The system of kinematic equations which describes Isaacs' Game of Two Cars has been extended to the case of a three-dimensional pursuit-evasion game between players with bounded curvature. It is shown that in the three-dimensional version of the Homicidal Chauffeur game, both players, when playing optimally, strive to steer the system into a common plane and will remain on this plane until game termination. The situation is somewhat different for the three-dimensional version of the Game of Two Cars, where it is not always advantageous to steer an initially three-dimensional dynamic system into a plane. Nevertheless, if at any instant the velocity vectors and the line of sight between players are coplanar, both players strive to remain on this plane.
[1]
Touvia Miloh,et al.
MARITIME COLLISION AVOIDANCE AS A DIFFERENTIAL GAME
,
1975
.
[2]
A. Merz.
The game of two identical cars
,
1972
.
[3]
A. W. Merz,et al.
Minimum Required Capture Radius in a Coplanar Model of the Aerial Combat Problem
,
1977
.
[4]
G. Rublein.
On Pursuit with Curvature Constraints
,
1972
.
[5]
J. V. Breakwell,et al.
Role determination in an aerial dogfight
,
1974
.
[6]
M. Pachter,et al.
The geometry of the barrier in the ‘game of two cars’
,
1980
.