WITHDRAWN: Deep Reinforcement Learning for Target Enclosing Under Limited Sensing and Autopilot Lag

This paper proposes a deep reinforcement learning (RL) based solution for the target enclosing problem for a non-holonomic unmanned aerial vehicle (UAV) operating under limited sensing and system lag. Our approach enables an end-to-end learning-based agent to autonomously interact with the environment and develop enclosing strategies that ensure safety and containment around a stationary target. To better account for temporal dependencies arising from vehicle dynamics and autopilot lag, we propose a history-augmented policy architecture based on Proximal Policy Optimization (HA-PPO) that incorporates observation history into the policy input. A carefully designed reward function guides the learning agent by combining three reward components: a quadratic distance-based reward penalizing deviation from the desired enclosing radius, a state-dependent velocity reward that promotes stability during radial transitions, and an acceleration penalty to enforce a smooth trajectory. Thus, the agent learns to trade off between maintaining the desired enclosing geometry and mitigating aggressive control responses, especially in the presence of autopilot lag. Our results demonstrate that the learned policy, achieved through our carefully designed reward function, achieves reliable target enclosing performance. Moreover, incorporating observation history leads to improved stability and better generalization ability as compared to standard PPO.