Algorithms for Cameras View-Frame Placement Problems in the Presence of an Adversary and Distributional Ambiguity

In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence of an adversary whose objective is to minimize the maximum coverage by $p$ cameras in response to input provided by $n$ autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution associated with the uncertain data, and varying levels of risk-appetite of the adversary. We present an exact cutting planes based algorithm to solve this problem and provide conditions under which it is finitely convergent. Since this approach solves deterministic CFP in each iteration, we also present improved exact method for CFP with $p=1$ , approximation algorithm and heuristics for Multi-CFP with $p\geq 2$ , and Multi-CFP with fixed tilt of the cameras. To evaluate the effectiveness and performance of the proposed approaches, we conduct computational experiments using randomly generated instances and simulation experiments where these approaches are utilized to find a hidden object in a remote location. Note to Practitioners —Telerobotic cameras have been widely used for a variety of applications in environment where it is tedious for humans to collect information such as surveillance, natural environment observation, search and rescue, satellite imaging, and many more. Therefore, computationally efficient approaches proposed in this paper for placement of view-frame of camera(s), by adjusting their pan, tilt, and zoom, will improve the effective utilization of a telerobotic cameras system. Additionally, before operating such systems in a military environment, a decision maker needs to analyze vulnerable cameras in the system whose disruption can significantly impact the information acquisition process. The algorithms presented for adversarial camera view-frame placement problem can identify the set of cameras (or vehicles carrying them) that are susceptible to attacks by a reasonable (risk-averse) attacker. Likewise, the proposed algebraic modeling framework and solution approaches are also applicable for planning interdiction actions to minimize the information acquisition by an evader/enemy. These results can be leveraged by autonomy solutions developed by the Army for both logistics (Autonomous Ground Resupply program) and combat missions (Combat Vehicle Robotics program).