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• Abstract

SECTION I

SECTION VII

## CONCLUSION

In this paper, we have presented algorithms and experimental validation on prototype vehicles for cooperative collision avoidance at intersections based on a formal control theoretic approach. Since the application considered is life critical, algorithms for collision avoidance should have safety certificates. The proposed approach provides these certificates, guaranteeing that the system stays collision free and that automatic control is not applied until absolutely necessary. This is achieved by keeping the system state always outside the capture set, which is the set of all states from which a collision is unavoidable given the vehicle dynamics and the limitations on the control efforts. A number of parameters can be chosen by the designer, including the maximal and minimal brake and throttle efforts for automatic control, maximal and minimal speeds, the size of the collision set (bad set), the bounds on the modeling uncertainty, the communication delay, and the bounds on the uncertainty on the driver control actions. For example, if acceleration is not considered suitable for preventing a collision, one can set the upper and lower bounds of the throttle input to zero in the calculation of the capture set and the control map, so that evasive maneuvers will only consider braking. Of course, the control action will be more conservative in this case as the capture set will be larger. Similarly, the size of the bad set is an input parameter to the algorithm, and it can be changed by the user depending on the specific intersection geometry. Experimentally, we have shown how to tune the prediction horizon and the number of prediction steps to adjust conservatism, that is, how soon the controller decides that automatic control is needed to prevent an imminent collision. The later the automatic control acts, the less conservative the algorithm is, but the closer the system trajectories come to a collision (while still averting it). This tradeoff can be decided depending on the system specifications. The experiments finally illustrate that the (linear complexity) algorithms for evaluating the capture set and control actions are fast enough for real-time implementation, which is a feature that is necessary for the practical applicability of our approach. A number of future research avenues are left to be explored. These include incorporating a warning phase that gives the opportunity to the driver to react before automatic control becomes necessary. Scalability to more than two vehicles needs to be studied, and initial results are promising [8]. Our approach can be applied where vehicles are on known crossing or merging paths, such as at intersections or when a vehicle merges onto a road from a parking lot or on the highway. Investigation should be carried out to extend the approach to road topologies other than intersections and merges and to situations where intended vehicle paths and collision zones cannot be identified a priori.

## Footnotes

The Associate Editor for this paper was F.-Y. Wang.

M. R. Hafner is with the Systems Laboratory, University of Michigan, Ann Arbor, MI 48109 USA.

D. Cunningham and L. Caminiti are with the Integrated Vehicle Systems Department, Toyota Motor Engineering and Manufacturing North America, Inc., Erlanger, KY 41018 USA (e-mail: drew.cunningham@tema.toyota.com; lorenzo.caminiti@tema.toyota.com).

D. Del Vecchio is with the Department of Mechanical Engineering and the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 USA.

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

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