Stability of a system of Volterra integro-differential equations

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.     

An asymptotically stable collision-avoidance system

Artificial potential fields, which are widely used in robotics for path planning and collision avoidance, are normally beset by difficulties arising from the existence of local minima. This article proposes a solution that involves an asymptotically stable point-mass system governed by differential equations. The system represents a planar point robot moving from its initial position to the desired goal whilst avoiding a static obstacle. Because the system is asymptotically stable, its Lyapunov function, which produces artificial potential fields around the goal and the obstacle, has no local minima other than the goal configuration in the pathwise-connected proper subset of free space which contains the goal configuration. As an application, we consider the point stabilization of a planar mobile car-like robot moving in the presence of a static obstacle.