3 research outputs found
Guarding a Subspace in High-Dimensional Space with Two Defenders and One Attacker
This paper considers a subspace guarding game in high-dimensional space which
consists of a play subspace and a target subspace. Two faster defenders
cooperate to protect the target subspace by capturing an attacker which strives
to enter the target subspace from the play subspace without being captured. A
closed-form solution is provided from the perspectives of kind and degree.
Contributions of the work include the use of the attack subspace (AS) method to
construct the barrier, by which the game winner can be perfectly predicted
before the game starts. In addition to this inclusion, with the priori
information about the game result, a critical payoff function is designed when
the defenders can win the game. Then, the optimal strategy for each player is
explicitly reformulated as a saddle-point equilibrium. Finally, we apply these
theoretical results to a half-space guarding game in three-dimensional space.
Since the whole achieved developments are analytical, they require a little
memory without computational burden and allow for real-time updates, beyond the
capacity of traditional Hamilton-Jacobi-Isaacs method. It is worth noting that
this is the first time in the current work to consider the target guarding
games for arbitrary high-dimensional space, and in a fully analytical form.Comment: 12 pages, 2 figure
Task Assignment for Multiplayer Reach-Avoid Games in Convex Domains via Analytical Barriers
This work considers a multiplayer reach-avoid game between two adversarial
teams in a general convex domain which consists of a target region and a play
region. The evasion team, initially lying in the play region, aims to send as
many its team members into the target region as possible, while the pursuit
team with its team members initially distributed in both play region and target
region, strives to prevent that by capturing the evaders. We aim at
investigating a task assignment about the pursuer-evader matching, which can
maximize the number of the evaders who can be captured before reaching the
target region safely when both teams play optimally. To address this, two
winning regions for a group of pursuers to intercept an evader are determined
by constructing an analytical barrier which divides these two parts. Then, a
task assignment to guarantee the most evaders intercepted is provided by
solving a simplified 0-1 integer programming instead of a non-deterministic
polynomial problem, easing the computation burden dramatically. It is worth
noting that except the task assignment, the whole analysis is analytical.
Finally, simulation results are also presented
A time-optimal feedback control for a particular case of the game of two cars
In this paper, a time-optimal feedback solution to the game of two cars, for
the case where the pursuer is faster and more agile than the evader, is
presented. The concept of continuous subsets of the reachable set is introduced
to characterize the time-optimal pursuit-evasion game under feedback
strategies. Using these subsets it is shown that, if initially the pursuer is
distant enough from the evader, then the feedback saddle point strategies for
both the pursuer and the evader are coincident with one of the common tangents
from the minimum radius turning circles of the pursuer to the minimum radius
turning circles of the evader. Using geometry, four feasible tangents are
identified and the feedback min-max strategy for the pursuer and the max-min
strategy for the evader are derived by solving a matrix game at
each instant. Insignificant computational effort is involved in evaluating the
pursuer and evader inputs using the proposed feedback control law and hence it
is suitable for real-time implementation. The proposed law is validated further
by comparing the resulting trajectories with those obtained by solving the
differential game using numerical techniques