Greedy Heuristics for Rapidly Exploring Random Trees in High-Dimensional State Spaces

Core Concepts

This article presents Greedy RRT* (G-RRT*), an asymptotically optimal sampling-based planning algorithm that leverages greedy heuristics and bidirectional search to quickly find high-quality solutions in complex high-dimensional state spaces.

Abstract

The article addresses the computational burden associated with the informed hyperellipsoid proposed in Informed RRT* by introducing a new direct informed sampling procedure. The proposed approach, Greedy RRT* (G-RRT*), biases the sampling based on the heuristic information of the states in the current solution path, regardless of the cost, to mitigate the impact of tortuous initial solution paths.
Key highlights:

G-RRT* maintains two rapidly growing trees, one rooted in the start and one in the goal, and uses a greedy connection heuristic to guide the trees towards each other to find initial solutions quickly.
It introduces a greedy informed set, a subset of the informed set, which greedily exploits the information from the current solution path to rapidly reduce the size of the informed exploration hyperellipsoid, enhancing sampling efficiency.
G-RRT* applies the direct informed sampling technique to the greedy informed set to focus the search on the promising regions of the problem domain based on heuristics, accelerating the convergence rate.
The article proves the completeness and asymptotic optimality of G-RRT* and demonstrates its benefits through simulations and experiments on a self-reconfigurable robot, Panthera, showing improved success and convergence rates compared to state-of-the-art algorithms.

Stats

The planning problems are tested with the objective of minimizing path length.

Quotes

None

Key Insights Distilled From

Greedy Heuristics for Sampling-based Motion Planning in High-Dimensional State Spaces

by Phone Thiha ... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.03411.pdf

Deeper Inquiries

How can the greedy informed set be further improved to maintain global optimality guarantees while enhancing the exploitation of the current solution path

To further improve the greedy informed set in maintaining global optimality guarantees while enhancing the exploitation of the current solution path, several strategies can be implemented. One approach is to incorporate a dynamic adjustment mechanism for the greedy biasing ratio, ϵ, based on the progress of the algorithm. By dynamically adapting ϵ during the planning process, the algorithm can balance between exploration and exploitation more effectively. Additionally, introducing a mechanism to periodically reassess the informed set based on the current solution path's progress can help in refining the subset to focus on states that are more likely to lead to improved solutions. This adaptive approach can enhance the exploitation of the current solution path while ensuring that the algorithm maintains global optimality guarantees.

What are the potential drawbacks of the greedy heuristics in G-RRT* and how can they be addressed to ensure robust performance across diverse planning scenarios

One potential drawback of the greedy heuristics in G-RRT* is the risk of getting trapped in local minima due to the algorithm's focus on exploiting the current solution path. To address this, a mechanism for periodically introducing randomness in the sampling process can be implemented to encourage exploration and prevent the algorithm from converging prematurely. Additionally, incorporating a mechanism to diversify the search space by occasionally expanding the search beyond the greedy informed set can help in discovering alternative paths that may lead to better solutions. By balancing the exploitation of the current solution path with periodic exploration, the algorithm can mitigate the risk of local minima and ensure robust performance across diverse planning scenarios.

Can the concepts of G-RRT* be extended to other sampling-based planning algorithms beyond RRT* to achieve faster convergence in high-dimensional problems

The concepts of G-RRT* can be extended to other sampling-based planning algorithms beyond RRT* to achieve faster convergence in high-dimensional problems. For instance, variants of PRM (Probabilistic Roadmaps) and other sampling-based planners can benefit from incorporating greedy heuristics and bidirectional search strategies similar to G-RRT*. By leveraging the principles of exploiting the current solution path information and focusing the sampling on promising regions of the state space, these algorithms can improve their convergence rates and solution quality. Additionally, integrating the adaptive greedy biasing ratio and dynamic informed set adjustments can further enhance the performance of these algorithms in high-dimensional planning scenarios. By extending the concepts of G-RRT* to other sampling-based planners, a broader range of algorithms can achieve faster convergence and improved solution paths in complex state spaces.