  In this paper, the collision avoidance problem for non-holonomic robots
moving at constant linear speeds in the 2-D plane is considered. The maneuvers
to avoid collisions are designed using dynamic vortex potential fields (PFs)
and their negative gradients; this formulation leads to a reciprocal behaviour
between the robots, denoted as being cooperative. The repulsive field is
selected as a function of the velocity and position of a robot relative to
another and introducing vorticity in its definition guarantees the absence of
local minima. Such a repulsive field is activated by a robot only when it is on
a collision path with other mobile robots or stationary obstacles. By analysing
the kinematics-based engagement dynamics in polar coordinates, it is shown that
a cooperative robot is able to avoid collisions with non-cooperating robots,
such as stationary and constant velocity robots, as well as those actively
seeking to collide with it. Conditions on the PF parameters are identified that
ensure collision avoidance for all cases. Experimental results acquired using a
mobile robot platform support the theoretical contributions.
