A Closed-Form Approach to Tracking Control of Nonlinear Uncertain Systems Using the Fundamental Equation

Udwadia, Firdaus E.; Wanichanon, Thanapat

doi:10.1061/9780784412190.143

Cited by 19 publications

(12 citation statements)

References 6 publications

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“…6,7 Moreover, it is not an issue for Udwadia-Kalaba equation based on the Gauss' principle of least constraint, and the optimal value of the generalized variables solution can still be obtained by the Moore-Penrose generalized inverse when the number of the constraint equations is not equal to the number of generalized variables. Udwadia and colleagues [8][9][10][11] also effectively dealt with the dynamics and control of nonlinear uncertain systems to benefit the basic research and further application of this method. It has been studied in some application fields, such as industrial robot, 12 parallel robot, 13 flexible multibody systems, 14 railway vehicles collision, 15 machine fish, 1 control of tethered satellites, 16 rigid multibody systems, 17 and mobile robots.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Liu

2017

Advances in Mechanical Engineering

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With the aim of dynamic modeling of the SCARA robot subjected to space trajectory constraint to satisfy repetitive tasks with higher accuracy, a succinct and explicit equation of motion based on Udwadia-Kalaba theory is established. The trajectory constraint, which is regarded as the external constraints imposed on the system, is integrated into the dynamic modeling of the system dexterously. The explicit expression of constraint torques required to satisfy constraints and explicit dynamic equation of the system without Lagrange multiplier are obtained. However, constraint violation arises when the initial conditions are incompatible with the constraint equations. Baumgarte stabilization method is considered for constraint violation suppression. Simulations of the varying law of the generalized coordinate variables and the trajectories of the SCARA robot are performed to demonstrate the simplicity and accuracy of the method.

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Section: Introductionmentioning

confidence: 99%

Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Liu

2017

Advances in Mechanical Engineering

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“…Using the fundamental equation, Udwadia et al also successfully addressed the control of nonlinear multibody mechanical systems in the presence of system uncertainties [36][37][38][39][40]. This control methodology now is well known to many researchers in this field.…”

Section: Introductionmentioning

confidence: 96%

Application of the Udwadia–Kalaba approach to tracking control of mobile robots

et al. 2015

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Udwadia-Kalaba approach which presents a new, general and explicit equation of motion for constrained mechanical systems with holonomic or nonholonomic constraints is applied to the trajectory tracking control of the mobile robot in this paper. Unlike any other nonlinear control methods, the inspiration for this methodology which does not make any linearization or approximations comes from a different, though closely allied, field, namely analytical dynamics. The control torques required to control the mobile robot so that it precisely satisfies the trajectory requirements which are represented by an arbitrary (sufficiently smooth) function of time are obtained explicitly and in closed form by solving Udwadia-Kalaba equation. Numerical simulations are performed to show the simplicity, efficacy and accuracy of this closed-form method.

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“…There are many contributions which deal with uncertainty based on constraint motion ( e.g. , and their bibliographies).…”

Section: Introductionmentioning

confidence: 99%

A New High‐Order Adaptive Robust Control for Constraint Following of Mechanical Systems

Yang

Zhao

Sun

et al. 2017

Asian Journal of Control

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A mechanical system is to follow a class of prescribed holonomic or nonholonomic constraints. The system contains time‐varying bounded uncertainty. However, the bound is unknown. The objective is to design a control which renders constraint following. A new high‐order adaptive robust control is proposed. The control guarantees uniform boundedness and uniform ultimate boundedness even in the presence of the uncertainty. Significant advantages of this new control are demonstrated both analytically and numerically. It is shown that the system performance, including the finite entering time, constraint‐following error, and control magnitude, can be improved by tuning the control order.

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A Closed-Form Approach to Tracking Control of Nonlinear Uncertain Systems Using the Fundamental Equation

Cited by 19 publications

References 6 publications

Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

Application of the Udwadia–Kalaba approach to tracking control of mobile robots

A New High‐Order Adaptive Robust Control for Constraint Following of Mechanical Systems

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