ABSTRACT:Uncertainties widely exist in engineering structural analysis and mechanical equipment designs, and they cannot always be neglected. The probabilistic method, the fuzzy method and the interval method are the three major approaches to model uncertainties at present. By representing all the uncertain length and the uncertain twist of the link parameters, and the uncertain distance and the uncertain angle between the links as interval numbers, the static pose (position and orientation) of the robot end effector in space was obtained accurately by evaluating interval functions. Overestimation is a major drawback in interval computation. A reliable computation approach is proposed to overcome it. The presented approach is based on the inclusion monotone property of interval mathematics and the physical/real means expressed by the interval function. The interval function was evaluated by solving the corresponding optimization problems to determine the endpoints / bounds of every interval element of the solution. Moreover, an intelligent algorithm named as real-code genetic algorithm was used to locate the global optima of these optimization problems. Before using the present approach to determine the response interval of uncertain robot system, some mathematical examples were used to examine its efficiency also.
Key words: robot kinematics; interval analysis; global optimization; uncertain geometry parameter

Introduction

 

When computing the robot forward kinematic, the nominal values for the link and joint parameters provided in the user manuals are used. Due to the manufacturing tolerance, the assembling error and part wear, the actual values for the kinematic parameters are always different from the given one. So the actual working envelop is different from the one reading from the robot controller computing with the nominal parameters. The Monte Carlo method is applied in a statistic way, but the computation is time-consuming to emulate all states [1].

The probabilistic method, the fuzzy method and the interval method are the three major approaches to model uncertainties at present [3]. Probabilistic approaches are not deliver reliable results at the required precision without sufficient experimenta

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