SMA-driven Flexible Robot Arm Switching System and Gain Allocation Control Method

Abstract

The present invention provides an SMA-driven flexible robotic arm switching system and a gain allocation control method, including an SMA spring constitutive characteristic module, an SMA-driven robotic arm state equation module, a model subsystem and a gain allocation control module, and a MIMO-PID module optimized based on a genetic algorithm; the SMA spring constitutive characteristic module considers the switching characteristics introduced by SMA; the SMA-driven robotic arm state equation module combines the constitutive model of SMA; the model subsystem and the gain allocation control module define the concept of a switching subsystem and introduce the gain allocation control technology; the MIMO-PID module optimized based on a genetic algorithm discusses the PID controller of the MIMO system and the objective optimization function; and combines the gain allocation control technology. By considering the constitutive characteristics of the SMA spring, the present invention clarifies the location and cause of the switching phenomenon and establishes a dynamic state equation of the flexible robotic arm including the switching phenomenon. This state equation can provide a theoretical basis and a mathematical model for the research on the nonlinearity and control of the switching system.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control, and specifically, to a switching system of a flexible robotic arm driven by SMA and a gain allocation control method. Background Art

[0002] With the development of fields such as aerospace, automation control, and industrial manufacturing, higher standards are required for the compliance, safety, and flexibility of robots. SMA is an intelligent material with a shape memory effect that can change its own shape and mechanical properties under certain conditions. Compared with traditional rigid robots, SMA has a large power density and a strong driving force, enabling the robotic arm to move more flexibly. However, due to its special constitutive characteristics, it exhibits high nonlinearity, theoretically infinite degrees of freedom, and discontinuity. There are significant challenges in the control method of a robotic arm driven by SMA.

[0003] 1. Discontinuity of the system

[0004] Due to its special constitutive characteristics, SMA has different mechanical properties in the compressed and stretched states. At the critical position of switching between the two, a small deformation can generate a huge axial output force, manifested as the discontinuity of the output force, resulting in the phenomenon of system switching during the movement of the robotic arm. For the movement of the switching system, using the same control scheme may face the phenomena of control failure or system instability. Therefore, it is crucial to design a control scheme for the switching system according to the state of SMA in the robotic arm.

[0005] 2. High nonlinearity and multiple degrees of freedom of the system

[0006] The robotic arm controlled by SMA can bend with a high curvature and theoretically has an infinite number of degrees of freedom. Moreover, the relationship between the deformation amount, deflection angle of the SMA spring itself and the input shows highly nonlinear characteristics. Therefore, it is relatively difficult to model the forward and inverse kinematics and dynamics of the robotic arm. At the same time, multiple groups of SMA are coupled with each other. In this case with complex motion characteristics, it is necessary to set a control method with strong robustness, simple parameter adjustment, and conforming to multiple inputs and multiple outputs. The MIMO-PID gain allocation control method based on genetic algorithm optimization can meet the system requirements.

[0007] Therefore, a new technical solution needs to be proposed. Summary of the Invention

[0008] Aiming at the defects in the prior art, the purpose of the present invention is to provide a switching system of a flexible robotic arm driven by SMA and a gain allocation control method.

[0009] An SMA-driven flexible robotic arm switching system provided according to the present invention includes an SMA spring constitutive characteristic module, an SMA-driven robotic arm state equation module, a model subsystem and a gain allocation control module, and a MIMO-PID module optimized based on a genetic algorithm;

[0010] The SMA spring constitutive characteristic module considers the switching characteristics introduced by SMA, elaborates on the location and cause of switching and its function expression, and analyzes the influence of the switching characteristics and strong nonlinear characteristics of SMA on the control of the flexible robotic arm;

[0011] The SMA-driven robotic arm state equation module combines the constitutive model of SMA to establish a state equation of the flexible robotic arm with switching phenomena for dynamic analysis or control;

[0012] The model subsystem and gain allocation control module define the concept of a switching subsystem, introduce gain allocation control technology, and adjust control parameters correspondingly by monitoring the state of the dynamic system in real time;

[0013] The MIMO-PID module optimized based on a genetic algorithm discusses the PID controller of the MIMO system, the objective optimization function, genetic algorithm optimization and its assignment; combined with gain allocation control technology, the PID parameters optimized by the genetic algorithm are assigned to each subsystem to achieve the goal of trajectory tracking of the switching system.

[0014] Preferably, the SMA spring constitutive characteristic module:

[0015] SMA has a shape memory effect through the phase transformation and reverse transformation of martensite. When SMA is axially stretched by an external force, axial deformation occurs. After unloading the external force, residual deformation remains. When heated to a certain temperature, the residual deformation can be eliminated, and work is done on the external force at the same time; when SMA is axially compressed by an external force, the form of its force is opposite to that during stretching after being heated to a certain temperature; at the critical position between compression and stretching, there is a large jump in its output force, showing a discontinuous phenomenon; when the i-th platform and the j-th group of SMA springs are both stretched and compressed axially, the output force F ij :

[0016]

[0017] where ξ ij represents the martensite volume fraction of the i-th platform and the j-th group of SMA springs, ξ0 represents the initial martensite volume fraction, T ij represents the temperature of the i-th platform and the j-th group of SMA springs, T0 is the ambient temperature, Ω represents the phase change coefficient, Θ represents the thermoelastic coefficient, σ e is the elastic stress limit of SMA, F e and Y eThe proportional parameter determined by the SMA spring structure.

[0018] Preferably, the martensite volume fraction and temperature are controlled by an external voltage or current signal. Define the controllable input quantity uij of the jth group of SMA springs on the ith platform as:

[0019]

[0020] Preferably, the state equation module of the SMA-driven robotic arm:

[0021] For the ith platform, define its Euler angles relative to the fixed coordinate system as Perform dynamic modeling on the SMA-driven robotic arm by the Lagrange method or the Newton-Euler method. The dynamic model is transformed into the form of a state equation. For the ith platform, the state equation has the following form:

[0022]

[0023] where f1, f2, f3 describe the influence of the system parameters of the dynamic model, k1, k2, k3 represent the influence of the control quantity on the dynamic model, ξ1, ξ2, ξ3 represent the system model error and external disturbance, ΔY ij represents the deformation of the jth group of SMA springs on the ith platform, uij represents the controllable input quantity of the jth group of SMA springs on the ith platform, sign(·) represents the sign function, and the sign function is introduced by the discontinuity of the SMA output force.

[0024] Preferably, the model subsystem and the gain allocation control module:

[0025] The SMA-driven robotic arm includes M platforms, and each platform contains N groups of SMA springs below it. Each SMA is in a compressed or stretched state. Then there are 2MN subsystems in this robotic arm; from Equation (1), it can be seen that the SMA under the ith platform only acts on the ith platform, so each joint can be independently controlled. For the ith platform, there are a total of 2N sub-cases, and the sub-cases The subscript i represents the platform where it is located. The number 1 indicates that the corresponding SMA is in a stretched state, and the number 0 indicates that the corresponding SMA is in a compressed state.

[0026] Preferably, from the SMA constitutive characteristics of Equation (2), when the SMA spring switches between the compressed and stretched states, the corresponding sub-cases also change. The change of the sign function sign(·) in the state equation of Equation (3) represents that the dynamic model has changed, and at the same time, the corresponding control method or parameters are adjusted accordingly.

[0027] Preferably, by monitoring the sub - situation where the system is located and calling the corresponding control parameters; when the system switches, the corresponding control parameters are switched, and the flexible robotic arm driven by SMA can track the desired signal in any situation to complete the control of the MIMO switching system.

[0028] Preferably, the MIMO - PID module optimized based on the genetic algorithm:

[0029] For the i - th platform, the desired trajectory is given as Define the trajectory tracking error of the dynamic system as:

[0030]

[0031] Then the state equation of Equation (3) is rewritten as the following error dynamic equation:

[0032]

[0033] For the MIMO system of the robotic arm, apply the PID controller to the controllable input quantity uij of Equation (2):

[0034]

[0035] where, P ij 、I ij 、D ij represent the control parameters of the j - th group of SMA springs of the i - th platform; select the ITAE (Integrated Time and Absolute Error) index as the optimization function:

[0036]

[0037] Preferably, the genetic algorithm simulates the natural selection and genetic mechanism of evolution theory, searches for the optimal solution by simulating the natural evolution process, including the initialization, selection, crossover, and mutation processes of chromosome genes. Facing complex combinatorial optimization problems, it can obtain better optimization results; based on the Matlab 2021a platform, use the genetic algorithm GA toolbox to optimize the control parameters to make the ITAE index reach the optimal; call the genetic algorithm GA toolbox:

[0038] x = ga(fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (8)

[0039] where, the configuration of each parameter is as follows: fun represents the optimization function, that is, Equation (7) J ITAE; nvars represents the number of elements of the x vector. For the i-th platform, N groups of SMA springs contain 3N PID control parameters; IntCon represents the subscript of positive integers in the x vector, which ranges from 1 to 3N here; A, b, Aeq, and beq represent linear constraints, that is nonlcon is the non-linear function constraint. Since there is no constraint in this model, they are all empty matrices; lb and ub represent the upper and lower bounds of the variable x, that is lb ≤ x ≤ ub. The upper and lower bound constraints of the PID control parameters are adjusted according to the external voltage or current signal. The default interval is taken as ±100 and adjusted according to the actual situation; options represent the optimization parameters.

[0040] The present invention also provides a gain allocation control method for an SMA-driven flexible robotic arm switching system. The method is applied to the SMA-driven flexible robotic arm switching system described above, and the method includes the following steps:

[0041] Step S1: Input the constitutive parameters of the SMA spring, the physical configuration of the robotic arm, and the desired trajectory of the robotic arm;

[0042] Step S2: Construct the state equation of the robotic arm;

[0043] Step S3: Identify the states of each SMA spring;

[0044] Step S4: Determine whether each platform sub-case has changed. If it has changed, look up the LUT; if it has not changed, output the MIMO-PID control parameters;

[0045] Step S5: After looking up the LUT, determine whether the corresponding MIMO-PID control parameters exist. If they exist, update the error dynamics equation of the robotic arm; if they do not exist, construct the ITAE optimization function;

[0046] Step S6: After constructing the ITAE optimization function, call the genetic algorithm for optimization and output the MIMO-PID control parameters;

[0047] Step S7: After updating the error dynamics equation of the robotic arm, determine whether the trajectory tracking is completed and meets the accuracy requirements. If it meets, output the MIMO-PID time-sequence control quantity; if it does not meet, return to Step S5.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. By considering the constitutive characteristics of the SMA spring, the present invention clarifies the location and cause of the switching phenomenon and establishes a dynamic state equation of the flexible robotic arm including the switching phenomenon. This state equation can provide a theoretical basis and a mathematical model for the research on the non-linearity and control of the switching system;

[0050] 2. The present invention designs a MIMO-PID controller through the error dynamics equation, constructs an ITAE optimization function, and uses a genetic algorithm for optimization; it solves the problem that the robotic arm has multiple Euler angle inputs, multiple control quantity outputs, and the control quantities are coupled with each other, making it difficult to manually adjust the control parameters. The genetic algorithm can quickly obtain a better control effect, provide reasonable control parameters, and ensure control stability.

[0051] 3. The present invention introduces the gain scheduling control technology, monitors the state of the system in real time, and updates the control parameters accordingly to achieve the goal of system trajectory tracking; when system switching occurs, the dynamic model changes. If the control method or parameters are not adjusted accordingly, it may cause system instability or control failure. By monitoring the system state, such situations can be avoided; when combined with the MIMO-PID control method, each model subsystem can better track the dynamic target.

[0052] 4. The present invention combines the gain scheduling control technology, MIMO-PID, and genetic algorithm for optimizing control parameters, which can provide a reference for other robotic arms with switching systems, MIMO systems, and those driven by intelligent materials, such as pneumatic artificial muscles, in terms of control methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Other features, objectives, and advantages of the present invention will become more apparent by reading the detailed description of the non-limiting embodiments with reference to the following drawings:

[0054] Figure 1 It is the process schematic diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0056] Example 1:

[0057] According to a switching system of an SMA-driven flexible robotic arm provided by the present invention, it includes an SMA spring constitutive characteristic module, an SMA-driven robotic arm state equation module, a model subsystem and a gain scheduling control module, and a MIMO-PID module optimized based on a genetic algorithm.

[0058] The SMA spring constitutive characteristic module takes into account the switching characteristics introduced by SMA, elaborates on the location and causes of switching and its function expression, and analyzes the influence of the switching characteristics and strong nonlinear characteristics of SMA on the control of flexible robotic arms;

[0059] The robotic arm state equation module driven by SMA combines the constitutive model of SMA to establish the state equation of the flexible robotic arm with switching phenomena for dynamic analysis or control;

[0060] The model subsystem and gain allocation control module define the concept of the switching subsystem, introduce the gain allocation control technology, and adjust the control parameters correspondingly by real-time monitoring the state of the dynamic system;

[0061] The MIMO-PID module based on genetic algorithm optimization discusses the PID controller of the MIMO system, the objective optimization function, genetic algorithm optimization and its assignment; combined with the gain allocation control technology, the PID parameters optimized by the genetic algorithm are assigned to each subsystem to achieve the goal of trajectory tracking of the switching system.

[0062] SMA spring constitutive characteristic module: SMA has shape memory effect through martensitic phase transformation and inverse transformation. When SMA is axially stretched by an external force, axial deformation occurs. After unloading the external force, residual deformation remains. When heated to a certain temperature, the residual deformation can be eliminated and work is done on the external force; when SMA is axially compressed by an external force, the force manifestation after heating to a certain temperature is opposite to that in tension; at the critical position of compression and tension, there is a large jump in its output force, showing a discontinuous phenomenon; when both the tension and compression of the jth group of SMA springs on the ith platform occur axially, its output force F ij :

[0063]

[0064] where ξ ij represents the martensite volume fraction of the jth group of SMA springs on the ith platform, ξ0 represents the initial martensite volume fraction, T ij represents the temperature of the jth group of SMA springs on the ith platform, T0 is the ambient temperature, Ω represents the phase transformation coefficient, Θ represents the thermoelastic coefficient, σ e is the elastic stress limit of SMA, F e and Y e are proportional parameters determined by the SMA spring structure.

[0065] The martensite volume fraction and temperature are controlled by external voltage or current signals. Define the controllable input quantity uij of the jth group of SMA springs on the ith platform as:

[0066]

[0067] SMA-driven robotic arm state equation module: For the i-th platform, define its Euler angles relative to the fixed coordinate system as Perform dynamic modeling on the SMA-driven robotic arm by Lagrangian method or Newton-Euler method, and transform the dynamic model into the form of state equation. For the i-th platform, the state equation has the following form:

[0068]

[0069] where f1, f2, f3 describe the influence of the system parameters of the dynamic model, k1, k2, k3 represent the influence of the control quantity on the dynamic model, ξ1, ξ2, ξ3 represent the system model error and external disturbance, ΔY ij represents the deformation of the j-th group of SMA springs of the i-th platform, uij represents the controllable input quantity of the j-th group of SMA springs of the i-th platform, sign(·) represents the sign function, and the sign function is introduced by the discontinuity of the SMA output force.

[0070] Model subsystem and gain allocation control module: The SMA-driven robotic arm contains M platforms, and each platform has N groups of SMA springs below it. Each SMA is in a compressed or stretched state, so there are 2MN subsystems in this robotic arm; from equation (1), it can be seen that the SMA under the i-th platform only acts on the i-th platform, so each joint can be independently controlled. For the i-th platform, there are 2N sub-cases in total, and the sub-cases The subscript i represents the platform where it is located, the number 1 represents that the corresponding SMA is in the stretched state, and the number 0 represents that the corresponding SMA is in the compressed state.

[0071] From the SMA constitutive characteristics of equation (2), when the SMA spring switches between the compressed and stretched states, the corresponding sub-cases also change. The change of the sign function sign(·) in equation (3) of the state equation represents that the dynamic model has changed, and at the same time, the corresponding control method or parameters are adjusted accordingly.

[0072] By monitoring the sub-case where the system is located and calling the corresponding control parameters; when the system switches, the corresponding control parameters are switched, and the SMA-driven flexible robotic arm can track the desired signal in any case and complete the control of the MIMO switching system.

[0073] MIMO-PID module based on genetic algorithm optimization: For the i-th platform, the desired trajectory is given as Define the trajectory tracking error of the dynamic system as:

[0074]

[0075] The state equation of Equation (3) is rewritten as the following error dynamics equation:

[0076]

[0077] For the MIMO system of the robotic arm, apply the PID controller to the controllable input uij of Equation (2):

[0078]

[0079] where P ij , I ij , D ij represent the control parameters of the jth group of SMA springs on the ith platform; select the ITAE (Integrated Time and Absolute Error) index as the optimization function:

[0080]

[0081] The genetic algorithm simulates the natural selection and genetic mechanism of evolution theory, searches for the optimal solution by simulating the natural evolution process, including the initialization, selection, crossover, and mutation processes of chromosome genes. Facing complex combinatorial optimization problems, it can obtain better optimization results. Based on the Matlab 2021a platform, use the genetic algorithm GA toolbox to optimize the control parameters to make the ITAE index reach the optimal; call the genetic algorithm GA toolbox:

[0082] x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,IntCon,options) (8)

[0083] where the parameter configurations are as follows: fun represents the optimization function, that is, Equation (7) J ITAE ; nvars represents the number of elements of the x vector. For the ith platform, N groups of SMA springs contain 3N PID control parameters; IntCon represents the subscript of the positive integers in the x vector, which is from 1 to 3N here; A, b, Aeq, and beq represent linear constraints, that is nonlcon is the nonlinear function constraint. Since there is no constraint in this model, they are all empty matrices; lb and ub represent the upper and lower bounds of the variable x, that is, lb ≤ x ≤ ub. Adjust the upper and lower bound constraints of the PID control parameters according to the external voltage or current signal. The default interval is taken as ±100 and adjusted according to the actual situation; options represent the optimization parameters.

[0084] The present invention also provides a gain allocation control method for an SMA-driven flexible robotic arm switching system. The method is applied to the SMA-driven flexible robotic arm switching system described above. The method includes the following steps:

[0085] Step S1: Input the constitutive parameters of the SMA spring, the physical configuration of the robotic arm, and the desired trajectory of the robotic arm.

[0086] Step S2: Construct the state equation of the robotic arm.

[0087] Step S3: Identify the states of each SMA spring.

[0088] Step S4: Determine whether each platform sub - case has changed. If it has changed, look up the Look - Up Table (LUT); if not, output the MIMO - PID control parameters.

[0089] After looking up the LUT in Step S5, determine whether the corresponding MIMO - PID control parameters exist. If they exist, update the error dynamics equation of the robotic arm; if not, construct the ITAE optimization function.

[0090] After constructing the ITAE optimization function in Step S6, call the genetic algorithm for optimization and output the MIMO - PID control parameters.

[0091] After updating the error dynamics equation of the robotic arm in Step S7, determine whether the trajectory tracking has ended and meets the accuracy requirements. If it meets the requirements, output the MIMO - PID time - series control quantity; if not, return to Step S5.

[0092] Example 2:

[0093] Embodiment 2 is a preferred example of Embodiment 1, which is used to illustrate the present invention more specifically.

[0094] The present invention provides a gain - allocation control method for an SMA - driven flexible robotic arm switching system, which relates to the technical field of robotic arm control. The method includes: considering the discontinuity of the output force of the SMA at the critical position of tension and compression, establishing the state equation of the robotic arm by combining the physical configuration of the flexible robotic arm and the constitutive parameters of the SMA; introducing the switching subsystem and the gain - allocation control technology, and adjusting the control parameters accordingly when the system switches by real - time monitoring of the system parameters to achieve the control stability of the system; constructing a MIMO - PID controller, selecting the ITAE optimization objective, calling the genetic algorithm, and optimizing the optimal control parameters of the subsystem and storing them in the look - up table. The gain - allocation control method for the SMA - driven flexible robotic arm switching system proposed in this patent can avoid the phenomenon of system instability or control failure caused by the discontinuity of the output force of the SMA at the critical position, and achieve the goal of end - trajectory tracking of the flexible robotic arm switching system. This patent can provide theoretical guidance and control reference for other flexible robotic arm systems with switching phenomena.

[0095] Considering that the robotic arm has multiple joints, which are connected end to end in sequence. In each joint, there are several groups of shape memory alloys (SMA), disk platforms, ball hinge straight rods, etc. This SMA-driven robotic arm is considered to contain M platforms, and each platform has N groups of SMA springs below it. At the same time, the robotic arm has multiple Euler angle inputs and multiple SMA spring outputs, making it a multiple input multiple output (MIMO) system. Combining forward and inverse kinematics and trajectory planning, specific tasks such as target grasping and spatial obstacle avoidance can be completed by the robotic arm. However, due to the non-linearity of the height of the SMA spring itself and the system switching phenomenon at the critical position of compression and tension, both bring challenges to the control of the flexible robotic arm. The control parameters or methods need to be adjusted in combination with the system switching to avoid system instability or uncontrollable phenomena.

[0096] This patent is divided into four modules. In the first module, the switching characteristics introduced by SMA are mainly considered. The position and cause of the switching and its function expression are described, and the influence of the switching characteristics and strong non-linear characteristics of SMA on the control of the flexible robotic arm is analyzed. In the second module, combined with the constitutive model of SMA, a general state equation of the flexible robotic arm with switching phenomenon is established for dynamic analysis or control. In the third module, the concept of the switching subsystem is defined, and the gain allocation control technology is introduced. By monitoring the state of the dynamic system in real time, the control parameters are adjusted accordingly. In the fourth module, the PID controller, target optimization function, genetic algorithm optimization and its assignment of the MIMO system are discussed. Combining the gain allocation control technology, the PID parameters optimized by the genetic algorithm are assigned to each subsystem to achieve the goal of trajectory tracking of the switching system.

[0097] SMA spring constitutive characteristic module:

[0098] Shape Memory Alloy (SMA) has shape memory effect through martensitic phase transformation and reverse transformation. When SMA is axially stretched by an external force, it undergoes axial deformation. After unloading the external force, residual deformation remains. When heated to a certain temperature, the residual deformation can be eliminated and work is done against the external force. When SMA is axially compressed by an external force, after heating to a certain temperature, the force manifestation is opposite to that in tension. However, at the critical position between compression and tension, there is a large jump in its output force, showing a discontinuous phenomenon. According to experimental data, even a very small deformation will generate a huge axial output force near the critical position. This axial output force has an almost jump-like impact on the flexible robotic arm system, and its mathematical manifestation is a step, thus causing system switching. If this switching phenomenon is not fully understood and results in a mismatch between the switching subsystem and the controller, it will lead to unpredictable system dynamics and possible instability. When both the tension and compression of the j-th group of SMA springs on the i-th platform occur axially, its output force F ij :

[0099]

[0100] where ξ ij represents the martensite volume fraction of the j-th group of SMA springs on the i-th platform, ξ0 represents the initial martensite volume fraction, T ij represents the temperature of the j-th group of SMA springs on the i-th platform, T0 is the ambient temperature, Ω represents the phase transformation coefficient, Θ represents the thermoelastic coefficient, σ e is the elastic stress limit of SMA, F e and Y e are proportional parameters determined by the SMA spring structure.

[0101] The martensite volume fraction and temperature can be controlled by external voltage or current signals. Define the controllable input quantity uij of the j-th group of SMA springs on the i-th platform as:

[0102]

[0103] SMA-driven robotic arm state equation module:

[0104] For the i-th platform, define its Euler angles relative to the fixed coordinate system as For the convenience of writing, the time (t) in the following formulas is omitted. By using the Lagrangian method or Newton-Euler method to perform dynamic modeling on the SMA-driven robotic arm, the dynamic model can be transformed into the form of a state equation. For the i-th platform, the state equation has the following form:

[0105]

[0106] Among them, f1, f2, and f3 describe the influence of the dynamic model system parameters, k1, k2, and k3 represent the influence of the control quantity on the dynamic model, ξ1, ξ2, and ξ3 represent the system model error and external disturbance, and ΔY ij represents the deformation of the j -th group of SMA springs on the i -th platform, uij represents the controllable input quantity of the j -th group of SMA springs on the i -th platform, sign(·) represents the sign function, and the sign function is introduced by the discontinuity of the SMA output force.

[0107] Model subsystem and gain - allocation control module:

[0108] The SMA - driven robotic arm contains M platforms, and each platform has N groups of SMA springs below it. Each SMA can be in a compressed or stretched state. Then, there are 2MN subsystems in this robotic arm. From Equation (1), it can be seen that the SMA under the i -th platform only acts on the i -th platform. Therefore, each joint can be independently controlled. For the i -th platform, there are a total of 2N sub - cases. The sub - cases The subscript i represents the platform where it is located. The number 1 represents that the corresponding SMA is in a stretched state, and the number 0 represents that the corresponding SMA is in a compressed state. The correspondence between the sub - cases and the SMA is as follows in the table.

[0109]

[0110] From the SMA constitutive characteristics of Equation (2), when the SMA spring switches between the compressed and stretched states, the corresponding sub - cases also change. The change of the sign function sign(·) in the state equation of Equation (3) represents that the dynamic model has changed, and at the same time, the corresponding control method or parameters also need to be adjusted accordingly.

[0111] By monitoring the sub - case where the system is located and calling the corresponding control parameters, this is the idea of gain - allocation control. When the system switches, the corresponding control parameters are switched. Based on this, the SMA - driven flexible robotic arm can track the desired signal in any case and complete the control of the MIMO switching system.

[0112] MIMO - PID module based on genetic - algorithm optimization:

[0113] For the i -th platform, the desired trajectory is given as Define the trajectory - tracking error of the dynamic system as:

[0114]

[0115] Then, the state equation of Equation (3) can be rewritten as the following error - dynamics equation:

[0116]

[0117] A PID controller that controls by the proportional (P), integral (I), and derivative (D) of the error has a simple principle, wide application, and independent parameters. For the MIMO system of the robotic arm, the PID controller is applied to the controllable input uij in Equation (2):

[0118]

[0119] where P ij , I ij , D ij represent the control parameters of the jth group of SMA springs on the ith platform. By selecting appropriate control parameters, the error performance index can be optimized. The ITAE (Integrated Time and Absolute Error) index is selected as the optimization function:

[0120]

[0121] The genetic algorithm simulates the natural selection and genetic mechanisms of evolution theory, searches for the optimal solution by simulating the natural evolution process, and includes processes such as the initialization, selection, crossover, and mutation of chromosome genes. Facing complex combinatorial optimization problems, it can usually obtain better optimization results quickly. Based on the Matlab 2021a platform, the genetic algorithm GA toolbox is used to optimize the control parameters to make the ITAE index optimal. Call the genetic algorithm GA toolbox:

[0122] x = ga(fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (8)

[0123] where the configurations of each parameter are as follows: fun represents the optimization function, that is, Equation (7) J ITAE ; nvars represents the number of elements in the x vector. For the ith platform, N groups of SMA springs contain 3N PID control parameters; IntCon represents the subscripts of positive integers in the x vector, which is from 1 to 3N here; A, b, Aeq, beq represent linear constraints, that is nonlcon is the nonlinear function constraint. Since there is no constraint in this model, they are all empty matrices; lb and ub represent the upper and lower bounds of the variable x, that is, lb ≤ x ≤ ub. The upper and lower bound constraints of the PID control parameters can be adjusted according to the external voltage or current signal. The default interval is taken as ±100 and can be adjusted according to the actual situation; options represent the optimization parameters, and the default values can be used without special requirements.

[0124] The performance of the PID controller depends on the proper selection of the proportional, integral, and derivative parameters, which can optimize the objective optimization function. At this time, the model control effect is also relatively ideal. By using the genetic algorithm for optimization, it avoids the time-consuming and inaccurate manual adjustment of PID parameters. At the same time, the PID parameters and the corresponding situations after each optimization are stored in the Look Up Table (LUT) for future calls to avoid duplicate work.

[0125] Combining the above four modules, establish the state equation of the robotic arm including the SMA switching phenomenon, and call the MIMO-PID optimized by the genetic algorithm to control each model subsystem. Real-time monitor the system state, adopt the gain allocation control technology to ensure the system stability, and achieve the goal of the switching system tracking the desired trajectory.

[0126] By considering the constitutive characteristics of the SMA spring, the location and cause of the switching phenomenon are clarified, and the dynamic state equation of the flexible robotic arm including the switching phenomenon is established. This state equation can provide a theoretical basis and a mathematical model for the research on the nonlinearity and control of the switching system.

[0127] Through the error dynamics equation, design the MIMO-PID controller, construct the ITAE optimization function, and use the genetic algorithm for optimization. It solves the problem that the robotic arm has multiple Euler angle inputs, multiple control quantity outputs, and the control quantities are coupled with each other, making it difficult to manually adjust the control parameters. The genetic algorithm can quickly obtain better control effects, provide reasonable control parameters, and ensure control stability.

[0128] By introducing the gain allocation control technology, real-time monitor the state of the system, and update the control parameters accordingly to achieve the goal of system trajectory tracking. When the system switches, the dynamic model changes. If the control method or parameters are not adjusted accordingly, it may cause the system to become unstable or the control to fail. By monitoring the system state, similar situations can be avoided. Combined with the MIMO-PID control method, each model subsystem can better track the dynamic target.

[0129] This patent combines the gain allocation control technology, MIMO-PID, and genetic algorithm to optimize the control parameters, which can provide a reference for the control methods of other robotic arms with switching systems, MIMO systems, and intelligent material-driven systems, such as pneumatic artificial muscles.

[0130] Those skilled in the art can understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0131] Those skilled in the art know that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0132] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. An SMA-driven flexible robotic arm switching system, characterized in that, It includes an SMA spring constitutive characteristic module, an SMA-driven robotic arm state equation module, a model subsystem and gain allocation control module, and a MIMO-PID module optimized based on a genetic algorithm; The constitutive characteristic module of the SMA spring defines the position and cause of the switching occurrence based on the phase change characteristics of SMA, and establishes the function expression of the SMA output force through formula (1) to quantify the influence of the switching characteristics and non-linear characteristics of SMA on the dynamic model of the flexible robotic arm; SMA has shape memory effect through the phase transformation and reverse transformation of martensite. When SMA is axially stretched by an external force, axial deformation occurs. After unloading the external force, residual deformation remains. When heated to a certain temperature, the residual deformation can be eliminated and work is done on the external force at the same time; when SMA is axially compressed by an external force, the force manifestation form after heating to a certain temperature is opposite to that during stretching; at the critical position of compression and stretching, there is a large jump in its output force, showing a discontinuous phenomenon; when both the stretching and compression of the j-th group of SMA springs in the i-th platform occur axially, the function expression F of the SMA output force ij is as follows: where ξ ij represents the martensite volume fraction of the j -th group of SMA springs on the i -th platform, ξ0 represents the initial martensite volume fraction, T ij represents the temperature of the j -th group of SMA springs on the i -th platform, T0 is the ambient temperature, Ω represents the phase transformation coefficient, Θ represents the thermo - elastic coefficient, σ e is the SMA elastic stress limit, F e and Y e are the proportional parameters determined by the SMA spring structure, ΔY ij is the deformation amount; The SMA-driven robotic arm state equation module combines the function expression of the SMA output force to establish a flexible robotic arm state equation with switching phenomena; The model subsystem and gain allocation control module define the concept of a switching subsystem and adjust the control parameters through gain allocation control technology based on the real-time monitored system state; The MIMO-PID module optimized based on a genetic algorithm aims at a multi-input multi-output PID controller, optimizes the ITAE objective function through a genetic algorithm, and allocates the optimized PID parameters to each subsystem to achieve the trajectory tracking of the switching system; In the model subsystem and the gain allocation control module, the SMA-driven robotic arm includes M platforms, and each platform is equipped with N groups of SMA springs below. Each SMA is in a compressed or stretched state, so there are 2MN subsystems in this robotic arm. From Equation (1), it can be seen that the SMA under the i-th platform only acts on the i-th platform, so each joint can be independently controlled. For the i-th platform, there are a total of 2N subsystems, and the subsystem The subscript i represents the platform where it is located. The number 1 indicates that the corresponding SMA is in a stretched state, and the number 0 indicates that the corresponding SMA is in a compressed state.

2. The SMA-driven flexible robotic arm switching system according to claim 1, wherein The martensite volume fraction and temperature are controlled by an external voltage or current signal, and the control input u for adjusting the martensite volume fraction and temperature of the jth group of SMA springs in the ith platform is defined as follows: ij as follows:

3. The SMA-driven flexible robotic arm switching system according to claim 2, characterized in that In the state equation module of the SMA-driven robotic arm, for the i-th platform, the Euler angles relative to the fixed coordinate system are defined as By using the Lagrangian method or the Newton-Euler method to perform dynamic modeling on the SMA-driven robotic arm, a dynamic model of the flexible robotic arm is obtained. The dynamic model of the flexible robotic arm is transformed into the state equation of the flexible robotic arm. For the i-th platform, the state equation has the following form: Among them, f1, f2, f3 describe the influence of the dynamic model system parameters, k1, k2, k3 represent the influence of the control quantity on the dynamic model, ξ1, ξ2, ξ3 represent the system model error and external disturbance, ΔT ij represents the deformation of the j-th group of SMA springs on the i-th platform, u ij represents the controllable input quantity of the j-th group of SMA springs on the i-th platform, sign(·) represents the sign function, which is introduced by the discontinuity of the SMA output force and reflects the discontinuity of the SMA output force.

4. The SMA-driven flexible robotic arm switching system according to claim 3, wherein It can be seen from the functional expression of the SMA output force in Equation (1) that when the SMA spring switches between the compressed and stretched states, the corresponding subsystem also changes. The change in the sign function sign(·) in the state equation of Equation (3) represents that the dynamic model has changed, and at the same time, the corresponding control method or parameters are adjusted accordingly.

5. The SMA-driven flexible robotic arm switching system according to claim 4, wherein By monitoring the subsystem where the system is located and calling the corresponding control parameters; when the system switches, the corresponding control parameters are switched, and the SMA-driven flexible robotic arm can track the desired signal in any situation to complete the control of the switching system.

6. The SMA-driven flexible robotic arm switching system according to claim 5, wherein In the MIMO-PID module optimized by the genetic algorithm, for the i-th platform, the desired trajectory is given as Define the trajectory tracking error of the dynamic system as: Then the state equation of Equation (3) is rewritten as the following error dynamics equation: For the robotic arm, which is a MIMO system, apply the PID controller to the control input u in Equation (2). ij : Among them, P ij , I ij , D ij represent the control parameters of the jth group of SMA springs on the ith platform; the ITAE (Integrated Time and Absolute Error) index is selected as the optimization function:

7. The SMA-driven flexible robotic arm switching system according to claim 6, wherein, Based on the Matlab2021a platform, use the genetic algorithm GA toolbox to optimize the control parameters to make the ITAE index reach the optimal; call the genetic algorithm GA toolbox: x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,IntCon,options) (8) Among them, the parameter configurations are as follows: fun represents the optimization function, i.e., Equation (7) J ITAE ; nvars represents the number of elements of the x vector. For the i-th platform, N groups of SMA springs contain 3N PID control parameters; IntCon represents the subscripts of positive integers of the x vector, which starts from 1 to 3N here; A, b, Aeq, and beq represent linear constraints, i.e., nonlcon is the non-linear function constraint. Since there is no constraint in this model, they are all empty matrices; lb and ub represent the upper and lower bounds of the variable x, i.e., lb ≤ x ≤ ub. The upper and lower bound constraints of the PID control parameters are adjusted according to the external voltage or current signal. The default interval is taken as ±100 and adjusted according to the actual situation; options represents the optimization parameters.

8. A gain allocation control method for a SMA-driven flexible robotic arm switching system, characterized in that, The method is applied to the SMA-driven flexible robotic arm switching system described in Claim 7, and the method includes the following steps: Step S1: Input the SMA spring constitutive parameters, the physical configuration of the robotic arm, and the desired trajectory of the robotic arm; Step S2: Construct the robotic arm state equation; Step S3: Identify the states of each SMA spring; Step S4: Determine whether the subsystem has changed. If it has changed, look up the look-up table LUT; if it has not changed, output the MIMO-PID control parameters; After looking up the look-up table LUT, determine whether the corresponding MIMO-PID control parameters exist. If they exist, update the robotic arm error dynamics equation; if they do not exist, select the ITAE optimization function; After selecting the ITAE optimization function, call the genetic algorithm to optimize and output the MIMO-PID control parameters; After updating the robotic arm error dynamics equation, determine whether the trajectory tracking is over and whether the accuracy requirement is met. If it is met, output the MIMO-PID time-series control quantity; if it is not met, return to Step S5.

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