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Model-based feedforward precompensation and VS-type robust nonlinear postcompensation for uncertain robotic systems with/without knowledge of uncertainty bounds(I)

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Abstract

In this paper, a robust motion tracking control algorithm for robotic manipulators is proposed where the higher-order system uncertainties are taken into account. The control structure consists of two main parts: a model-based precompensation part and a robust nonlinear controller one. Specifically, with knowledge of possible upper bounds on uncertainties, we propose the nonadaptive version of robust controller. Stability and robustness issues of the controllers have been investigated via a Lyapunov method and it is shown that the proposed control algorithms are highly robust in the presence of significant system uncertainties. Finally, the computer simulation results are presented to validate the proposed algorithm.

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Abbreviations

R + :

Set of non-negative real number;R +:=[0, +∞)

R n :

n-dimensional vector space with real elements R

R n×m :

Set of all real-valued (n×m) matrices

inf:

Infimum, the greatest lower bound

sup:

Supremum, the least upper bound

x:

A vector; x=[x 1 x 2...x n ]T,x 1∈R

‖x‖:

Euclidean norm of a vector x; ‖x‖=[x7x]1/2, ∨x∈R n

A>0(<0):

Positive (negative) definite matrix A

‖A‖:

Induced norm of a real matrix A∈R n×m; ‖A‖=[λmax (A T A)]1/2

Ω r (x):

Closed ball inR n of radiusr∈R + centered at x=0:Ω r (x)=(x∈R n: ‖x‖≤r)

C p :

Set ofp-times continuously differentiable functions

E n :

(n×n) Identity matrix

L p :

The function norm in the Lebesgue space; Let f(t):R −→R n be Lebesgue measurable function, then theL p -norm ‖f‖ p is defined as ‖f‖ p , forp∈[1, ∞). Whenp=∞,f∈L ∞ if and only if\(\left\| f \right\|_\infty = \mathop {\sup }\limits_{t \in [0, + \infty )} \left\| {f(t)} \right\|< \infty \)

λmax(A):

Maximum eigenvalue of A:\(\lambda _{\max } (A) = \mathop {\max }\limits_i \{ \lambda _i (A)\} \), where λi(A) is theith eigenvalue of matrix A

λmax(A):

Minimum eigenvalue of A;\(\lambda _{\min } (A) = \mathop {\max }\limits_i \{ \lambda _i (A)\} \)

(•)C :

Complement of (•)

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Authors and Affiliations

  1. Department of Mechanieal Engineering, Korea Maritime University, Yeongdo-Ku, 606-791, Pusan, Korea

    Sam-Sang You

  2. Research Center for Ocean Industrial Development, Pukyong National University, 599-1 Daeyeon-dong, Nam-gu, Pusan, Korea

    Seok-Kwon Jeong

Authors
  1. Sam-Sang You
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  2. Seok-Kwon Jeong
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You, SS., Jeong, SK. Model-based feedforward precompensation and VS-type robust nonlinear postcompensation for uncertain robotic systems with/without knowledge of uncertainty bounds(I). KSME Journal 10, 296–304 (1996). https://doi.org/10.1007/BF02942638

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  • DOI: https://doi.org/10.1007/BF02942638

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