This paper describes and analyzes a reactive navigation framework for mobile robots in unknown environments. The approach does not rely on a global map and only considers the local occupancy in its robot-centered 3D grid structure. The proposed algorithm enables fast navigation by heuristic evaluations of pre-sampled trajectories on-the-fly. At each cycle, these paths are evaluated by a weighted cost function, based on heuristic features such as closeness to the goal, previously selected trajectories, and nearby obstacles. This paper introduces a systematic method to calculate a feasible pose on the selected trajectory, before sending it to the controller for the motion execution. Defining the structures in the framework and providing the implementation details, the paper also explains how to adjust its offline and online parameters. To demonstrate the versatility and adaptability of the algorithm in unknown environments, physics-based simulations on various maps are presented. Benchmark tests show the superior performance of the proposed algorithm over its previous iteration and another state-of-art method. The open-source implementation of the algorithm and the benchmark data can be found at \url{https://github.com/RIVeR-Lab/tentabot}.