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

Felix Herrmann, Sebastian Zach, Jacopo Banfi,

Jan Peters, Georgia Chalvatzaki and Davide Tateo

Paper

Code

Appendix

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 to the training step, allowing for fast neural network evaluation of the constraints during planning. In extensive experiments, we show that Deep Collision Probability Fields can produce reasonably accurate collision probabilities (up to 1e-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.

Network Structure

Input data is processed using Fourier features. The processed features are given in input to a deep neural network with 5 fully connected 1024-dimensional hidden layers. An additional set of 3 fully connected 512-dimensional hidden layers computes the input for the shaping functions α and ρ, which influence the mode switching of the two regularizers σ1 and σ2.

Planning with DCPF

random_obstacle.mp4

Random obstacles

In this experiment, we generate random obstacles and we plan trajectories using Hybrid A*

tight_junction.mp4

Narrow Passage

In this experiment, we consider a hard planning problem where the robot must pass between a narrow passage. We show that the homotopy class of the trajectory changes by reducing the maximum collision probability allowed.

overtake.mp4

Dynamic obstacles

In this experiment we assume to plan in the setting where the obstacles are dynamic, using Hybrid A*. Here we consider an overtake scenario, where we control a car and try to perform an overtake. Reducing the allowed collision probability makes the car more cautious, waiting for the car coming from the opposite lane before committing to the overtake.

dcpf_static_map.mov

Real-world Maps - static obstacles

In this experiment, we generate random obstacles in 10 different real-world maps and we plan trajectories using Hybrid A*

dcpf_dynamic_map_2.mov

Real-world Maps - dynamic obstacles

In this experiment, we perform planning using Hybrid A* on 10 different real-world maps with dynamic obstacles populating the environment with position uncertainty growing over time.

tiago_planner.mp4

Overtake planner

In video, we show our proposed overtake planner to be used in the real-world setting, to exploit the parallelization capabilities of our approach and be able to plan real-time on the real system

tiago_experiment.mp4

Real-world Experiments

Overtaking results on the Tiago robot in the real world. Here the controlled robot recieves an estimate of the position and velocity of the other robot and plans an overtake wich considers also robot bounding box variability (caused by the moving arm) to plan safely.

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