• 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.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• 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 the Korean Society for Precision Engineering
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• v.15 no.3
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• pp.127-132
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• 1998

Mobile wheeled robots are nonholonomically constrained systems. Generally, it is very difficult to describe the motion of mechanical systems with nonintegrable nonholonomic constraints. An objective of this study is to describe the motion of a robot with a free wheel. The motion of holonomically and/or nonholonomically constrained system can be simply determined by Generalized Inverse Method presented by Udwadia and Kalaba in 1992. Using the method, we describe the exact motion of the robot and determine the constraint force exerted on the robot for satisfying constraints imposed on it. The application illustrates the ease with which the Generalized Inverse Method can be utilized for the purpose of control of nonlinear system without depending on any linearization, maintaining precision tracking motion and explicit determination of control forces of nonholonomically constrained system.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.346-349
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• 1994

This paper is concerned with a motion control of a manipulator under parametric uncertainties and external disturbances. The parametric uncertainties are regarded as internally generated disturbances in the manipulator. Based on this idea, we formulate a model reference control problem with desired disturbance attenuation. The solution of this control problem not only reduces the worst-case effect on tracking error due to internal and external disturbances (combined disturbances) as much as possible, but also achieve optimal tracking when perturbations are absent. In order to solve the control problem which is formulated in this paper we reduce it to a constrained minmax cost control problem. A differential game theory is used to treat this constrained minmax cost control problem. The differential game theory leads to a sufficient condition for the global solvability of the model reference control problem with desired disturbance attenuation.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.7
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• pp.154-162
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• 1997

본 논문은 구속된 기계 시스템의 운동 제어 설계를 위한 새로운 방법을 제안한다. 구속된 기계 시스템의 운동 제어에는 지금까지 주로 사용되어온 Lagrange의 운동 방정식에 의한 모델링 보다 Udwadia와 Kalaba에 의해 제안된 운동 방정식에 의한 모델링이 더욱 적합함을 보였으며 이는 Holonomic 및 Nonholonomic 구속 조건을 비롯한 대부분의 구속 조건이 포함된다. 문헌에 잘 알려진 두 시스템을 시뮬레이션을 통하여 비교 함으로써 본 논문에 제안된 방법이 보다 우수한 결과를 보여줌을 확인 할 수 있었다. 또한 지금까지 불가능 하였던 비선형 일반 속도(gereralized velocity)를 포함한 구속 조건도 용이하게 제어됨을 보임으로써 광범위한 구속된 기계 시스템의 제어 문제를 통일된 방법으로 접근 할 수 있음을 제시하였다.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.69-72
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• 1996

This paper considers a global resolution of kinematic redundancy under inequality constraints as a constrained optimal control. In this formulation, joint limits and obstacles are regarded as state variable inequality constraints, and joint velocity limits as control variable inequality constraints. Necessary and sufficient conditions are derived by using Pontryagin's minimum principle and penalty function method. These conditions leads to a two-point boundary-value problem (TPBVP) with natural, periodic and inequality boundary conditions. In order to solve the TPBVP and to find a global minimum, a numerical algorithm, named two-stage algorithm, is presented. Given initial joint pose, the first stage finds the optimal joint trajectory and its corresponding minimum performance cost. The second stage searches for the optimal initial joint pose with globally minimum cost in the self-motion manifold. The effectiveness of the proposed algorithm is demonstrated through a simulation with a 3-dof planar redundant manipulator.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.35 no.11
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• pp.1199-1204
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• 2011

The capability to bilaterally telemanipulate soft-tissues for medical applications could increase the quality of telemanipulation systems. Since most soft-tissue manipulation tasks include constrained motion interacting with an unknown and dynamic bioenvironment through contact, bilateral telemanipulation raises problems due to stability and transparency issues. It is well understood that knowledge of environments plays an important role in pursuing transparent telemanipulation and achieving telepresence, and in particular, online estimation of environmental parameters with an explicit environment model can improve these systems' performance. In this study, a continuum mechanics-based environment model with an online environmental property estimation algorithm and an adaptive telemanipulation control scheme is proposed. The proposed method can improve the telemanipulation performance in terms of stability and transparency and can offer valuable information (e.g., elastic modulus of soft tissues) pertaining to diagnostic examinations.