Quantifying Risk
Calculating Reach Tube
This is a bird-eye-view of the traffic where four cars are present. The bottom car is grayed out to signify that it is removed due to counterfactual reasoning. The initial state of the ego vehicle starting with 0 velocity is represented by a dashed circle at the original position. As time advances, possible potential states of the ego vehicle is calculated iteratively following the bicycle model using sampled controls (accleration and steering), which are represented using blue dots.
After aggregating all possible states throughout time steps (color-coded for different steps), the reach tube is the bounding polygon of all the possible states, presented in light gray.
Calculating Risks
To calculate the risk of each actor, we first calculate the reach tube of the ego actor removing other actor one at a time, and finally removing all the other actors.
The risk of an actor posed on the ego actor is calculated counterfactually by the increase in reach tube when removing that actor. The scene risk is calculated by finding the increase in reach tube when removing all other vehicles. Risks are always normalized. This example can be found in the GitHub repo as well.
STI in Action
The above animation demonstrates that as a metric, STI also works in Argoverse, a real-world dataset. It shows the risk of other actors are inherently low.
Results
| Metric | Ghost Cut-In | Lead Cut-In | Lead Slowdown | Rear-End | All Scenarios |
|---|---|---|---|---|---|
| TTC | 0.00 (0.00) | 0.00 (0.00) | 3.30 (0.89) | 0.02 (0.17) | 0.83 |
| Dist. CIPA | 0.00 (0.00) | 0.00 (0.00) | 5.50 (0.89) | 0.02 (0.17) | 1.38 |
| PKL-All | 0.75 (0.30) | 1.01 (0.76) | 1.22 (0.62) | 0.01 (0.12) | 0.75 |
| PKL-Holdout | 0.14 (0.21) | 3.36 (4.18) | 1.23 (0.69) | 0.01 (0.12) | 1.19 |
| STI (ours) | 2.94 (0.33) | 8.37 (0.70) | 2.22 (0.23) | 1.23 (0.11) | 3.69 |
- PKL-Holdout: trained on all scenarios except the ghost cut-in and the lead cut-in scenarios.
- In the front accident scenario, the ego actor’s ADS (LBC agent) avoided the accident, resulting in no LTFMA metric to report.
- SD stands for standard deviation.
The above table demonstrates the comparative analysis of Lead-Time-for-Mitigating-Accident (LTFMA) in seconds across various risk metrics. The average time in seconds and the standard deviation are provided. PKL-All: trained on all scenarios. We used LBC agent as the ADS to control the ego actor to obtain these results.