Potential Functions based Sampling Heuristic For Optimal Path Planning (1704.00264v1)

Abstract: Rapidly-exploring Random Tree Star(RRT*) is a recently proposed extension of Rapidly-exploring Random Tree (RRT) algorithm that provides a collision-free, asymptotically optimal path regardless of obstacle's geometry in a given environment. However, one of the limitations in the RRT* algorithm is slow convergence to optimal path solution. As a result, it consumes high memory as well as time due to a large number of iterations utilised in achieving optimal path solution. To overcome these limitations, we propose the Potential Function Based-RRT* (P-RRT*) that incorporates the Artificial Potential Field Algorithm in RRT*. The proposed algorithm allows a considerable decrease in the number of iterations and thus leads to more efficient memory utilization and an accelerated convergence rate. In order to illustrate the usefulness of the proposed algorithm in terms of space execution and convergence rate, this paper presents rigorous simulation based comparisons between the proposed techniques and RRT* under different environmental conditions. Moreover, both algorithms are also tested and compared under non-holonomic differential constraints.

• The paper introduces the P-RRT* algorithm, which enhances RRT* by integrating artificial potential fields to accelerate convergence to optimal paths.
• It employs attractive and repulsive gradients to guide sampling away from obstacles, thereby reducing memory use and computational iterations.
• Empirical results confirm that P-RRT* maintains probabilistic completeness and asymptotic optimality while delivering faster and more efficient path planning.

Potential Functions for Sampling Heuristics in Optimal Path Planning

The research paper authored by Ahmed Hussain Qureshi and Yasar Ayaz presents an enhanced version of the Rapidly-exploring Random Tree Star algorithm (RRT*) dedicated to optimal path planning problems in robotics and similar fields. Given the critical role that motion planning plays across robotics, computer animation, and medical applications, the work tackles some significant limitations inherent to current solutions—most notably, the slow convergence to an optimal path noted in RRT*.

Key Contributions

1. P-RRT* Algorithm: The core proposition is the Potential Function Based-RRT* (P-RRT*) algorithm, which incorporates Artificial Potential Fields (APF) to guide the sampling process within RRT*. This is aimed at accelerating convergence to optimal solutions and reducing memory use by minimizing iterations required.
2. Artificial Potential Field Integration: The APF algorithm effectively combines attractive and repulsive potential gradients to navigate a robot away from obstacles and towards goals quickly. The use of these fields in P-RRT* introduces directionalized sampling, intended to reduce the dispersion of samples in the configuration space and optimize solution paths.
3. Probabilistic Completeness: The paper asserts that P-RRT* maintains the probabilistic completeness characteristic of RRT*, implying it consistently finds solutions if they exist within finite iterations, as the number of samples approaches infinity.
4. Asymptotic Optimality: The P-RRT* algorithm inherits the asymptotic optimality of RRT*. Under the assumptions of cost function additivity, continuity, and obstacle $\delta$-spacing, P-RRT* is confirmed to converge almost surely to an optimal solution as samples approach infinity.
5. Computational Complexity: The authors demonstrate that while P-RRT* improves convergence rates, it maintains a computational complexity similar to that of RRT*, suggesting that enhanced performance constrains do not translate to increased computational burdens.

Empirical Validation

Through extensive simulation across varied environments, P-RRT* exhibits significantly reduced computational time and memory requirements compared to RRT*, with fewer failures to identify optimal paths in complex environments. Key evaluations depicted how the potential-guided, goal-oriented sampling in P-RRT* aids its efficiency over environments characterized by narrow passages, multiple barriers, and maze-like configurations.

Implications and Future Research

This paper provides a compelling enhancement to the existing RRT* framework by introducing a sampling heuristic rooted in potential functions. The practical implications span real-time robotics applications where faster convergence to path solutions holds critical importance. Future research could focus on integrating this approach into dynamic or unpredictable environments, pushing towards deploying P-RRT* in live scenarios where online motion planning demands immediate responses to changing conditions.

The paper underscores an essential evolutionary step in motion planning algorithms, suggesting a trajectory for future developments that maintains efficiency while reducing computational overhead, potentially unlocking new realms in AI-driven path planning tightly coupled with dynamic heuristic adjustments. Researchers and practitioners in robotics and related fields might find the proposed algorithm attractive for applications seeking robust, optimal path solutions efficiently.