Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields (2409.04306v1)

Abstract: Estimating collision probabilities between robots and environmental obstacles or other moving agents is crucial to ensure safety during path planning. This is an important building block of modern planning algorithms in many application scenarios such as autonomous driving, where noisy sensors perceive obstacles. While many approaches exist, they either provide too conservative estimates of the collision probabilities or are computationally intensive due to their sampling-based nature. To deal with these issues, we introduce Deep Collision Probability Fields, a neural-based approach for computing collision probabilities of arbitrary objects with arbitrary unimodal uncertainty distributions. Our approach relegates the computationally intensive estimation of collision probabilities via sampling at the training step, allowing for fast neural network inference of the constraints during planning. In extensive experiments, we show that Deep Collision Probability Fields can produce reasonably accurate collision probabilities (up to 10^{-3}) for planning and that our approach can be easily plugged into standard path planning approaches to plan safe paths on 2-D maps containing uncertain static and dynamic obstacles. Additional material, code, and videos are available at https://sites.google.com/view/ral-dcpf.

• The paper introduces DCPF, a deep learning framework that shifts heavy collision probability computation to an offline training phase for efficient real-time planning.
• It leverages a signed distance-inspired neural architecture to provide smooth and accurate collision probability estimates with a MAE on the order of 10⁻³.
• Experimental results demonstrate robust integration with Hybrid-A* and effective performance in complex, uncertain environments for safe trajectory planning.

Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields

The paper "Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields" presents a neural network-based approach called Deep Collision Probability Fields (DCPF). The primary challenge addressed is the accurate estimation of collision probabilities (CPs) between a robot and various obstacles in an uncertain environment, which is a critical requirement for the safe deployment of autonomous agents.

Summary and Key Contributions

DCPF is designed to estimate CPs efficiently, circumventing the conservativeness of traditional approximate methods and the computational intensity of sampling-based methods. The fundamental innovation of DCPF is to offload the computationally heavy task of CP estimation to a training phase using a neural network, thereby enabling swift neural inference during path planning.

Core Contributions:

1. Efficient Learning Framework: The paper introduces a method to train a neural network off-line to learn collision probabilities effectively. This framework relies on a Monte Carlo (MC) sampling approach during the data generation phase, therefore allowing the heavy computational work to be completed before deployment.
2. Deep Learning Architecture: The DCPF model utilizes a specially designed neural network architecture inspired by Signed Distance Functions (SDFs). This architecture guarantees a collision probability estimation that smoothly transitions to zero as the distance between objects increases, and approaches one when objects overlap.
3. Practical Implementation: The trained DCPF can be integrated into existing path planners to offer quick and accurate CP assessments in real-time. The authors showcase integration with Hybrid-A*, a well-known path planning algorithm.

Experimental Validation

The authors executed extensive experiments covering various scenarios to validate the accuracy and efficiency of DCPF.

Key Results:

1. Accuracy: The trained DCPF models provide CP estimates with a Mean Absolute Error (MAE) up to the order of $10^{-3}$. This level of accuracy is suitable for practical deployment in settings where high precision in collision avoidance is essential.
2. Efficiency: Benchmarking against traditional methods such as z-test and Sequential Probability Ratio Test (SPRT) demonstrates that DCPF significantly reduces computation time, especially when assessing low-probability events. Inferred times on GPU for small batches (e.g., batch size 16) reach the order of milliseconds per sample, highlighting potential for real-time applications.
3. Robustness: The DCPF's robustness is evident from its performance across different configurations, including narrow passage and dynamic overtake scenarios. The planner, incorporating DCPF, consistently produced safe trajectories even under stringent CP constraints (as low as $10^{-3}$).

Practical and Theoretical Implications

Practical Implications:

• Scalability: By offloading computation to a training phase and leveraging GPUs during inference, DCPF offers scalability for solving large-scale path planning problems.
• Integration: The approach can be seamlessly integrated with existing planners, enhancing the safety and efficiency of autonomous systems in dynamic and uncertain environments.
• Deployment: Successful real-world deployment, demonstrated with the TIAGo robots, underscores the readiness level of DCPF for practical applications.

Theoretical Implications:

• CP Generalization: The DCPF model extends CP estimation capabilities by supporting arbitrary obstacle shapes and distributions, potentially generalizable to more complex autonomous systems.
• Future Research: This work opens avenues for investigating more sophisticated network architectures and data generation techniques to further refine CP estimates.

Future Directions

Further research could extend DCPF by:

• Exploring broader classes of obstacle shapes and higher-dimensional spaces.
• Improving the robustness of DCPF in unknown environments where real-time sensor data dynamically alters the occupancy grid.
• Combining with advanced planning algorithms to exploit the parallelization potential inherent in neural network inference.

Conclusion

The DCPF model represents a significant step towards safer and more efficient path planning under uncertainty. The shift from real-time sampling to offline computation, paired with fast neural inference, positions DCPF as a promising solution in the trajectory optimization landscape. Future enhancements will likely solidify its role in advanced autonomous navigation systems, bridging the gap between theoretical safety guarantees and practical real-world deployment.