FAST RRT* 3D-Sliced Planner for Autonomous Exploration Using MAVs

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.

Effective Geometric Algorithms for Immersed Boundary Method Using Signed Distance Field

We present three algorithms for robust and efficient geometric calculations in the context of immersed boundary method (IBM), including classification of mesh cells as inside/outside of a closed surface, projection of points onto a surface, and accurate calculation of the solid volume fraction field created by a closed surface overlapping with a background Cartesian mesh. The algorithms use the signed distance field (SDF) to represent the surface and remove the intersection tests, which are usually required by other algorithms developed before, no matter the surface is described in analytic or discrete form. The errors of the algorithms are analyzed. We also develop an approximate method on efficient SDF field calculation for complex geometries. We demonstrate how the algorithms can be implemented within the framework of IBM with a volume-average discrete-forcing scheme and applied to simulate fluid–structure interaction problems.