Learning Barrier Certificates for Neural Path Tracking Control of Self Driving Vehicles - Extension

An extension of paper Learning Barrier Certificates for Neural Path Tracking Control of Self Driving Vehicles is contained in the PDF file, with the following sections

1. Pseudocodes
2. Policy Learning
3. Learning Low-Dimensional Barriers under Partial Observability
4. Estimating Range of Dynamics near Samples
5. Finding Boundary Counterexamples for Retraining
6. Using the Learned Barrier Function for Safety Monitor
7. Hyper-parameters and Details of Experiments

Below we present figures contained in the original and extended paper.

Pseudocodes

Training the Barrier Function

Cerifying the Barrier Function

Dynamic Model Trajectories Illustration

Plotting of trajectories of the dynamic model, with x, y axes as angle and distance errors, and z axis as:

Longitudinal Speed | Lateral Speed | Yaw Rate :-------------------------:|:------------------------:|:-------------------------: | |

Flow Chart of Overall Pipeline

Vehicle Dynamics Models

Kinematic Model | Dynamic Model
:-------------------------:|:------------------------: |

Barrier Functions

The barrier functions on kinematic model, dynamic model and TORCS environment

Kinematic Model (3D) | Dynamic Model (2D) | TORCS (2D) :-------------------------:|:------------------------:|:-------------------------: | |

Safety Monitor

Backward reachable states for dynamic model, evaluated on a maximum curvature of 0.15, for 50 time steps

Path with Curvature 0.15 (Curve to Left) | Path with Curvature 0.15 (Curve to Right) | Safety Monitor :-------------------------:|:------------------------:|:-------------------------: | |

Importance of Retraining

The barrier function for dynamic model obtained after the initial training and after the final retraining, projected in the dimensions of angle and distance error

Initial Barrier | Final Barrier
:-------------------------:|:------------------------: |

Vector Fields of Dynamic Model

Close to Collected Trajectories | Whole Certification Grid
:-------------------------:|:------------------------: |

Barrier Behavior of TORCS Environment