Working in crowded environments is a challenging task for mobile robotic systems as the robot may have a collision to other moving or stationary objects. One of the practical issues is that robots should not have any collision while they are performing their tasks. A general collision avoidance algorithm which can be used everywhere can be very useful. In this thesis a controller, which can avoid the collision between two vehicles modelled as unicycles, is presented and it is shown that if this controller cannot avoid collision, no other controller can do it. This controller is called a least restrictive controller. This controller is not unique and therefore we may find another controller which is least restrictive, however the set of the states, for which a collision is unavoidable, is the same for all least restrictive controllers.