Implementation of the Rapidly-exploring Random Belief Tree and Statistical Analysis of Functionality

In this paper, we implement the Rapidly-exploring Random Belief Tree (RRBT) in a test environment from the original work. The algorithm is modified to utilize a more formal definition of domination when performing partial ordering of beliefs, improving the method for appending and rewiring the tree. We also consider the probabilistic guarantees of the Rapidly-exploring Random Tree (RRT) algorithm compared to those clearly stated in the RRBT development, and more importantly, which are not included. Monte Carlo simulation of the RRBT algorithm in the test environment provides evidence for the exponential decay in the probability of failure as the number of planning iterations increases. If this assertion would prove true universally, future work can focus on computing minimum number of iterations necessary for a valid solution, and thus a minimum time to compute for safe paths through complex environments while accounting for agent, measurement, and environment uncertainties.