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
In the last 20 years, both of the algorithmic components of interval arithmetic and their relation on computers were further developed. However, overestimation of an interval function is still a major drawback in interval analysis.