Tracking control for lower limb rehabilitation robots based on polynomial nonlinear uncertain models

Abstract

This paper aims to propose a novel idea for the modeling and trajectory tracking control of a lower limb rehabilitation robot. A polynomial nonlinear uncertain model is established to deal with the difficulty of accurate modeling for the lower limb rehabilitation robot with complex dynamic characteristics. A high‐order nonlinear disturbance observer (HONDO) is utilized to estimate the lumped disturbance with fast time‐varying and the corresponding observer gain matrix is obtained by H∞ performance. Then an HONDO‐based composite tracking controller is designed to achieve good tracking performance of the lower limb rehabilitation robot. In addition, all solvability conditions can be directly handled by sum of squares programming, effectively avoiding the calculation problem. Finally, numerical simulations are conducted to verify the validity of the proposed method.

Adaptive output feedback fault‐tolerant control for nonlinear stochastic systems with output constraint

“…Remark Many real physical systems can be expressed into the mathematical models in system (2), such as single‐link manipulators 32 and inverted pendulums. Different from the exiting works, 4‐6 the unideal sensors and actuator failure are taken into account. Due to the manufacturing technology, it is difficult to guarantee that the sensor is completely ideal.…”

“…Moreover, the existence of unknown output measurement sensitivity and complex nonlinear function will make the existing K-filter algorithms 14,15 ineffective, and then how to establish a reduced-order K-filter is a challenging problem. To deal with the unknown output measurement sensitivity, we design the reconstructed state variable as (6). Since the nonlinear function c k (y)x k is directly related to unmeasurable state variables, it will render that the term cannot be handled under the traditional algorithm.…”

“…In recent years, research on nonlinear systems has attracted considerable attention since almost all physical systems are nonlinear in nature 1‐3 . The existing research on nonlinear system can be roughly divided into two categories: one is stabilization problem, 4,5 the other is tracking problem 6,7 . As the basis of nonlinear system research, the stabilization problem has been vigorously studied in References 8,9.…”

“…[1][2][3] The existing research on nonlinear system can be roughly divided into two categories: one is stabilization problem, 4,5 the other is tracking problem. 6,7 As the basis of nonlinear system research, the stabilization problem has been vigorously studied in References 8,9. Tracking problem, as a generalization of stabilization, has attracted great interests of researchers because of its strong ability to track the desired trajectory. The work 10 constructed a robust tracking controller for uncertain nonlinear system.…”

Robust adaptive control Lyapunov‐barrier function for non‐collocated control and safety of underactuated robotic systems

“…In recent years, researchers have become increasingly interested in controlling of underactuated robotic systems due to their important applications such as aerial and underwater vehicles, [1][2][3] flexible-joint robots, 4,5 and walking and rehabilitation robots. [6][7][8] Herein, underactuated systems mean systems that have fewer degrees of actuation (DoA) than degrees of freedom (DoF). The lack of actuation is, clearly, a challenging control problem with underactuated robots.…”