Output feedback control method and system for flexible-joint robotic arms

Abstract

The application discloses a kind of output feedback control method and system of flexible joint mechanical arm, method includes: the state space general model of flexible joint mechanical arm is constructed;It is converted from the state space model of flexible joint mechanical arm into linear state observer, and linear state observer is used to output link angular velocity auxiliary estimation state and motor angular velocity auxiliary estimation state;Step-by-step definition trajectory tracking error variable;With trajectory tracking error variable, link angular position, motor angular position, link angular velocity auxiliary estimation state and motor angular velocity auxiliary estimation state as foundation, first virtual control law to third virtual control law is gradually deduced and constructed by backstepping method, and linear feedback closed-loop controller is formed according to the solution of final control input instruction to first virtual control law to third virtual control law;The present application can realize output feedback control only by conventional position sensor, and can greatly improve the trajectory tracking accuracy and engineering robustness of flexible joint servo system.

Description

Technical Field

[0001] This invention belongs to the field of flexible joint servo control technology, specifically relating to the output feedback control method and system for flexible joint robotic arms. Background Technology

[0002] Flexible joint robotic arms are widely used in collaborative robots and precision manufacturing due to their advantages such as low inertia and high compliance. For example... Figure 1 As shown, the existing flexible joint robotic arm includes a motor 1, a flexible joint 2, and a link 3. The motor 1 drives the link 3 through the flexible joint 2. The underactuated characteristics introduced by the elastic deformation of the flexible joint, the strong coupling between the link and the motor and the non-minimum phase zero dynamic, plus uncertainties such as inertial perturbation, nonlinear friction and time-varying external load, significantly increase the control difficulty.

[0003] Existing high-performance nonlinear control methods rely on full-state feedback, requiring real-time acquisition of the position and angular velocity signals of the linkage and motor. In engineering practice, encoders can accurately measure position, but angular velocity is difficult to obtain directly at low cost: numerical differentiation of the position signal severely amplifies high-frequency noise, leading to distortion of the velocity signal; adding a tachometer increases hardware cost, size, and failure rate, making it unsuitable for miniaturized industrial scenarios. Therefore, output feedback control relying solely on position measurement has become the core research direction for the practical application of flexible joint servo control engineering.

[0004] Current observation schemes for unmeasurable velocity states mainly rely on high-gain observers, but they have an inherent initial peak phenomenon, which can easily lead to control saturation and system instability. Furthermore, excessively high observation gain can severely amplify sensor noise and degrade the steady-state performance of the system. The Kreisselmeier observer does not consider the nonlinear characteristics of flexible joints, resulting in a significant decrease in estimation accuracy in large-scale motion scenarios. Nonlinear schemes such as sliding mode observers and neural network adaptive observers have problems such as control chattering, large online computation, complex parameter tuning, and poor engineering portability, making it difficult to implement in large quantities in industrial scenarios. Summary of the Invention

[0005] This invention provides an output feedback control method and system for a flexible joint robotic arm. It can achieve full system output feedback control with only a position sensor. The linear state observer can significantly improve the trajectory tracking accuracy and engineering robustness of the flexible joint servo system, and is suitable for engineering scenarios such as industrial collaborative robots, precision manufacturing equipment, and aerospace servo mechanisms.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The first aspect of this invention provides an output feedback control method for a flexible joint robotic arm, comprising:

[0008] A general dynamic model of a flexible joint robotic arm is constructed based on the angular position and angular velocity of the motor and the angular position and angular velocity of the connecting rod.

[0009] The motor angular velocity and the link angular velocity are selected as state terms that cannot be directly measured, while the motor angular position and the link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state space model of the flexible joint manipulator.

[0010] The state-space model of the flexible joint robotic arm is converted into a linear state observer. The linear state observer is used to output the auxiliary estimation states of the link angular velocity and the motor angular velocity. Specifically, an adjustable gain of the observer corresponding to the angular position of the link is introduced to reconstruct the state of the link angular velocity to obtain the auxiliary estimation state of the link angular velocity; an adjustable gain of the observer corresponding to the angular position of the motor is introduced to reconstruct the state of the motor angular velocity to obtain the auxiliary estimation state of the motor angular velocity.

[0011] The trajectory tracking error variables are defined step by step based on the deviation of the link angular position from the desired trajectory, the auxiliary estimation state of the link angular velocity and the deviation of the first virtual control law, the deviation of the motor angular position from the second virtual control law, and the auxiliary estimation state of the motor angular velocity and the deviation of the third virtual control law.

[0012] Based on the trajectory tracking error variables, link angular position, motor angular position, link angular velocity auxiliary estimation state, and motor angular velocity auxiliary estimation state, the first to third virtual control laws are derived and constructed step by step through the backstepping method. The final control input command is solved according to the first to third virtual control laws to form a linear feedback closed-loop controller.

[0013] Furthermore, a general dynamic model of the flexible joint manipulator is constructed based on the angular position and angular velocity of the motor and the angular position and angular velocity of the connecting rod, expressed by the following formula:

[0014] ;

[0015] ;

[0016] In the formula, This refers to the link angle position. The angular velocity of the connecting rod, This refers to the angular acceleration of the connecting rod. This refers to the motor's angular position. The angular velocity of the motor. This refers to the angular acceleration of the motor. Let the moment of inertia of the connecting rod be _____. This refers to the moment of inertia of the motor. For the mass of the connecting rod, It is the acceleration due to gravity. This is the distance from the joint to the center of mass of the connecting rod; This refers to the stiffness coefficient of the flexible joint. This is the viscous damping coefficient on the connecting rod side. This refers to the viscous damping coefficient on the motor side. The input control torque for the flexible joint robotic arm. External torque disturbance on the connecting rod side This is the lumped term of the inherent uncertainties and disturbances on the motor side.

[0017] Furthermore, the general dynamic model of the flexible joint manipulator is transformed into a state-space model of the flexible joint manipulator, specifically including:

[0018] ;

[0019] In the formula, , , , , , To simplify the system constant parameters, where, , , , , , ; For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. and For the system disturbance of the flexible joint robotic arm. This is the input control torque for the flexible joint robotic arm.

[0020] Furthermore, an adjustable gain of the observer corresponding to the link angular position is introduced to reconstruct the link angular velocity state and obtain the auxiliary estimation state of the link angular velocity, specifically including:

[0021] ;

[0022] ;

[0023] In the formula, To aid in estimating the state of the connecting rod angular velocity, For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. The adjustable gain of the observer corresponding to the link angle position; , , To simplify the constant parameters of the system; The first derivative is used to help estimate the state of the connecting rod angular velocity.

[0024] Furthermore, an adjustable gain of the observer corresponding to the motor angular position is introduced to reconstruct the state of the motor angular velocity and obtain the auxiliary estimation state of the motor angular velocity, specifically including:

[0025] ;

[0026] ;

[0027] In the formula, To assist in estimating the state of the motor's angular velocity, For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. The adjustable gain of the observer corresponding to the motor's angular position; , and To simplify the constant parameters of the system; The input control torque for the flexible joint robotic arm. The first derivative is used to estimate the state of the motor's angular velocity.

[0028] Furthermore, the first to third virtual control laws are derived and constructed step-by-step using the backstepping method, specifically including:

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula, This is the first virtual control law. For the differentiable term of the first virtual control law, This is the second virtual control law. For the differentiable term of the second virtual control law, This is the third virtual control law; The desired trajectory for the link's angular position. The observer's adjustable gain corresponds to the link angle position. The adjustable gain of the observer corresponding to the motor's angular position. , and The adjustable positive gain of the linear feedback closed-loop controller; For the link angular position status item that can be directly measured, For motor angular position status items that can be directly measured, , , To simplify the constant parameters of the system, The deviation between the link angular position and the desired trajectory. To aid in estimating the state and deviation of the first virtual control law based on the link angular velocity, The deviation between the motor angular position and the second virtual control law. It helps estimate the state of the connecting rod angular velocity.

[0033] Furthermore, based on the first to third virtual control laws, the final control input command is solved to form a linear feedback closed-loop controller, specifically including:

[0034] ;

[0035] In the formula, , and To simplify the constant parameters of the system, The input control torque for the flexible joint robotic arm. The adjustable gain of the observer corresponding to the motor's angular position. To assist in estimating the state of the motor's angular velocity, For the link angular position status item that can be directly measured, For motor angular position status items that can be directly measured, This is a differentiable term of the third virtual control law; The adjustable positive gain is for a linear feedback closed-loop controller. The deviation between the motor angular position and the second virtual control law. The deviation between the motor angular velocity state and the third virtual control law is estimated.

[0036] A second aspect of the present invention provides an output feedback control system for a flexible joint robotic arm, comprising:

[0037] The model building module is used to construct a general dynamic model of the flexible joint manipulator based on the motor angular position and angular velocity, as well as the link angular position and angular velocity. The motor angular velocity and link angular velocity are selected as state terms that cannot be directly measured, while the motor angular position and link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state space model of the flexible joint manipulator.

[0038] The state observation module is used to convert the state-space model of the flexible joint manipulator into a linear state observer. The linear state observer is used to output the auxiliary estimated state of the link angular velocity and the auxiliary estimated state of the motor angular velocity. Specifically, an adjustable gain corresponding to the angular position of the link is introduced to reconstruct the state of the link angular velocity to obtain the auxiliary estimated state of the link angular velocity; an adjustable gain corresponding to the angular position of the motor is introduced to reconstruct the state of the motor angular velocity to obtain the auxiliary estimated state of the motor angular velocity.

[0039] The error tracking module is used to define trajectory tracking error variables step by step based on the following: the deviation between the link angular position and the desired trajectory, the auxiliary estimation state of the link angular velocity and the deviation of the first virtual control law, the deviation between the motor angular position and the second virtual control law, and the auxiliary estimation state of the motor angular velocity and the deviation of the third virtual control law.

[0040] The instruction output module is used to derive and construct the first to third virtual control laws step by step using the trajectory tracking error variables, link angular position, motor angular position, link angular velocity auxiliary estimation state and motor angular velocity auxiliary estimation state as a basis, and solve the final control input instruction according to the first to third virtual control laws to form a linear feedback closed-loop controller.

[0041] A third aspect of the present invention provides an electronic terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the output feedback control method for the flexible joint robotic arm described in the first aspect of the present invention.

[0042] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] This invention introduces an adjustable gain for the observer corresponding to the angular position of the connecting rod, and reconstructs the state of the connecting rod angular velocity to obtain an auxiliary estimation state of the connecting rod angular velocity; it also introduces an adjustable gain for the observer corresponding to the angular position of the motor, and reconstructs the state of the motor angular velocity to obtain an auxiliary estimation state of the motor angular velocity. This enables accurate linear estimation of unmeasurable angular velocities without using a speed sensor, effectively avoiding the initial peak value and sensor noise amplification problems of traditional high-gain observers, making the observation error exponentially stable and uniformly bounded. At the same time, the gain adjustment is simple and the computational load is small, greatly improving the system estimation accuracy, dynamic response and engineering practicality.

[0045] This invention is based on trajectory tracking error variables, link angular position, motor angular position, auxiliary estimation states of link angular velocity and motor angular velocity. It derives and constructs the first to third virtual control laws step by step through backstepping. Based on the first to third virtual control laws, the final control input command is solved to form a linear feedback closed-loop controller. It does not require additional nonlinear robust terms and disturbance observation compensation links. The control output is continuous, smooth and jitter-free. Only conventional position sensors are needed to achieve output feedback control, which can significantly improve the trajectory tracking accuracy and engineering robustness of flexible joint servo systems. Attached Figure Description

[0046] Figure 1 This is a simplified model diagram of the flexible joint robotic arm provided in Embodiment 1 of the present invention;

[0047] Figure 2 This is a flowchart of the output feedback control of the flexible joint robotic arm provided in Embodiment 1 of the present invention;

[0048] Figure 3 This is the desired trajectory tracking curve provided in Embodiment 1 of the present invention;

[0049] Figure 4 This is a trajectory tracking error curve of the OFRC controller provided in Embodiment 1 of the present invention;

[0050] Figure 5 This is a graph showing the change in the input control torque of the OFRC controller provided in Embodiment 1 of the present invention;

[0051] Figure 6 This is provided in Embodiment 1 of the present invention. and The curve showing the change in the estimated value;

[0052] Figure 7 This is provided in Embodiment 1 of the present invention. The estimation error curve;

[0053] Figure 8 This is provided in Embodiment 1 of the present invention. and The curve showing the change in the estimated value;

[0054] Figure 9 This is provided in Embodiment 1 of the present invention. The estimation error curve;

[0055] Figure 10 This is a comparison curve of the tracking error of the PI controller provided in Embodiment 1 of the present invention;

[0056] Figure 11This is a graph showing the change in the input control torque of the PI controller provided in Embodiment 1 of the present invention;

[0057] In the diagram, 1 is the motor, 2 is the flexible joint, and 3 is the connecting rod. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0059] like Figure 1 As shown, the existing flexible joint robotic arm includes a motor 1, a flexible joint 2, and a connecting rod 3. The motor 1 drives the connecting rod 3 through the flexible joint 2. In a specific embodiment, the output feedback control method is applied to the flexible joint robotic arm.

[0060] Example 1

[0061] like Figure 2 As shown, this embodiment provides an output feedback control method for a flexible joint robotic arm, including:

[0062] A general dynamic model of a flexible joint robotic arm is constructed based on the angular position and angular velocity of the motor and the angular position and angular velocity of the connecting rod. The formula is as follows:

[0063] ;

[0064] ;

[0065] In the formula, This refers to the link angle position. The angular velocity of the connecting rod, This refers to the angular acceleration of the connecting rod. This refers to the motor's angular position. The angular velocity of the motor. This refers to the angular acceleration of the motor. Let the moment of inertia of the connecting rod be _____. This refers to the moment of inertia of the motor. For the mass of the connecting rod, It is the acceleration due to gravity. This is the distance from the joint to the center of mass of the connecting rod; This refers to the stiffness coefficient of the flexible joint. This is the viscous damping coefficient on the connecting rod side. This refers to the viscous damping coefficient on the motor side. The input control torque for the flexible joint robotic arm. External torque disturbance on the connecting rod side This represents the lumped term of inherent uncertainties and disturbances on the motor side. It should be further noted that... This represents the first derivative of the parameter X set in this embodiment. Subsequent variables of the same type will be defined according to this rule, and will not be described again.

[0066] Motor angular velocity and link angular velocity are selected as state terms that cannot be directly measured, while motor angular position and link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state-space model of the flexible joint manipulator, specifically including:

[0067] ;

[0068] In the formula, , , , , , To simplify the system constant parameters, where, , , , , , ; For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. and For the system disturbance of the flexible joint robotic arm. This is the input control torque for the flexible joint robotic arm.

[0069] The state-space model of the flexible joint robotic arm is converted into a linear state observer. This linear state observer outputs auxiliary estimation states for the link angular velocity and the motor angular velocity. Specifically, an adjustable gain corresponding to the link angular position is introduced to reconstruct the link angular velocity state and obtain the auxiliary estimation states.

[0070] ;

[0071] ;

[0072] In the formula, To aid in estimating the state of the connecting rod angular velocity, For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. The adjustable gain of the observer corresponding to the link angle position; , , To simplify the constant parameters of the system; The first derivative is used to help estimate the state of the connecting rod angular velocity.

[0073] By introducing an adjustable gain for the observer corresponding to the motor's angular position, and reconstructing the state of the motor's angular velocity to obtain the auxiliary estimation state of the motor's angular velocity, the following steps are taken:

[0074] ;

[0075] ;

[0076] In the formula, To assist in estimating the state of the motor's angular velocity, For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. The adjustable gain of the observer corresponding to the motor's angular position; , and To simplify the constant parameters of the system; The input control torque for the flexible joint robotic arm. The first derivative is used to estimate the state of the motor's angular velocity.

[0077] The linear state observer can achieve accurate linear estimation of unmeasurable angular velocity without using a velocity sensor. It effectively avoids the problems of initial peak and sensor noise amplification that exist in traditional high-gain observers, making the observation error exponential stable and uniformly bounded. At the same time, the gain adjustment is simple and the computation is small, which greatly improves the system estimation accuracy, dynamic response and engineering practicality.

[0078] The trajectory tracking error variables are defined step by step. The trajectory tracking error variables include the deviation between the link angular position and the desired trajectory, the deviation between the auxiliary estimation state of the link angular velocity and the first virtual control law, the deviation between the motor angular position and the second virtual control law, and the deviation between the auxiliary estimation state of the motor angular velocity and the third virtual control law.

[0079] , , , ;

[0080] In the formula, The deviation between the link angular position and the desired trajectory. To aid in estimating the state and deviation of the first virtual control law based on the link angular velocity, The deviation between the motor angular position and the second virtual control law. The deviation between the motor angular velocity and the state and the third virtual control law is estimated. The desired trajectory for the link angle position; This is the first virtual control law. This is the second virtual control law. This is the third virtual control law;

[0081] Based on the trajectory tracking error variable, the link angular position, the motor angular position, the auxiliary estimation states of the link angular velocity and the motor angular velocity, the first to third virtual control laws are derived and constructed step by step using the backstepping method, along with the final control input command output by the linear feedback closed-loop controller. The formula is as follows:

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] In the formula, This is the first virtual control law. For the differentiable term of the first virtual control law, This is the second virtual control law. For the differentiable term of the second virtual control law, This is the third virtual control law. This is a differentiable term of the third virtual control law; The desired trajectory for the link's angular position. The observer's adjustable gain corresponds to the link angle position. The adjustable gain of the observer corresponding to the motor's angular position. , , and The adjustable positive gain of the linear feedback closed-loop controller; For the link angular position status item that can be directly measured, For motor angular position status items that can be directly measured, To aid in estimating the state of the connecting rod angular velocity, To assist in estimating the state of the motor's angular velocity; This is the input control torque for the flexible joint robotic arm.

[0087] When inherent perturbations exist in the system, the Lyapunov function is constructed as follows:

[0088] ;

[0089] After differentiation, the cross terms are handled using Young's inequality to obtain... This proves that the tracking error of the closed-loop control system is consistent and eventually bounded, and that increasing the feedback gain can arbitrarily reduce the bounded range of the error.

[0090] When there are no inherent system disturbances and no modeled dynamics, the augmented Lyapunov function is constructed as follows:

[0091] ;

[0092] In the formula, To aid in estimating the state observation error of the connecting rod angular velocity, To assist in estimating the state observation error of the motor angular velocity;

[0093] After differentiation, the cross terms are handled using Young's inequality to obtain... This proves that the tracking error and observation error of the closed-loop control system converge asymptotically to zero globally; among them, and is a positive definite constant, and C is a bounded positive constant related to the upper bound of the perturbation derivative.

[0094] The linear feedback closed-loop controller requires no additional nonlinear robust terms or disturbance observation compensation circuits. The control output is continuous, smooth, and jitter-free. It can achieve output feedback control with only conventional position sensors, which can significantly improve the trajectory tracking accuracy and engineering robustness of flexible joint servo systems.

[0095] The present invention will be further described in detail below with reference to simulation embodiments. This embodiment adopts a single-link flexible joint robotic arm, which is a general standard model for industrial collaborative robots. The system physical parameters are shown in Table 1.

[0096] Table 1. Operating parameters of the flexible joint robotic arm;

[0097]

[0098] Observer Gain = 20、 = 40; Controller gain k 1s1 = 500, k 2s1 = 500, k 3s1 = 500, k 4s1 = 1000; the simulation sampling time is 0.5ms, and the total simulation duration is 30s.

[0099] To verify the effectiveness of the method of the present invention, two sets of comparison schemes were set up: the method proposed in this embodiment (referred to as OFRC controller) and the traditional PI controller.

[0100] like Figure 3 As shown, the desired link angular position trajectory is set as follows:

[0101] ;

[0102] Simulation results are as follows: 1. Trajectory tracking performance: such as Figure 4 As shown, the trajectory tracking error of the OFRC controller proposed in this invention is stable at... Within rad; such as Figure 10 As shown, the maximum tracking error of a traditional PI controller reaches The rad is 150 times that of the method proposed in this invention;

[0103] 2. Velocity observation performance: such as Figures 6 to 9 As shown, the linear state observer proposed in this invention can quickly converge to the true velocity value, with a steady-state observation error of around 1% and no initial peak phenomenon.

[0104] 3. Control output performance: such as Figure 5 As shown, the controller proposed in this invention provides a continuous and smooth output without any jitter, which meets the output limitations of industrial servo drives; Figure 11 As shown, the traditional PI scheme has obvious control chattering, which can easily cause resonance and mechanical wear in the servo system.

[0105] Simulation results fully verify the effectiveness and superiority of the method proposed in this invention. It can achieve high-precision trajectory tracking of flexible joint servo systems using only position sensors, and is fully adapted to the needs of industrial engineering applications.

[0106] Example 2

[0107] This embodiment provides an output feedback control system for a flexible joint robotic arm. The control system is used to execute the control method described in Embodiment 1. The control system includes:

[0108] The model building module is used to construct a general dynamic model of the flexible joint manipulator based on the motor angular position and angular velocity, as well as the link angular position and angular velocity. The motor angular velocity and link angular velocity are selected as state terms that cannot be directly measured, while the motor angular position and link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state space model of the flexible joint manipulator.

[0109] The state observation module is used to convert the state-space model of the flexible joint manipulator into a linear state observer. The linear state observer is used to output the auxiliary estimated state of the link angular velocity and the auxiliary estimated state of the motor angular velocity. Specifically, an adjustable gain corresponding to the angular position of the link is introduced to reconstruct the state of the link angular velocity to obtain the auxiliary estimated state of the link angular velocity; an adjustable gain corresponding to the angular position of the motor is introduced to reconstruct the state of the motor angular velocity to obtain the auxiliary estimated state of the motor angular velocity.

[0110] The error tracking module is used to define trajectory tracking error variables step by step based on the following: the deviation between the link angular position and the desired trajectory, the auxiliary estimation state of the link angular velocity and the deviation of the first virtual control law, the deviation between the motor angular position and the second virtual control law, and the auxiliary estimation state of the motor angular velocity and the deviation of the third virtual control law.

[0111] The instruction output module is used to derive and construct the first to third virtual control laws step by step using the trajectory tracking error variables, link angular position, motor angular position, link angular velocity auxiliary estimation state and motor angular velocity auxiliary estimation state as a basis, and solve the final control input instruction according to the first to third virtual control laws to form a linear feedback closed-loop controller.

[0112] Example 3

[0113] This embodiment provides an electronic terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the output feedback control method of the flexible joint robotic arm described in Embodiment 1.

[0114] Example 4

[0115] This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0116] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0117] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0118] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0119] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0120] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An output feedback control method for a flexible joint robotic arm, characterized in that, include: A general dynamic model of a flexible joint robotic arm is constructed based on the angular position and angular velocity of the motor and the angular position and angular velocity of the connecting rod. The motor angular velocity and the link angular velocity are selected as state terms that cannot be directly measured, while the motor angular position and the link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state space model of the flexible joint manipulator. The state-space model of the flexible joint robotic arm is converted into a linear state observer, which is used to output the link angular velocity to assist in estimating the state and the motor angular velocity to assist in estimating the state. Specifically, an adjustable gain of the observer corresponding to the link angular position is introduced to reconstruct the link angular velocity state and obtain the auxiliary estimation state of the link angular velocity. This includes: ； ； In the formula, To aid in estimating the state of the connecting rod angular velocity, For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. The adjustable gain of the observer corresponding to the link angle position; , , To simplify the constant parameters of the system; The first derivative of the state is used to assist in estimating the angular velocity of the connecting rod; Specifically, by introducing an adjustable gain of the observer corresponding to the motor angular position, and reconstructing the state of the motor angular velocity to obtain the auxiliary estimation state of the motor angular velocity, the following steps are taken: ； ； In the formula, To assist in estimating the state of the motor's angular velocity, For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. The adjustable gain of the observer corresponding to the motor's angular position; , and To simplify the constant parameters of the system; The input control torque for the flexible joint robotic arm. The first derivative of the state estimation auxiliary function for the motor's angular velocity; The trajectory tracking error variables are defined step by step based on the deviation of the link angular position from the desired trajectory, the auxiliary estimation state of the link angular velocity and the deviation of the first virtual control law, the deviation of the motor angular position from the second virtual control law, and the auxiliary estimation state of the motor angular velocity and the deviation of the third virtual control law. Based on the trajectory tracking error variables, link angular position, motor angular position, link angular velocity auxiliary estimation state, and motor angular velocity auxiliary estimation state, the first to third virtual control laws are derived and constructed step by step using the backstepping method, specifically including: ； ； ； In the formula, This is the first virtual control law. For the differentiable term of the first virtual control law, This is the second virtual control law. For the differentiable term of the second virtual control law, This is the third virtual control law; The desired trajectory for the link's angular position. The observer's adjustable gain corresponds to the link angle position. The adjustable gain of the observer corresponding to the motor's angular position. , and The adjustable positive gain of the linear feedback closed-loop controller; For the link angular position status item that can be directly measured, For motor angular position status items that can be directly measured, , , To simplify the constant parameters of the system, The deviation between the link angular position and the desired trajectory. To aid in estimating the state and deviation of the first virtual control law based on the link angular velocity, The deviation between the motor angular position and the second virtual control law. To aid in estimating the state of the connecting rod angular velocity; The final control input command is solved based on the first to third virtual control laws to form a linear feedback closed-loop controller.

2. The output feedback control method for the flexible joint robotic arm according to claim 1, characterized in that, A general dynamic model of a flexible joint robotic arm is constructed based on the angular position and angular velocity of the motor and the angular position and angular velocity of the connecting rod. The formula is as follows: ； ； In the formula, This refers to the link angle position. The angular velocity of the connecting rod, This refers to the angular acceleration of the connecting rod. This refers to the motor's angular position. The angular velocity of the motor. This refers to the angular acceleration of the motor. Let the moment of inertia of the connecting rod be _____. This refers to the moment of inertia of the motor. For the mass of the connecting rod, It is the acceleration due to gravity. This is the distance from the joint to the center of mass of the connecting rod; This refers to the stiffness coefficient of the flexible joint. This is the viscous damping coefficient on the connecting rod side. This refers to the viscous damping coefficient on the motor side. The input control torque for the flexible joint robotic arm. External torque disturbance on the connecting rod side This is the lumped term of the inherent uncertainties and disturbances on the motor side.

3. The output feedback control method for the flexible joint robotic arm according to claim 2, characterized in that, The general dynamic model of the flexible joint manipulator is transformed into a state-space model of the flexible joint manipulator, specifically including: ； In the formula, , , , , , To simplify the system constant parameters, where, , , , , , ; For the link angular position status item that can be directly measured, This refers to the link angular velocity state term, which cannot be directly measured. For motor angular position status items that can be directly measured, This refers to the motor angular velocity state item, which cannot be directly measured. and For the system disturbance of the flexible joint robotic arm. This is the input control torque for the flexible joint robotic arm.

4. The output feedback control method for the flexible joint robotic arm according to claim 1, characterized in that, The final control input command is solved based on the first to third virtual control laws to form a linear feedback closed-loop controller, specifically including: ； In the formula, , and To simplify the constant parameters of the system, The input control torque for the flexible joint robotic arm. The adjustable gain of the observer corresponding to the motor's angular position. To assist in estimating the state of the motor's angular velocity, For the link angular position status item that can be directly measured, For motor angular position status items that can be directly measured, This is a differentiable term of the third virtual control law; The adjustable positive gain is for a linear feedback closed-loop controller. The deviation between the motor angular position and the second virtual control law. The deviation between the motor angular velocity state and the third virtual control law is estimated.

5. An output feedback control system for a flexible joint robotic arm, characterized in that, The output feedback control system performs the output feedback control method according to any one of claims 1 to 4, and the output feedback control system includes: The model building module is used to construct a general dynamic model of the flexible joint manipulator based on the motor angular position and angular velocity, as well as the link angular position and angular velocity. The motor angular velocity and link angular velocity are selected as state terms that cannot be directly measured, while the motor angular position and link angular position are determined as state terms that can be directly measured. The general dynamic model of the flexible joint manipulator is then converted into a state space model of the flexible joint manipulator. The state observation module is used to convert the state-space model of the flexible joint manipulator into a linear state observer. The linear state observer is used to output the auxiliary estimated state of the link angular velocity and the auxiliary estimated state of the motor angular velocity. Specifically, an adjustable gain corresponding to the angular position of the link is introduced to reconstruct the state of the link angular velocity to obtain the auxiliary estimated state of the link angular velocity; an adjustable gain corresponding to the angular position of the motor is introduced to reconstruct the state of the motor angular velocity to obtain the auxiliary estimated state of the motor angular velocity. The error tracking module is used to define trajectory tracking error variables step by step based on the following: the deviation between the link angular position and the desired trajectory, the auxiliary estimation state of the link angular velocity and the deviation of the first virtual control law, the deviation between the motor angular position and the second virtual control law, and the auxiliary estimation state of the motor angular velocity and the deviation of the third virtual control law. The instruction output module is used to derive and construct the first to third virtual control laws step by step using the trajectory tracking error variables, link angular position, motor angular position, link angular velocity auxiliary estimation state and motor angular velocity auxiliary estimation state as a basis, and solve the final control input instruction according to the first to third virtual control laws to form a linear feedback closed-loop controller.

6. An electronic terminal, comprising a processor and a storage medium; said storage medium being used to store instructions; characterized in that, The processor is configured to operate according to the instructions to perform the steps of the output feedback control method for the flexible joint robotic arm according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 4.

Images