Autonomous navigation and obstacle avoidance are key technologies for indoor mobile robots to complete tasks, and their importance is increasingly emphasized. However, the trajectory planning module in current navigation systems typically generates trajectories that deviate significantly from the original geometric path, resulting in severe trajectory offset. In addition, although visual sensors offer advantages such as rich perceptual information and low cost, they face challenges related to large data volumes and complex processing. This study proposes a visual-based navigation and obstacle avoidance method, utilizing a trajectory planning algorithm based on Bezier curves. Segmented trajectories are represented using Bernstein basis functions, and safety constraints as well as dynamic feasibility constraints are applied to the entire trajectory to effectively avoid collisions. The method for generating safety corridors is also improved to address the issue of severe trajectory deviation. For obstacle recognition and avoidance in indoor environments, the study introduces the “nearest depth method” and the “depth comparison method”, which eliminate interference from ground-level obstacle recognition and reduce computational resource requirements. Finally, experimental verification is conducted on an indoor mobile robot platform, relying solely on a depth camera to perceive and avoid low obstacles within the field of view, without the need for Lidar hardware, thus completing navigation tasks.