Deepen the control theory of nonlinear systems: PAM is a typical strong nonlinear and hysteresis system. In-depth research on its control algorithm will enrich and develop the theoretical system of nonlinear control, adaptive control and intelligent control, and provide theoretical reference for solving a class of engineering control problems with similar characteristics [6].

Promoting the integration of “physical model-data-driven” model building: exploring a hybrid modeling method that deeply integrates first principles and machine learning will help establish a more accurate and efficient software driver model and provide complex system modeling methodological innovation.

Expanding the perception-control framework of human-machine collaboration: studying the deep fusion mechanism of EMG signals and fatigue characteristics and machine control will lay the foundation for the establishment of a new generation of intelligent human-computer interaction theory based on biofeedback.

Overcome the core technology of PAM high-precision control: Through the development of new intelligent control algorithms and compensation strategies, break through the performance bottleneck of PAM under time delay, creep and disturbance, and achieve sub-millimeter positioning accuracy and millisecond dynamic response, reaching the international advanced level [6].

Build a research paradigm for digital twin empowerment: establish a set of “modeling-simulation-control-optimization” full-chain technical process based on digital twins, significantly improve the development efficiency and system reliability of control algorithms, and provide an efficient tool chain for the research and development of soft robots.

Realize low-cost, high-performance localized solutions: the research results are expected to replace expensive imported precision pneumatic actuators, greatly reduce the cost of rehabilitation exoskeletons, flexible production lines and other equipment, and promote the upgrading of related industries.

Serving people’s livelihood and health and national strategic needs: develop low-cost, high-performance rehabilitation assistive equipment, which can benefit tens of millions of patients with physical disabilities in my country; The space flexible operation technology developed can provide technical support for major national projects such as deep space exploration and on-orbit services.

Promote interdisciplinary and talent training: This research involves robotics, control theory, artificial intelligence, biomedical engineering and other disciplines. The implementation of the project will cultivate compound talents with interdisciplinary vision and innovative ability.

International research has developed from simple geometrical static models to dynamic high-fidelity models with coupling of multiple physical fields (Figure 2Figure 2 Development History of System Modeling Methods). The Massachusetts Institute of Technology (MIT) team proposed a multi-scale modeling framework for fiber-reinforced composite soft actuators in Science Robotics, which significantly improved the prediction accuracy of the model [7]. In terms of hysteresis modeling, parameterized models based on operators such as Prandtl-Ishlinskii and Bouc-Wen and data-driven models based on long-term and short-term memory networks (LSTM) have become mainstream [8]. Domestic modeling research has made rapid progress in recent years, but in terms of refinement, especially in the model considering the dynamic effect of filament winding and thermal-mechanical coupling, it still relies on empirical formulas, which is far behind the top level abroad. The development trend is the deep mixing of mechanism models and data-driven models [9], and the use of digital twins to realize online calibration and update of model parameters.

Figure 2. Development history of system modeling methods.

The control method has undergone the evolution from PID to modern robust/adaptive control, and then to intelligent control. The University of Tokyo in Japan took the lead in applying reinforcement learning to PAM control, realizing adaptive force control under unknown disturbances [10]. Fuzzy logic, neural networks (especially recurrent neural networks) are widely used for hysteresis feedforward compensation and direct inverse control. Domestic research is relatively mature in the improvement of traditional PID and the application of fuzzy control, but relatively weak in the original research and system integration of autonomous intelligent algorithms (such as deep reinforcement learning). The current frontiers focus on the combination of deep reinforcement learning and model predictive control, and the use of digital twins as “training grounds” to safely and efficiently optimize control strategies.

International research attaches great importance to multimodal perception and biological signal fusion. The development of flexible electronics has made distributed proprioception possible [11]. In terms of biological signal interaction, sEMG-based motion intention recognition is relatively mature, but how to process the impact of muscle fatigue on signals in real time is the key to improving the practicability of the system. The research of Yan Shijia et al. (2024) shows that the fusion of real-time muscle fatigue features can significantly improve the robustness of gesture recognition, which provides important enlightenment for the adaptive control of PAM rehabilitation system. China keeps up with the international pace in the application of flexible sensing and sEMG, but the systematic work in the deep fusion of multi-modal information and closed-loop control still needs to be strengthened. The future direction is to develop “smart materials” that integrate driving, sensing, and computing, and build a context-aware collaborative control system that can understand the user’s physiological state (such as fatigue).

To ensure the reproducibility of the proposed framework integrating “multiphysics modeling, reinforcement learning optimization, digital twin verification, and sEMG feature fusion,” this paper designs the following data and control flow:

Input Layer:

Raw surface electromyography (sEMG) signalsDesired displacement/force commandsPressure sensor feedback values

Processing Layer:

1) Multiphysics Modeling Module → Reinforcement Learning Module: Outputs the nonlinear dynamics model of the PAM (including Bouc‑Wen hysteresis parameters and the dynamic equation of braid angle variation), which serves as the simulation environment for the DDPG agent.

2) Reinforcement Learning Module → Digital Twin Module: Outputs the trained control policy network (in.pt or.onnx format) along with hyperparameter configurations, which are imported into the digital twin platform (e.g., Simulink + Unity) for virtual validation.

3) Digital Twin Module → sEMG Fusion Module: Outputs the validated control parameters (e.g., assistive force ratio, impedance coefficients) and receives fatigue features (median frequency slope, root mean square value) as online adjustment signals.

Output Layer:

Compensated desired pressure value → proportional valve drive voltageClosed‑loop feedback of actual displacement/forceHuman‑robot collaborative adaptive strategy (fatigue → decrease assistive force/increase impedance)

Objective: To establish a high-fidelity dynamic model of PAM which can accurately reflect filament winding effect thermodynamic process and material nonlinearity.

Research Content:

1) Establishing the governing equations of integrated thermodynamics-mechanics:

Thermodynamic model: The PAM chamber is regarded as a variable capacitance adiabatic system, and the mass flow and energy exchange in and out of the gas are considered.

Where P is the intracavity pressure, T is the temperature, V(L) is the volume geometric function related to the muscle length L, γ is the specific heat capacity ratio of the gas, R is the gas constant, and m_in/out is the inlet and outlet mass flow rate.

Structural Mechanics Models: Fusion of Hyperelastic Constitutive and Fiber Constraints.

where d₀ 、θ₀is the initial diameter and braiding angle, and F_elastic is the elastic force term of the rubber liner described based on the Mooney-Rivlin model:

2) Modeling the dynamic effect of filament winding angle: study the dynamic change (unconstant) of braiding angle θ in actual deformation, establish the relationship model between θ and axial strain ϵ, and substitute it into the above mechanical model to more accurately predict the stiffness and output of different deformation stages [12].

3) Global identification of parameters based on Bayesian optimization: Quasi-static and dynamic tensile tests at different strain rates (10%, 20%, 30%) are carried out on Instron material testing machine to obtain force-displacement data. Construct an optimization problem including model parameters, Bouc-Wen parameters, take experimental data as observations, use Markov chain Monte Carlo method for Bayesian inference, obtain a posterior probability distribution of parameters, and give 95% confidence interval, quantify model uncertainty [13].

Objective: To develop an intelligent control algorithm that can effectively compensate for nonlinearity and hysteresis, and can adapt to environmental changes online.

Research Content:

1) Double Closed-Loop Controller Architecture Design

Inner ring (pressure fast tracking ring): A high-order sliding mode observer is used to design the pressure controller [14].

where P_des is the expected pressure, the observer can converge in a finite time and estimate the disturbance, and the controller is designed based on the output of the observer to achieve a chattering suppression rate of >90%.

Outer loop (displacement/force control loop): A controller based on adaptive neuro-fuzzy inference system (ANFIS) is designed. The ANFIS structure combines the interpretability of fuzzy logic and the learning ability of neural networks, and its rule 1 output is:

2) LSTM-Based Hysteresis Feedforward Compensator

Construct an LSTM network whose inputs are the barometric pressure sequence { P t − N , ⋯ , P t − 1 } and the current expected displacement d_des(t) at the last N moments, and whose outputs are the hysteresis compensated displacement

To ensure the reproducibility and robustness of the proposed LSTM compensator, the minimum training specifications are supplemented as follows:

1) Training Data Acquisition Protocol

Excitation Signals: A composite sinusoidal sweep signal (0.5 - 5 Hz) and a multi-amplitude pseudo-random binary sequence (PRBS) are adopted as the desired displacement inputs to sufficiently excite the nonlinearity and hysteresis characteristics of the PAM. Each signal lasts for 60 seconds with a sampling frequency of 1 kHz.

Loading Conditions: Data are collected under three static loading conditions: no load (0 N), low load (20 N), and high load (50 N). Additionally, dynamic transition data are collected during sudden load changes (20 N ↔ 50 N step).

Data Partitioning: 70% of the data is used for training, 15% for validation, and 15% for testing.

2) Cross-Condition Generalization Capability Validation

Three methods are used to check generalization capability:

Load Generalization: Tests are performed under intermediate loads not seen during training (10 N, 35 N). The relative increase in the root mean square error (RMSE) of displacement tracking is calculated, and the increase is required to be ≤20%.

Frequency Generalization: Sinusoidal tracking at constant frequencies outside the training range (0.2 Hz, 6 Hz) is performed to evaluate phase lag and amplitude attenuation.

Long-Term Drift Test: A continuous 10-minute run (3000 control cycles) is conducted. The mean and standard deviation of the post-compensation displacement error are monitored for any monotonic increasing trend (linear fit slope < 0.01 mm/s).

Objective: Build a high-performance real-time control experimental platform, and verify the effectiveness of the algorithm in typical application scenarios.

Research Content:

1) Hardware Platform Development

Drive and sensing: The drive unit is built with Festo MPVE proportional valve and custom silicone muscle. Integrated laser displacement sensor and micro pressure sensor, and through the NI cRIO-9068 real-time controller to synchronously collect all sensor data and execute control algorithms in a 1 ms cycle.

Real-time software architecture: Implement deterministic real-time loops in LabVIEW RT. The TensorRT-accelerated LSTM and DDPG policy network inference engine is integrated internally to ensure that the forward propagation time of the neural network is less than 0.5 ms.

2) Adaptive Human-Machine Interface Fusing Myoelectric Fatigue Features (Innovative Application Verification) [15]

sEMG signal processing and fatigue feature extraction: Referring to the method of Yan Shijia et al. (2024), the median frequency (MDF) slope and root mean square (RMS) value are extracted in real time from the collected forearm sEMG signal as the estimation of muscle fatigue F_level.

Adaptive adjustment of the control law: the F_level as an additional state input to the DRL agent or a direct design of the fuzzy regulator. When the user’s fatigue degree is detected to increase, the system automatically adjusts the auxiliary force ratio of the exoskeleton or the impedance parameter of the controller to provide more supportive assistance and realize the “people-oriented” adaptive collaborative control.

3) Systematic Performance Verification Experiment

Benchmark performance test: Step response, sinusoidal tracking (1 - 5 Hz), load mutation (0 - 50N) experiments, quantization positioning accuracy (target ± 0. 8 mm), response time (target ≤ 0. 3 s) and force control error (target < 2%).

Application scenario validation:

Rehabilitation glove scenario: Subjects wear soft gloves with integrated PAM drivers and perform grip-release tasks. Before and after the introduction of EMG fatigue feature adaptive adjustment, the changes of muscle activation degree and subjective fatigue feeling of users during long-term training were compared.

Microgravity simulation scene: Cooperate with the Space Environment Simulation Center of the Chinese Academy of Sciences to test the ability of the PAM manipulator to grasp and control floating targets under the microgravity conditions of hanging wire counterweight or parabolic flight simulation, and verify its robustness in extreme environments sex.