# From structured english to robot motion.

**ABSTRACT** Recently, Linear Temporal Logic (LTL) has been successfully applied to high-level task and motion planning problems for mobile robots. One of the main attributes of LTL is its close relationship with fragments of natural language. In this paper, we take the first steps toward building a natural language interface for LTL planning methods with mobile robots as the application domain. For this purpose, we built a structured English language which maps directly to a fragment of LTL.

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**ABSTRACT:**In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over timed sequences of states. For systems whose states are equipped with nontrivial metrics, such as continuous, hybrid, or general metric transition systems, robustness is not only natural, but also a critical measure of system performance. In this paper, we define robust, multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other timed trace which remains ε-close to the initial one also satisfies the same MTL specification with the usual Boolean semantics. We derive a computational procedure for determining an under-approximation to the robustness degree ε of the specification with respect to a given finite timed state sequence. Our approach can be used for robust system simulation and testing, as well as form the basis for simulation-based verification. KeywordsRobustness-Metric spaces-Monitoring-Timed State Sequences-Metric and Linear Temporal Logic01/1970: pages 178-192; - SourceAvailable from: symlogical.com[Show abstract] [Hide abstract]

**ABSTRACT:**A temporal logic paradigm to specify the mission objectives and then to automatically derive the high level control definition required for an abstract robotic system is presented. Such paradigms for defining mission con-troller have been advocated by several researchers for mobile robots since the obtained controller can be proved to be correct by construction, provided that a correct specification formula is given. In this paper the problem of translating a Linear Temporal Logic (LTL) formula into a mission controller implementation is analyzed. One finding is that all the published solutions for that problem follow a static approach when the formula is used off-line to define a complete controller and then implemented as a fixed controller. Dynamic approaches for this problem are unknown, even though potentially they have several advantages, like the progressive construction of the solution, the ability to deal with changeable specifications and unknown environments, and the advantage of not having to visit the entire state space for finding a working solution. The paper also deals with the actual application of mission control specification through LTL formulae including the use of temporal commands, how to convert different robotic modes -like reactive or behavior control -into logic formulation, and how to deal with dynamic definitions. Finally typical mission specification patterns are studied. The main conclusion is that the LTL formulation is a very powerful tool for defining high level control for robotic abstractions, since the formula can be translated automatically into the desired mission controller, and most of the situations with mission control can be solved. However the necessity to improve or change currently available static conversion approaches is observed, and a dynamic approach solution for that problem suggested here is the main original contribution of this article. -
##### Conference Paper: Improving the continuous execution of reactive LTL-based controllers

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**ABSTRACT:**Recently, formal methods have been used to transform high-level robot tasks into correct-by-construction controllers. While correctness is guaranteed, these inherently discrete methods often lead to behaviors that are not optimal in the continuous sense, i.e. they induce robot paths that are significantly suboptimal. This paper proposes an algorithm for dynamically reordering the robot goals and connecting them via the shortest path with respect to a given continuous metric. The generated robot trajectories are close-to-optimal while satisfying the task specification in a dynamic environment. This method is implemented and simulation results are shown.Robotics and Automation (ICRA), 2013 IEEE International Conference on; 01/2013

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From Structured English to Robot Motion∗

Hadas Kress-Gazit, Georgios E. Fainekos and George J. Pappas

GRASP Laboratory, University of Pennsylvania

Philadelphia, PA 19104, USA

{hadaskg,fainekos,pappasg}@grasp.upenn.edu

Abstract—Recently, Linear Temporal Logic (LTL) has been

successfully applied to high-level task and motion planning

problems for mobile robots. One of the main attributes of LTL is

its close relationship with fragments of natural language. In this

paper, we take the first steps toward building a natural language

interface for LTL planning methods with mobile robots as the

application domain. For this purpose, we built a structured

English language which maps directly to a fragment of LTL.

I. INTRODUCTION

Successful paradigms for task and motion planning for

robots require the verifiable composition of high level plan-

ning with low level controllers that take into account the

dynamics of the system. Most research up to now has

targeted either high level discrete planning or low level

controller design that handles complicated robot dynamics

(for an overview see [2], [16]). Recent advances [1], [4], [6],

[17] try to bridge the gap between the two distinct approaches

by imposing a level of discretization and taking into account

the dynamics of the robot.

The aforementioned approaches in motion planning can

incorporate at the highest level any discrete planning method-

ology [2], [16]. One such framework, is based on automata

theory where the specification language is the so-called

Linear Temporal Logic (LTL) [3]. In the case of known

and static environments, LTL planning has been successfully

employed for the non-reactive path planning problem of a

single robot [8], [9] or even robotic swarms [12]. For robots

operating in the real world, one would like them to act

according to the state of the environment, as they sense it, in

a reactive way. In our recent work [14], we have shifted to a

framework that solves the planning problem for a fragment

of LTL [21], but now it can handle and react to sensory

information from the environment.

One of the main advantages of using this logic as a spec-

ification language is that LTL has a structural resemblance

to natural language1. Nevertheless LTL is a mathematical

formalism which requires expert knowledge of the subject

if one seeks to tame its full expressive power and avoid

mistakes. This is even more imperative in the case of the

fragment of Linear Temporal Logic that we consider in this

paper. This fragment has an assume-guarantee structure that

makes it difficult for the non-expert user even to understand

a specification, let alone formulate one.

∗This work is partially supported by National Science Foundation EHS

0311123, National Science Foundation ITR 0324977, and Army Research

Office MURI DAAD 19-02-01-0383.

1A. N. Prior - the father of modern temporal logic - actually believed that

tense logic should be related as closely as possible to intuitions embodied

in everyday communications.

Ultimately, the human-robot interaction will be part of the

every day life. Nevertheless, most of the end users, that is the

humans, will not have the required mathematical background

in formal methods in order to communicate with the robots.

In other words, nobody wants to communicate with a robot

using logical symbols - hopefully not even the experts in

Linear Temporal Logic. Therefore, in this paper we advocate

that structured English should act as a mediator between the

logical formalism that the robots accept as input and the

natural language that the humans are accustomed to.

From a more practical point of view, structured English

helps even the robot savvy to understand better and faster

the capabilities of the robot without having an intimate

knowledge of the system. This is the case since structured

English can be tailored to the capabilities of the robotic

system, which eventually restricts the possible sentences in

the language. Moreover, since different notations are used

for the same temporal operators, a structured English frame-

work targeted for robotic applications can offer a uniform

representation of temporal logic formulas. Finally, usage

of a controlled language minimizes the problems that are

introduced in the system due to ambiguities inherent in

natural language [22]. The last point can be of paramount

importance in safety-critical applications.

Related research moves along two distinct directions. First,

in the context of human-robotinteraction through natural lan-

guage, there has been research that converts natural language

input to some form of logic (but not temporal) and then maps

the logic statements to basic control primitives for the robot

[15], [18]. The authors in [20] show how human actions

and demonstrations are translated to behavioral primitives.

Note that these approaches lack the mathematical guarantees

that our work provides for the composition of the low level

control primitives for the motion planning problem. The

other direction of research deals with controlled language. In

[11], [13], whose application domain is model checking [3],

the language is mapped to some temporal logic formula. In

[23] it is used to convey user specific spatial representations.

In this work we assume the robot has perfect sensors that

give it the information it needs. In practice one would have

to deal with uncertainties and unknowns. The work in [19]

describes a system in which language as well as sensing can

be used to get a more reliable description of the world.

II. PROBLEM FORMULATION

Our goal is to devise a human-robot interface where the

humans will be able to instruct the robots in a controlled

language environment. The end result of our procedure

Page 2

should be a set of low level controllers for mobile robots

that generate continuous behaviors satisfying the user speci-

fications. Such specifications can depend on the state of the

environment as sensed by the robot. Furthermore, they can

address both robot motion, i.e. the continuous trajectories,

and robot actions, such as making a sound or flashing a light.

To achieve this, we need to specify the robot’s workspace and

dynamics, assumptions on admissible environments, and the

desired user specification.

Robot workspace and dynamics: We assume that a mobile

robot (or possibly several mobile robots) is operating in

a polygonal workspace P. We partition P using a finite

number of convex polygonal regions P1,...,Pn, where

P = ∪n

the position of the robot by creating boolean propositions

Reg = {r1,r2,...,rn}. Here, ri is true if and only if

the robot is located in Pi. Since {Pi} is a partition of

P, exactly one ri is true at any time. We also discretize

other actions the robot can perform, such as operating the

video camera or transmitter. We denote these propositions

as Act = {a1,a2...,ak} which are true if the robot is

performing the action and false otherwise. In this paper we

assume that such actions can be turned on and off at any

time, i.e., there is no minimum or maximum duration for the

action. We denote all the propositions that the robot can act

upon by Y = {Reg,Act}.

Admissible environments: The robot interacts with its

environment using sensors, which in this paper are assumed

to be binary. This is a reasonable assumption to make since

decision making in the continuous world always involves

some kind of abstraction. We denote the sensor propositions

by X = {x1,x2,...,xm}. An example of such sensor

propositions might be TargetDetected when the sensor

is a vision camera. The user may specify assumptions on

the possible behavior of these propositions, thus making

implicit assumptions on the behavior of the environment.

We guarantee that the robot will behave as desired only if

the environment behaves as expected, i.e., is admissible, as

explained in Section III.

User Specification: The desired behavior of the robot is

given by the user in structured English. It can include motion,

for example “Go to rooms [1, 2, 3] infinitely often”. It can

include an action that the robot must perform, for example

“If you are in room 5, then play music”. It can also depend

on the environment, for example “If you see Mika, go to

room 3 and stay there”.

Problem 1 (From Language to Motion): Given the robot

workspace, initial conditions, and a suitable specification in

structured English, construct (if possible) a controller so that

the robot’s resulting trajectories satisfy the user specification

in any admissible environment.

i=1Pi and Pi∩ Pj = ∅ if i ?= j. We discretize

III. APPROACH

In this section we give an overview of our approach to

creating the desired controller for the robot. Figure 1 shows

the three main steps. First, the user specification, together

with the environment assumptions and robot workspace and

dynamics, are translated into a temporal logic formula ϕ.

Temporal Logic Formula

Synthesis Algorithm

Hybrid Controller

ϕ

User

Automaton A

Continuous Trajectories and Actions

Satisfying the User Specification

Environment

Assumptions

Robot

Workspace Specification

Fig. 1: Overview of the approach

Next, an automaton A that implements ϕ is synthesized.

Finally, a hybrid controller based on the the automaton A

is created.

The first step, the translation, is the main focus of this

paper. In Section IV, we give a detailed description of the

logic that we use and in Section VI we show how some

behaviors can be automatically translated. For now, let us

assume we have constructed the temporal logic formula ϕ

and that its atomic propositions are the sensor propositions

X and the robot’s propositions Y. The other two steps, i.e.

the synthesis of the automaton and creation of the controller,

are addressed in [14]. Here, we give a high level description

of the process through an illustrative example.

Hide and Seek: Our robot is moving in the workspace

depicted in Figure 3. It can detect people (through a camera)

and it can “beep” (using it’s speaker). We want the robot to

play “Hide and Seek” with Mika, so we want the robot to

search for Mika in rooms 1, 2 and 3. If it sees her, we want it

to stay where she is and start beeping. If she disappears, we

want the robot to stop beeping and look for her again. We

do not assume Mika is willing to play as well. Therefore, if

she is not around, we expect the robot to keep looking until

we shut it off.

This specification is encoded in a logic formula ϕ that

includes the sensor proposition X = {Mika} and the robot’s

propositions Y = {r1,...,r4,Beep}. The synthesis algo-

rithm outputs an automaton A that implements the desired

behavior, if this behavior can be achieved. The automaton

can be non-deterministic, and is not necessarily unique, i.e.

there could be a different automaton that satisfies ϕ as well.

The automaton for the Hide and Seek example is shown in

Figure 2. The circles represent the automaton states and the

propositions that are written inside each circle are the robot

propositions that are true in that state. The edges are labelled

with the sensor propositions that enable that transition, that is

a transition labelled with “Mika” can be taken only if Mika

is seen. A run of this automaton can start, for example, at

the top most state. In this state the robot proposition r1 is

true indicating that the robot is in room 1. From there, if the

sensor proposition Mika is true a transition is taken to the

Page 3

r1

r4

r1 Beep

Mika

r2

r4

r1

r4

r3

Mika

r3 Beep

Mika

r3

Mika

r2 Beep

Mika

r2

Mika

Fig. 2: Automaton for the Hide and Seek example

1

2

3

4

(a) The robot found Mika in 2

1

2

3

4

(b) Mika disappeared from 2 and

the robot found her again in 3

Fig. 3: Simulation for the Hide and Seek example

state that has both r1and Beep true meaning that the robot

is in room 1 and is beeping, otherwise, a transition is made

to the state in which r4 is true indicating the robot is now

in room 4 and so on.

The hybridcontroller used to drive the robot and control its

actions continuously executes the discrete automaton. When

the automaton transitions from a state in which riis true to

a state in which rj is true, the hybrid controller envokes a

simple continuous controller that is gueranteed to drive the

robot from Pito Pjwithout going through any other cell [1],

[6], [17]. Based on the current automaton state, the hybrid

controller also activates actions whose propositions are true

in that state and deactivates all other robot actions.

Returning to our example, Figure 3 shows a sample

simulation. Here Mika is first found in room 2, therefore

the robot is beeping (indicated by the lighter colored stars)

and staying in that room (Figure 3.a). Then, Mika disappears

so the robot stops beeping (indicated by the dark dots) and

looks for her again. It finds her in room 3 where it resumes

the beeping (Figure 3.b).

IV. TEMPORAL LOGIC

We use a fragment of Linear Temporal Logic (LTL) [3]

to formally describe the assumptions on the environment,

the dynamics of the robot and the desired behavior of the

robot, as specified by the user. We first give the syntax and

semantics of the full LTL. Then, following [21], we describe

the specific structure of the LTL formulas that will be used

in this paper.

A. LTL Syntax and Semantics

Syntax: Let AP be a set of atomic propositions. In our

setting AP = X ∪ Y, including both sensor and robot

propositions. LTL formulas are constructed from atomic

propositions π ∈ AP according to the following grammar

ϕ ::= π | ¬ϕ | ϕ ∨ ϕ | ? ϕ | 3ϕ

where ? is the next time operator and 3 is the eventually

operator. As usual, the boolean constants True and False

are defined as True = ϕ ∨ ¬ϕ and False = ¬True

respectively. Given negation (¬) and disjunction (∨), we can

define conjunction (∧), implication (⇒), and equivalence

(⇔). Furthermore, we can also derive the always operator

as 2ϕ = ¬3¬ϕ.

Semantics: The semantics of an LTL formula ϕ is defined

on an infinite sequence σ of truth assignments to the atomic

propositions π ∈ AP. For a formal definition of the seman-

tics we refer the reader to [3]. Informally, the formula ?ϕ

expresses that ϕ is true in the next “step” (the next position

in the sequence). The sequence σ satisfies formula 2ϕ if ϕ

is true in every position of the sequence, and satisfies the

formula 3ϕ if ϕ is true at some position of the sequence.

Sequence σ satisfies the formula 23ϕ if ϕ is true infinitely

often.

B. Special class of LTL formulas

Following [21], we consider a special class of temporal

logic formulas. These LTL formulas are of the form ϕ =

ϕe ⇒ ϕs. The formula ϕeacts as an assumption about the

sensor propositions and, thus, as an assumption about the

environment, and ϕs represents the desired robot behavior.

The formula ϕ is true if ϕs is true, i.e., the desired robot

behavior is satisfied, or ϕe is false, i.e., the environment

did not behave as expected. This means that when the

environment does not satisfy ϕeand is thus not admissible,

there is no guarantee about the behavior of the robot. Both

ϕeand ϕshave the following structure

ϕe= ϕe

i∧ ϕe

t∧ ϕe

g; ϕs= ϕs

i∧ ϕs

t∧ ϕs

g

ϕe

iand ϕs

ment and the robot. ϕe

environement by constraining the next possible sensor values

based on the current sensor and robot values. ϕs

the moves the robot can make and ϕe

assumed goals of the environment and the desired goals of

the robot, respectively. For a detailed description of these

formulas the reader is referred to [14].

Despite the structural restrictions of this class of LTL

formulas, there does not seem to be a significant loss in

expressivity as most specifications encountered in practice

can be either directly expressed or translated to this format.

Furthermore, the structure of the formulas very naturally

reflects the structure of most sensor-based robotic tasks.

idescribe the initial condition of the environ-

trepresents the assumptions on the

tconstrains

grepresent the

gand ϕs

V. ENVIRONMENT AND MOTION CONSTRAINTS

As mentioned before, we can view the LTL formulas as

encoding three components. First, ϕerepresents the assump-

tions we make on the behavior of the environment, as sensed

Page 4

by the robot. Second, ϕs

condition and dynamics. Finally, ϕs

behavior of the robot. Note that in some cases, the desired

behavior is also encoded in ϕs

iand ϕs

tdescribe the robot’s initial

grepresents the desired

tas discussed in Section VI.

A. Environment Assumptions

In this paper we allow the user to choose between two

types of environments. The first, which is the most general

case, is when we have no assumptions on the behavior of the

environment, just initial conditions of the sensors. The user

input in this case is “Environment with initial conditions”

E“.” where E is the set of all sensors that are initially true.

In this case

ϕe

General= ∧x∈Ex ∧x?∈E¬x ∧ 2True ∧ 23True

The second is the case in which the robot behavior does

not depend on it’s environment, for example “go to room

4” (no sensing specified). The user input in this case is

“Any Environment.”. Here a dummy sensor proposition must

be defined for the completeness of this special class of

LTL formulas. We arbitrarily choose it to be always false.

Therefore, we have

ϕe

NoSensors= ¬Dummy ∧ 2¬Dummy ∧ 23True

The logic formulation allows much richer environment as-

sumptions. Creating a language interface for them is a topic

for future work.

B. Motion Constraints

The position of the robot is represented by the propositions

ri∈ Y. The robot can only move, at each discrete step, from

one cell to an adjacent cell and it can not be in two cells at the

same time (mutual exclusion). We can automatically translate

these constraints from a description of the workspace into a

logic formula. A transition is encoded as

ϕs

tTransition(i)= 2(ri⇒ (?ri∨r∈N?r))

where N is the set of all the regions that are adja-

cent to ri. All transitions are encoded as ϕs

∧i=1,...,nϕs

ϕs

tTransitions=

tTransition(i). The mutual exclusion is encoded as

tMutualExclusion= 2(∨1≤i≤n(ri∧1≤j≤n,i?=j¬rj))

Constraints on the other actions of the robots, if such exist,

should be encoded into ϕs

there are no such constraints.

tas well. In this paper we assume

VI. DESIRED BEHAVIOR

Our goal in this section is to design a controlled language

for the motion and task planning problems for a mobile robot.

Similar to [10], [13], we first give a simple grammar (Table

I) that produces the sentences in our controlled language and

then we give the semantics of some of the sentences in the

language with respect to the LTL formulas. We distinguish

between two forms of behaviors, Safety and Liveness. Safety

includes all behaviors that the robot must always satisfy, such

as “Always avoid corridor 2” or “If Mika is found, then stay

there”. These behaviors are encoded in ϕs

form 2(formula). The other behavior, liveness, includes

tand are of the

things the robot should always eventually satisfy, such as

“Go to room 4 infinitely often” or “Go to room 1 infinitely

often unless Mika is seen”. These behaviors are encoded in

ϕs

Some of the rules of the grammar for our controlled

language L appear in Table I. Note that L is actually an

infinite language. The literal terminals are marked using

quotation marks “...”, the non-literal terminals are denoted by

bold face (capital letters denote lists of symbols while small

letters just one symbol) and non-terminals by italics. In some

cases, we allow for synonyms in the literal terminals. For

example, “go to” can be replaced by “visit” or “reach”, while

“detected” by “found” or “seen”. The terminal R ranges over

subsets of Reg, i.e., over sets of regions of interest. For

example R can be replaced by {room 1, corridor 2}. C ranges

over sets of active actions at the initial state. The terminal

s ranges over the predicates for the sensors, for example

“Mika”, “fire”, “person” and so on, while the terminals a1,

a2, ... range over predicates for the actions, for example

“beep”, “picture”, “medic”, “fireman” and so on. A point

that we should make is that the grammar is designed so as

the user can write specifications for only one robot. Any

inter-robot interaction comes into play through the sensor

propisitions. For example we can add a sensor proposition

“Robot2in4”, which is true whenever the other robot is in

room 4, and then refer to that proposition: “If Robot2in4,

then go to room 1”.

We now show how several simple commands are translated

automatically to an LTL formula ϕ.

Initial Conditions: The initial condition of the robot is

given by the user by specifying the initial region that the

robot is in and all other output propositions that are initially

True. Let Rr= Reg − {r}, then the sentence “You start in

r with initial conditions C” is translated to

gand are of the form 23(formula).

ϕs

i= r ∧¯ r∈Rr¬¯ r ∧a∈Ca ∧a∈Act\C¬a

Motion Rules: The requirement “go to r infinitely often”

is mapped to the temporal formula:

ϕs

gGoTo(r)= 23r

This formula makes sure the robot visits room r infinitely

often. We can request the robot to visit multiple rooms, such

as “go to R?infinitely often” for R?⊆ Reg, by taking

conjunctions of “go to” specifications. Note that such a

conjunction does not specify in which order the rooms must

be visited. It only requests that all rooms be visited infinitely

often.

The “go to” specification does not make the robot stay

in room r, once it arrived there. If we want to specify “go

to room r and always stay there”2, we must add a safety

behavior that requires the robot to stay in room r once it

arrives there. The specification is translated to

ϕs

tgGoStay(r)= 23r ∧ 2(r ⇒ ?r)

2Note that the simple grammar in Table I allows for “go to r infinitely

often and go to q and always stay there”. This is an infeasible specification,

and the synthesis algorithm will inform the user that it is unrealizable.

Page 5

Start

::=

::=

“You start in” r “with initial conditions” C “.” (Conditional | Motion “.” | Motion “.” Conditional)

Conditional Conditional | “If” Condition “, then” (Motion+| Action) “.” |

| (Motion+| Action) “unless” Condition “.” | (Motion+| Action) “iff” Condition

Condition “and” Condition | Condition “or” Condition | “you are in” R |

| “you are not in” R | “You detect” s | s “is detected” | ...

Action “and” Action | Action+

Action−| “do not” Action−

a1| “take” a2 | “call” a3| ...

Motion “and” Motion | Motion−| “go to” r “and always stay there”

Motion−| “stay there”

“go to” R “infinitely often” | “always avoid” R | ...

TABLE I: The basic grammar rules for the motion planning problem.

Conditional

Condition

::=

Action

Action+

Action−

Motion

Motion+

Motion−

::=

::=

::=

::=

::=

::=

This formula states that if the robot is in room r, in the next

step it must be in room r as well. We define both Motion

and Motion+to allow sentences of the form “If you sense

Mika, then stay there” while prohibiting combinations such

as “always avoid r and stay there”.

Another motion primitive is avoidance. Since avoidance

is a safety behavior, it is encoded in ϕs

“always avoid r” is translated into

t. The specification

ϕs

tAvoid(r)= 2(¬ ? r)

meaning, the robot will not be in room r in the next step.

Again, as before, we can tell the robot to avoid several rooms

taking a conjunction of ϕs

tAvoid(r)

Conditional Rules: We can translate “if ... then ...” or “...

unless ...” commands using temporal logic by connecting the

condition and the requirement with the appropriate logical

connective. As an example for a condition, the sentence

“you are in R?”, where R?⊆ Reg, translates to the boolean

formula

ϕin(R?)= ∨r∈R?r

The semantics of the conditional rules depend on the rules

used in the consequence. For example, “If condition, then go

to r” converts to

ϕs

gIfGoTo(Condition,r)= 23(Condition ⇒ r)

While “If condition then avoid r” translates to

ϕs

tIfAvoid(Condition,r)= 2(Condition ⇒ ¬ ? r)

For lack of space we will not discuss further how such

conditionals are translated to LTL.

Now we turn to the composition of conditionals with

action primitives. Turning on or off other outputs of the robot

will typically be a safety behavior of the form “If on(off)-

condition, then (do not) action”.

ϕs

tDo(a)

=

=

2( OnCondition ⇒ ?a)

2( OffCondition ⇒ ¬ ? a)

ϕs

tDoNot(a)

The conditional “... iff ... ” is short for if and only if and is

created by taking the conjunction of “If” Condition “, then”

(Motion+| Action) “.” and “If” NOT Condition “, then” NOT

(Motion+| Action) “.”

One final note is that the different sentences in the Start

rule are converted to a temporal formula by taking conjunc-

tions of the respective temporal subformulas. We give several

examples in the next section.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Fig. 4: Simulation for the Visit and Beep example

VII. EXAMPLES

In the following, we assume that the workspace of the

robot contains 24 rooms (Figures 4, 5). Given this workspace

we automatically generate ϕs

relating to the motion constraints

No Sensors: Here we assume the robot has no sensor

inputs, therefore we will automatically generate the dummy

proposition and ϕe= ϕe

NoSensors

Visit and Beep: In this example the robot can move

and beep, therefore Y = {r1,...,r24,Beep}. The user

specification is: “Any Environment. You start in r1 with

initial conditions ∅. Go to {r1,r3,r5,r7} infinitely often.

Beep iff you are in {r9,r12,r17,r23}.”

The behavior of the above example is first automatically

translated into the formula ϕ:

tTransitionsand ϕs

tMutualExclusion

ϕe

=

¬Dummy ∧ 2¬Dummy ∧ 23True

⎧

⎪

Then an automaton is synthesized and a hybrid controller is

constructed. Sample simulations are shown in Figure 4. As

before, beeping is indicated by lighter colored stars.

Sensors: Let us assume that the robot has two sensors, a

camera that can detect an injured person and another sensor

that can detect a gas leak, therefore X = {Person, Gas}.

Search and Rescue: Here, other than moving, the robot can

communicate to the base station a request for either a medic

or a fireman. We assume that the base station can track the

robot therefore it does not need to transmit it’s location. We

ϕs

=

⎪

⎪

⎪

⎪

⎪

⎩

⎨

r1∧i=2,...,24¬ri∧ ¬Beep

∧ϕs

∧23(r1) ∧ 23(r3) ∧ 23(r5) ∧ 23(r7)

∧2((r9∨ r12∨ r17∨ r23) ⇒ ?Beep)

∧2(¬(r9∨ r12∨ r17∨ r23) ⇒ ¬ ? Beep)

tTransitions∧ ϕs

tMutualExclusion

Page 6

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Fig. 5: Simulation for the Search and Rescue example

define Y = {r1,...,r24,Medic,Fireman}. The user speci-

fication is “Environment with initial conditions ∅. You start

in r1with initial conditions ∅. Go to {r1,...,r24} infinitely

often. Call Medic iff Person is found. Call Fireman iff Gas

is detected.”

A sample simulation is shown in Figure 5. Here, a person

was detected in region 10 resulting in a call for a Medic

(light cross). A gas leak was detected in region 24 resulting

in a call for a Fireman (light squares). In region 12, both a

person and a gas leak were detected resulting in a call for

both a Medic and a Fireman (dark circles)

VIII. CONCLUSIONS - FUTURE WORK

In this paper we have described a method for automatically

translating robot behaviors from a user specified description

in structured English to actual robot controllers and trajecto-

ries. Furthermore, this framework allows the user to specify

reactive behaviors that depend on the information the robot

gathers from its environment at run time. We have shown

how several complex robot behaviors can be expressed using

structured English and how these phrases can be translated

into temporal logic. The extension of the results in this paper

to deal with complex dynamics [7] as well as non-holonomic

vehicles [5] follows naturally.

As mentioned in this paper, we have not yet captured

the full expressive power of the special class of LTL for-

mulas. This logic allows the user to specify sequences of

behaviors, different environment assumptions and other robot

constraints. This is a topic of future work.

We also intend to construct a corpus of what people

would typically ask a robot to do and use it to explore if

and how natural language might be translated into the logic

formulation.

IX. ACKNOWLEDGMENTS

We would like to thank David Conner for allowing us

to use his code for the potential field controllers and Nir

Piterman, Amir Pnueli and Yaniv Sa’ar for allowing us to

use their code for the synthesis algorithm.

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Facilitating the construction of

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