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This paper addresses the challenge to build an autonomous exploration system using Micro-Aerial Vehicles (MAVs). MAVs are capable of flying autonomously, generating collision-free paths to navigate in unknown areas and also reconstructing the environment at which they are deployed. One of the contributions of our system is the “3D-Sliced Planner” for exploration. The main innovation is the low computational resources needed. This is because Optimal-Frontier-Points (OFP) to explore are computed in 2D slices of the 3D environment using a global Rapidly-exploring Random Tree (RRT) frontier detector. Then, the MAV can plan path routes to these points to explore the surroundings with our new proposed local “FAST RRT* Planner” that uses a tree reconnection algorithm based on cost, and a collision checking algorithm based on Signed Distance Field (SDF). The results show the proposed explorer takes 43.95% less time to compute exploration points and paths when compared with the State-of-the-Art represented by the Receding Horizon Next Best View Planner (RH-NBVP) in Gazebo simulations.