Input Mapping-Based Model Predictive Control with Event-Triggered Adaptive Strategy for Rigid-Soft Hybrid Manipulator

doi:10.1007/s12204-026-2902-4

Abstract

Abstract: Uncertain loads of the rigid-soft hybrid manipulator directly affect working configurations, which will alter the system model parameters, and thereby degrade control accuracy and efficiency. This paper introduces an event-triggered adaptive model predictive control strategy, which integrates with a data-driven approach to control hybrid robots with a cable-driven soft component. In the presence of model uncertainty and mismatch, adaptive identification is employed to improve the nominal model within the controller. Meanwhile, an event-triggered scheme is utilized to reduce redundant identification frequency and improve computing efficiency. Furthermore, an online data-driven method, called input mapping, uses the relationship between the historical input and output data to compensate for the minor model error in the controller via linear combination. The optimization problem is efficiently solved by designing the attenuation coefficient in an infinite-domain situation. Comparative simulation and experimental results demonstrate that the proposed method achieves improved accuracy and faster convergence speed.

Key words: rigid-soft hybrid robot, input mapping, event-triggered, adaptive model predictive control, recursive feasibility, stability

摘要： 不确定性负载会直接影响刚柔混合机械臂的工作配置，改变系统模型参数，从而降低其控制精度和效率。介绍了一种带有事件触发自适应策略的模型预测控制，并结合数据驱动方法控制刚柔混合机器人，其中软体部分由电缆驱动。在模型不确定性和匹配失真的情况下，使用自适应辨识方法改进控制器内的名义模型；同时使用事件触发方法以降低冗余的辨识频率，以提高计算效率。此外，使用了一种在线数据驱动方法，即输入映射，利用历史输入和输出数据的关系，并通过线性组合补偿了控制器中的轻微模型误差。在无限时域中，设计了衰减系数以高效解决优化问题。对比仿真和实验结果表明：本文所提方法在精度和收敛速度上都实现了更好的效果。

关键词: 刚柔混合机器人，输入映射，事件触发，自适应模型预测控制，递归可行性，稳定性

CLC Number:

TP241

Li Guolin, Chen Tong, He Shaoying, Yin Debin. Input Mapping-Based Model Predictive Control with Event-Triggered Adaptive Strategy for Rigid-Soft Hybrid Manipulator[J]. J Shanghai Jiaotong Univ Sci, 2026, 31(1): 36-47.

References

[1] Renda F, Giorelli M, Calisti M, et al. Dynamic model of a multibending soft robot arm driven by cables [J]. IEEE Transactions on Robotics, 2014, 30(5): 1109-1122.
[2] Rus D, Tolley M T. Design, fabrication and control of soft robots [J]. Nature, 2015, 521(7553): 467-475.
[3] Bruder D, Graule M A, Teeple C B, et al. Increasing the payload capacity of soft robot arms by localized stiffening [J]. Science Robotics, 2023, 8(81): eadf9001.
[4] Ma X, Wang X C, Zhang Z H, et al. Design and experimental validation of a novel hybrid continuum robot with enhanced dexterity and manipulability in confined space [J]. IEEE/ASME Transactions on Mechatronics, 2023, 28(4): 1826-1835.
[5] Almanzor E, Ye F, Shi J L, et al. Static shape control of soft continuum robots using deep visual inverse kinematic models [J]. IEEE Transactions on Robotics, 2023, 39(4): 2973-2988.
[6] Huang X J, Zou J, Gu G Y. Kinematic modeling and control of variable curvature soft continuum robots [J]. IEEE/ASME Transactions on Mechatronics, 2021, 26(6): 3175-3185.
[7] Jiang H, Wang Z C, Jin Y S, et al. Hierarchical control of soft manipulators towards unstructured interactions [J]. The International Journal of Robotics Research, 2021, 40(1): 411-434.
[8] Caasenbrood B, Pogromsky A, Nijmeijer H. Control-oriented models for hyperelastic soft robots through differential geometry of curves [J]. Soft Robotics, 2023, 10(1): 129-148.
[9] Raisch A, Mayer A, Müller D, et al. A model-based cascaded control concept for the bionic motion robot [C]//2020 American Control Conference. Denver: IEEE, 2020: 2049-2054.
[10] Wang H S, Yang B H, Liu Y T, et al. Visual servoing of soft robot manipulator in constrained environments with an adaptive controller [J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(1): 41-50.
[11] Sefati S, Hegeman R, Alambeigi F, et al. A surgical robotic system for treatment of pelvic osteolysis using an FBG-equipped continuum manipulator and flexible instruments [J]. ASME Transactions on Mechatronics, 2021, 26(1): 369-380.
[12] Coevoet E, Adagolodjo Y, Lin M C, et al. Planning of soft-rigid hybrid arms in contact with compliant environment: Application to the transrectal biopsy of the prostate [J]. IEEE Robotics and Automation Letters, 2022, 7(2): 4853-4860.
[13] Jin Z H, Qin D D, Liu A D, et al. Model predictive variable impedance control of manipulators for adaptive precision-compliance tradeoff [J]. IEEE/ASME Transactions on Mechatronics, 2023, 28(2): 1174-1186.
[14] Mayne D Q, Rawlings J B, Rao C V, et al. Constrained model predictive control: Stability and optimality [J]. Automatica, 2000, 36(6): 789-814.
[15] Rubagotti M, Taunyazov T, Omarali B, et al. Semi-autonomous robot teleoperation with obstacle avoidance via model predictive control [J]. IEEE Robotics and Automation Letters, 2019, 4(3): 2746-2753.
[16] Best C M, Gillespie M T, Hyatt P, et al. A new soft robot control method: Using model predictive control for a pneumatically actuated humanoid [J]. IEEE Robotics & Automation Magazine, 2016, 23(3): 75-84.
[17] Wu K, Zheng G. FEM-based gain-scheduling control of a soft trunk robot [J]. IEEE Robotics and Automation Letters, 2021, 6(2): 3081-3088.
[18] Spinelli F A, Katzschmann R K. A unified and modular model predictive control framework for soft continuum manipulators under internal and external constraints [C]//2022 IEEE/RSJ International Conference on Intelligent Robots and Systems. Kyoto: IEEE, 2022: 9393-9400.
[19] Mayne D Q. Model predictive control: Recent developments and future promise [J]. Automatica, 2014, 50(12): 2967-2986.
[20] Dai Y, Yu S H, Yan Y, et al. An EKF-based fast tube MPC scheme for moving target tracking of a redundant underwater vehicle-manipulator system [J]. IEEE/ASME Transactions on Mechatronics, 2019, 24(6): 2803-2814.
[21] Bhattacharya D, Hashem R, Cheng L K, et al. Nonlinear model predictive control of a robotic soft esophagus [J]. IEEE Transactions on Industrial Electronics, 2022, 69(10): 10363-10373.
[22] El-Hussieny H, Hameed I A, Ryu J H. Nonlinear model predictive growth control of a class of plant-inspired soft growing robots [J]. IEEE Access, 2020, 8: 214495-214503.
[23] Amouri A, Cherfia A, Merabti H, et al. Nonlinear model predictive control of a class of continuum robots using kinematic and dynamic models [J]. FME Transactions, 2022, 50(2): 339-350.
[24] Li F H, Hou Z S. Event-triggered model-free adaptive predictive control for networked control systems under deception attacks [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(2): 1325-1334.
[25] Hui Y, Chi R H, Huang B, et al. Observer-based sampled-data model-free adaptive control for continuous-time nonlinear nonaffine systems with input rate constraints [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(12): 7813-7822.
[26] Zhu B, Zheng Z W, Xia X H. Constrained adaptive model-predictive control for a class of discrete-time linear systems with parametric uncertainties [J]. IEEE Transactions on Automatic Control, 2020, 65(5): 2223-2229.
[27] He S Y, Sun L L, Xu Y W, et al. A modeling and data-driven control framework for rigid-soft hybrid robot with visual servoing [J]. IEEE Robotics and Automation Letters, 2023, 8(11): 7281-7288.
[28] Hou Z S, Jin S T. Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems [J]. IEEE Transactions on Neural Networks, 2011, 22(12): 2173-2188.
[29] He S Y, Xu Y W, Li D W, et al. Eye-in-hand visual servoing control of robot manipulators based on an input mapping method [J]. IEEE Transactions on Control Systems Technology, 2023, 31(1): 402-409.
[30] Zhu B, Xia X H. Adaptive model predictive control for unconstrained discrete-time linear systems with parametric uncertainties [J]. IEEE Transactions on Automatic Control, 2016, 61(10): 3171-3176.
[31] Li D W, Xi Y G, Lu J Y, et al. Synthesis of real-time-feedback-based 2D iterative learning control–model predictive control for constrained batch processes with unknown input nonlinearity [J]. Industrial & Engineering Chemistry Research, 2016, 55(51): 13074-13084.
[32] Guo Y, Hou Z S, Liu S D, et al. Data-driven model-free adaptive predictive control for a class of MIMO nonlinear discrete-time systems with stability analysis [J]. IEEE Access, 2019, 7: 102852-102866.