Ultimately 1/12 Simplifying Assumptions Vehicles have positive - PowerPoint PPT Presentation

Safe Intersections: At the Crossing of Hybrid Systems and Verification Sarah M. Loos and André Platzer Computer Science Department Carnegie Mellon University October, 2011

Ultimately… 1/12

Simplifying Assumptions • Vehicles have positive velocity • Accurate sensing • Instantaneous braking and acceleration • Time synchronization • Delay for sensor updates is bounded • Straight lane dynamics • Cars represented as points, lanes as lines 2/12

Previous Work: Highway Control • Verified multilane highway system • Arbitrary number of cars • Arbitrary number of lanes • Proof of safety for distributed control built from two-car “building blocks.” 3/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks 4/12

Intersection Building Blocks This is similar to a merge on the highway. 4/12

T-Intersection Building Block 5/12

Intersection Building Blocks 6/12

Intersection Building Blocks 6/12

Intersection Building Blocks 6/12

Intersection Building Blocks 6/12

Straight Lane Building Block 7/12

Di Different ntial Dyna l Dynami mic L Logic * * * The he s sho hort v version. n. Initial Conditions → [Model] Requirements 8/12

Di Different ntial Dyna l Dynami mic L Logic Initial Conditions → [Model] Requirements 8/12

Di Different ntial Dyna l Dynami mic L Logic Initial Conditions → [Model] Requirements logical formula logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic Initial Conditions → [Model] Requirements logical formula logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic Initial Conditions → [Model] Requirements logical formula logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic Initial Conditions → [Model] Requirements logical formula hybrid program logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic discrete control continuous dynamics Initial Conditions → [Model] Requirements logical formula hybrid program logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic discrete control continuous dynamics → [(ctrl;dyn) * ] logical formula hybrid program logical formula 8/12

Di Different ntial Dyna l Dynami mic L Logic continuous dynamics discrete control → [(ctrl; x’= v; v’= a ) * ] logical formula hybrid program logical formula 8/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: Initial Conditions → [Model] Requirements 9/12

Single Lane Stoplight To Prove: ✔ h Initial Conditions → [Model] Requirements 9/12

Intersection To Prove: Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: No collision Cars can stop initially Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision Initial Conditions → [Model] Requirements 10/12

Intersection To Prove: Cars can stop initially No collision ✔ h Initial Conditions → [Model] Requirements 10/12

Conclusions Future Work  Curved road dynamics  Distributed car dynamics  Combinations of merge and cross protocols  Noisy and delayed sensor data  Delayed braking and acceleration reaction  Non-synchronized time  Non-zero car lengths and lane widths 11/12

Conclusions Cha halle lleng nges Solu lutions ns  Infinite, continuous, and evolving  We give a formal proof for a two-lane state space, R ∞ intersection with one car on each lane  Simulation and testing only  Semi-automated proof generation partially prove safety  Variations in system design  Continuous dynamics  Demonstrated potential for formal  Discrete control decisions safety verification in car control, even when models have high branching  Large branching factor factor 12/12

Conclusions Thank You! 12/12

Conclusions Reference The full length paper for this research can be found here: Sarah M. Loos and André Platzer. Safe Intersections: At the Crossing of Hybrid Systems and Verification. In the 14th International IEEE Conference on Intelligent Transportation Systems, ITSC 2011, Washington, D.C., USA, Proceedings, 2011. 12/12