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Autonomous mobile robots are usually faced with challenging situations when driving in complex environments. Namely, they have to recognize the static and dynamic obstacles, plan the driving path and execute their motion. For addressing the issue of perception and path planning, in this paper, we introduce OctoPath, which is an encoder-decoder deep neural network, trained in a self-supervised manner to predict the local optimal trajectory for the ego-vehicle. Using the discretization provided by a 3D octree environment model, our approach reformulates trajectory prediction as a classification problem with a configurable resolution. During training, OctoPath minimizes the error between the predicted and the manually driven trajectories in a given training dataset. This allows us to avoid the pitfall of regression-based trajectory estimation, in which there is an infinite state space for the output trajectory points. Environment sensing is performed using a 40-channel mechanical LiDAR sensor, fused with an inertial measurement unit and wheels odometry for state estimation. The experiments are performed both in simulation and real-life, using our own developed GridSim simulator and RovisLab's Autonomous Mobile Test Unit platform. We evaluate the predictions of OctoPath in different driving scenarios, both indoor and outdoor, while benchmarking our system against a baseline hybrid A-Star algorithm and a regression-based supervised learning method, as well as against a CNN learning-based optimal path planning method. [ABSTRACT FROM AUTHOR]