Families of semipermeable curves in differential games with the homicidal chauffeur dynamics

Semipermeable Curves and Level Sets of the Value Function in Differential Games with the Homicidal Chauffeur Dynamics

A classical and a modified (acoustic) variants of the differential game “homicidal chauffeur” are considered. An interesting peculiarity of the letter variant consists, in particular, in the presence of holes located strictly inside the victory domain of the pursuit-evasion game. In the paper, an explanation to this phenomenon is given. The explanation is based on an analysis of families of sem...

Numerical Solution to the Acoustic Homicidal Chauffeur Game

A well-known differential game in the theory of differential games is the “homicidal chauffeur” problem which was introduced by Isaacs [7]. It is a pursuit-evasion game. In the paper, a variant of this problem proposed by Bernhard [3] is considered. The computation of level sets of the value function in this variant becomes difficult since holes in the “victory domains” of the pursuer can appea...

Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer

The paper is devoted to the investigation of a time-optimal differential game in which the pursuer possesses increased control capabilities comparing to the classical homicidal chauffeur problem. Namely, the pursuer steers not only the angular velocity of turn but can additionally change the magnitude of his linear velocity. For such a new variant of the dynamics with non-scalar control of the ...

Level Sets of the Value Function in differential Games with the Homicidal Chauffeur Dynamics

On the Suicidal Pedestrian Differential Game

We consider the following differential game of pursuit and evasion involving two participating players: an evader, which has limited maneuverability, and an agile pursuer. The agents move on the Euclidean plane with different but constant speeds. Whereas the pursuer can change the orientation of its velocity vector arbitrarily fast, that is, he is a “pedestrian” á la Isaacs, the evader cannot m...