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Intelligent Behavior Correctness and perceived correctness of
continuous execution of synthesized plans
Vasu Raman Cornell University
Joint work with Cameron Finucane, Gangyuan Jing and Hadas Kress-Gazit
Synthesizable
Unsynthesizable
(FSA)
Synthesis
Specification Analysis
(Physical Robot) (Simulation)
Hybrid Controller
Specification Map Robot
Synthesizable
Unsynthesizable
(FSA)
Synthesis
Specification Analysis
(Physical Robot) (Simulation)
Hybrid Controller
Specification Map Robot
Example:
“Robot starts in region r1 with the camera off”
“Activate the camera if and only if you see a person”
“Go to r2 infinitely often”
Continuous Execution
– Camera turns on
– Motion from r1 to r2
How to execute:
Assume all actions except motion instantaneous
Do motion first, then everything else
Camera turns on Motion from r1 to r2
Continuous Execution
PART I Correctness of Execution for Actions with
Different Durations
Original Approach: actions after motion
Camera turns on Motion from r1 to r2
Why is this undesirable?
- Delayed reactivity
- Potentially unsafe states
Alternative Approach: simultaneous actions
Camera turns on
Motion from r1 to r2
Why is this undesirable?
- Potentially unsafe executions
“Do not activate the camera in r1”
What we really want:
• Automatically check for safe continuous execution
during synthesis
• Provide feedback for unrealizability due to continuous
execution
Goal:
Implicit intermediate state
“Slow” = motion, “Fast” = everything else
Synthesis for Fast/Slow Actions
Synthesis for Fast/Slow Actions
For fast and slow actions!
Implicit intermediate states are safe!
Raman, Finucane and Kress-Gazit, IROS 2012
Synthesizable
Unsynthesizable
(FSA)
Synthesis
Specification Analysis
(Physical Robot) (Simulation)
Hybrid Controller
Specification Map Robot
- Explaining unsynthesizability arising from different
controller execution durations
e.g. OK with instantaneous actions, not without
- More that two relative action completion durations
Robot actions (in order of duration):
– Turning on/off the camera
– Waving hand
– Motion between regions
New framework: • Explicitly model action initiation/completion
• Small computational overhead
Raman, Piterman and Kress-Gazit, Submitted
PART II Optimality of Continuous Executions
(“perceived correctness”)
Non-optimality in the continuous execution
Classroom2 Classroom1
Hall1
Office1
Hall2
Hall3 Office2
Classroom2 Classroom1
Hall1
Office1
Hall2
Hall3 Office2
Trajectory when “people” is false Trajectory when “people” is true
Overview of solutions
• Add continuous metric when synthesizing the discrete automaton.
• Minimize cost in continuous domain between consecutive robot goals
• Frame the problem of minimizing cost to satisfy all robot goals as a Travelling Purchaser Problem.
• Reorder robot goals based on approximate solution.
Jing and Kress-Gazit, Submitted
Non-optimal path between goals Non-optimal goal order
Reorder robot goals based on TPP solution
Find shortest path between goals for a specific environment state
3
3 1
3
5
1
2
1
𝑞5 𝑞6
𝑞1 𝑞8
5
9
1
11
6 7 9
2
6
3
10 3
𝑞2
𝑞3
𝑞4
𝑞5
𝑞6
𝑞1
𝑞7
𝑞8
Jing and Kress-Gazit, Submitted
Non-optimal path between goals Non-optimal goal order
Reactive controller for dynamic environment
Reordered Liveness
Extract goal
states
Reorder robot
goals
Synthesize
weighted
automaton
Compute and
follow the
reasonable path
Topological
Map
Specification
State
Synthesize
weighted
automaton
Automaton
New Environment
New Weighted
State
Initial Environment
States
Set of Goals
Automaton Weighted
New Weighted Automaton
Jing and Kress-Gazit, Submitted
Reasonable continuous robot trajectories
Classroom2 Classroom1
Hall1
Office1
Hall2
Hall3 Office2
Classroom2 Classroom1
Hall1
Office1
Hall2
Hall3 Office2
Trajectory when “people” is false Trajectory when “people” is true
Jing and Kress-Gazit, Submitted
Intelligent Behavior Correctness and perceived correctness of
continuous execution of synthesized plans
Vasu Raman Cornell University
Joint work with Cameron Finucane, Gangyuan Jing and Hadas Kress-Gazit