# Multi-Layered Interactive Target Guidance with Visual Safety in Convex-Shaped Obstacle Environments
## 1 Introduction  
In nature, pursuit and evasion are fundamental behaviors that have been observed across various species [1; 2; 3]. Pursuit and evasion involve the problem of devising strategies for the pursuer to eventually capture the target that is attempting to escape. This problem is also a significant challenge in robotics, with applications such as search and rescue operations or security surveillance [4]. An advanced variation of this problem is known as shepherding or herding. In shepherding, the evaders are a flock of sheep, and the pursuers are dogs, using a traditional herding technique to drive the flock into an enclosure. The attempt to replace sheep dogs with robots is initiated by [PERSON] et al. [5; 6], and many research results are still being reported in recent times [7; 8; 9]. Additionally, there is the guarding problem, where the pursuer prevents the evader from entering a certain area [10]. The common point in these problems is the indirect guidance of agents, which cannot be directly controlled, by robots. In this paper, we refer to these tasks as interactive guidance and propose an approach to address this task. In interactive guidance, the basic setting involves a group of evaders and a group of pursuers moving on a two-dimensional plane without obstacles. Recently, studies have begun to be reported that aim to achieve interactive guidance in environments where obstacles are present. In [11; 12; 13; 14], the authors address this issue by using path-planning methods to generate collision-free paths. [PERSON] et al. [15] proposed a method for deriving collision-free guidance laws using deep reinforcement learning. The presence of obstacles not only poses a risk of collision but also creates the risk of the pursuers losing sight of the evaders due to occlusion by obstacles. [PERSON] et al. [16] considered this in the context of pursuit-evasion. [PERSON] et al. [17] and [PERSON] et al. [18] addressed this risk in pursuit control by using control barrier functions. However, to the best of the authors' knowledge, no method exists that considers obstacle occlusion in interactive guidance. In this paper, we define a system as being \"visually safe\" when it consistently keeps the evaders within the field of view, even in environments with obstacles. Achieving interactive guidance is challenging with reactive behavior based solely on feedback control as it requires planning paths or trajectories. A significant challenge of planning algorithms in robotic systems is real-time performance, where the output typically consists of waypoints [19]. Therefore, visual safety between waypoints must be ensured through other methods, and the integration of planning and feedback control becomes an effective approach to address this issue. The aforementioned issues resulting from differences in the operating cycles of algorithms are common across many engineering control systems. To systematically address this issue, a new research direction has emerged focusing on control architecture theory [20]. [PERSON] et al. [21] proposed a multi-layered structure for advanced robotic tasks using algorithms with different operating cycles. This structure typically includes a decision-making layer, a trajectory planning layer, and a safety layer. The decision-making layer often uses tools such as temporal logic and Markov decision processes [22; 23]. Optimal control is often adopted in the trajectory planning layer [24; 25], whereas methods involving control barrier functions and Hamilton-Jacobi reachability are gaining popularity in the safety layer [26]. Other layers, such as an action recognition layer for human interaction [27] and a learning layer for trajectory improvement [28], have also been proposed. In this paper, we propose a multi-layered control architecture consisting of a trajectory planning layer and a safety layer to achieve interactive guidance tasks in environments with obstacles.