Fast End-to-End Generation of Belief Space Paths for Minimum Sensing Navigation (2409.12902v1)

Abstract: We revisit the problem of motion planning in the Gaussian belief space. Motivated by the fact that most existing sampling-based planners suffer from high computational costs due to the high-dimensional nature of the problem, we propose an approach that leverages a deep learning model to predict optimal path candidates directly from the problem description. Our proposed approach consists of three steps. First, we prepare a training dataset comprising a large number of input-output pairs: the input image encodes the problem to be solved (e.g., start states, goal states, and obstacle locations), whereas the output image encodes the solution (i.e., the ground truth of the shortest path). Any existing planner can be used to generate this training dataset. Next, we leverage the U-Net architecture to learn the dependencies between the input and output data. Finally, a trained U-Net model is applied to a new problem encoded as an input image. From the U-Net's output image, which is interpreted as a distribution of paths,an optimal path candidate is reconstructed. The proposed method significantly reduces computation time compared to the sampling-based baseline algorithm.

• The paper presents a deep learning approach using U-Net to generate optimal belief space paths, substantially reducing computational effort compared to RI-RRT*.
• The method processes environmental inputs like start/goal configurations and obstacle maps to predict collision-free paths with minimal sensing.
• Experimental results indicate a 12–15× speedup over sampling-based planners while maintaining path quality for real-time navigation.

Fast End-to-End Generation of Belief Space Paths for Minimum Sensing Navigation

The paper "Fast End-to-End Generation of Belief Space Paths for Minimum Sensing Navigation" addresses the computational challenges inherent in belief space planning, a critical aspect for the operation of robotic systems under Gaussian uncertainty. The authors propose a deep learning approach utilizing the U-Net architecture to predict optimal paths directly from environmental inputs, substantially reducing computational overhead compared to traditional sampling-based planners such as the Rationally Inattentive RRT* (RI-RRT*).

Problem Statement

The core problem explored in this paper is the computational inefficiency associated with traditional belief space planners. These planners must account for the high-dimensional nature of belief spaces—comprising both states and covariance matrices—which makes real-time implementation problematic. Given an initial belief state, a target belief region, and a set of obstacles, the task is to find a collision-free path minimizing both the physical path length and the information gain needed for the path plan.

Proposed Approach

The authors' approach encompasses three key steps:

1. Data Collection: A comprehensive dataset is compiled using RI-RRT* to solve numerous planning scenarios. Each scenario includes start and goal configurations along with obstacle locations, represented as occupancy grids.
2. Path Prediction: The U-Net model is employed to predict optimal path distributions from the input images. The input to the U-Net includes start configurations, goal configurations, and obstacle maps, while the output is interpreted as a probability distribution over possible paths.
3. Path Reconstruction: The predicted distribution is used to sample potential path points, from which an optimal path is reconstructed. This involves constructing a graph where vertices represent sampled points and edge weights reflect the cost function, which is then optimized to find the best path.

Experimental Results

The trained U-Net demonstrated strong performance in predicting feasible paths, generalizing well even to scenarios with obstacle geometries outside the training distribution. Quantitatively, the paths generated by the neural network were comparable in quality to those produced by RI-RRT*, as measured by path length.

Numerical Results: The computational time for generating paths using the U-Net approach was substantially faster, achieving approximately 12 to 15 times speedup over RI-RRT*. This efficiency suggests that further optimizations, particularly in graph construction and collision checking, could enhance this figure significantly.

Implications and Future Work

The practical implications of this research are significant. In real-time applications such as autonomous driving or aerial surveillance, where rapid decision-making under uncertainty is paramount, this approach could offer a robust solution to navigating complex environments efficiently. From a theoretical perspective, this paper bridges techniques from deep learning and belief space planning, expanding the toolkit available for solving high-dimensional planning problems.

Future developments might include extending the approach to higher-dimensional spaces and further refining the path reconstruction algorithm to ensure completeness more efficiently. There is ample scope for integrating improved sampling techniques and collision-checking methods, which could bolster both the accuracy and speed of the proposed approach.

Conclusion

This paper presents a compelling case for leveraging deep learning to address computational inefficiencies in belief space planning. The U-Net based method not only retains the quality of traditional planners but also substantially minimizes the computational burden, paving the way for real-time applications in uncertain environments. As such, it represents a noteworthy step towards practical, efficient robotic navigation under uncertainty.

The work is supported by grants from the Air Force Office of Scientific Research and the Army Research Office, demonstrating significant interest and backing from defense-related entities to solve these critical computational problems.