In this paper, the investigation aims to experimentally simulate the navigation of line-following robots in different environmental conditions using a fuzzy inf In this paper, the investigation aims to experimentally simulate the navigation of line-following robots in different environmental conditions using a fuzzy inf

Unmanned Aerial Vehicles (UAVs) have become indispensable in fields such as disaster response, precision agriculture, environmental monitoring, and surveillance. Their ability to navigate complex and dynamic environments makes them essential for autonomous operations. However, ensuring accurate and reliable state estimation remains a significant challenge, particularly in GPS-denied environments, where traditional navigation systems suffer from drift, localization errors, and trajectory inconsistencies. Addressing these limitations is crucial for improving UAV autonomy and operational efficiency. This study aims to enhance UAV autonomy and trajectory optimization by integrating a Satellite-Based Augmentation System (SBAS) with monocular visual-inertial odometry (VIO) within a factor graph optimization framework. The proposed methodology fuses visual and inertial sensor data, incorporating state constraints and prior knowledge to improve localization accuracy, reduce drift, and manage uncertainty. Experimental evaluations were conducted under different path optimization conditions to assess system performance. Results show that Path 1 achieved the highest optimization score of 0.481, Path 2 showed moderate optimization at 0.130, while Paths 3, 4, and 5 exhibited minimal improvements, with scores of −6.176, −0.041, and −0.113, respectively. These findings confirm the effectiveness of the proposed approach in optimizing UAV trajectories and enhancing real-time navigation accuracy. The study concludes that integrating SBAS with VIO significantly enhances UAV state estimation, offering a promising solution for autonomous aerial operations in both indoor and outdoor environments. This approach provides a robust and scalable framework for improving UAV navigation in critical applications, ensuring greater reliability under GPS-denied conditions.

Graphical abstract Abstract Multi-robot path planning must adapt to difficult situations, allowing autonomous navigation in both static and dynamic barriers in complicated environments. However, defining the best planning strategies for certain applications remains unsolved. This study focused at three methods for learning complex robotic decision-making principles such as Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), and Deep Reinforcement Learning (DRL). Furthermore, proposed a novel technique for obstacle avoidance and autonomous navigation called Dynamic Improvement Trust Region Policy Optimization with Covariance Grid Adaptation (DITRPO-CGA). Initially, created the Dynamic Improvement Proximal Policy Optimization with Covariance Grid Adaptation (DIPPO-CGA) based on PPO to assure collision-free policies. Next, developed a DRL technique that integrates DIPPO-CGA, resulting in the DITRPO-CGA algorithm, which improved the flexibility of multi-robot systems in different situations. During training process, DIPPO-CGA is utilized to optimize the multi-robot multi-task policies, ensuring least distance obstacle avoidance and target completion. The proposed DIPPO-CGA algorithm reaches the target within minimum distance. The findings showed that when compared to PPO, TRPO, and DIPPO-CGA, the proposed DITRPO-CGA algorithm achieves a higher convergence rate, faster target achievement and reaches the positions more quickly.