ARRT/ARRT*: A path planning variant that combines multiple techniques to achieve fast convergence to an initial solution

Abstract

The path planning problem is a fundamental problem in robotics and has been studied extensively in the literature. In this thesis, we propose a novel sampling-based algorithm called ARRT (All Rapidly-exploring Random Tree) for solving the path planning problem in complex environments. ARRT combines multiple approaches from different variants of sampling based motion planners to provide an efficient path in the smallest amount of time possible. Its novelty lies in its use of grid based techniques to provide an initial estimate of the cost to reach the goal from a given configuration, and then using informed sampling to guide the search. Our claim is that ARRT has a fast convergence to a feasible path and also provides a path that is more optimal or efficient than other state of the art algorithms in terms of number of iterations. We evaluate the performance of ARRT against several state-of-the-art algorithms, including RRT, BIT*, and ABIT*, in various environments, including cluttered environments and narrow passage problems. Our results show that ARRT outperforms these algorithms in terms of both computational time and path cost, demonstrating its effectiveness in solving the path planning problem in complex environments. We also analyze the convergence properties of ARRT and show that it can be made to be asymptotically optimal, meaning that it will converge to the optimal solution as the number of iterations increases. Finally, we discuss the implications of our findings and suggest directions for future research in the field of path planning.