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