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

TL;DR

Deep Collision Probability Fields is introduced, a neural-based approach for computing collision probabilities of arbitrary objects with arbitrary unimodal uncertainty distributions that 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.

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.

Figures (13)

• Figure 1: The network structure of : input data is processed using Fourier features. The processed features are fed to a deep neural network with 5 fully connected 1024-dimensional hidden layers. An additional set of 3 fully connected 512-dimensional hidden layers compute the input for the shaping functions $\alpha$ and $\rho$, which influence the mode switching of the two regularizers $\sigma_{\bm{\theta}}^1$ and $\sigma_{\bm{\theta}}^2$, that implement the euclidean distance bias.
• Figure 2: Box plot of absolute error evaluated on test dataset
• Figure 3: Comparison of paths generated using A* using different sampling algorithms. Blue rectangles represent obstacles sampled from the obstacle distribution, while the other rectangles represent a configuration of the robot checked by the planner. The configurations chosen as part of the solution are marked in dark green. samples a maximum of $4\times10^6$ and the Z-Test uses $10^5$ samples at most.
• Figure 4: The distance of the constraint $p_{\max}$ to the $p_{gt}$, computed with the -based method outlined in \ref{['sec:data-gen']}, during the planned trajectories seen in figure \ref{['fig:a_star_paths']}. More conservative methods will have a higher minimal distance. For values below the precision threshold it cannot be verified whether the constraint is respected, due to the uncertainty of $p_{gt}$
• Figure 5: Error of estimate during the planned trajectory for in figure \ref{['fig:a_star_paths']} The green bar represents an estimation error inside the confidence interval of the ground truth calculation, while the red bar represents an error outside the confidence interval.