Robust Constraint Following Control of Lower Limb Rehabilitation Robots Based on the Generalized Udwadia-Kalaba Method

SUN Hao; WANG Xin; HU Aohua; MA Chao

doi:10.21656/1000-0887.450085

Volume 46 Issue 4

Apr. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(4): 451-464

SUN Hao, WANG Xin, HU Aohua, MA Chao. Robust Constraint Following Control of Lower Limb Rehabilitation Robots Based on the Generalized Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2025, 46(4): 451-464. doi: 10.21656/1000-0887.450085

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Robust Constraint Following Control of Lower Limb Rehabilitation Robots Based on the Generalized Udwadia-Kalaba Method

doi: 10.21656/1000-0887.450085

SUN Hao^{1, 2
,},
WANG Xin^{1, 2},
HU Aohua^{1, 2},
MA Chao^{1, 2
,
,}

1.
School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, P.R.China
2.
Anhui Key Laboratory of Digit Design and Manufacture, Hefei 230009, P.R.China

Received Date: 2024-04-07
Rev Recd Date: 2025-03-08
Publish Date: 2025-04-01

Abstract

Abstract

A robust constraint following controller based on the generalized Udwadia-Kalaba (U-K) equation was proposed for the problem of equality constraints and inequality constraints in the lower limb rehabilitation robot system, to make the system meet the equality constraints and inequality constraints at the same time, solve the uncertainty in the system, and achieve good constraint following effects on the robot. During the working process of the robot, the traditional control method is difficult to ensure that the motion range of the robot is within the boundary conditions, resulting in secondary injury to the patient during use. To solve the influence of boundary problems, a control method was proposed to use the diffeomorphism transformation to incorporate the equality constraint and inequality constraint system into the U-K equation, with the generalized U-K equation established mathematically. On this basis, a robust constraint tracking strategy was presented to ensure satisfactory performances of the system in the presence of uncertainties and various constraints. In addition, the stability of the robust control method was theoretically proved with the Lyapunov function. The simulation results show that, the robust control method has high-precision tracking control of a given trajectory under non-ideal conditions.
- generalized Udwadia-Kalaba equation,
- inequality constraint,
- robust control,
- lower limb rehabilitation robot

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References(29)

References

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