In this paper, a nonlinear model predictive controller (NMPC) with input saturation is designed and modified for a rehabilitative exoskeleton for paraplegic individuals. An analytical solution for the NMPC optimization problem is obtained for small prediction horizons ( $$N < 3$$ N < 3 ). Additionally, an iterative solution for longer horizon problems ( $$N \ge 3$$ N ≥ 3 ) is performed by employing the linear time-varying approach and using the active set method to include the constraints. Real-time guarantee for the implementation of both NMPC solutions is derived, and the robustness and stability of the closed-loop system are discussed. Finally, the proposed controller is successfully simulated and implemented on a real exoskeleton robot with 1 ms sampling time. The results show that the proposed controller is more effective than PID and adaptive fuzzy controllers.

中文翻译：

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输入饱和下肢外骨骼实时非线性模型预测控制器的设计与实现

在本文中，针对截瘫患者的康复外骨骼设计并修改了具有输入饱和度的非线性模型预测控制器（NMPC）。对于小预测范围 ( $$N < 3$$ N < 3 )，可以获得 NMPC 优化问题的解析解。此外，通过采用线性时变方法并使用活动集方法包括约束来执行更长范围问题（$$N \ge 3$$ N ≥ 3 ）的迭代解决方案。推导出两种NMPC解决方案的实时性保证，并讨论了闭环系统的鲁棒性和稳定性。最后，所提出的控制器在具有 1 ms 采样时间的真实外骨骼机器人上成功模拟和实现。