Avoidance trajectories using reachable sets and parametric sensitivity analysis

M. Gerdts,I. Xausa: Avoidance trajectories using reachable sets and parametric sensitivity analysis
in: System modeling and optimization. 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 12–16, 2011. Revised Selected Papers, D. Hömberg, F. Tröltzsch (eds.)
IFIP Advances in Information and Communication Technology 391, 2013, 491 - 500

Smart-Link: http://link.springer.com/chapter/10.1007/978-3-642-36062-6_49
DOI: 10.1007/978-3-642-36062-6_49
Zentralblattnummer: 1266.49059
Keywords: driver assistance; collision avoidance; optimal control; reachable sets; parametric sensitivity analysis
Mathematics Subject Classification Code: 49M30 (90C31 49N90)


The article suggests a model-based simulation method that allows to detect collision of cars in all-day road traffic. The benefit of the method within a driver assistance system is twofold. Firstly, unavoidable accidents can be detected and appropriate actions like full braking maneuvers can be initiated in due course. Secondly, in case of an avoidable accident the algorithm is able to suggest an evasion trajectory that can be tracked by a future active steering driver assistance system. The algorithm exploits numerical optimal control techniques and reachable set analysis. A parametric sensitivity analysis is employed to investigate the influence of inaccurate sensor measurements.


1. Introduction
2. Model Scenarios
3. Model of the Car
4. Collision Detection and Collision Avoidance
4.1 Approach 1: Reaching a Safe Target Position for Scenario 1
4.2 Approach 2: Computing the Projected Reachable Set
4.3 Approach 3: Feasibility Problem for Scenario 2
5. Sensor Influence
6. Outlook

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