Minimalism Distribution Sup ermo dularity
Bruce Donald Jim Jennings
Department of Computer Science Department of Computer Science
Cornell University Tulane University
Ithaca NY New Orleans LA
Daniela Rus
Department of Computer Science
Dartmouth College
Hanover NH
April
mechanically based rob ot algorithm for pushing and Abstract
grasping e g Mas While quite general in prin
We have designed and implemented multi agent
ciple these o line algorithms are usually designed for
strategies for manipulation tasks by distributing
rob otics devices such as gripp ers or ngers attached to
mechanical ly based sequential algorithms across sev
a traditional rob ot arm To extend these results for
eral autonomous spatial ly separated agents such as
distributed manipulation de ned in this pap er in Sec
mobile robots Our experience using mobile robots for
tion there are several challenges Autonomous
the manipulation of large objects couches boxes le
mobile rob ots mob ots have a suite of sensing and
cabinets etc leads us to recommend a minimalist
control mo dalities that di er across rob ot architec
architecture for multi agent programming In particu
tures Mob ots are often b etter suited to on line
lar our methodology has led us to derive asynchronous
approaches and hence the algorithms must b e adapted
distributed strategies that require no direct communi
to rely less extensively on geometrical and dynamical
cation between agents and very sparse geometric and
mo dels A host of di culties arises when a task
dynamic models of the objects our robots manipulate
must b e p erformed by a distributed team instead of
We argue for a design principle cal led sup ermo du
a single agent and hence the algorithms must com
larity which is orthogonal both to the notion of modu
p ensate by changing their communication sensing
larity in cognitive AI and also to horizontal decompo
or knowledge requirements Don DJR DJR a
sition the non modularity advocated in the subsump
RDJ
tion connectionist literature
We have rep orted on several sets of manipulation
Final ly we discuss a simple mobot Scheme in
strategies which we call protocols and also on the
frastructure to implement supermodular architectures
+
metho dology which generated them Don BBD
In the past few years we have programmed many su
RDJ Jen Our most interesting proto cols are
permodular manipulation protocols and tested them ex
asynchronous and do not require communication b e
tensively on our team of mobile robots We describe
tween the agents In this pap er we address the ar
why we think the supermodular infrastructure results
chitecture and the programming environment we used
in robust simple readable manipulation strategies
to develop our proto cols We also discuss how the
that can be recycled and reused
class of distributed manipulation algorithms we have
Intro duction
develop ed leads naturally to certain architectural con
straints
In rob otics most manipulation algorithms are de
signed to execute in a single pro cess on a single com This pap er is organized as follows We b egin with
puter that takes input from all the sensors and con a discussion on minimalism and sup ermo dularity We
trols all the e ectors To develop distributed ma continue by describing three di erent minimalist ma
nipulation strategies we b egan with a sequential but nipulation proto cols we have implemented and ana
lyzed in the information invariants framework and we sp ond to the data paths through which the informa
highlight their sup ermo dular structure Then we de tion passes Circuits can b e transformed by changing
scrib e the infrastructure we used for developing our the edge or vertex structure of their graphs Di er
strategies Finally we discuss how sup ermo dularity ent immersions of the graphs corresp ond to di erent
and minimalism a ect distributed rob ot architectures spatial allo cations of resources An imp ortant class
of transformations consists of p ermutations A circuit
Minimalism
p ermutation is a vertex p ermutation followed by an
Minimalism pursues the following agenda For a
edge p ermutation of its graph
given rob otics task nd the minimal con guration of
Roughly sp eaking a subroutine is modular if it can
resources required to solve the task Thus minimal
b e reused without changing the interface We say a
ism attempts to reduce the resource signature for a
circuit is supermodular if it can b e relo cated to a di er
task in the same way that say Stealth technology de
ent physical lo cation and still function correctly even
creases the radar signature of an aircraft Minimalism
in the absence of circuits that formerly surrounded it
is interesting b ecause doing task A without resource B
and in the presence of new circuits at this new lo
proves that B is somehow inessential to the informa
cation In this pap er we will describ e sup ermo dular
tion structure of the task We will discuss our exp eri
circuits according to the following hierarchy of circuit
mental demonstrations and show how their implemen
transformations A circuit is replicated when it is du
tation relates to our theoretical pro ofs of minimalist
plicated at the same or at a di erent lo cation A cir
systems In particular we will describ e our Mobot
cuit is distributed when it is split up and the parts are
Scheme system a distributed multi threaded high
recombined to form di erent circuits A supermodular
level rob ot programming environment
permutation consists of moving circuits around while
In rob otics minimalism has b ecome increasingly
resp ecting sup ermo dular b oundaries
in uential Marc Raib ert showed that walking and
The chief debate b etween cognitive AI and archi
running machines could b e built without static sta
tecturally constrained approaches such as subsump
bility Erdmann and Mason showed how to do dex
tionism and connectionism is as follows cognitive AI
trous manipulation without sensing Tad McGeer
advo cates that skills should b e mo dular Connection
built a bip ed kneed walker without sensors com
ism subsumption enforces a particular architecture
puters or actuators Ro d Bro oks has develop ed on
ab ove all else and this architecture may violate mo d
line algorithms that rely less extensively on planning
ularity We maintain that this so called dichotomy
and world mo dels Canny and Goldb erg have demon
opp oses the wrong categories the issue is not mo du
strated rob ot systems of minimal complexity We have
larity vs non mo dularity this faux dichotomy arises
taken a minimalist approach to distributed manipula
from only considering single agent systems in which all
tion de ned in this pap er in Section and also to
resources are physically co lo cated in this case sup er
our choice of a software architecture for writing our
mo dularity reduces or more accurately masquerades
rob ot programs We claim that the resulting proto
as simple naked mo dularity
cols consume a near minimum amount of resources
On the other hand in distributed systems re
The accompanying software development debugging
sources are of course not physically co lo cated
and execution time system are concomitantly parsi
In order to achieve the following goals
monious and lean
simplicity
Sup ermo dularity
ease of reuse
This pap er intro duces the concept of sup ermo du
larity and in particular it brings to the foreground
p erformance guarantees
the sup ermo dularity of our manipulation strategies
In programming it is natural to talk ab out units of
fault tolerance
organization called subroutines In mobile rob otics
we cho ose the design constraint of sup ermo dularity
particularly for distributed strategies we have devel
We will show how sup ermo dularity achieves this goal
op ed analysis and synthesis to ols for units of orga
Since this design constraint de nes an architecture
nization called circuits Don Intuitively a circuit
our architecture could also b e called sup ermo dular
is a sensori computational unit consisting of sensors
ity
and actuators connected by data paths We mo del
our circuits as graphs Vertices corresp ond to di er As an example of a sup ermo dular circuit illustrat
ent sensori computational comp onents Edges corre ing these p oints we discuss in detail two circuits
called align and push track see Section has a predictable functionality for example it p er
align is a virtual orientation sensor which by ac forms to within sp eci ed accuracy as in the case of the
tively exerting compliant control changes the rob ot s align circuit discussed in Section In addition
heading to lie at a particular desired angular relation ii ensures that the circuit has the same functional
to a manipulated ob ject push track is a virtual ef ity when moved to a di erent lo cation The goal here
fector that given a velo city control executes a guarded is to show that under any p ermutation that resp ects
move while in contact to apply a force along a desired co designation constraints Don the sup ermo du
line of pushing to a manipulated ob ject We will de lar circuits retain at least lo cally their p erformance
scrib e a sup ermo dular proto col called Async Online guarantees Finally iii ensures that the p erformance
that uses push track for multi rob ot reorienting of guarantees of a sup ermo dular circuit are preserved in
large ob jects the presence of other circuits or agents that might a
Sup ermo dularity is a continuum A circuit X is said priori interfere with its basic functionality
to b e more supermodular than circuit Y if the region
We have already derived p erformance guarantees
C X of the con guration space C in which X func for sequential and single agent circuits An example
tions correctly strictly contains C Y A completely is align whose analysis is describ ed in JR see
supermodular circuit Z has C Z C Hence sup er Section Arguments that rely on geometry and
mo dularity is a partial order on circuits In this pap er task mechanics can also b e made ab out our other su
we will informally use the term circuit X is often
p ermo dular circuits We b elieve that b ecause our ma
supermodular to connote that C X is large This
nipulation strategies are p erformed in quasi static en
concept may b e quanti ed precisely by measuring the vironments Section given velo city b ounds the
relative volume of C X in C DRJ In this pap er p erformance guarantees of single agent sequential cir
we describ e a partial order on the circuits we describ e cuits will b e preserved when distributed We tried to
in detail Some circuits are completely sup ermo dular
demonstrate this p oint empirically by running a large
for the manipulation tasks we consider while other
numb er of tests and exp eriments While these results
circuits are not sup ermo dular at all We will show are yet to b e proved rigorously we b elieve that the
that Async Online is completely sup ermo dular and sup ermo dular framework is the right architecture for
more sup ermo dular than push track which in turn addressing p erformance guarantees
is more sup ermo dular than prim push the circuit
Previous Work
for applying a force along a pre sp eci ed line of push
There has b een much work on co op erative systems
ing
of rob ots For an excellent review see CFKM
Our mantra for this pap er is as follows
Previous work on co op erative manipulation has fo
Minimalism Distribution Sup ermo dularity
cused mostly on pushing usually in the context of
b ox pushing by multiple mobile rob ots e g Par
In other words simplicity do es not arise from su
Nor
p ermo dularity but rather from minimalism Simi
Rob otic Manipulation
larly the transformations we p ermit circuits to un
dergo are constrained by the information invariants MS presents extensive analysis of grasping and
pushing op erations under a quasi static mo del Ma
theory That is minimalism de nes what it means for
son s analyses of the mechanics of pushing and grasp
circuits to b e simple and information invariants de ne
what it means for circuits to b e distributed When ing have led to many practical manipulation strate
the two are combined the optimal kind of circuits gies implemented most often on anthrop omorphic
are the sup ermo dular ones rob ot arms with simple two nger gripp ers Simi
larly Bro and others have analyzed the geometry
Sup ermo dularity yields recyclable and p ortable
and mechanics of quasi static pushing and squeeze
co de The greatest challenge is to formulate a metho d
for authoring optimal sup ermo dular circuits with per grasping of planar ob jects with common parallel jaw
formance guarantees Our research agenda for p erfor gripp ers
mance guarantees is i to ensure p erformance guaran Some work has b een done on large scale manipula
tees for individual circuits ii to show that a sup er tion using a single mobile rob ot such as LM and
mo dular circuit with p erformance guarantees retains OY The former analyze the mechanics of planar
these guarantees when relo cated and iii to show that pushing with line contact e g a mobile rob ot with a
a sup ermo dular circuit with p erformance guarantees xed at blade pushing a b ox and demonstrate a ma
retains these guarantees when distributed and paral nipulation planner which maintains this contact con
lelized More sp eci cally i ensures that a circuit guration
Co op erating Mobile Rob ots tions that follow we discuss our fo cus on minimalism
our rob ot programming philosophy and the nature of
Other recent work investigates tasks in which mul
the distributed manipulation algorithms we have im
tiple mobile rob ots co op erate such as SB manip
plemented
ulation of pallets by many small rob ots in simulation
Mat study of group b ehaviors such as disp ersion
Three Distributed Minimalist Ma
and o cking ABN simulation of foraging agents
nipulation Proto cols
with and without communication
This section describ es our exp erience in building
Work combining co op eration with mob ot manipu
minimalist distributed strategies for mob ots that p er
lation includes Nor Par and DJR DJR a
form manipulation tasks We describ e the circuits that
DJR b RDJ Jen Each demonstrates the ma
implement the proto cols we develop ed for three ma
nipulation of a b ox or other large ob ject using two
nipulation tasks and highlight their sup ermo dularity
mobile rob ots Nor describ es a task in which one
We di erentiate b etween the prop erties of manipula
rob ot pushes a b ox and another rob ot clears obstacles
tion proto cols by rob ots according to the following hi
out of the way Par builds an architecture designed
erarchy In a manipulation task rob ots use forces to
to achieve fault tolerant co op eration within teams of
reorganize the rob ots space In a paral lel manipula
heterogeneous mobile rob ots and applies that archi
tion protocol two or more rob ots apply forces to the
tecture to a numb er of tasks mostly in simulation
same coupled dynamical system In a distributed ma
including hazardous waste cleanup in which several
nipulation protocol the computation and control are
mob ots co op erate to pick up a numb er of small ob jects
distributed among the rob ots in a way that quali es
and move them near a designated site
as a distributed computation
One task from Par implemented on real phys
We present three di erent tasks the proto cols we
ical rob ots is a two rob ot b ox pushing task Each
develop ed for these tasks and two examples of sup er
rob ot pushes its own end of the b ox by some xed
mo dular circuits that we recycled and reused for each
amount then waits for the other rob ot to push its end
task proto col The exp eriments provide empirical evi
This strategy can b e executed by a single rob ot in the
dence for our b elief that co de authored in sup ermo du
event of failure of the other rob ot the key feature of
lar architectures is simple predictable parallelizable
the strategy and indeed of Parker s architecture is its
and reusable
fault tolerance
Sp eci cally we describ e proto cols that allow a team
We note that although much work has b een done
of small autonomous mobile rob ots to co op erate to
in simulation of co op erative manipulation there is
move large ob jects such as couches The rob ots run
1 1
little evidence that the results re ect the b ehav
SPMD and MPMD manipulation proto cols with
ior of physical rob ots p erforming similar tasks Of
no explicit communication We develop ed these pro
ten the mechanics and dynamics are p o orly mo d
to cols by distributing o line sequential algorithms
eled and unreasonable assumptions are made ab out
requiring geometric mo dels and planning The result
available communication and sensing devices How
ing parallel proto cols are more on line have reduced
ever Lynch and Mason LM present a simulator
dep endence on a priori geometric mo dels require no
and motion planner for single rob ot pushing that is
communication and are typically robust resistant to
based in sound mechanics and this simulator may yet
uncertainty in control sensing and initial conditions
b e extended to multiple rob ot manipulation Also
We will discuss the circuits needed to implement
DJR DJR a DJR c DJR b Jen present
the proto cols In particular we will intro duce the fol
algorithms for two rob ot pushing and for multi rob ot
lowing circuits
reorientation They analyze their proto cols with re
M the proto col for two rob ot straight line
sp ect to usage of such resources as computation re
pushing
tained state e g mo dels sensors and communica
tion Much of this work has the theme of minimalism
prim push the circuit for applying a force
asking such questions as Can we design a manipula
along a sp eci ed line of pushing
tion strategy that requires no communication b etween
align the circuit that allows a rob ot to p osi
the agents
tion itself at a sp eci ed relative orientation with
In the next section we summarize our most in
resp ect to a surface
teresting implemented manipulation proto cols those
1
for multi rob ot pushing reorientation and push
SPMD MPMD S ingle Multiple Program Multiple
ata D ing steering manipulation of large ob jects In the sec
of friction lies b etween the ngers The actual con
dition for stable straight line pushing is slightly more
complicated See MS for a complete analysis An
advantage of the two nger pushing strategy is that
the COF can drift around some and yet the rob ot can
keep pushing since we only need ensure the COF lies
a b
in some region b etween the lines of pushing of the n
gers see Figure a instead of on a line If the COF
Figure Two pushing tasks the goal in each case is
moves outside the region then the ngers can move
to push the blo ck in in the direction indicated by the
sideways to capture it again We have implemented
dashed arrows a In the two nger pushing task
a control lo op for this task on our force controlled
as seen from ab ove the ngers drawn as circles are
Puma manipulator The basic idea is to sense the
kinematically connected in the common parallel jaw
reaction torque ab out the p oint in Figure a If
gripp er con guration b Although similar in ap
push forward in direction of the arrow If
p earance the two rob ot pushing task is quite dif
move the ngers to the right else move the ngers to
ferent Each of the mobile rob ots drawn as circles
the left
is an autonomous machine and there may b e little or
We now derive a di erent version of this pushing
no explicit communication b etween them
strategy with a parallel jaw gripp er for a system of
two autonomous rob ots that can push an ob ject This
new strategy relies on the observation that the infor
mation needed to determine the motion of the b ox
SPR the circuit for a single pushing rob ot
is present in the angle b etween the normal to the
Async online the proto col for two rob ot reori
face of the b ox n and the direction of pushing p See
entation
Figure We wish the new proto col to run on two
autonomous mobile rob ots which will replace the n
push track the circuit for compliant pushing
gers as in Figure b We can adapt the control lo op to
at an angle while sliding on the face
servo on instead of b ecause our rob ots can use their
pushbutton bump ers to measure the relative angle b e
Pusher Steerer the circuit for the MPMD
tween their heading and the orientation of the face of
manipulation system
the b ox JR Actually the rob ots rst measure
0
the initial angle b etween n and p and subsequently
We will discuss how we used these circuits to imple
compare this value to the angle t measured at time
ment the proto cols for our three manipulation tasks
t in order to infer the direction of motion of the b ox
we will show how these circuits relate to each other
A negative change in the value of this angle implies a
and we will discuss their sup ermo dularity
clo ckwise rotation of the b ox A p ositive change im
For all of our proto cols the manipulated ob jects
plies a counterclo ckwise rotation The rob ots adjust
have comparable size and dynamic complexity to the
their pushing lo cation along the face of the b ox accord
rob ots Ob jects used in our exp eriments are up to six
ingly This is an example of how the rob ots can use
rob ot diameters in length and up to twice the mass of
2
the task dynamics to determine their next actions
one of the rob ots Rep ositioning and reorientation of
Pseudo co de for this strategy called Proto col M is
these ob jects may b e p ossible only through active co
shown in Figure and the circuit for the proto col is
op eration of a team of mobile rob ots Employing mul
shown in Figure
tiple rob ots may yield p erformance b ene ts or other
This pushing proto col dep ends crucially on two re
advantages such as ease of programming
sources for the mob ots the ability to sense the rel
Pushing
ative orientation of the ob ject at the p oint of con
Consider a task in which a single rob ot manipu
tact and the ability to apply a force along a sp eci ed
lator must push a b ox in a straight line Figure a
line of pushing The relative orientation sensor is im
depicts this task p osed for a two nger rob otic ma
plemented by using the circuit align describ ed in
nipulator We do not assume that the rob ot p ossesses
2
An alternative to using task dynamics is to use explicit
a complete mo del geometric and physical of the ob
communication The rob ots could exchange the sensed torque
ject it is pushing or of the supp orting surface With a
at their p oints of contact to determine the b est contact p oint
two ngered push see Figure a the b ox will trans
on the face of the ob ject A detailed description of this metho d
is presented in DJR DJR a late in a straight line so long as the COF the center
p n p n
Left robot Right robot
θ θ
0 0
repeat repeat
push f f
push θ
measure t measure t
g g
until t until t
0 0
Figure The critical quantities for the servo lo op in
if t if t
0 0
Proto col M
translate left translate left
else translate right else translate right
A
Figure Proto col M A strategy for two au
tonomous rob ots to push an ob ject in a straight line
without communication
B
Figure A single pushing rob ot is not a sup ermo dular
t
circuit Relo cating the circuit from A to B results in
comm
the application of the wrong torque sign
b
init run init run
0
0
where the comp osition of align and prim push
is parallel
sgn sgn
SPR is mo dular it can b e replicated on other
s
s
rob ots for the same functionality In our lab we
case s case s
have equipp ed three rob ots with similar but di er
3
ent architectures Tommy Lily and Camel with
R
L
prim push
Figure Sensor system for Proto col M This is a
prim push is not a sup ermo dular circuit as
manipulation circuit for Proto col M
its functionality quanti ed by the applied torque
dep ends on its spatial lo cation When relo cated
prim push do es not impart the same torque see
Figure Moreover a multiple rob ot system where
detail in Section and Figure Pushing is imple
each rob ot is SPR may e ect translations rotations
mented by a circuit called prim push describ ed in
or the null op eration i e the ob ject stays in place
RD
dep ending on their physical lo cation prim push
is our rst example of a mo dular circuit that is not
Sup ermo dularity in Pushing
sup ermo dular
In contrast to prim push align is a sup er
prim push gives us a simple version of pushing it
mo dular circuit The e ect of align is to p osition a
applies a force at a xed direction with resp ect to the
rob ot at a sp eci ed relative orientation with resp ect
surface of the ob ject prim push is a sub circuit that
to a surface align adapts to the surface normal to
implements Proto col M for co op erative straight line
determine the heading of the rob ot no matter where
pushing In other words prim push M
the rob ot is lo cated
A single rob ot system equipp ed with the circuit
In the following section we describ e circuits
prim push is denoted by SPR SPR e ects trans
that are sup ermo dular Sp eci cally we show how
lations This circuit is related to prim push by the
following information invariant equation
3
Camel s di ers mechanically from Tommy and Lily in that
it is a treaded rather than wheel based rob ot and it contact
SPR align prim push bump ers are distributed on a line rather than a circular surface
0
end-of-face
prim push can b e generalized to a circuit we call
push-track spin
push track so that it can apply a force at any de
sired orientation with resp ect to the surface of the
y
This generalization is achieved by combining ob ject push-track x
spin
the circuits prim push and align in a sequential
end-of-face
rather than parallel fashion The sequential comp osi
(b)
tion of align and prim push results in a circuit
su cient for the reorientation task the parallel com
COF
p osition of align and prim push results in a cir
Y
cuit su cient for the MPMD manipulation task The
X
details of the comp ositions will b e given in Sections
and (a)
a b
Reorientation
We are also interested in the reorientation of ob jects
Figure a Reorientation by one rob ot executing
by teams of mobile rob ots Consider the task whose
pushing tracking b A system of two rob ots reori
goal is to change the orientation of a large ob ject by
enting a couch The rob ot motions are shown in an
a given amount This is called the reorientation task
ob ject centered frame Each rob ot executes a pushing
We have describ ed and analyzed in detail the reori
tracking motion Rob ots recognize when they reach
entation task in RDJ Figure depicts one rob ot
the end of a face by breaking contact and execute a
reorienting a large ob ject A rob ot can generate a ro
spinning motion to turn around and reacquire contact
tation by applying a force that is displaced from the
center of friction This prop erty relates the dynamics
and the geometry of reorientations Mas and it can
cuted by each rob ot asynchronously and in parallel to
b e used to e ect continuous reorientations with mo
achieve the desired reorientation
bile rob ots The idea is to compliantly apply a sliding
4
Each rob ot
force on the face of the ob ject We call this action a
push track step
push track until contact break or imp ediment
When the end of the face is reached the rob ot may
turn around to reacquire contact and rep eat the push
if contact break then spin
tracking A rob ot that has gone past the end of a face
if imp ediment then graze
e ectively losing contact with the ob ject has broken
contact with the ob ject A rob ot whose maximum
The intuition is that the rob ots try to maintain
applied force de ned by a threshold do es not change
the push tracking state When the end of the face
the p ose of the ob ject has encountered an impediment
is reached the spinning motion is employed to reac
One rob ot may e ect any desired reorientation by
quire contact see Figure b When an imp ediment
rep eated push tracking steps if it can apply a large
is encountered the rob ot executes a guarded move
enough force but it may require a large workspace
near parallel to but towards the face of the ob ject
area for the rotation We are interested in multi rob ot
e ectively grazing the ob ject Graze terminates when
strategies that can overcome such limitations
the rob ot recontacts the ob ject or when it detects that
We now present a robust implemented reorienta
it has traveled past the end of the face Hence graze
tion proto col which relies on the ability of our rob ots
terminates in I reacquiring the ob ject at a contact
to execute push tracking motions The proto col is on
with a longer moment arm or I I missing altogether
line do es not rely on a priori geometric mo dels is
I is detected with a guarded move I I is detected
SPMD asynchronous and requires no communication
using a sonar based wall corner detection algorithm of
b etween the agents
JR When I I o ccurs the rob ot executes spin
For this proto col called Async online two
The comp osition of these three circuits constitutes the
rob ots su ce Assuming that the rob ots b egin in con
circuit for a reorienting rob ot Asynch online con
tact with the ob ject the following algorithm is exe
sists of two reorienting rob ot circuits
We have executed this proto col on our rob ots to
4
This strategy can b e implemented by a force that forms an
reorient couches le cabinets and large b oxes some
acute angle on the contacting edge outside the friction cone
times through more than three complete revolutions
This is similar to hybrid control RC which would b e used
for a dexterous hand Rus degrees contact Bumpers contact mode angle
desired contact contact angle mode
initial desired Rotational heading change Odometry θ ∆θ
Random sign
=0?
{#t,#f}
Rotate v|| x {#t,#f}
Until
Figure Two mobile rob ots co op erating to reorient
a couch a snapshot taken from a couch reorientation
exp eriment
Figure Circuit for align The rob ot has a ring
of contact bump ers and the goal is to p osition the
rob ot so that the two front bump ers for example are
This algorithm dep ends on the robust implemen
compressed The rob ot reads its bump er con gura
tation of push track This is realized as the se
tion and either terminates rotates clo ckwise rotates
quential comp osition of align and prim push
counterclo ckwise or randomly rep ositions itself on the
de ned in Section align is invoked rst to
face of the ob ject dep ending on the bump er values If
orient the rob ot to the face and to cho ose the correct
the two front bump ers are compressed it terminates
pushing direction Then keeping that heading xed
If a subset of the right bump ers are compressed it ro
prim push is invoked
tates counterclo ckwise If a subset of the left bump ers
Figure describ es in detail the align circuit We
are compressed it rotates clo ckwise If the rob ot fails
have run hundreds of exp eriments in which the rob ots
to align after several rotates it reacquires contact by
reliably execute align asynchronously and in par
randomization
allel We b elieve that reliability and ease of reuse of
our virtual orientation sensor come from its p erfor
may not apply the correct torque This only happ ens
mance guarantees In JR we prove that align
when the friction b etween the rob ot and the ob ject
is robust and reliable in that for the geometry of our
is such that no sliding is p ossible on the ob ject sur
rob ots the sensed angle is always accurate to within
face push track can b e extended to b e completely
three degrees Our exp eriments provide empirical evi
sup ermo dular always in the following manner An in
dence that these guarantees transfer when align is
dep endent sensor can b e added to detect the situation
immersed in di erent fashions
where the rob ot applies a force that is within the fric
Similar analyses can b e carried for the other circuits
tion cone at the p oint of contact graze which
used by the reorientation proto col e g spin and
moves the rob ot without contact can then b e invoked
graze
0
to place the rob ot to B for a b etter lever arm
Let us consider now the circuit Async online
Sup ermo dularity of Reorientation
Async online consists of push track spin
and graze replicated on two spatially separated
Unlike prim push push track is often su
rob ots Async online is more sup ermo dular than
p ermo dular The reason is that when relo cated
push track it is guaranteed to reorient the ob
push track adapts to the lo cal surface and cho oses
ject no matter what the starting con guration of the
a pushing direction by using align that imparts
two rob ots is RDJ Async online is thus more
the correct torque see Figure The relo cation of
sup ermo dular than push track since there are no
the push track circuit from con guration A to B
constraints on where this circuit can b e relo cated so
eventually results in the same net torque on the ob
0
long as it is on the b o dy of the ob ject
ject as B will slide to B This assumes that the rob ot
slides If the rob ot do es not slide then push track We can quantify the sup ermo dularity of a circuit by
A
given in BJ Bro
The system consists of two rob ots Each of the two
rob ots executing this proto col either takes on
the role of the Pusher in which
Torque controlled translations push the ob ject in
front of the rob ot
B' B
the rob ot follows the ob ject by continually turn
ing to align its front bump ers with the rear face of
Figure The sup ermo dularity of the push track
the ob ject the rotational and translational mo
circuit In the left image the rob ot A executes
tions here are decoupled and o ccur in parallel
push track and imparts the torque shown in the
and
gure The right image shows push track relo
the rob ot do es not know the path that the ob ject
0
cated to B Eventually B will slide to B resulting
is supp osed to follow
in the correct torque
or the role of the Steerer in which
The rob ot knows a path that it is supp osed to
(prim-push)
follow
the rob ot is translationally compliant it controls
the heading of its wheels but do es not control
(push-track) their rate of rotation and
the rob ot moves forward as a result of b eing
pushed by the ob ject which is itself b eing pushed
by the Pusher
SUPERMODULARITY
shows two rob ots moving a rectangular
ASYNC-ONLINE (align) Figure
ob ject through a circular arc
Now it is sometimes p ossible to navigate an ob ject
Figure A partial order with resp ect to sup ermo d
in a straight line or along a circular arc using a single
ularity The arrow indicates more sup ermo dularity
rob ot If the ob ject s center of friction COF is known
prim push is not sup ermo dular push track
and xed and the rob ot has little control error then
is often sup ermo dular and align and Async
the rob ot can plan a control strategy to manipulate
Online are always sup ermo dular
the ob ject along a desired tra jectory with acceptably
small error However if the lo cation of the COF is not
known precisely or changes with time generally the
case then the rob ot cannot simply plan and execute
the fraction of con guration space where the circuit
a reliable tra jectory but must continually sense the
can b e relo cated and still function correctly In our
ob ject s relative orientation and p osition and comp en
forthcoming work we will characterize this prop erty
sate for drift On the other hand the forces exerted
algebraically DRJ Here we develop the follow
by the rob ots in the two rob ot Pusher Steerer system
ing partial order on sup ermo dular circuits We have
can constrain the ob ject reliably in the presence of
given examples of circuits that are not sup ermo dular
greater uncertainties e g in the lo cation of the COF
at all such as prim push circuits that are often
and under coarser control and sensing
sup ermo dular such as push track and circuits
In his monograph on information invariants
that are always sup ermo dular such as align and
Don Donald claims that the spatial distribution
Async Online The partial order on these circuits
of resources has a critical e ect on the capabilities of
with resp ect to sup ermo dularity is shown in Figure
a system The Pusher Steerer system validates that
MPMD Manipulation
claim Consider a single robot manipulation algorithm
Section presents an implemented and tested such as LM As implemented on the Cornell mo
SPMD manipulation proto col We now present an bile rob ots the execution system consists of the fol
MPMD proto col called the Pusher Steerer system lowing resources each of which can b e represented as
A detailed description and analysis of this system is a circuit
circuit and the prim push circuit are comp osed in
parallel then the resulting sup ercircuit is su cient to
implement a single pushing rob ot that can for exam
ple push a couch along a path When the circuits
are distributed across two rob ots broken up as de
scrib ed ab ove then neither rob ot alone can manip
a b c d
ulate a couch but b oth rob ots together can manip
ulate large ob jects dexterously along a path In ad
dition the resulting distributed system reaps b ene ts
in terms of greater controllability and reduced sensing
and knowledge requirements
Role Trading
e f g h
In the Pusher Steerer system the manipulated ob ject
Figure This series of gures depict a b ox b eing
sits b etween the rob ots One feature of this system
guided through a degree arc by a steering rob ot in
is that there is no direct communication b etween the
front following the arc and a pushing rob ot The
two rob ots they interact with indirect communica
b ox b egins with its front and rear faces approximately
tion through the mechanics of the rob ots and ob ject
p erp endicular to the path In b and c the b ox ro
system The con guration is conceptually similar to a
tates in the wrong direction due to p o or initial place
rear wheel drive automobile that has b een sliced into
ment of the Pusher relative to the Steerer By d the
three sections the rear wheels push the passenger
Pusher with no mo del of the b ox or the path and with
compartment forward in a direction determined by
no communication has comp ensated for the p o or ini
the front wheels The challenge to this con guration
tial con guration By h the b ox has traversed the
is that the pieces are separate the rob ots have to
arc and rotated until its front and rear faces are ap
b e programmed to allow exible tra jectory following
proximately p erp endicular to the path
while keeping the ob ject b etween them The advan
tage is that the rob ots can trade roles the Pusher
can b ecome the Steerer and vice versa This increases
a pushing primitive prim push see Sec
the exibility of the proto col by allowing such maneu
tion
vers as the back and ll that automobile drivers use
for turning cars around on narrow roads It also p er
align see Section
mits the rob ots and ob ject system to reverse direction
a steering primitive steer and
without the rob ots having to move to di erent faces
on the ob ject
a priori path information
Role trading adds exibility to the system but dou
bles the resource requirements Each rob ot has to b e
Sup ermo dularity in the Pusher Steerer
equipp ed with all the circuits necessary for the Pusher
System
role and for the Steerer Role A system so equipp ed it
The Pusher s entire control system is obtained by
is sup ermo dular so long as the Pusher and the Steerer
the paral lel comp osition of the circuits align and
have the same direction of action
prim push The rob ot skill represented by the cir
We have p erformed over manipulation exp eri
cuit push track used in Section consists of the
ments using the Pusher Steere r proto col running on
sequential comp osition of align and prim push
several pairs of Cornell mobile rob ots In these ex
Thus the Pusher is equivalent to a single pushing rob ot
p eriments b oxes and similar ob jects of varying size
SPR in Section This constitutes another exam
mass mass distribution and material prop erties were
ple of sup ermo dularity here the vertex immersion
manipulated along complicated paths up to feet
for the align circuit is the same as in the reorien
in length On the basis of these exp eriments along
tation circuit but the graph p ermutation is di erent
with others which are describ ed in Bro we have
The Steerer s entire control system consists of the
observed the system to b e quite robust in practice
steer circuit and path information
In each case the co de that each rob ot executed re
mained the same there was no reco ding or tuning If all the circuits listed ab ove are co lo cated that
for di erent ob jects or paths Additional exp eriments is implemented on a single rob ot and if the align
using on line navigation metho ds human guidance in synchronization and communication b etween pro
one case and visual landmark recognition in another cesses
have demonstrated the exibility of the system
Since rob ot control algorithms can b e quite general
Despite conventional wisdom regarding the com
we chose a general programming language in which
plexities of programming a multi rob ot system a key
to express them and provide architectural supp ort for
feature of the Pusher Steerer system is its ease of
the p oints ab ove as follows
use the actual rob ot co de is simple and elegant and
yet there remains great exibility in metho ds of path
and library calls
sp eci cation
and light weight pro cesses threads im
Infrastructure
plemented using continuations Lo cks and condi
The programs that implement our distributed ma
tion variables provide synchronization
nipulation strategies were easy to generate and are
Automatic memory management with garbage
robust In this section we discuss our development
collection of a xed physical address space no
infrastructure
virtual memory
We b egin with two architectural decisions that we
rst rep orted in our pap er Program mobile rob ots
The last p oint yields a xed upp er b ound for
in Scheme RD For details see RD These
garbage collection delays p ermitting rigorous reason
decisions concern
ing ab out real time programs
This section describ es how well our design decisions
Why extend a general purp ose programming lan
worked and their implications for the infrastructure
guage instead of using or inventing a sp ecial
of manipulation proto cols We will describ e domain
purp ose rob ot language such as ALPHA Gat
constraints that must b e satis ed to makes the use of
or the b ehavior language Bro
Scheme practical The programming infrastructure
Of the general purp ose languages why Scheme
has resulted in a particular set of manipulation idioms
which p ermeate our co de We will describ e how using
We regard rob ots as computers that can exert
higher order functions we can implement termination
forces In particular we are interested only in the
predicates control parameter caches action cues and
case these forces are external to the rob ot system
event based exception handling
this excludes devices like clo cks from b eing consid
Mob ot Scheme The Software Logic
ered rob ots More sp eci cally we fo cus on devices
Analyzer
where these external forces are programmable this
In Sections ab ove we describ ed several dis
excludes devices like VCRs which are electronically
tributed systems in which a team of mob ots co op er
but not mechanically programmable Most sp eci
ates in manipulation tasks The programs that imple
cally we are interested in using these programmable
ment the strategies for Pushing Reorientation and
external forces for manipulation tasks that is to re
Pusher Steerer are written in Mobot Scheme a
arrange the environment external to the rob ot e g to
customized Scheme designed by Jonathan Rees for
move furniture p erform assemblies sort parts etc
the Cornell Mobile Rob ots RD Mobot Scheme
Naturally such rob ots typically use internal state to
co de for Proto col M Section is shown in Fig
enco de assumptions mo dels and exp ectations ab out
ure The most interesting feature from a develop
the external physical world Equally often sensors
ment standp oint is the distributed nature of the pro
are employed not only to build such internal state but
gramming environment The rob ots act as Scheme
also to comp ensate for errors in actuation and a priori
servers our workstations run a Scheme byte co de
mo dels
compiler and maintain serial connections to the rob ots
As such the internal state and control strategies
by wire or by radio mo dem The serial connection
can range from very simple to arbitrarily complex
is used only during debugging the rob ots are oth
The language must supp ort the following op erations
erwise completely autonomous p ossessing complete
Scheme virtual machines on b oard
access to e ectors
A typical rob ot exp eriment session consists of in
teracting with the rob ot by typing on the worksta
access to sensors
tion The user works in an interactive Scheme en
ability to satisfy real time constraints vironment usually running inside GnuEmacs The
Both Robots Execute
remove layers of abstraction by applying a pro cedure
to its arguments The entire language de nition in
define M theta
cluding its history co de examples macro do cumenta
let initial angle measure theta
tion formal syntax and semantics and extensive bibli
let repeat
ography ts into pages CR Scheme is a mo dern
if positive
high level functional language with automatic mem
push until
ory management rst class functions blo ck structure
lambda theta
static scoping closures p olymorphism and dynamic
if not approx theta
initial angle typing
sign theta initial angle
Early manipulation programs for commercial an
f
throp omorphic rob ot arms were written in a Basic
translate left
like language which lacked virtually every desirable
translate right
5
feature of mo dern programming languages More re
repeat
cently manipulators and mobile rob ots have b een pro
6
grammed in the C language The application of lan
guages like Scheme Lisp or ML to rob ot control may
Figure Proto col M co de for two mobile rob ots
have b een primarily hindered by one particular fea
with relative orientation sensing capability to execute
ture automatic memory management Systems with
the straight line pushing task This co de is an imple
this feature require p erio dic garbage collection which
mentation of the circuit shown in Figure
often stalls or at least slows other pro cessing Since
rob ot programming was assumed to require real time
resp onse garbage collecting systems were avoided
The reasons were Robots need programs which
user has access to b oth the workstation facilities e g
meet real time constraints and A language that
graphics sound lesystems and the mobile rob ot
garbage col lects can introduce arbitrarily long delays
Interaction with the rob ot b egins by invoking the
For many rob ots and many tasks these reasons are
mob ot read eval print lo op Scheme forms are
not valid First many rob ots execute tasks which do
typ ed interactively at the workstation which compiles
not require real time resp onses to sensory input For
them and sends them to the rob ot for evaluation The
example most mobile rob ots do not need to do dge
reply is interpreted by the workstation and displayed
tra c on busy streets or play tennis In particular
on the screen Therefore the read and print steps
much manipulation work can b e mo deled as quasi
o ccur on the workstation while the eval is p erformed
static meaning that inertial e ects are negligible
by the rob ot While a program is b eing executed
When this is the case largely b ecause sp eeds are low
the serial communications link b etween the rob ot and
and friction is signi cant ob jects in the task stop
workstation is not required It can b e disconnected
moving as so on as the rob ot stops And so the rob ot
at anytime and the rob ot will continue to run inde
may stop and think for arbitrarily long p erio ds with
p endent of the workstation Of course debugging in
out upsetting the task Thus pausing for garbage col
formation cannot b e displayed during this time and
lection do es not break the strategy but instead merely
the rob ot s program cannot b e altered But b oth of
slows it down
these activities may resume any time the communica
Now there are quasi static tasks in which the
tions cable is reconnected The design of the program
rob ots cannot pause for arbitrary p erio ds of time In
ming environment also p ermits remote pro cedure calls
a dynamic environment a rob ot may have to resp ond
to take place b etween the rob ot and workstation in
to conditions e g the presence of a human b eing or
either direction The end result is that the full de
the sudden app earance of an obstacle in the world
bugging facilities of the workstation are available for
apart from the actual manipulation The interaction
development and yet the rob ot remains autonomous
able to execute programs untethered
5
The most common example is the VAL I I language which
Our choice of Mobot Scheme for development re
runs the Unimation Puma series of manipulators
6
ects a minimalist approach to multi rob ot program
The Zebra Zero manipulator arm is supplied with a C li
brary of rob ot control functions and many mobile rob ots are
ming As a programming language Scheme is con
programmed in C due to the abundance of C compilers for
sidered minimal Scheme comprises of a small set of
small micropro cessors The Intel family and the Motorola
functions that enable the programmer to build layers
family of pro cessors including emb edded controller vari
ations are frequently used of abstraction by evaluating lamb da expressions and
b etween the rob ot and the manipulated ob ject may Termination predicates have b een intro duced in the
remain accurately describ ed as quasi static We have pre image motion planning framework of LPMT
found that garbage collection do es not vitiate the ro An extensive discussion of the relative p ower of these
bustness or even signi cantly degrade the p erformance termination predicates in the context of motion plan
of distributed manipulation proto cols a close exami ning may b e found in Erd
nation of current mobile rob ots reveals that very few
In the LPMT framework actions are pairs of
employ pro cessors with virtual memory In most cases
the form v tp where v is a velo city vector and tp
memory size is xed and is often small by worksta
is a termination predicate The motion continues in
tion standards As we p ointed out in RD with a
the direction v until the termination predicate returns
constant amount of memory needing garbage collec
true The predicate then is a function of all of the
tion we can easily calculate an upp er b ound on how
information available to the rob ot through sensors and
long this pro cess could p ossibly take Thus we know
a priori mo dels In the idealized mo del the predicate
8
in advance how long a pause may o ccur as the rob ot
is evaluated continuously in the background
executes its strategy and so we can predict just how
All of our motion control functions follow the
e ectively in the worst case the rob ot could react to
same style for any e ector including e g a camera
7
changing conditions
which may pan or tilt Bro Examples of Mobot
Scheme co de for various mo des of translation for
A rob ot running a garbage collecting programming
ward motion are in Figure We deviated from
system can execute complex co ordinated strategies
typical Scheme style by intro ducing keyword argu
in dynamic environments Each co op erative strategy
ments which mo dify the e ects of the motion Hence
presented in this pap er is an example The programs
a set of defaults must b e maintained and there are that implement our strategies must of course access
set default and get default functions for this
motors and sensors on our rob ots In the next setion
purp ose Default values are used for any argument
we describ e this interface
not given explicitly in the call to translate
Higher Order Functions
Our motion control functions represent sensor
The most critical features of our Mobot Scheme
based control lo ops They initiate the rob ot s motion
system are higher order functions sensor based con
which is usually controlled by another pro cessor and
trol structures and event based exception handling
at the same time evaluate the appropriate termination
In this section we describ e how using higher order
predicate The motion is halted when the termination
functions we can implement termination predicates
predicate returns a value other than false In order
control parameter caches and action cues Figure
for access to the motors to remain completely general
is an example of how higher order functions are used
many keywords exist and may b e used in arbitrary
in Mobot Scheme
combinations See Figure
As indicated by the examples in the gure key
words such as by and vel for velocity are followed
Termination Predicates
by integer values On the other hand keywords such
In our system the rob ot programmer can write pro
as until are followed by functions In the sp eci c
grams in which arbitrary termination predicates func
case of until a function of one argument is given
tions are passed as arguments to motion control rou
and the rob ot s motion stops when this function eval
tines Intermediate layers of the motion control sys
uates to something other than false The argument
tem build more complicated predicates out of these
to the predicate is supplied by the system when the
and pass along the resulting functions to the next
predicate function is called and represents the cur
lower layer As describ ed in RD we use higher
rent knowledge of the status of the motion The mo
order function to implement termination predicates
tion controller a separate pro cessor rep orts this sta
tus information to Mob ot Scheme In one example
7
Moreover rob ots like the Cornell Mobile Rob ots which con
from Figure we check to see whether the rob ot s
tain a lo osely connected network of or more on average pro
bump ers have contacted an obstacle in another we
cessors have a distinct advantage in that time critical pro cesses
may b e o oaded to a pro cessor which do es not garbage collect check to see if sonar unit rep orts a value that ex
Our rob ot s impediment sensor for example detects when a
8
On a real rob ot the frequency at which the termination sp eci ed amount of current would have to b e applied to the
predicate is evaluated will of course critically a ect its accu motors in order for the rob ot to continue moving The pro
racy However the pre image planning framework anticipated cessor which detects this situation and shuts down the motors
the general problem of control error from the start Control executes a simple feedback lo op at a high frequency and do es
error is already part of the input to the problem not garbage collect
Example Distance Velo city Termination Predicate
translate indet default impediment
translate by mm default or impediment
lambda status
stopped
status
translate vel indet mm s impediment
translate by vel m mm s or impediment
lambda status
stopped
status
translate until indet default or impediment
lambda status lambda status
not not
zero zero
read bumpers read bumpers
translate until mm mm s or impediment
lambda status lambda status
threshold or threshold
read sonar read sonar
by stopped
vel status
Figure Mobot Scheme motion control examples using the translate function For simplicity only three
keyword arguments are shown Any or all of the valid arguments may b e combined however When no distance
argument is given using the by option the distance the rob ot will travel is indeterminate When a distance is
sp eci ed the termination predicate consists of a check for the status of the motor controller which is triggered
by checking o dometry Note that the system always checks for the impediment condition The action taken when
impediment returns true is to invoke the imp ediment handler see Section
ceeds threshold when an imp ediment is detected is sp eci ed by the im
p ediment handler b ecause the situation is treated as
Keyword Description Default value
an exception see Section The system always
by distance to travel mm none
checks for the imp ediment condition Since the user
vel velo city mm s
may supply several other terminating conditions such
2
accel acceleration mm s
as a sp eci ed distance traveled or some other arbi
dir direction to travel
trary predicate the system constructs at run time
forward is p ositive
the prop er predicate to use
torque motor torque limit
in obscure units
Write through Cache
until termination predicate impediment
We may use higher order functions to mo dify the low
on exit termination action stop
level b ehavior of individual pro cessors in the rob ot
halt the robot
while still maintaining the single Scheme pro cessor ab
straction at the user level The mechanism we use is a
Figure Motion control system keywords The key
write through cache which can b e implemented to b e
words may b e used in arbitrary combinations and
transparent to higher levels of co de Its sole utility is
each has a reasonable and changeable default value
to b o ost p erformance and works as follows
Each rob ot contains on average more than nine
The default termination predicate impediment
9
individual pro cessors each of which is directly con
rep orts whether the rob ot s motors are stalled due to
nected to a small numb er of sensors or motors
contact with an immovable obstacle The action taken
This heterogeneous collection of computers are pro
9
The level of motor current that must b e exceeded to meet
grammed to make each sensor or motor smart As
the stalled condition may b e set by software an additional key
word argument torque exists for this purp ose much pro cessing as p ossible is done lo cally with every
sensori motor mo dule providing a high level interface
define wb state table make table
to the rest of the rob ot Consequently the rob ot s
define write wb state
critical system parameters are distributed across many
write cache wb state table
pro cessors When a Scheme program accesses a sen
define translate speed
sor or motor at the lowest level a form of remote
cache set translate speed
pro cedure call RPC is executed to the pro cessor
wb state table
which controls the hardware of interest The inter
define translate accel
pro cessor communication and RPC are of course hid
cache set translate accel
den to higher levels of Scheme programs such as
wb state table
the the user programming level Each time an RPC
define translate torque
o ccurs many parameters may b e needed which in
cache set translate torque
creases the amount of communication necessary and
Wb State Table
slows down the system As a result most pro ces
sors store their own state variables and the remote
calling machine needs only pass along the changes
Figure Examples of using a simple write through
in state
cache implemented using a macro and higher or
der functions
We now present a brief case study of using Mobot
Scheme to tune a control library thereby improv
ing real time p erformance In our initial library any
b etween pro cessors and also to the higher levels of
Scheme function invoking a wheelbase motion would
the system such as the user programming environ
rst set each parameter in turn and then nally start
ment The cache may b e trivially removed in the event
the motion This was ine cient We observed that al
that we decide not to trust the remote pro cessor to
most always the parameters remain the same through
retain its state b etween successive motions e g due
many successive motions Therefore we decided to
10
to a susp ected faulty piece of hardware On the
cache them on the Scheme computer using a standard
other hand the macro is general enough to b e used
write through cache We implemented a simple macro
in other caching applications Our cache illustrates
cache see Figure which accepts as its argument
that standard software design techniques are also ap
the function used to set a parameter It mo di es this
plicable to rob ot programming We are far from the
function to use the cache and also constructs a func
days of programming a single bit pro cessor in as
tion to read the current value of the parameter from
sembly language in order to make our rob ots move
the cache Its use is illustrated in Figure What
is interesting is that even this kind of low level op
Action Cues
timization may b e done in Mobot Scheme using
higher order pro cedures
Our nal example of higher order functions lies in the
The cache macro takes two arguments the func
interface to the Cornell Mobile Rob ots set of push
tion which sets the parameter to b e cached and the
buttons which along with multi colored LEDs re
table to use Two things happ en a the set function
side on top of the rob ot for interaction with users
is mo di ed to set the current value in the cache table
Esp ecially when op erating untethered the informa
and then the original set function is called and b a
tion displayed by the lights and entered via the but
get value function thunk is returned Each entry in
tons provides useful communication b etween the rob ot
the cache table has a key and an entry The key is
and the researcher At the user programming level
the new set function and the entry is always a pair
the set button action pro cedure takes two argu
value original set fcn The value is kept
ments the rst identi es a particular button on the
in a one element list so that it will b e null if no value
rob ot and the second is a function of no arguments
has b een set The original set function is kept around
technically a thunk When the appropriate button
so that i we can get it back if we need it and ii we
is pressed the asso ciated function is executed in its
can call it to write the cache out to force a write
own thread concurrently with whatever other threads
pro cesses are running on the rob ot The mechanism
Because we used a mo dern general purp ose pro
gramming language with higher order functions im
10
On the Cornell Mobile Rob ots the Scheme pro cessor can
plementing cache was easy The cache is transpar
detect when the wheelbase pro cessor resets and a complete
ent to the low level layers of the rob ot control sys
cache write automatically o ccurs after those events along with
a warning message displayed on the workstation tem which p erforms the necessary communications
define syntax cache
lambda exp rename compare
let set fcn cadr exp
state table caddr exp
let original set fcn set fcn
set set fcn lambda x
let value table ref state table set fcn
if or null car value not equal car value list x
original set fcn x
table set state table set fcn cons list x cdr value
if not table set state table set fcn cons original set fcn
begin
set set fcn original set fcn
error Cache error table full set fcn state table
lambda
let value table ref state table set fcn
if null car value
error Cache error the referenced value has not been set set fcn state table
car car value
define write cache cache table
table walk
lambda set fcn value
if not null car value
apply cdr value car value
cache table
Figure A simple write through cache implemented using a Scheme macro
allows complete freedom in deciding what the buttons of event that convolves the internal imp ediment and
should do The exibility is provided by the passing the external contact change More precisely a col li
of an arbitrary Scheme function directly into the next sion is the sp ecial case of an imp ediment caused by a
lower layer of the sensor control system In fact many p ositive contact change
of our sensors are programmed in this manner includ
Unexp ected collisions should b e treated as excep
ing the pushbutton bump ers that detect collisions with
tions The idea is straightforward we can either ll
ob jects and measure the relative orientation of ob ject
our programs with conditionals which check for unex
faces with resp ect to the rob ot s heading In writ
p ected situations or we can invoke the exception han
ing a program which p olls the bump ers we rst write
dler and make our programming task that much easier
a function which when a bump er button is pressed
Also we must b e able to easily mo dify this b ehavior
simply up dates a global dynamic variable The p olling
for those circumstances under which the programmer
pro cess then reads this variable to determine the cur
fully exp ects that a given situation might o ccur and
rent state of the bump er sensor
wishes to trap it so that the program can continue to
execute taking appropriate action
Collisions as Exceptions
We say a contact change o ccurs at time t when the
A global variable called impediment handler is de
rob ot is in contact with a di erent numb er of surfaces
ned as a function which is called when the motion
b efore t than after t We say the contact change is pos
control system detects the imp ediment condition The
itive when the numb er of contacting surfaces increases
default value for the handler is a function which rst
Hence a contact change is an external event to the
stops the rob ot s motors and then calls the system ex
rob ot in other words ground truth observable to
ception handler presenting all relevant information to
an outsider but p otentially undetectable by the rob ot
the user and leaving them in the symb olic debugger
An imp ediment on the other hand see Sec see Figure Example From within the debug
tion is an internal event signaled by and for the ger the user may continue e g after removing the
rob ot itself We de ne a col lision as a sp ecial kind o ending obstacle from the rob ot s path ab ort or
p erform almost any other action such as recompiling handler with a di erent function while a collision is
a piece of co de or using the insp ector to examine the a predicted p ossibility and should b e trapp ed In
stack our exp erience the most common alternative to the
function which calls the exception handler is a func
So the default reaction to a collision is for the rob ot
tion which simply returns the symb ol impediment
to stop and the user to b e presented with status in
The user program needs only check for this symb ol to
formation displayed through the debugger In other
b e returned by a motion control routine in order to
words the situation is treated as any other run time
branch on whether a collision o ccurred or some other
error would b e such as division by zero or a typ e mis
situation terminated the motion Because we use this
match It remains to b e explained how the user may
mechanism frequently we have de ned a macro called
write a program which traps exp ected collision errors
tolerate impediments see Figure Example
which replaces the default imp ediment handler with a
function that returns impediment while the b o dy of
Example
the macro is b eing executed Consequently one may
mo dify any motion control function call by wrapping
Move until the bumpers detect a collision
tolerate impediments around it as shown in the ex
Lily translate until
ample
lambda s
The exibility of Mobot Scheme p ermits the use
not zero read bumpers
of this mechanism which can b e seen in virtually ev
t
ery manipulation program our rob ots run All we have
done was to adapt a traditional technique to our ap
Example
plication of programming rob ots Our programs are
short and simple as a result of this technique
Move forever monitoring the motor current
against a current threshold
Architecture
Here we grab the robot and force it to stop
When the minimalist philosophy is applied to rob ot
which invokes the debugger that allows us
manipulation algorithms it yields proto cols with sur
us to examine variables redefine functions
prisingly low resource consumption that is the re
etc a aborts out of the debugger
sulting proto cols often disp ense with a resource such
Lily translate
as sensing communication or geometric mo dels that
Error Impediment
a naive analysis would have predicted was essential
translate
DJR DJR a RDJ DJR b When applied to
the programming environment and architectural sup
Debugging job number
p ort for rob ot manipulation minimalism results in a
Lily a
development and execution system that is spare and
lean in other words something more like Scheme and
Example
less like C Section In this section we discuss
the use of our Scheme based minimalist infrastructure
Expected collisions can be trapped We use
in sup ermo dular architectures
a tolerate impediments wrapper around the
The greatest challenge for sup ermo dular architec
function that might generate a collision
tures is to supp ort co de distribution across multiple
The impediment handling system will stop
spatially separated rob ots It is di cult to ensure
the robot and the motion function return
co de p ortability across rob ot architectures and the
impediment
result of the execution in distributed systems of mul
Lily tolerate impediments translate
tiple rob ots is even harder to predict Even for sin
impediment
gle rob ot systems that are mechanically similar such
as our rob ots Tommy and Lily it is not trivial to
share co de as this often entails adjusting constants
Figure Three examples of imp ediments han
that involve mass gear ratios etc Furthermore for
dling It is straight forward to substitute an arbi
manipulation tasks the output of a distributed sys
trary function for the imp ediment handler
tem of rob ots often dep ends on the numb er of rob ots
and their relative p ositions
The mechanism we use replaces the imp ediment Consider for example a system in which a rob ot
pushes an ob ject to e ect a desired translation and circuit to achieve the same task we must demon
the circuit implementation of this system we describ e strate that the emb edded circuits e ect the same
in Section This system is mo dular but not su strategy
p ermo dular The reason is that when distributed on
For our particular domain of manipulation tasks
multiple rob ots the output of the system dep ends in
we must account for the mechanical interactions
timately on the lo cation of the rob ots To see this
b etween the rob ots and their environment On
imagine a two rob ot system consisting of the original
a rob ot such as Camel whose bump er geome
rob ot and a second rob ot that acts on a face of the
try is essentially a at blade the e ect of push
ob ject opp osite to the rst rob ot The presence of
ing against an ob ject may b e di erent from that
the second rob ot interferes with the action of the rst
of say Tommy whose bump er is in the shap e
rob ot e g it may cause the b ox to rotate This is not
of a semi circle For manipulation then we ob
a sup ermo dular system in other words prim push
serve that compatible mechanical architectures
Section is mo dular but not sup ermo dular
are required when distributing a circuit across
A contrasting example is the reorientation task
several agents However by transforming circuits
Here one rob ot alone can cause reorientations by ex
into other equivalent circuits we have p orted
ecuting push track Section but this may re
our strategies without di culty from Tommy to
quire a large workspace area When the same co de
11
Camel and vice versa The transformation op
is distributed over multiple rob ots the output of the
erates at the circuit level so in the nal analysis
system is the same e g the ob ject rotates but p er
we are still moving a transformed circuit from
haps at a faster rate The resulting circuit Async
one rob ot to another
Online is completely sup ermo dular In our hierarchy
We have identi ed that the rob ot s mechanical
of sup ermo dular examples Async Online is more
architecture may limit sup ermo dularity for ma
sup ermo dular than push track which is more su
nipulation tasks b ecause di erent strategies are
p ermo dular than prim push
required for di erent mechanical interfaces to the
This is a sup ermo dular system in other words
world An imp ortant line of inquiry remains
push track is mo dular and sup ermo dular
which is to ask how the necessary architectural
Sup ermo dularity has made it easy for us to share
supp ort for sup ermo dularity varies with the task
and distribute co de across similar but not identical
domain
rob ots that op erate in parallel This is b ecause the
abstract principles of sup ermo dularity translate into
What development environment best supports the
concrete b ene ts in terms of co de recycling and pre
authoring of supermodular circuits and protocols
dictability in distributed rob ot systems By de ni
Our authoring environment is develop ed on top of
tion sup ermo dular circuits can b e relo cated to di er
an intrastructure Section that enforces min
ent physical lo cations and still function correctly In
imal constraints on programming The system
addition we b elieve that the p erformance guarantees
we advo cate is orthogonal b oth to the notion of
of sup ermo dular circuits transfer when the circuits are
mo dularity in cognitive AI and also to the hori
distributed
zontal decomp osition of Subsumptionism Sp ecif
The pushing vs reorienting example describ ed
ically our development environment is structured
ab ove shows that sup ermo dularity and distribution
by the following categories mo dular circuits su
impact architecture We now discuss this connection
p ermo dular circuits and strategies comp osed of
with emphasis on the following questions
sup ermo dular circuits or sup ercircuits
What architectural support is required to dis
The rst category comprises the mo dular circuits
tribute the circuits over several agents
for the interaction b etween rob ots and ob jects
and for navigation Conceptually these circuits
We cannot b egin to answer this question until we
can represent a wide range of rob ot skills of vary
understand what it means to distribute a circuit
ing degree of abstraction and complexity A cir
over several agents The installation and calibra
cuit in this category is a single agent circuit that
tion of resources must b e sp eci ed and commu
is safe for relo cation on other single agent sys
nications pathways across spatially separate lo ca
tems but there are no degrees of freedom the
tions must b e available The precise de nition
11
of these op erations is given in the information in
Camel is a Cornell mobile rob ot that uses treads instead of
wheels for lo comotion variants theory Don But for a distributed
circuit must b e immersed identically An example We have exp erimental evidence for these prop erties
of a mo dular manipulation circuit in this category for example the reuse of align in the reorientation
is prim push proto cols and the Pusher Steerer proto cols Similarly
we have p erformance guarantees For example for
The second category comprises the manipulation
align the p erformance guarantees transfer nicely
circuits that are often sup ermo dular In our
once align in immersed in a di erent fashion
hierarchy measured by the fraction of the con
the degrees of freedom of the new immersion are
guration space that allows relo cation Async
controlled by the kinds of p ermutations p ermitted in
Online and align are completely sup ermo d
the information invariants theory in the form of co
ular push track is often sup ermo dular A
designation constraints and the niceness of the trans
circuit in this category is safe for relo cation even
fer is ensured by sup ermo dularity
when the circuit is immersed in a di erent fash
ion The degrees of freedom of this immersion
Acknowledgements
are controlled by the kinds of p ermutations p er
This pap er describ es research done in the Rob otics and
Vision Lab oratory at Cornell University Russell Brown is
mitted in the information invariants theory in
one of the develop ers of the Pusher Steerer system We
the form of co designation constraints
thank Jonathan Rees for developing the Mobot Scheme
The third category comprises the circuits for ma
system We thank Jean Claude Latomb e for his hospitality
nipulation strategies A circuit in this category is
at the Stanford Rob otics Lab oratory
a multiple agent circuit consisting of sup ermo d
Supp ort for our rob otics research was provided in part
ular circuits The resulting sup ercircuit may or
by the National Science Foundation under grants No IRI
may not b e sup ermo dular Examples are Proto IRI IRI and by a Presidential
Young Investigator award to Bruce Donald and in part
col M proto col Async Online and Pusher
by the Air Force O ce of Sp onsored Research the Math
Steerer which are sup ermo dular
ematical Sciences Institute Intel Corp and AT T Bell
lab oratories
How can the architectural support and authoring
environment be realized in such a way that the
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