Real-Time Decision Making in Hybrid Systems
summary
Computes conservative safety envelopes via a backwards reachable set (HJ-Isaacs PDE) and runs real-time 3D solves on a laptop; decomposes a 10-D quadrotor model into two 3-D plus one 1-D subsystems using decoupling disturbances to get exact 10-D results. Demonstrations: four quadrotors switch to automated collision-avoidance when reachable sets touch, platooning routes form organically from reach-avoid ops, and a lab quadrotor uses Gaussian-process updates to shrink/expand a safe envelope while learning and never crashes.
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chapters (29)
- 0:00Intro
- 0:47Air traffic in Oakland Center
- 3:26Controller must keep aircraft separated
- 6:01Growing numbers of UAV applications
- 10:32Outline
- 11:17Backwards Reachable Set All states for which, for all possible control actions, there is a disturbance action which can drive the system state into a region G(0) in timet
- 14:14A discrete game
- 17:47Reachable Set Propagation
- 19:56Level set interpretation
- 21:35Partitions the state space
- 21:58Numerical computation of reachable sets
- 22:28Collision Avoidance Pilots instructed to attempt to collide vehicles
- 24:01Backwards Reachable Set: Capture Backwards Reachable Set
- 24:34Mode sequencing and reach-avoid
- 25:24Dealing with the curse of dimensionality • Impose practical constraints - Protocol, ditional problem structure
- 27:18Platooning UAVs
- 30:21Merge and join
- 32:26Intruder
- 33:15Fast Approximations using Decoupling Disturbances
- 34:34Acrobatic Quadrotor in Vertical Plane
- 34:48Near-Hover Quadrotor
- 37:04Example 3: Forced Landing System
- 38:23Data-driven
- 42:47Learn models from data...
- 43:25Safe Policy Gradient Reinforcement Learning
- 45:26Gaussian Processes (GP) (a Gaussian distribution over functions)
- 46:10Online Disturbance Model Validation
- 48:12Safe Learning
- 50:26Summary: Safety, simplicity, with data driven components Safety, from reachability analysis Simplicity, from hybrid system representation scrat. • Ability to learn from new information
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