Abstract
Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road—a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart. We leverage reachability analysis to construct a real-time (100 Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein the two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner’s expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.
M. Chen—Work performed as a postdoctoral scholar at Stanford University.
K. Leung and E. Schmerling—Contributed equally to this work. This work was supported by the Office of Naval Research (Grant N00014-17-1-2433), by Qualcomm, and by the Toyota Research Institute (“TRI”). This article solely reflects the opinions and conclusions of its authors and not ONR, Qualcomm, TRI, or any other Toyota entity. The authors would like to thank Thunderhill Raceway Park for accommodating testing.
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Notes
- 1.
The HJI PDE is solved starting from the boundary condition \(V(0, x_{_\mathscr {R}})\), the sign of which reflects set membership of \(x_{_\mathscr {R}}\) in \(\mathscr {T}\); see Sect. 5 for discussion of specific choices of \(V(0, x_{_\mathscr {R}})\).
- 2.
For ease of notation going forward we will often write \(V := V_\infty \).
- 3.
The computation becomes notoriously expensive past five or more states without compromising on grid discretization or employing some decoupling strategy. We use a grid size of \(13\times 13\times 9\times 9\times 9\times 9\times 9\) for our 7D system uniformly spaced over \((x_\mathrm {rel}, y_\mathrm {rel}, \psi _\mathrm {rel}, U_{x_\mathrm {R}}, U_{y_\mathrm {R}}, v_{_\mathrm {H}}, r_{_\mathrm {R}}) \in [-15, 15] \times [-5, 5] \times [-\pi /2, \pi /2] \times [1, 12] \times [-2, 2] \times [1, 12] \times [-1, 1]\); computing the BRS with this discretization takes approximately 16 hours on a 3.6 GHz octocore AMD Ryzen 1800X CPU.
- 4.
Only a single iteration of SQP is solved for the tracking problem at each MPC step, rather than the usual iteration until convergence. Since the tracking problems are so similar from one MPC step to the next, we find that this approach yields sufficient performance for our purposes.
- 5.
We scaled the highway traffic-weaving scenario (mean speed \(\sim \)28 m/s) in [11] down to a mean speed of \(\sim \)8 m/s by shortening the track (reducing longitudinal velocity by a constant) and scaling time by a factor of 4/3 (with the effect of scaling speeds by 3/4 and accelerations by 9/16).
- 6.
For comparative purposes, the controllers were simulated with the displayed nominal trajectory held fixed, but in reality, the nominal trajectory in these experiments was updated at \(\sim \)4 Hz.
- 7.
By literature standards we already use a relatively coarse discretization grid for solving the HJI PDE; associated numerical inaccuracies may be another source of the observed safety mismatch.
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Leung, K., Schmerling, E., Chen, M., Talbot, J., Gerdes, J.C., Pavone, M. (2020). On Infusing Reachability-Based Safety Assurance Within Probabilistic Planning Frameworks for Human-Robot Vehicle Interactions. In: Xiao, J., Kröger, T., Khatib, O. (eds) Proceedings of the 2018 International Symposium on Experimental Robotics. ISER 2018. Springer Proceedings in Advanced Robotics, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-33950-0_48
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