The problem of motion planning of an autonomous vehicle amidst other vehicles on a straight road is considered. Traffic in a number of countries is unorganized, where the vehicles do not move within predefined speed lanes. In this paper, we formulate a mechanism wherein an autonomous vehicle may travel on the “wrong” side in order to overtake a vehicle. Challenges include assessing a possible overtaking opportunity, cooperating with other vehicles, partial driving on the “wrong” side of the road and safely going to and returning from the “wrong” side. The experimental results presented show vehicles cooperating to accomplish overtaking manoeuvres.