Hybrid Systems Controller Synthesis Examples EE291E Tomlin/Sastry

Example 1: Aircraft Collision Avoidance Two identical aircraft at fixed altitude & speed: ‘evader’ (control) ‘pursuer’ (disturbance) x y u v  d v

Continuous Reachable Set  x y

Collision Avoidance Filter Simple demonstration –Pursuer: turn to head toward evader –Evader: turn to head right pursuer safety filter’s input modification pursuer’s inputevader’s desired input evader evader’s actual input unsafe set collision set Movies…

Collision Avoidance Control

Overapproximating Reachable Sets [Khrustalev, Varaiya, Kurzhanski] Overapproximative reachable set: Exact: Approximate: ~1 sec on 700MHz Pentium III (vs 4 minutes for exact) Polytopic overapproximations for nonlinear games Subsystem level set functions “Norm-like” functions with identical strategies to exact [Hwang, Stipanović, Tomlin]

Can separation assurance be automated? Requires provably safe protocols for aircraft interaction Must take into account: Uncertainties in sensed information, in actions of the other vehicle Potential loss of communication Intent, or non-intent

unsafe set with choice to maneuver or not? Example 2: Protocol design unsafe set with maneuver unsafe set without maneuver ? unsafe safe

Protocol Safety Analysis Ability to choose maneuver start time further reduces unsafe set safe without switch unsafe to switch safe with switch unsafe with or without switch

Implementation: a finite automaton It can be easier to analyze discrete systems than continuous: use reachable set information to abstract away continuous details q1q1 safe at present will become unsafe unsafe to  1 q5q5 safe at present always safe safe to  1 q3q3 safe at present will become unsafe safe to  1 q4q4 safe at present always safe unsafe to  1 q2q2 unsafe at present will become unsafe unsafe to  1 qsqs SAFE ququ UNSAFE forced transition controlled transition (  1 ) q1q1 q5q5 q3q3 ququ q4q4 q2q2

Example 3: Closely Spaced Approaches Photo courtesy of Sharon Houck

Example 3: Closely Spaced Approaches evader EEM Maneuver 1: accelerate EEM Maneuver 2: turn 45 deg, accelerate EEM Maneuver 3: turn 60 deg [Rodney Teo]

Sample Trajectories Segment 1 Segment 2 Segment 3

Dragonfly 3Dragonfly 2 Ground Station Tested on the Stanford DragonFly UAVs

EEM alert Separation distance (m) North (m) East (m) time (s) Above threshold Accelerate and turn EEM Put video here Tested at Moffett Federal Airfield

EEM alert Separation distance (m) North (m) East (m) time (s) Above threshold Put video here Coast and turn EEM Tested at Moffett Federal Airfield

Tested at Edwards Air Force Base T-33 Cockpit [DARPA/Boeing SEC Final Demonstration: F-15 (blunderer), T-33 (evader)]

Photo courtesy of Sharon Houck; Tests conducted with Chad Jennings

Implementation: Display design courtesy of Chad Jennings, Andy Barrows, David Powell R. Teo’s Blunder Zone is shown by the yellow contour Red Zone in the green tunnel is the intersection of the BZ with approach path. The Red Zone corresponds to an assumed 2 second pilot delay. The Yellow Zone corresponds to an 8 second pilot delay

R. Teo’s Blunder Zone is shown by the yellow contour Red Zone in the green tunnel is the intersection of the BZ with approach path. The Red Zone corresponds to an assumed 2 second pilot delay. The Yellow Zone corresponds to an 8 second pilot delay

Map View showing a blunder The BZ calculations are performed in real time (40Hz) so that the contour is updated with each video frame.

Map View with Color Strips The pilots only need to know which portion of their tunnel is off limits. The color strips are more efficient method of communicating the relevant extent of the Blunder zone

Aircraft must stay within safe flight envelope during landing: –Bounds on velocity ( ), flight path angle (  ), height ( ) –Control over engine thrust ( ), angle of attack (  ), flap settings –Model flap settings as discrete modes –Terms in continuous dynamics depend on flap setting Example 4: Aircraft Autolander inertial frame wind frame body frame

Autolander: Synthesizing Control For states at the boundary of the safe set, results of reach-avoid computation determine –What continuous inputs (if any) maintain safety –What discrete jumps (if any) are safe to perform –Level set values and gradients provide all relevant data

Application to Autoland Interface Controllable flight envelopes for landing and Take Off / Go Around (TOGA) maneuvers may not be the same Pilot’s cockpit display may not contain sufficient information to distinguish whether TOGA can be initiated flare flaps extended minimum thrust rollout flaps extended reverse thrust slow TOGA flaps extended maximum thrust TOGA flaps retracted maximum thrust flare flaps extended minimum thrust rollout flaps extended reverse thrust TOGA flaps retracted maximum thrust revised interface existing interface controllable flare envelope controllable TOGA envelope intersection