In this paper we develop a compilant system that permits robotic assembly of chamferless pieces. The idea is to absorb the positioning error between parts to be inserted by giving one of them a planar random movement. An actuator consisting of two axes (X and y) operated by an electromagnetic System is fitted to the work table; when its inputs are pseudo-random binary signais (P.R.B.S.) random motion is obtained. The trajectories of the actuator are analysed depending upon the P.R.B.S. parameters and a peg-in-a-hole assembly task is carried out. Experimental results show that large positioning errors can be compensated for chamferless insertions.