Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs (1405.5848v7)

Abstract: In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.

• The paper introduces BIT*, a unified framework that merges heuristic graph search with sampling-based planning for optimal robot motion.
• The paper details a batch processing method that intelligently balances exploration and exploitation to converge on lower-cost solutions.
• The paper demonstrates BIT*'s asymptotic optimality and improved performance in complex robotic tasks through rigorous empirical evaluations.

Overview of Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

The paper presents Batch Informed Trees (BIT*), a novel algorithm formulated to address path planning in robotics through an overview of graph-based and sampling-based techniques. Specifically, BIT* efficiently combines the heuristic search capabilities of algorithms like A* with the probabilistic completeness and anytime performance of sampling-based planners such as Rapidly-exploring Random Trees (RRT*).

Main Contributions

1. Unified Framework: BIT* leverages the concept of implicit Random Geometric Graphs (RGG), allowing for the combination of the ordered nature of graph-based search with the scalability of sampling-based methods. This framework is extendable to continuous domains, advancing techniques such as Lifelong Planning A* (LPA*).
2. Algorithm Details: BIT* constructs a tree iteratively by processing batches of samples. It intelligently balances between exploration and exploitation by focusing computational resources on promising regions of the search space. This is achieved via heuristics that estimate path cost, including cost-to-come, edge cost, and cost-to-go.
3. Asymptotic Optimality: The algorithm is demonstrated theoretically to be asymptotically optimal and probabilistically complete. It employs strategies that ensure convergence towards the optimal solution as the sample size increases indefinitely.
4. Empirical Evaluation: BIT* was tested in simulated environments and on the CMU HERB robot, navigating both configuration space obstacles (random worlds) and real-world manipulation tasks (15-DOF problems). It consistently surpassed non-optimization planners and optimal planners in terms of convergence speed and quality of solutions.

Key Numerical Results

In difficult dual-arm manipulation tasks on HERB, BIT* achieved a success rate of 68% with a median solution cost significantly lower than RRT* variants. In a separate one-arm task, BIT* outperformed both heuristic and optimal planners in solution cost, showcasing its robust application across different robotic settings.

Implications and Future Directions

BIT* exemplifies an advanced approach to motion planning that integrates known benefits of established algorithms. The potential to incrementally refine solutions while maintaining a focus on promising regions could mitigate the high-dimensional state-space challenge, a persistent issue in robotics.

Through further refinement, BIT* could be enhanced to manage dynamic environments and improve overall efficiency by exploiting failed connections intelligently. Additionally, exploring related modifications, such as extending to kinodynamic planning or integrating with local planners, could broaden its applicability in real-time robotic systems.

In conclusion, BIT* stands as a versatile and efficient planning algorithm suitable for complex robotic domains. By bridging heuristic-informed searches with sampling-based adaptability, it offers promising advancements for both theoretical research and practical applications in autonomous systems.