• International Journal of Precision Engineering and Manufacturing
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• v.2 no.4
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• pp.61-68
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• 2001

A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.209-209
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• 2000

In this paper, we show that some of 2- or higher-dimensional systems cannot be asymptotically stabilized on the constrained asymptotically stabilizable set via linear feedback.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.12
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• pp.991-997
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• 2002

The concept of feasible & invariant region plays an important role to derive closed loop stability and achie adequate performance of constrained receding horizon predictive control. In this paper, we define a complex polyhedral feasible & invariant set for all stabilizable input-constrained linear systems by using a complex transform and propose a one-norm based receding horizon control scheme using these invariant sets. In order to get a larger stabilizable set, a convex hull of invariant sets which are defined for different state feedback gains is used as a target invariant set of the constrained receding horizon control. The proposed constrained receding horizon control scheme is formulated so that it can be solved via linear programming.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.374-381
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• 1995

In this paper, integration methods for stiff constrained mechanical systems are studied to analyze dynamic response of the stiff mechanical system efficiently. The stiff, non-stiff systems are identified by using eigenvalues of the Jacobian of the systems. To integrate both stiff system and non-stiff system efficiently a new switching method between the non-stiff differential equation solver and the stiff differential equation solver is presented.

• Journal of Mechanical Science and Technology
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• v.18 no.11
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• pp.1891-1899
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• 2004

The characteristics of dynamic systems subjected to multiple linear constraints are determined by considering the constrained effects. Although there have been many researches to investigate the dynamic characteristics of constrained systems, most of them depend on numerical analysis like Lagrange multipliers method. In 1992, Udwadia and Kalaba presented an explicit form to describe the motion for constrained discrete systems. Starting from the method, this study determines the dynamic characteristics of the systems to have positive semidefinite mass matrix and the continuous systems. And this study presents a closed form to calculate frequency response matrix for constrained systems subjected to harmonic forces. The proposed methods that do not depend on any numerical schemes take more generalized forms than other research results.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.52-57
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• 1993

Conventional active control algorithm for duct system is developed without considering problems of constrained structure. Therefore it destroys the constrained structures of the weights or parameters. A new LMS algorithm, which does keep the constraints, is proposed for systems with known constrained structure. It is based on error-back propagation. The stability analysis and simulation example are also included.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.705-713
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• 1999

In this paper, we propose a new motion and force control methodology for constrained robots as an approach of hybrid discrete-continuous dynamical system. The hybrid dynamic system modeling of robotic manipulation tasks with constraints is presented, and the hybrid system control architecture for unconstrained and constrained motion system with parametric uncertainties is synthesized. The optimal reference stiffness of robot manipulator is generated by the hybrid automata as a discrete state system and the control behavior of constrained system which has poor modeling information and time-varying constraint function is improved by the constrained robots as a continuous state system. The performance of the proposed constrained motion control system is successfully evaluated via experimental studies to the constraint tasks.

• Journal of Mechanical Science and Technology
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• v.18 no.10
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• pp.1691-1699
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• 2004

The objective of this study is to present an accurate and simple method to describe the motion of constrained mechanical or structural systems. The proposed method is an elimination method to require less effort in computing Moore-Penrose inverse matrix than the generalized inverse method provided by Udwadia and Kalaba. Considering that the results by numerical integration of the derived second-order differential equation to describe constrained motion veer away the constrained trajectories, this study presents a numerical integration scheme to obtain more accurate results. Applications of holonomically or nonholonomically constrained systems illustrate the validity and effectiveness of the proposed method.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1086-1093
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• 2004

The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.