Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Platzer, André; Clarke, Edmund M.

doi:10.1007/978-3-642-05089-3_35

Cited by 88 publications

(83 citation statements)

References 22 publications

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“…This analysis yields new results for the analysis of collision avoidance protocols and generalizes previous related work [18].…”

Section: B the Keymaera Theorem Prover For Hybrid Systemssupporting

confidence: 77%

“…KeYmaera has been used successfully for verifying properties of systems involving cars, trains, aircraft, and robots: local lane controllers for highway car traffic [14], left-turn assist controllers for cars at intersections [15], intelligent speed adaptation for variable speed limit control and incident management by traffic centers on highways [16], cooperation protocols of the European Train Control System [17], airplane collision avoidance [18,19], obstacle avoidance for ground robots [20], and force feedback to the surgeon from a surgical robot [21].…”

Section: B the Keymaera Theorem Prover For Hybrid Systemsmentioning

confidence: 99%

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Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

Ghorbal

Jeannin

Zawadzki

et al. 2014

Journal of Aerospace Information Systems

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Complex software systems are becoming increasingly prevalent in aerospace applications, in particular to accomplish critical tasks. Ensuring the safety of these systems is crucial, while they can have subtly different behavior under slight variations in operating conditions. In this paper we advocate the use of formal verification techniques and in particular theorem proving for hybrid software-intensive systems as a wellfounded complementary approach to the classical aerospace verification and validation techniques such as testing or simulation. As an illustration of these techniques, we study a novel lateral mid-air collision avoidance maneuver in an ideal setting, without accounting for the uncertainties of the physical reality. We then detail the challenges that naturally arise when applying such technology to industrial-scale applications and our proposals on how to address these issues.

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“…This analysis yields new results for the analysis of collision avoidance protocols and generalizes previous related work [18].…”

Section: B the Keymaera Theorem Prover For Hybrid Systemssupporting

confidence: 77%

Section: B the Keymaera Theorem Prover For Hybrid Systemsmentioning

confidence: 99%

Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

Ghorbal

Jeannin

Zawadzki

et al. 2014

Journal of Aerospace Information Systems

Self Cite

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“…Differential invariant proofs of more involved properties of rotational and curved flight dynamics can be found in previous work [Pla10a,PC09b,Pla10b].…”

Section: F Fmentioning

confidence: 99%

The Structure of Differential Invariants and Differential Cut Elimination

Platzer¹

2012

Logical Methods in Computer Science

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Abstract. The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable verification. Search procedures for these proof certificates are still rather ad-hoc, though, because the problem structure is only understood poorly. We investigate differential invariants, which define an induction principle for differential equations and which can be checked for invariance along a differential equation just by using their differential structure, without having to solve them. We study the structural properties of differential invariants. To analyze trade-offs for proof search complexity, we identify more than a dozen relations between several classes of differential invariants and compare their deductive power. As our main results, we analyze the deductive power of differential cuts and the deductive power of differential invariants with auxiliary differential variables. We refute the differential cut elimination hypothesis and show that, unlike standard cuts, differential cuts are fundamental proof principles that strictly increase the deductive power. We also prove that the deductive power increases further when adding auxiliary differential variables to the dynamics.

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“…Since those robots are designed for environments that occupy stationary as well as moving obstacles, motion safety and obstacle avoidance are vital safety features for such robots [3,22,25,27].…”

Section: Introductionmentioning

confidence: 99%

On Provably Safe Obstacle Avoidance for Autonomous Robotic Ground Vehicles

Mitsch

Ghorbal

Platzer

2013

Robotics: Science and Systems IX

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Abstract-Nowadays, robots interact more frequently with a dynamic environment outside limited manufacturing sites and in close proximity with humans. Thus, safety of motion and obstacle avoidance are vital safety features of such robots. We formally study two safety properties of avoiding both stationary and moving obstacles: (i) passive safety, which ensures that no collisions can happen while the robot moves, and (ii) the stronger passive friendly safety in which the robot further maintains sufficient maneuvering distance for obstacles to avoid collision as well. We use hybrid system models and theorem proving techniques that describe and formally verify the robot's discrete control decisions along with its continuous, physical motion. Moreover, we formally prove that safety can still be guaranteed despite location and actuator uncertainty.

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Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study

Cited by 88 publications

References 22 publications

Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

Hybrid Theorem Proving of Aerospace Systems: Applications and Challenges

The Structure of Differential Invariants and Differential Cut Elimination

On Provably Safe Obstacle Avoidance for Autonomous Robotic Ground Vehicles

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