint driving torque of the robotic arm according to the expected joint angular velocity includes: Setting a second control input criterion function; According to the second pseudo-Jacobian matrix term and the second total disturbance term corresponding to the second data-driven model, the second control input criterion function is transformed, and an optimization solution is performed to obtain an expression corresponding to the joint angle controller; According to the desired joint angular velocity, the joint driving torque is calculated by an expression corresponding to the joint angle controller.

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