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Probabilistic Safety Analysis of Sensor-Driven



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Submitted 2009 Hybrid Systems Computation and Control HSCC http www cds caltech edu murray papers 2008s hm09 hscc html Probabilistic Safety Analysis of Sensor Driven Hybrid Automata Julia M B Braman and Richard M Murray Dept of Mechanical Engineering California Institute of Technology braman caltech edu Abstract The control programs of complex autonomous systems that have conditional branching can be modeled as linear hybrid systems When the state knowledge is perfect linear hybrid systems with statebased transition conditions can be verified against a specified unsafe set using existing model checking software This paper introduces a formal method for calculating the failure probability due to state estimation uncertainty of these sensor driven hybrid systems Problem complexity is described and some reduction techniques for the failure probability calculation are given An example goal based control program is given and the failure probability for that system is calculated 1 Introduction Autonomous robotic missions generally have complex fault tolerant control systems There are several ways to incorporate the necessary fault tolerance in a control architecture One way is to create a flexible control system that can reconfigure itself based on the state of the system and environment in the presence of faults However if the control system cannot be analyzed for safety in the presence of estimator error the added complexity of the system s reconfigurability could reduce the system s effective fault tolerance One particularly useful way to model a fault tolerant control system is as a hybrid system When the continuous dynamics of these systems are sufficiently simple it is possible to verify that the execution of the hybrid control system will not fall into an unsafe regime 1 There are several software packages that can be used for this analysis including HyTech 2 UPPAAL 3 and PHAVer 4 all of which are symbolic model checkers PHAVer in particular is able to exactly



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