A Random Exploration Approach for Automatic Chamferless Insertion

The stochastic approach strategy to realize the robotized in sertion of low-clearance, chamferless parts is studied in both the analytical and experimental contexts. The analytical ap proach is discussed in terms of stochastic differential equations that involve Gaussian white and colored noises processes to model a planar random search. Special attention is devoted to characterize the time required for the insertion, a random variable whose first moment calculation (i.e., the mean) is dealt with. In the mathematical modelization context adopted, it is remarkable that the calculated mean mating time grows slowly (i.e., logarithmically), with the precision required to perform an insertion. The. theoretical results are validated on a robo tized assembly system, also presented in this article. In this experimental system, the random movements are generated by pseudorandom binary sequences that, for the time scales con sidered, are large band processes. The experimental data are observed to sustain the logarithmic behavior obtained analyt ically. Hence, in addition to its simplicity and flexibility, the random strategy approach appears to be very efficient when high mating precision is required.