Rehabilitation lower limb exoskeleton joint safety constraint trajectory tracking control method

Abstract

The embodiment of the application provides a rehabilitation lower limb exoskeleton joint safety constraint trajectory tracking control method, and belongs to the technical field of exoskeleton robot control. The method comprises the following steps: acquiring the state of the lower limb exoskeleton at the current moment, and constructing a dynamics model; constructing a differential homeomorphism mapping according to the bilateral boundary condition, performing coordinate transformation on each joint angle, and constructing a dynamics model and a servo constraint model in the transformed domain based on the transformed coordinate variables; uniformly representing the uncertain action in the dynamics model in the transformed domain, and adopting a deep recurrent neural network to perform online estimation on the comprehensive uncertain term; constructing an adaptive robust controller that fuses deep recurrent neural network estimation compensation and residual error adaptive robust compensation; optimizing the key parameters of the adaptive robust controller through a Nash game parameter optimization mechanism to obtain optimal parameters; and substituting the optimal parameters into the adaptive robust controller to obtain joint driving input. The application can reduce driving energy consumption.

Description

Technical Field

[0001] This invention relates to the field of exoskeleton robot control technology, specifically to a method for tracking and controlling the safety constraint trajectory of a lower limb exoskeleton joint for rehabilitation. Background Technology

[0002] Lower limb rehabilitation exoskeletons are wearable robotic devices designed to assist patients in lower limb joint flexion and extension, gait training, and motor function recovery. They are widely used in rehabilitation settings such as nerve injury, post-orthopedic surgery, and motor dysfunction. These devices improve the standardization, repeatability, and efficiency of rehabilitation training by driving lower limb joints along predetermined trajectories. Because the exoskeleton acts directly on the lower limbs, and the patient's limb status, muscle tone changes, and human-machine interaction continuously affect joint movement response during training, its control performance not only impacts trajectory tracking effectiveness but also relates to safety, stability, and comfort during training. Therefore, achieving stable trajectory tracking while ensuring joint movement safety has become a crucial technical challenge in this field.

[0003] In existing technologies, trajectory tracking control of lower limb rehabilitative exoskeletons typically employs methods such as PID control, adaptive control, robust control, and impedance control. While these methods can improve system control performance to some extent, rehabilitative exoskeletons often experience various influencing factors during actual operation, including parameter perturbations, external disturbances, and interactions. This results in significant system uncertainty, leading to problems such as insufficient tracking accuracy, large control input fluctuations, and limited adaptability in practical applications. Some robust control or adaptive robust control methods often require compensation using an upper bound on the uncertainty term. When the estimate of the comprehensive uncertainty term upper bound is too conservative, it can easily lead to increased control input or uneven torque changes; conversely, when the upper bound estimate is insufficient, it is difficult to suppress disturbances during training in a timely manner. For control methods that use neural networks to estimate the uncertainty term, if the neural network estimation results are not combined with a residual compensation mechanism, the estimation error may still affect the uncertainty term compensation effect. Meanwhile, rehabilitation training has clear safety requirements for joint range of motion. In some existing lower limb exoskeleton control schemes, joint movement is usually constrained by methods such as amplitude limiting, saturation, or threshold protection. These methods are mostly additional restrictions and make it difficult to directly incorporate joint safety boundary requirements into control system modeling and controller design. Therefore, it is still difficult to fully guarantee that joint movement remains within the safe range during dynamic processes. In addition, the values ​​of multiple key parameters in the exoskeleton controller usually affect trajectory tracking accuracy, control input magnitude, and motion smoothness simultaneously. In existing control schemes, the determination of relevant parameters still relies heavily on manual experience tuning or adjustment based on a single performance index, making it difficult to simultaneously meet multiple performance requirements. Summary of the Invention

[0004] The purpose of this invention is to provide a trajectory tracking control method for lower limb exoskeletons under joint safety constraints, addressing the challenge of simultaneously achieving high trajectory tracking accuracy, joint motion safety, and smoothness of joint drive input under the combined influence of joint safety angle constraints, model uncertainty, human-computer interaction, and other time-varying uncertainties during rehabilitation training. This invention performs transform domain modeling based on joint safety constraints and implements trajectory tracking control based on the transform domain model. It combines online estimation compensation using deep recurrent neural networks, adaptive robust residual compensation, and collaborative optimization of key parameters to improve the system's adaptability to comprehensive uncertainties, reduce the adverse effects of conservative compensation on control input, and enhance trajectory tracking performance and overall control effectiveness under joint safety constraints.

[0005] To achieve the above objectives, embodiments of the present invention provide a method for tracking and controlling the safety constraint trajectory of a lower limb exoskeleton joint in rehabilitation, comprising: Obtain the current state of the lower limb exoskeleton and construct a dynamic model of the rehabilitation lower limb exoskeleton system; The trajectory tracking servo constraint is constructed based on the preset rehabilitation training reference trajectory, and the bilateral boundary conditions of each joint are constructed based on the joint safety angle range. Based on the bilateral boundary conditions, a differential homeomorphism is constructed, a coordinate transformation is performed on each joint angle, and a dynamic model and a servo constraint model in the transformation domain are constructed based on the transformed coordinate variables. Uncertainty effects in the dynamic model under the transformed domain are uniformly characterized, and a deep recurrent neural network is used to estimate the comprehensive uncertainty term online. Construct an adaptive robust controller that integrates deep recurrent neural network estimation compensation and residual adaptive robust compensation; The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain the optimal parameters; The optimal parameters are substituted back into the adaptive robust controller to obtain the joint drive input, thereby realizing trajectory tracking control of the rehabilitation lower limb exoskeleton within the safe range of the joint.

[0006] Optionally, the current state of the lower limb exoskeleton is obtained, and a dynamic model of the rehabilitation lower limb exoskeleton system is constructed, including: A dynamic model of the lower limb exoskeleton system for rehabilitation is established based on formula (1). (1) in, , and Let represent the joint angle vector, joint angular velocity vector, and joint angular acceleration vector of each controlled joint of the lower limb exoskeleton, respectively. The system inertia matrix is ​​positive definite. For Coriolis eccentricity matrix, For gravity, This is a bounded uncertain parameter vector used to characterize system parameter deviations and other time-varying uncertainties. The control torque output by the motors of each joint of the exoskeleton. This refers to the human-machine interaction torque generated between the human body and the exoskeleton during rehabilitation training. For time.

[0007] Optionally, trajectory tracking servo constraints are constructed based on a preset rehabilitation training reference trajectory, and bilateral boundary conditions for each joint are constructed based on the joint safety angle range, including: The servo constraint equations are established according to formula (2). (2) in, For the l-th servo constraint function Each component item l , Joint angle vector, This represents the sequence number of the servo constraint equation. The number of servo constraint equations. Number of controlled joints; The servo constraint equations are rearranged into constraint vector form, and their derivatives with respect to time are obtained, yielding the second-order constraint form shown in formula (3). (3) in, The constraint coefficient matrix, The joint angular acceleration vector. The target constraint vector for the acceleration layer; Based on the range of joint safety angles, establish the bilateral boundary conditions shown in formula (4). , (4) in, For the first Joint angle The lower boundary of safety, For the first Joint angle The upper boundary of safety, .

[0008] Optionally, a differential homeomorphism is constructed based on the bilateral boundary conditions, a coordinate transformation is performed on each joint angle, and a dynamic model and a servo constraint model in the transformation domain are constructed based on the transformed coordinate variables, including: According to formula (5), the first The transformation domain coordinate variables of each joint angle map the bounded joint angles in the original joint space, which are constrained by bilateral boundary conditions, to unbounded coordinate variables in the transformation domain. (5) in, For the first Transform domain coordinate variables of each joint angle It is a differential homeomorphism mapping; The specific form of the differential homeomorphic transformation can be obtained according to formula (6). (6) in, , , Transformation parameters; By performing the inverse solution of the differential homeomorphism of formula (6), the inverse transformation relation corresponding to formula (7) can be obtained. (7); Substituting the inverse transformation relationship into the dynamic model of the rehabilitation lower limb exoskeleton system established by formula (1), and combining it with human-computer interaction, the dynamic model in the transformation domain of formula (8) is obtained. (8) in, The equivalent inertia matrix in the transformation domain, For the coordinate acceleration variable in the transformation domain, For the velocity vector in the transformation domain, The coordinate vector in the transformation domain; The servo constraint relationships in the original joint space are synchronously transformed to the transform domain to obtain the constraint models in the transform domain of equations (9) to (11). (9) (10) (11) in, Let the vector be the position constraint function in the transform domain. The target constraint vector for the transformation domain position layer. Let be the full-rank transformation domain constraint coefficient matrix. For the coordinate vector in the transformation domain, For the velocity vector in the transformation domain, For the coordinate acceleration vector in the transformation domain, For the target constraint vector of the velocity layer in the transform domain, This is the target constraint vector for the acceleration layer in the transform domain.

[0009] Optionally, the uncertainties in the dynamic model under the transformed domain are uniformly characterized, and a deep recurrent neural network is used to estimate the comprehensive uncertainty term online, including: According to formula (12), the equivalent inertia matrix in the transformation domain is decomposed into a nominal part and an uncertain deviation part. (12) in, The equivalent inertia matrix in the transformation domain, The nominal part of the equivalent inertia matrix in the positive definite transformation domain. This represents the uncertain deviation portion of the equivalent inertia matrix in the transformation domain. According to formula (13), the transform domain comprehensive torque term including the influence of human-computer interaction is decomposed into a nominal part and an uncertain deviation part. (13) in, For the transformed domain composite torque term, For the nominal part of the synthesized torque term in the transform domain, This represents the uncertain deviation portion of the synthesized torque term in the transformed domain; Construct a composite error variable in the transform domain according to formula (14). (14) in, For the composite error vector in the transform domain, For error adjustment parameters, To constrain position following error, To constrain speed following error; The uncertainties and their coupling effects in the equivalent inertia matrix and the comprehensive moment term in the transformed domain are collectively denoted as the comprehensive uncertainty term, which is expressed according to formula (15). (15) in, To encompass the uncertainties, To predetermine the positive definite weight matrix, The inverse matrix corresponding to the nominal equivalent inertia matrix in the transformation domain. The uncertain deviation component of the inverse of the equivalent inertia matrix in the transformation domain. For nominal control items, For feedback correction items; According to formula (16), a deep recurrent neural network is used to perform a nonlinear approximation of the comprehensive uncertainty term. (16) in, This is the output layer weight matrix. This is the feature output vector of a deep recurrent neural network. This is the output vector of the deep recurrent neural network; The output layer weights, hidden layer base width parameters, hidden layer center parameters, and output feedback weights of the deep recurrent neural network are updated online based on the transform domain composite error variable.

[0010] Optionally, an adaptive robust controller integrating deep recurrent neural network estimation compensation and residual adaptive robust compensation is constructed, including: The control input of the adaptive robust controller is determined according to formula (17). (17) in, To control the input, For nominal control items, For feedback correction items, For deep recurrent neural network compensation terms, This is the adaptive robust compensation term for the residuals; The nominal control term is obtained according to formula (18). (18) in, Moore–Penrose generalized inverse; The feedback correction term is obtained according to formula (19). (19) in, This is the convergence adjustment coefficient; The compensation term for the deep recurrent neural network is obtained according to formula (20). , (20).

[0011] Optionally, an adaptive robust controller integrating deep recurrent neural network estimation compensation and residual adaptive robust compensation is constructed, including: The residual uncertainty term after estimation and compensation by the deep recurrent neural network is obtained according to formula (21). ,(twenty one) in, This refers to the residual uncertainty term after compensation by the deep recurrent neural network. The bounded upper bound function of the residual uncertainty term is determined according to formula (22). ,(twenty two) in, This is a lower bound parameter for the influence of the uncertain deviation of the inverse of the equivalent inertia matrix in the transform domain on the adaptive robust compensation of the residual. Uncertain parameters of the system The bounded domain of discourse, Θ, is the torque for human-computer interaction. Bounded domain of discourse Let be the upper bound function of the residual uncertainty term. The boundary parameter vector for the residual uncertainty term; To update the adaptive estimate of the boundary parameter vector of the residual uncertainty term online, an adaptive law as shown in formula (23) is designed. ,(twenty three) in, The boundary parameter vector of the residual uncertainty term The adaptive estimate, Design parameters for the adaptive law. For adaptive laws, The preset dead zone threshold; The adaptive robust compensation term for the residual is obtained according to formula (24). ,(twenty four) in, For the cooperative suppression gain coefficient, , For auxiliary functions, This is the upper bound estimation function for the residual uncertainty term determined based on the adaptive estimate.

[0012] Optionally, the key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters, including: The two key parameters of the adaptive robust controller, the convergence adjustment coefficient and the cooperative disturbance suppression gain coefficient, are used as two decision variables in the Nash game. Based on formula (25), a comprehensive performance evaluation upper bound function for Nash game parameter optimization is constructed. (25) in, This is the upper bound function for comprehensive performance evaluation. For residual compensation evaluation items, This is an evaluation item for online learning of deep recurrent neural networks; Based on the aforementioned comprehensive performance evaluation upper bound function, the transient comprehensive performance function and the steady-state comprehensive performance function are constructed according to formulas (26) and (27). (25) (26) in, For transient composite performance function, For steady-state comprehensive performance function, At the initial moment, From the initial moment The initial composite error energy is jointly determined by the transform domain composite error and the residual uncertainty term boundary parameter estimation error. This is the state convergence gain term; According to formula (28), a defuzzification operator is introduced to transform the performance function containing boundary parameters with residual uncertainties into a deterministic performance index. (28) in, To defuzzify the operator, Let be the function to be deblurred. For fuzzy sets, For fuzzy variables Regarding fuzzy sets membership function, It is a fuzzy variable; Based on the transient comprehensive performance function and the steady-state comprehensive performance function, the transient comprehensive performance index and the steady-state comprehensive performance index as shown in formula (29) and formula (30) are constructed respectively. (29) (30) in, For transient comprehensive performance indicators, For steady-state comprehensive performance indicators; Based on formulas (31) and (32), construct the cost functions corresponding to the two key parameters respectively. (31) (32) in, The cost function corresponding to the convergence adjustment coefficient. The cost function corresponding to the cooperative suppression gain coefficient. and To control the cost item.

[0013] Optionally, the key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters, including: Based on the decision variables, establish the optimal response model according to formula (33). (33) in, The feasible region for the convergence adjustment coefficient. The feasible region for the cooperative suppression gain coefficient, , The optimal parameters; Construct a joint objective function based on formula (34). (34) in, The joint objective function; The optimal parameters are obtained according to formula (35). (35) in, This represents the optimal parameter pair.

[0014] Optionally, the optimal parameters are substituted back into the adaptive robust controller to obtain joint drive inputs, thereby achieving trajectory tracking control of the rehabilitation lower limb exoskeleton within the joint safety range, including: Substituting the optimal parameters back into the adaptive robust controller, we obtain the joint drive input represented by formula (36). (36) in, This is the joint drive input after parameter coordination and optimization.

[0015] Through the above technical solution, embodiments of the present invention provide a method for trajectory tracking control of a lower limb exoskeleton joint with safety constraints. By acquiring the current state of the lower limb exoskeleton, a dynamic model of the lower limb exoskeleton system is constructed. A preset rehabilitation training reference trajectory is used as a servo constraint, and bilateral boundary conditions are established based on the range of joint safety angles. Differential homeomorphism is performed on each joint angle according to the bilateral boundary conditions to construct a transform domain dynamic model and a constraint model. Uncertain factors in the transform domain are uniformly described, and an adaptive robust controller integrating a deep recurrent neural network is constructed. The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters. These optimal parameters are then substituted back into the adaptive robust controller to obtain the joint drive input, thereby achieving trajectory tracking control of the lower limb exoskeleton within the joint safety range. This invention maps the lower limb exoskeleton joint angle variables constrained by safety angles to the transform domain through differential homeomorphism, transforming the constrained trajectory tracking problem in the original joint space into an equivalent unconstrained trajectory tracking control problem in the transform domain. Based on this, a controller is designed to maintain joint movement within a preset safety range while meeting trajectory tracking requirements. Furthermore, this invention unifies model uncertainty, human-computer interaction, and other disturbance factors in the transform domain as a comprehensive uncertainty term, and introduces a deep recurrent neural network to estimate the comprehensive uncertainty term online to construct a corresponding estimation compensation term. Simultaneously, a residual adaptive robust compensation mechanism is used to compensate for the residual uncertainty term after estimation compensation, which helps reduce the conservatism of uncertainty term compensation and improves the lower limb exoskeleton's anti-disturbance capability, adaptability, and trajectory tracking performance under complex rehabilitation training conditions. Based on this, this invention optimizes the key parameters of the adaptive robust controller through a Nash game parameter optimization mechanism, enabling the system to meet joint safety constraints and trajectory tracking requirements while also considering control input costs. This helps improve control input smoothness and reduce the adverse effects of excessive driving torque input.

[0016] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a method for tracking and controlling the safety constraint trajectory of a lower limb exoskeleton joint in rehabilitation, according to one embodiment of the present invention. Figure 2 This is a flowchart illustrating the construction of trajectory tracking servo constraints and bilateral boundary conditions according to one embodiment of the present invention; Figure 3 This is a flowchart illustrating the construction of a dynamic model and a servo constraint model in the transformation domain according to one embodiment of the present invention. Figure 4 This is a flowchart of an embodiment of the present invention for uniformly describing the comprehensive uncertainty terms in a dynamic model under the transform domain; Figure 5 This is a flowchart of constructing an adaptive robust controller according to one embodiment of the present invention; Figure 6 This is a flowchart illustrating the process of obtaining optimal parameters according to one embodiment of the present invention. Detailed Implementation

[0018] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0019] In the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, they do not mean that the applicant has used or necessarily used the solution.

[0020] like Figure 1 The diagram shown is a flowchart of a method for tracking and controlling the safety constraint trajectory of a lower limb exoskeleton joint in rehabilitation, according to one embodiment of the present invention. Figure 1 In this context, the control method may include: In step S1, the current state of the lower limb exoskeleton is obtained, and a dynamic model of the rehabilitation lower limb exoskeleton system is constructed. In step S2, trajectory tracking servo constraints are constructed based on the preset rehabilitation training reference trajectory, and bilateral boundary conditions for each joint are constructed based on the joint safety angle range. In step S3, a differential homeomorphism is constructed based on the bilateral boundary conditions, coordinate transformation is performed on each joint angle, and a dynamic model and servo constraint model in the transformation domain are constructed based on the transformed coordinate variables. In step S4, the uncertainties in the dynamic model under the transform domain are uniformly characterized, and a deep recurrent neural network is used to estimate the comprehensive uncertainty terms online. In step S5, an adaptive robust controller that integrates deep recurrent neural network estimation compensation and residual adaptive robust compensation is constructed. In step S6, the key parameters of the adaptive robust controller are optimized through the Nash game parameter optimization mechanism to obtain the optimal parameters; In step S7, the optimal parameters are substituted back into the adaptive robust controller to obtain the joint drive input, so as to realize the trajectory tracking control of the rehabilitation lower limb exoskeleton within the safe range of the joint.

[0021] In Figure 1 The method described above acquires the current state of the lower limb exoskeleton and constructs a dynamic model of the rehabilitation lower limb exoskeleton system. It then constructs trajectory tracking servo constraints based on a preset rehabilitation training reference trajectory, and establishes bilateral boundary conditions for each joint based on the joint safety angle range. A differential homeomorphism is then constructed based on these boundary conditions, and coordinate transformation is performed on each joint angle. Based on the transformed coordinate variables, a dynamic model and servo constraint model in the transformation domain are constructed to keep joint movement within a preset safety range. Uncertainties in the dynamic model in the transformation domain are uniformly represented, and a deep recurrent neural network is used to estimate the comprehensive uncertainty online. An adaptive robust controller is constructed, integrating deep recurrent neural network estimation compensation and residual adaptive robust compensation. The residual adaptive robust compensation mechanism compensates for the network estimation residuals and remaining uncertainties. The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters. These optimal parameters are then substituted back into the adaptive robust controller to obtain joint drive input, thereby achieving trajectory tracking control of the rehabilitation lower limb exoskeleton within the joint safety range. This control method can achieve stable tracking of rehabilitation trajectory while ensuring joint movement safety, reduce reliance on passive protection methods such as mechanical limit, improve control input smoothness and overall system control performance, and help reduce drive energy.

[0022] In Figure 1 In the method shown, step S1 can be used to obtain the current state of the lower limb exoskeleton and construct a dynamic model of the rehabilitation lower limb exoskeleton system. The specific method for constructing the dynamic model of the rehabilitation lower limb exoskeleton system can be of various forms known to those skilled in the art. In one example of the present invention, the dynamic model of the rehabilitation lower limb exoskeleton system can be established according to formula (1). (1) in, Let be the joint angle vectors of each controlled joint of the lower limb exoskeleton. These are the joint angular velocity vector and the joint angular acceleration vector, respectively. The system inertia matrix is ​​positive definite. For Coriolis eccentricity matrix, For gravity, This is a bounded uncertain parameter vector used to characterize system parameter deviations and other time-varying uncertainties. The control torque output by the motors of each joint of the exoskeleton. This refers to the human-machine interaction torque generated between the human body and the exoskeleton during rehabilitation training. For time, The number of controlled joints.

[0023] Step S2 can be used to construct trajectory tracking servo constraints based on a preset rehabilitation training reference trajectory, and to construct bilateral boundary conditions for each joint based on the joint safety angle range. Based on the dynamic model of the rehabilitation lower limb exoskeleton system constructed in step S1, trajectory tracking servo constraints and bilateral boundary conditions are constructed. The specific methods for constructing these constraints and conditions can be of various forms known to those skilled in the art. In one example of this invention, the method for constructing trajectory tracking servo constraints and bilateral boundary conditions may include, for example... Figure 2 The steps are shown. Specifically: In step S11, the servo constraint equations are established according to formula (2). (2) in, For the l-th servo constraint function Each component item l , Joint angle vector, This represents the sequence number of the servo constraint equation. This represents the number of servo constraint equations. In step S12, the servo constraint equations are rearranged into constraint vector form, and their derivative with respect to time is taken to obtain the second-order constraint form shown in formula (3). (3) in, The constraint coefficient matrix, The joint angular acceleration vector. The target constraint vector for the acceleration layer; In step S13, the bilateral boundary conditions shown in formula (4) are established based on the range of joint safety angles. , (4) in, For the first Joint angle The lower boundary of safety, For the first Joint angle The upper boundary of safety, .

[0024] In Figure 2In the method shown, step S11 can be used to establish the servo constraint equation according to formula (2). Step S12 rearranges the servo constraint equation into a constraint vector form, and differentiates it with respect to time to obtain the second-order constraint form shown in formula (3). The constraint vector form can be expressed according to formula (37). (37) in, and These are the servo constraint vector and the target constraint vector obtained by rearranging from formula (2), and both belong to... ; Taking the derivative of formula (37) with respect to time, we can obtain the first-order constraint form shown in formula (38). (38) in, The joint angular velocity vector. For the velocity layer target constraint vector ; By further differentiating and rearranging the first-order constraint form shown in formula (38) with respect to time, we can obtain the second-order constraint form shown in formula (3). (3) in, The constraint coefficient matrix, The joint angular acceleration vector. For the acceleration layer target constraint vector, Furthermore, the second-order constraint equations satisfy the consistency condition.

[0025] Considering that each joint of the lower limb exoskeleton has a preset safe range of motion during rehabilitation training, in order to ensure that the joint movement is always within the corresponding safe range, step S13 can be used to establish the bilateral boundary conditions shown in formula (4) based on the range of joint safe angles.

[0026] Step S3 can be used to construct a differential homeomorphism based on the bilateral boundary conditions, perform coordinate transformation on each joint angle, and construct a dynamic model and servo constraint model in the transformation domain based on the transformed coordinate variables. The specific method for constructing the dynamic model and servo constraint model in the transformation domain can be of various forms known to those skilled in the art. In one example of the present invention, the method for constructing the dynamic model and servo constraint model in the transformation domain may include, for example... Figure 3 The steps are shown. Specifically: In step S21, the first is defined according to formula (5). The transformation domain coordinate variables of each joint angle map the bounded joint angles in the original joint space, which are constrained by bilateral boundary conditions, to unbounded coordinate variables in the transformation domain. (5) in, For the first Transform domain coordinate variables of each joint angle It is a differential homeomorphism mapping; In step S22, the specific form of the differential homeomorphism is obtained according to formula (6). (6) in, , , Transformation parameters; In step S23, the inverse transformation of the differential homeomorphism of formula (6) is solved to obtain the inverse transformation relation corresponding to formula (7). , (7).

[0027] In step S24, the inverse transformation relation is substituted into the dynamic model of the rehabilitation lower limb exoskeleton system established by formula (1), and combined with human-computer interaction, the dynamic model in the transformation domain of formula (8) is obtained. (8) in, The equivalent inertia matrix in the transformation domain, For the coordinate acceleration vector in the transformation domain, , For the velocity vector in the transformation domain, The coordinate vector in the transformation domain; In step S25, the servo constraint relationships in the original joint space are synchronously transformed to the transform domain to obtain the constraint models in the transform domain of formulas (9) to (11). (9) (10) (11) in, Let the vector be the position constraint function in the transform domain. The target constraint vector for the transformation domain position layer. Let be the full-rank transformation domain constraint coefficient matrix. For the coordinate vector in the transformation domain, For the velocity vector in the transformation domain, For the coordinate acceleration vector in the transformation domain, For the target constraint vector of the velocity layer in the transform domain, This is the target constraint vector for the acceleration layer in the transform domain.

[0028] In Figure 3 In the method shown, step S21 can be used to define the first according to formula (5). The coordinate variables in the transformation domain of each joint angle are transformed by introducing a class of differential homeomorphic transformations that satisfy the bijective condition, are continuously differentiable, and whose inverse mapping is also continuously differentiable. This transforms the bounded joint angles in the original joint space that are constrained by bilateral boundary conditions. Mapped to unbounded state variables in the transformation domain This transforms the trajectory tracking problem with joint safety constraints into an equivalent unconstrained trajectory tracking control problem in the transform domain. For the ... Joint angle The transformation function satisfies the following boundary and reference point mapping conditions: when hour, ;when hour, ;when hour, .in, For the pre-set number There are joint angle reference points, and they satisfy the following conditions: Based on this, the original bounded safe interval was realized. To the entire real number field Equivalent conversion.

[0029] Step S22 can be used to obtain the specific form of the differential homeomorphic transformation according to formula (6). To ensure the transformation satisfies the above boundary correspondence reference point alignment condition, the parameters... The following conditions must be met. , , , Thus, the transformation parameters represented by formulas (39) to (41) are obtained. (39) (40) (41) Therefore, the first one can be uniquely determined. The differential homeomorphic transformation of each joint. Step S23 can be used to solve the differential homeomorphic transformation of formula (6) to obtain the inverse transformation relationship corresponding to formula (7). By combining the above inverse transformation relationship with chain rule differentiation, the correspondence between joint angular velocity, joint angular acceleration and transformation domain variables and their derivatives can be obtained, and the dynamic equations and servo constraints in the original joint space can be synchronously mapped to the transformation domain accordingly. Step S24 can be used to substitute the inverse transformation relationship into the dynamic model of the rehabilitation lower limb exoskeleton system established by formula (1), and combined with human-computer interaction, to obtain the dynamic model in the transformation domain of formula (8). (8) in, , , The system inertia matrix is ​​positive definite. For Coriolis eccentricity matrix, For gravity, For differential homeomorphism mapping The inverse mapping of .

[0030] After completing the transformation of the dynamic equations, the servo constraint relationships in the original joint space are synchronously transformed to the transformation domain through step S25, thereby obtaining the constraint models in the transformation domain of equations (9) to (11). (9) (10) (11) in, , , , .

[0031] Therefore, joint safety angle constraints and trajectory tracking constraints are uniformly expressed in the transform domain, and subsequent operations revolve around transform domain variables. The design of a trajectory tracking controller was carried out to keep the original joint angle within a preset safe range and to achieve tracking control of the rehabilitation reference trajectory.

[0032] Step S4 can be used to uniformly characterize the uncertainties in the dynamic model in the transform domain and to estimate the comprehensive uncertainty term online using a deep recurrent neural network. In one example of the present invention, the method for uniformly characterizing the uncertainties in the dynamic model in the transform domain and obtaining the online estimation result of the comprehensive uncertainty term through a deep recurrent neural network may include, for example: Figure 4 The steps are shown. Specifically: In step S31, the equivalent inertia matrix in the transform domain is decomposed into a nominal part and an uncertain deviation part according to formula (12). (12) in, The equivalent inertia matrix in the transformation domain, The nominal part of the equivalent inertia matrix in the positive definite transformation domain. This represents the uncertain deviation portion of the equivalent inertia matrix in the transformation domain. In step S32, the transform domain comprehensive torque term containing the influence of human-computer interaction is decomposed into a nominal part and an uncertain deviation part according to formula (13). (13) in, for , For the nominal part of the synthesized torque term in the transform domain, This represents the uncertain deviation portion of the synthesized torque term in the transformed domain; In step S33, the composite error variable in the transform domain is constructed according to formula (14). (14) in, For the composite error vector in the transform domain, For error adjustment parameters, To constrain position following error, To constrain speed following error; In step S34, the uncertainties and their coupling effects in the equivalent inertia matrix of the transform domain and the comprehensive moment term are collectively denoted as the comprehensive uncertainty term, which is expressed according to formula (15). (15) in, To encompass the uncertainties, To predetermine the positive definite weight matrix, The inverse matrix corresponding to the nominal equivalent inertia matrix in the transformation domain. The uncertain deviation component of the inverse of the equivalent inertia matrix in the transformation domain. For nominal control items, For feedback correction items; In step S35, the comprehensive uncertainty term is nonlinearly approximated using a deep recurrent neural network according to formula (16). (16) in, This is the output layer weight matrix. This is the feature output vector of a deep recurrent neural network. This is the output vector of the deep recurrent neural network; In step S36, the output layer weights, hidden layer base width parameters, hidden layer center parameters, and output feedback weights of the deep recurrent neural network are updated online based on the transform domain composite error variables.

[0033] In Figure 4 In the method shown, step S31 can be used to decompose the equivalent inertia matrix of the transform domain into a nominal part and an uncertain deviation part according to formula (12). To characterize the deviation between the inverse matrix corresponding to the actual equivalent inertia matrix of the transform domain and the inverse matrix corresponding to the nominal equivalent inertia matrix of the transform domain, the inverse matrix corresponding to the nominal part of the equivalent inertia matrix of the transform domain is defined according to formula (42). The uncertain deviation part of the inverse matrix of the equivalent inertia matrix in the transformation domain is defined by formula (43). , (42) , (43).

[0034] Step S32 can be used to decompose the transform domain composite torque term containing the human-computer interaction influence into a nominal part and an uncertain deviation part according to formula (13). Step S33 can be used to construct the transform domain composite error variable according to formula (14). Wherein, in formula (14)... This is the error adjustment parameter, used to coordinate the weights of the constraint position following error and the constraint velocity following error in the composite error. The constraint position following error is defined according to formula (44), and the constraint velocity following error is defined according to formula (45). (44) (45) in, , , This represents the number of servo constraint equations.

[0035] Step S34 can be used to unify the uncertain deviations and their coupling effects in the equivalent inertia matrix and the comprehensive torque term in the transform domain into a comprehensive uncertainty term, which is represented by formula (15). The comprehensive uncertainty term is used to uniformly characterize the combined effects of uncertain factors such as the deviation of the equivalent inertia matrix in the transform domain, the deviation of the comprehensive torque term in the transform domain, and the change in human-machine interaction torque on the system.

[0036] Since the overall upper bound estimate of the comprehensive uncertainty term is usually conservative, directly using adaptive robust compensation can easily lead to an excessively large control torque, thereby increasing the human-computer interaction safety risk of the lower limb rehabilitation exoskeleton during joint safety constraint tracking. To reduce the conservatism of the compensation and decrease unnecessary control output, in step S35, the comprehensive uncertainty term is nonlinearly approximated using a deep recurrent neural network according to formula (16) to obtain the estimation result of the comprehensive uncertainty term. . Specifically: Construct the input vector of the deep recurrent neural network according to formula (46). (46) in, This is the input vector for the deep recurrent neural network; A deep recurrent neural network consists of an input layer, a first hidden layer, a second hidden layer, a third hidden layer, and an output layer. The input layer receives the input vector. and the network output feedback signal at the previous sampling time. According to formula (47), the input layer output is represented. (47) in, For the input layer output, To output the feedback weight matrix, This is the network output vector fed back to the input layer of the neural network at the previous sampling time.

[0037] The first, second, and third hidden layers all have preset quantities. Number of nodes, preset quantity The multi-layer nonlinear characteristic mapping for the comprehensive uncertainty term is determined based on the number of controlled degrees of freedom, the real-time computing capability of the controller, and the nonlinear complexity of the comprehensive uncertainty term. Formula (48) represents the output of the first hidden layer, formula (49) represents the output of the second hidden layer, and formula (50) represents the output of the third hidden layer. (48) (49) (50) in, These represent the output vectors of the first hidden layer, the second hidden layer, and the third hidden layer, respectively. , and The first hidden layer is respectively The node, the second hidden layer The node and the third hidden layer The output of each node, These are the centers of each hidden layer node. These represent the widths of each hidden layer node. Additionally... Indicates by the first The overall central parameter vector is formed by arranging the central parameters of each node in the hidden layer according to the node index. Indicates by the first The base width parameters of each node in the hidden layer are arranged according to their node numbers to form a base width parameter vector. Finally, the output layer outputs the vector from the third hidden layer. As feature input, the output vector of the deep recurrent neural network is obtained according to formula (16). .

[0038] To enable the output of the deep recurrent neural network to adjust to the dynamic changes of the system during rehabilitation training, step S36 can be used to composite the error variable in the transform domain. To provide a basis for correction, the output layer weights, hidden layer base width parameters, hidden layer center parameters, and output feedback weights of the deep recurrent neural network are updated online. The update law is as follows: , , , , , , , , in, The first derivative of the output layer weight matrix with respect to time; For the cooperative suppression gain coefficient, All are adaptive gain parameters. Output layer weight matrix Leakage adjustment coefficient, These are the first derivatives of the basis width parameters of the first, second, and third hidden layers with respect to time, respectively. These are the first-order derivatives of the center parameters of the first, second, and third hidden layers with respect to time, respectively. To output the first derivative of the feedback weight matrix with respect to time, To output the feedback weight matrix Leakage adjustment coefficient, These represent the first-order sensitivity matrices of the third hidden layer output to the base width parameters of each hidden layer. These represent the first-order sensitivity matrices of the third hidden layer output with respect to the center parameters of each hidden layer. This represents the first-order sensitivity of the third hidden layer output to the output feedback weights. Through the above online update process, the deep recurrent neural network approximates the comprehensive uncertainty term in the transform domain online, obtaining the estimation result. Based on this, a deep recurrent neural network compensation term is constructed. The residual uncertainties after deep recurrent neural network compensation are subsequently processed using residual adaptive robust compensation. Thus, the controller can improve its ability to compensate for time-varying uncertainties such as parameter perturbations, external disturbances, and human-computer interaction in the rehabilitation exoskeleton model.

[0039] To achieve trajectory tracking control of lower limb exoskeleton joints under safe angle constraints, step S5 can be used to construct an adaptive robust controller that integrates deep recurrent neural network estimation compensation and residual adaptive robust compensation. Based on the transform domain dynamics model, transform domain servo constraint model, and composite error variables, combined with deep recurrent neural network estimation compensation and residual adaptive robust compensation, an adaptive robust controller is constructed, and the driving torque control inputs for each joint of the exoskeleton are generated. The specific method for constructing the adaptive robust controller in step S5 can be of various forms known to those skilled in the art. In one example of the present invention, the method for constructing the adaptive robust controller may include, for example... Figure 5 The steps are shown. Specifically: In step S41, the control input of the adaptive robust controller is determined according to formula (17). (17) in, To control the input, The nominal control term, constructed based on the transform domain nominal model, is used to achieve basic tracking of the target trajectory and constraint relationships. This is a feedback correction term, used for feedback correction based on the composite error. This is a compensation term for the deep recurrent neural network, used to estimate the comprehensive uncertainty term based on the output of the deep recurrent neural network. Generate compensating control inputs to mitigate the effects of comprehensive uncertainty in the transform domain. This is the residual adaptive robust compensation term, used to robustly compensate for the residual uncertainties after compensation by the deep recurrent neural network; In step S42, the nominal control term is obtained according to formula (18). (18) in, For Moore–Penrose generalized inverse; In step S43, the feedback correction term is obtained according to formula (19). (19) in, This is the convergence adjustment coefficient; In step S44, the deep recurrent neural network compensation term is obtained according to formula (20). , (20).

[0040] In step S45, the residual uncertainty term after estimation and compensation by the deep recurrent neural network is obtained according to formula (21). ,(twenty one) in, This refers to the residual uncertainty term after compensation by the deep recurrent neural network. In step S46, the bounded upper bound function of the residual uncertainty term is determined according to formula (22). ,(twenty two) in, This is a lower bound parameter for the influence of the uncertain deviation of the inverse of the equivalent inertia matrix in the transform domain on the adaptive robust compensation of the residual. Uncertain parameters of the system The bounded domain of discourse, Θ, is the torque for human-computer interaction. Bounded domain of discourse Let be the upper bound function of the residual uncertainty term. The boundary parameter vector for the residual uncertainty term; In step S47, to update the adaptive estimate of the boundary parameter vector of the residual uncertainty term online, the adaptive law shown in formula (23) is designed. ,(twenty three) in, The boundary parameter vector of the residual uncertainty term The adaptive estimate, Design parameters for the adaptive law. For adaptive laws, The preset dead zone threshold; In step S48, the residual adaptive robust compensation term is obtained according to formula (24). ,(twenty four) in, This is the cooperative disturbance suppression gain coefficient, used to adjust the output strength of the residual adaptive robust compensation term. , For auxiliary functions, This is the upper bound estimation function for the residual uncertainty term determined based on the adaptive estimate.

[0041] In Figure 5In the method shown, step S41 can be used to determine the control input of the adaptive robust controller according to formula (17). Step S42 can be used to obtain the nominal control term according to formula (18). Step S43 can be used to obtain the feedback correction term according to formula (19). Step S44 can be used to obtain the deep recurrent neural network compensation term according to formula (20). Considering the output of the deep recurrent neural network... Synthetic uncertainty in the transform domain The approximation has an estimated residual. The residual uncertainty term, after estimation and compensation by the deep recurrent neural network, is obtained in step S45 according to formula (21). To suppress the influence of the residual uncertainty term on the constraint following error, an adaptive robust compensation term for the residual is further constructed. Suppose there exists an unknown parameter vector. and the pre-defined nonnegative function In step S46, the bounded upper bound function of the residual uncertainty term is determined according to formula (22). For parameter vectors It has first-order continuous differentiability, and the parameter vector Each component is described using fuzzy numbers. To estimate the upper bound of the residual uncertainty term for online adjustment, a boundary parameter vector of the residual uncertainty term is constructed. Adaptive estimator By using step S47 to adaptively estimate the boundary parameter vector of the residual uncertainty term online, the adaptive law shown in formula (23) is designed. In formula (23) This constitutes a leakage control term, used to suppress parameter drift and enhance numerical stability.

[0042] Based on adaptive estimator ,definition: , , , in, For auxiliary functions, For smoothing factor. Step S48 can be used to obtain the residual adaptive robust compensation term according to formula (24).

[0043] Step S6 can be used to optimize the key parameters of the adaptive robust controller through a Nash game parameter optimization mechanism to obtain the optimal parameters. The key parameters in the adaptive robust controller include the convergence adjustment coefficient. With cooperative suppression gain coefficient .in, Simultaneously acts on the feedback correction term An adaptive law for the adaptive estimate of the boundary parameter vector of the residual uncertainty term is used to adjust the strength of the feedback correction to the composite error and the strength of the online update of the boundary parameter estimate of the residual uncertainty term. Simultaneously affects the output weight update law and residual adaptive robust compensation term of the deep recurrent neural network. These parameters respectively affect the online learning strength of the neural network and the robust compensation strength of the residual uncertainty. The values ​​of these parameters directly affect the transient response, trajectory tracking accuracy, and driving torque input amplitude of the lower limb exoskeleton joint under safety angle constraints. Generally, enhanced feedback correction, online neural network learning, and robust compensation are beneficial for improving trajectory tracking accuracy; however, excessively large parameter values ​​may increase the driving torque input and affect control stability. Therefore, it is necessary to carefully consider these parameters. and Coordination and optimization are performed to obtain a parameter configuration that balances trajectory tracking performance and control costs. The specific methods for obtaining the optimal parameters can take many forms known to those skilled in the art. In one example of this invention, the method for obtaining the optimal parameters may include, for example... Figure 6 The steps are shown. Specifically: In step S51, the two key parameters of the adaptive robust controller, the convergence adjustment coefficient and the cooperative disturbance suppression gain coefficient, are used as two decision variables in the Nash game. In step S52, a comprehensive performance evaluation upper bound function for Nash game parameter optimization is constructed according to formula (25). (25) in, This is the upper bound function for comprehensive performance evaluation. For residual compensation evaluation items, This is an evaluation item for online learning of deep recurrent neural networks; In step S53, based on the upper bound function of the comprehensive performance evaluation, the transient comprehensive performance function and the steady-state comprehensive performance function are constructed according to formulas (26) and (27). (26) (27) in, For transient composite performance function, For steady-state comprehensive performance function, At the initial moment, From the initial moment The initial composite error energy is jointly determined by the transform domain composite error and the residual uncertainty term boundary parameter estimation error. This is the state convergence gain term; In step S54, a defuzzification operator is introduced according to formula (28) to transform the performance function containing boundary parameters with residual uncertainties into a deterministic performance index. (28) in, To defuzzify the operator, Let be the function to be deblurred. For fuzzy sets, For fuzzy variables Regarding fuzzy sets membership function, It is a fuzzy variable; In step S55, based on the transient comprehensive performance function and the steady-state comprehensive performance function, the transient comprehensive performance index and the steady-state comprehensive performance index as shown in formula (29) and formula (30) are constructed respectively. (29) (30) in, For transient comprehensive performance indicators, For steady-state comprehensive performance indicators; In step S56, cost functions corresponding to the two key parameters are constructed according to formulas (31) and (32), respectively. (31) (32) in, The cost function corresponding to the convergence adjustment coefficient. The cost function corresponding to the cooperative suppression gain coefficient. and To control the cost item.

[0044] In step S57, the optimal response model of formula (33) is established based on the decision variables. (33) in, The feasible region for the convergence adjustment coefficient. The feasible region for the cooperative suppression gain coefficient, , The optimal parameters; In step S58, a joint objective function is constructed according to formula (34). (34) in, The joint objective function; In step S59, the optimal parameters are obtained according to formula (35). (35) in, This represents the optimal parameter pair.

[0045] In Figure 6 In the method shown, step S51 can be used to adjust the convergence coefficients of the two key parameters of the adaptive robust controller. and cooperative suppression gain coefficient As two decision variables in a Nash game; among them... , Their feasible regions are denoted as follows: and . This is used to adjust the strength of feedback correction for composite errors and the strength of online updates of adaptive estimates of the boundary parameter vectors of residual uncertainties. This is used to adjust the online learning strength of the deep recurrent neural network for the comprehensive uncertainty term, and the compensation strength of the residual adaptive robust compensation term for the residual uncertainty term.

[0046] Step S52 can be used to construct an upper bound function for comprehensive performance evaluation of Nash game parameter optimization according to formula (25), so as to transform the comprehensive impact of error feedback adjustment and online estimation and compensation of uncertainty on the system control performance into a performance evaluation quantity related to key parameters. (25) in, This is a residual compensation evaluation term, used to characterize the evaluation effect of the residual adaptive robust compensation process on the upper bound of the comprehensive performance evaluation. This is an online learning evaluation term for deep recurrent neural networks (RNNs), used to characterize the evaluation effect of the online update process of the RNN's output weights on the upper bound of the overall performance evaluation. In this embodiment, combining the parameter form of the residual compensation evaluation term, the RNN's output weight update law, and the boundedness condition of the output weights, the residual compensation evaluation term... Online learning evaluation items for deep recurrent neural networks It can be organized as follows: , , in, , The boundary parameter vector of the residual uncertainty term The determined nonnegative bounded function, , , It is a non-negative finite constant obtained by combining the output weight update law, the boundedness condition of the output weight, and the evaluation weights of the deep recurrent neural network.

[0047] Step S53 can be used to construct the transient comprehensive performance function and the steady-state comprehensive performance function based on the upper bound function of the comprehensive performance evaluation, according to formulas (26) and (27). (26) (27) in, Let be the transient synthesis performance function, representing the transient decay term of the difference between the initial synthesis error energy and the upper bound of the steady-state synthesis performance. This is the steady-state comprehensive performance function, and its value is determined by the upper bound function of the comprehensive performance evaluation. At the initial moment, From the initial moment The initial composite error energy is jointly determined by the transform domain composite error and the residual uncertainty term boundary parameter estimation error. This is the state convergence gain term.

[0048] Considering the boundary parameter vector of the residual uncertainty term Given its fuzziness, step S54 can be used to introduce a defuzzification operator according to formula (28), transforming the performance function containing boundary parameters with residual uncertainties into a deterministic performance index. (28) in, To defuzzify the operator, Let be the function to be deblurred. For fuzzy sets, For fuzzy variables Regarding fuzzy sets membership function, It is a fuzzy variable.

[0049] Step S55 can be used to construct the transient comprehensive performance index and steady-state comprehensive performance index as shown in formula (29) and formula (30) respectively, based on the transient comprehensive performance function and the steady-state comprehensive performance function. (29) (30) in, For transient comprehensive performance indicators, This is a steady-state comprehensive performance index.

[0050] Transient comprehensive performance indicators and steady-state comprehensive performance index Summarized as a summary of convergence adjustment coefficients and cooperative suppression gain coefficient Explicit function form: , .

[0051] in, and These are the coefficient terms obtained by organizing the results of the defuzzification expansion of the transient and steady-state comprehensive performance indices, respectively. .

[0052] Step S56 can be used to construct the cost functions corresponding to the two key parameters according to formulas (31) and (32), respectively. (31) (32) in, The cost function corresponding to the convergence adjustment coefficient. The cost function corresponding to the cooperative suppression gain coefficient. and To control the cost term, they are used to characterize the parameters. and parameters The increased control input burden and energy consumption costs.

[0053] Step S57 can be used to establish the optimal response model of formula (33) based on the decision variables. Due to the cost function... and They share a common system comprehensive performance evaluation component, and the control cost item and Each is only related to its corresponding decision variable, so a joint objective function is constructed according to formula (34) in step S58. (34) And there is, , , in, For the joint objective function, since the joint objective function Only compare the cost function Additional decision variables irrelevant And only compared to the cost function Additional decision variables irrelevant Therefore, the minimization conditions of the joint objective function with respect to the two decision variables are consistent with the Nash optimal response conditions of the two cost functions, and the global minimum solution of the joint objective function constitutes the Nash equilibrium parameter pair. Step S59 can be used to obtain the optimal parameters according to formula (35).

[0054] Step S7 can be used to substitute the optimal parameters back into the adaptive robust controller to obtain the joint drive input, thereby achieving trajectory tracking control of the rehabilitation lower limb exoskeleton within the joint safety range, while balancing control smoothness and the cost of drive torque input. In one example of the present invention, by substituting the optimal parameters back into the adaptive robust controller, the joint drive input represented by formula (36) is obtained. (36) in, This is the joint drive input after parameter co-optimization. Through the above optimization configuration process, a balance is achieved between trajectory tracking performance and control input cost while meeting joint safety constraints and trajectory tracking requirements.

[0055] Through the above technical solution, embodiments of the present invention provide a method for trajectory tracking control of a lower limb exoskeleton joint with safety constraints. By acquiring the current state of the lower limb exoskeleton, a dynamic model of the lower limb exoskeleton system is constructed. A preset rehabilitation training reference trajectory is used as a servo constraint, and bilateral boundary conditions are established based on the range of joint safety angles. Differential homeomorphism is performed on each joint angle according to the bilateral boundary conditions to construct a transform domain dynamic model and a constraint model. Uncertain factors in the transform domain are uniformly described, and an adaptive robust controller integrating a deep recurrent neural network is constructed. The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters. These optimal parameters are then substituted back into the adaptive robust controller to obtain the joint drive input, thereby achieving trajectory tracking control of the lower limb exoskeleton within the joint safety range. This invention maps the lower limb exoskeleton joint angle variables constrained by safety angles to the transform domain through differential homeomorphism, transforming the constrained trajectory tracking problem in the original joint space into an equivalent unconstrained trajectory tracking control problem in the transform domain. Based on this, a controller is designed to maintain joint movement within a preset safety range while meeting trajectory tracking requirements. Furthermore, this invention unifies model uncertainty, human-computer interaction, and other disturbance factors in the transform domain as a comprehensive uncertainty term, and introduces a deep recurrent neural network to estimate the comprehensive uncertainty term online to construct a corresponding estimation compensation term. Simultaneously, a residual adaptive robust compensation mechanism is used to compensate for the residual uncertainty term after estimation compensation, which helps reduce the conservatism of uncertainty term compensation and improves the lower limb exoskeleton's anti-disturbance capability, adaptability, and trajectory tracking performance under complex rehabilitation training conditions. Based on this, this invention optimizes the key parameters of the adaptive robust controller through a Nash game parameter optimization mechanism, enabling the system to meet joint safety constraints and trajectory tracking requirements while also considering control input costs. This helps improve control input smoothness and reduce the adverse effects of excessive driving torque input.

[0056] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0057] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for tracking and controlling the safety constraint trajectory of a lower limb exoskeleton joint in rehabilitation, characterized in that, The control method includes: Obtain the current state of the lower limb exoskeleton and construct a dynamic model of the rehabilitation lower limb exoskeleton system; The trajectory tracking servo constraint is constructed based on the preset rehabilitation training reference trajectory, and the bilateral boundary conditions of each joint are constructed based on the joint safety angle range. Based on the bilateral boundary conditions, a differential homeomorphism is constructed, a coordinate transformation is performed on each joint angle, and a dynamic model and a servo constraint model in the transformation domain are constructed based on the transformed coordinate variables. Uncertainty effects in the dynamic model under the transformed domain are uniformly characterized, and a deep recurrent neural network is used to estimate the comprehensive uncertainty term online. Construct an adaptive robust controller that integrates deep recurrent neural network estimation compensation and residual adaptive robust compensation; The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain the optimal parameters; The optimal parameters are substituted back into the adaptive robust controller to obtain the joint drive input, thereby realizing trajectory tracking control of the rehabilitation lower limb exoskeleton within the safe range of the joint.

2. The control method according to claim 1, characterized in that, Obtain the current state of the lower limb exoskeleton and construct a dynamic model of the rehabilitation lower limb exoskeleton system, including: A dynamic model of the lower limb exoskeleton system for rehabilitation is established based on formula (1). ，（1） in, , and Let represent the joint angle vector, joint angular velocity vector, and joint angular acceleration vector of each controlled joint of the lower limb exoskeleton, respectively. The system inertia matrix is ​​positive definite. For the Coriolis eccentric matrix, For gravity, This is a bounded uncertain parameter vector used to characterize system parameter deviations and other time-varying uncertainties. The control torque output by the motors of each joint of the exoskeleton. This refers to the human-machine interaction torque generated between the human body and the exoskeleton during rehabilitation training. For time.

3. The control method according to claim 2, characterized in that, Trajectory tracking servo constraints are constructed based on a preset rehabilitation training reference trajectory, and bilateral boundary conditions for each joint are constructed based on the joint safety angle range, including: The servo constraint equations are established according to formula (2). ，（2） in, For the l-th servo constraint function Each component item l , Joint angle vector, This represents the sequence number of the servo constraint equation. The number of servo constraint equations. Number of controlled joints; The servo constraint equations are rearranged into constraint vector form, and their derivatives with respect to time are obtained, yielding the second-order constraint form shown in formula (3). ，（3） in, The constraint coefficient matrix, The joint angular acceleration vector. The target constraint vector for the acceleration layer; Based on the range of joint safety angles, establish the bilateral boundary conditions shown in formula (4). ， ，（4） in, For the first Joint angle The lower boundary of safety, For the first Joint angle The upper boundary of safety, .

4. The control method according to claim 3, characterized in that, Based on the aforementioned bilateral boundary conditions, a differential homeomorphism is constructed, a coordinate transformation is performed on each joint angle, and a dynamic model and a servo constraint model in the transformation domain are constructed based on the transformed coordinate variables, including: According to formula (5), the first The transformation domain coordinate variables of each joint angle map the bounded joint angles in the original joint space, which are constrained by bilateral boundary conditions, to unbounded coordinate variables in the transformation domain. ，（5） in, For the first Transform domain coordinate variables of each joint angle It is a differential homeomorphism mapping; The specific form of the differential homeomorphic transformation can be obtained according to formula (6). ，（6） in, , , For transformation parameters; By performing the inverse solution of the differential homeomorphism of formula (6), the inverse transformation relation corresponding to formula (7) can be obtained. ，（7）； Substituting the inverse transformation relationship into the dynamic model of the rehabilitation lower limb exoskeleton system established by formula (1), and combining it with human-computer interaction, the dynamic model in the transformation domain of formula (8) is obtained. ，（8） in, The equivalent inertia matrix in the transformation domain, For the coordinate acceleration vector in the transformation domain, For the velocity vector in the transformation domain, The coordinate vector in the transformation domain; The servo constraint relationships in the original joint space are synchronously transformed to the transform domain to obtain the constraint models in the transform domain of equations (9) to (11). ，（9） ，（10） ，（11） in, Let the vector be the position constraint function in the transform domain. The target constraint vector for the transformation domain position layer. Let be the full-rank transformation domain constraint coefficient matrix. For the coordinate vector in the transformation domain, For the velocity vector in the transformation domain, For the coordinate acceleration vector in the transformation domain, For the target constraint vector of the velocity layer in the transform domain, This is the target constraint vector for the acceleration layer in the transform domain.

5. The control method according to claim 4, characterized in that, Uncertainties in the dynamic model under the transformed domain are uniformly characterized, and a deep recurrent neural network is used to estimate the comprehensive uncertainty term online, including: According to formula (12), the equivalent inertia matrix in the transformation domain is decomposed into a nominal part and an uncertain deviation part. ，（12） in, The equivalent inertia matrix in the transformation domain, The nominal part of the equivalent inertia matrix in the positive definite transformation domain. This represents the uncertain deviation portion of the equivalent inertia matrix in the transformation domain. According to formula (13), the transform domain comprehensive torque term including the influence of human-computer interaction is decomposed into a nominal part and an uncertain deviation part. ，（13） in, For the transformed domain composite torque term, For the nominal part of the synthesized torque term in the transform domain, This represents the uncertain deviation portion of the synthesized torque term in the transformed domain; Construct a composite error variable in the transform domain according to formula (14). ，（14） in, For the composite error vector in the transform domain, For error adjustment parameters, To constrain position following error, To constrain speed following error; The uncertainties and their coupling effects in the equivalent inertia matrix and the comprehensive moment term in the transformed domain are collectively denoted as the comprehensive uncertainty term, which is expressed according to formula (15). ，（15） in, To encompass the uncertainties, To predetermine the positive definite weight matrix, The inverse matrix corresponding to the nominal equivalent inertia matrix in the transformation domain. The uncertain deviation component of the inverse of the equivalent inertia matrix in the transformation domain. For nominal control items, For feedback correction items; According to formula (16), a deep recurrent neural network is used to perform a nonlinear approximation of the comprehensive uncertainty term. ，（16） in, This is the output layer weight matrix. This is the feature output vector of a deep recurrent neural network. This is the output vector of the deep recurrent neural network; The output layer weights, hidden layer base width parameters, hidden layer center parameters, and output feedback weights of the deep recurrent neural network are updated online based on the transform domain composite error variable.

6. The control method according to claim 5, characterized in that, An adaptive robust controller is constructed that integrates deep recurrent neural network estimation compensation with residual adaptive robust compensation, including: The control input of the adaptive robust controller is determined according to formula (17). ，（17） in, To control the input, For nominal control items, For feedback correction items, For deep recurrent neural network compensation terms, This is the adaptive robust compensation term for the residuals; The nominal control term is obtained according to formula (18). ，（18） in, Moore–Penrose generalized inverse; The feedback correction term is obtained according to formula (19). ，（19） in, This is the convergence adjustment coefficient; The compensation term for the deep recurrent neural network is obtained according to formula (20). ，（20）。 7. The control method according to claim 6, characterized in that, An adaptive robust controller is constructed that integrates deep recurrent neural network estimation compensation with residual adaptive robust compensation, including: The residual uncertainty term after estimation and compensation by the deep recurrent neural network is obtained according to formula (21). ，（21） in, This refers to the residual uncertainty term after compensation by the deep recurrent neural network. The bounded upper bound function of the residual uncertainty term is determined according to formula (22). ，（22） in, This is a lower bound parameter for the influence of the uncertain deviation of the inverse of the equivalent inertia matrix in the transform domain on the adaptive robust compensation of the residual. Uncertain parameters of the system The bounded domain of discourse, Θ, is the torque for human-computer interaction. Bounded domain of discourse This is an upper bound function for the residual uncertainty term. The boundary parameter vector for the residual uncertainty term; To update the adaptive estimate of the boundary parameter vector of the residual uncertainty term online, an adaptive law as shown in formula (23) is designed. ，（23） in, The boundary parameter vector of the residual uncertainty term The adaptive estimate, Design parameters for the adaptive law. For adaptive laws, The preset dead zone threshold; The adaptive robust compensation term for the residual is obtained according to formula (24). ，（24） in, For the cooperative suppression gain coefficient, , For auxiliary functions, This is the upper bound estimation function for the residual uncertainty term determined based on the adaptive estimate.

8. The control method according to claim 7, characterized in that, The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters, including: The two key parameters of the adaptive robust controller, the convergence adjustment coefficient and the cooperative disturbance suppression gain coefficient, are used as two decision variables in the Nash game. Based on formula (25), a comprehensive performance evaluation upper bound function for Nash game parameter optimization is constructed. ，（25） in, This is the upper bound function for comprehensive performance evaluation. For residual compensation evaluation items, This is an evaluation item for online learning of deep recurrent neural networks; Based on the aforementioned comprehensive performance evaluation upper bound function, the transient comprehensive performance function and the steady-state comprehensive performance function are constructed according to formulas (26) and (27). ，（26） ，（27） in, For transient composite performance function, For steady-state comprehensive performance function, At the initial moment, From the initial moment The initial composite error energy is jointly determined by the transform domain composite error and the residual uncertainty term boundary parameter estimation error. This is the state convergence gain term; According to formula (28), a defuzzification operator is introduced to transform the performance function containing boundary parameters with residual uncertainties into a deterministic performance index. ，（28） in, To defuzzify the operator, Let be the function to be deblurred. For fuzzy sets, For fuzzy variables Regarding fuzzy sets membership function, It is a fuzzy variable; Based on the transient comprehensive performance function and the steady-state comprehensive performance function, the transient comprehensive performance index and the steady-state comprehensive performance index as shown in formula (29) and formula (30) are constructed respectively. ，（29） ，（30） in, For transient comprehensive performance indicators, For steady-state comprehensive performance indicators; Based on formulas (31) and (32), construct the cost functions corresponding to the two key parameters respectively. ，（31） ，（32） in, The cost function corresponding to the convergence adjustment coefficient. The cost function corresponding to the cooperative suppression gain coefficient. and To control the cost item.

9. The control method according to claim 8, characterized in that, The key parameters of the adaptive robust controller are optimized using a Nash game parameter optimization mechanism to obtain optimal parameters, including: Based on the decision variables, establish the optimal response model according to formula (33). ，（33） in, The feasible region for the convergence adjustment coefficient. The feasible region for the cooperative suppression gain coefficient, , The optimal parameters; Construct a joint objective function based on formula (34). ，（34） in, The joint objective function; The optimal parameters are obtained according to formula (35). ，（35） in, This represents the optimal parameter pair.

10. The control method according to claim 9, characterized in that, Substituting the optimal parameters back into the adaptive robust controller to obtain the joint drive input, thereby achieving trajectory tracking control of the rehabilitation lower limb exoskeleton within the safe range of the joint, including: Substituting the optimal parameters back into the adaptive robust controller, we obtain the joint drive input represented by formula (36). ，（36） in, This is the joint drive input after parameter coordination and optimization.

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