Uncrewed aerial vehicle (UAV)-enabled ISAC systems have received widespread attention due to the high mobility of UAVs with good line-of-sight (LoS) paths to ensure communication and sensing performance. However, the existing works on UAV-enabled ISAC mainly focus on optimizing communication performance (e.g., sum rate) and sensing performance, resulting in excessive energy consumption and reducing the flight endurance of the UAV. Motivated by this, we draw a trade-off between such performance and energy consumption to achieve robust and efficient UAV-enabled ISAC. In this work, we aim to maximize the worst-case energy efficiency in UAV-enabled ISAC by jointly designing the beamforming and the UAV trajectory, while ensuring the UAV energy constraints and the ISAC performance. Nevertheless, solving this problem is non-trivial due to its non-convex nature, and the high coupling of the transmit beamforming vectors and the UAV dynamics adds an additional layer of complexity. To effectively address this non-convex issue, we alternately optimize the transmit communication and sense beamforming, as well as the UAV dynamic variables to obtain a sub-optimal solution, and the algorithm complexity is lower than the existing algorithms. Experimental results show a trade-off between energy efficiency and average sum rate. Furthermore, they indicate the superiority of the proposed algorithm to enhance energy efficiency by significantly reducing energy consumption without causing excessive sum rate loss
