Full-Body Collision Detection and Reaction with Omnidirectional Mobile Platforms: A Step Towards Safe Human-Robot Interaction

6.3 MB·English

by  Kwan Suk Kim

Noname manuscript No.
(will be inserted by the editor)
Full-Body Collision Detection and Reaction with
Omnidirectional Mobile Platforms: A Step Towards Safe
Human-Robot Interaction
Kwan Suk Kim · Travis Llado · Luis Sentis
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1 Received:date/Accepted:date
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n Abstract In this paper, we develop estimation and presented here is the first of which we are aware to
a control methods for quickly reacting to collisions be- address, in depth, the mitigation of the effects of colli-
J
tween omnidirectional mobile platforms and their en- sions between these types of sizable robots and objects

0
vironment. To enable the full-body detection of exter- or people.
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nal forces, we use torque sensors located in the robot’s The majority of work addressing mobility in clut-

] drivetrain. Using model based techniques we estimate, tered environments has centered around the idea of
O
withgoodprecision,thelocation,direction,andmagni- avoiding collisions altogether. However, collisions be-
R tude of collision forces, and we develop an admittance tween robotic manipulators and objects and humans
. controller that achieves a low effective mass in reac- have been investigated before [9,29]. Push recovery in
s
c tiontothem.Forexperimentaltesting,weuseafacility humanoidrobotsallowsthemtoregainbalancebystep-
[
containing a calibrated collision dummy and our holo- pinginthedirectionofthepush[20]orquicklycrouch-

1 nomic mobile platform. We subsequently explore col- ing down [25]. Inherently unstable robots like ball-bots
v lisions with the dummy colliding against a stationary [18,14]andSegways[19]havebeenabletoeasilyrecover
7
baseandthebasecollidingagainstastationarydummy. frompushesandcollisionsusinginertialsensordata.A
0
0 Overall,weaccomplishfastreactiontimesandareduc- four-wheel robotic base with azimuth joint torque sen-
5 tion of impact forces. A proof of concept experiment sors [7] has been able to respond to human push inter-
0 presents various parts of the mobile platform, includ- actions, but only when its wheels are properly aligned
.
1 ing the wheels, colliding safely with humans. with respect to direction of the collision. Also, a non-
0
holonomic base with springs on the caster wheels was
Keywords Mobile Platform · Force Estimation ·
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recently developed [15] and reported to detect pushes
1 Admittance Control
: from a human, but with very preliminary results and
v
without the ability to detect forces in all directions or
i
X 1 Introduction detect contacts on the wheels themselves. In this work,
r we focus on non-stationary robots, as opposed to fixed
a
Asmobilerobotsprogressintoserviceapplications,their basemanipulators.Inthefieldofnon-stationaryrobotic
environmentsbecomelesscontrolledandlessorganized systems, such as statically or dynamically balancing
compared to traditional industrial use. In these envi- mobile bases and legged robots, one of the key defi-
ronments,collisionswillbeinevitable,requiringathor- ciencies is the availability of collision reaction methods
oughstudyoftheimplicationsofthistypeofinteraction that can be used across different platforms. Dynami-
as well as potential solutions for safe operation. With cally balancing mobile bases and humanoid robots rely
this in mind, we are interested in characterizing the on IMU sensing to detect the direction of a fall and
safety and collision capabilities of statically stable mo- then regain balance along that direction. However, this
bile bases moving in cluttered environments. The work type of method is limited to robots which naturally tip
over at the slightest disturbance.
K.Kim ·T.Llado · L.Sentis
TheUniversityofTexasatAustin The main objective of this paper is to develop gen-
E-mail:{kskim@,travisllado@,lsentis@austin}.utexas.edu eral sensing and control methods for quickly reacting
2 Kwan SukKimetal.
to collisions in statically stable mobile bases. Specifi-
cally,wedevelopmethodsthatrelyonjointleveltorque
sensing instead of inertial measurement sensing to de-
termine the direction and magnitude of the collision
forces. If IMUs were used, accelerations would only be
sensed accurately once the robot overcomes static fric-
tion which, for a sizable robot, could be quite large.
Torque sensors, which are mounted next to the wheels,
can quickly detect external forces sooner than IMUs
and therefore are more suitable for quick collision re-
sponse. Equally important is the fact that statically
stablemobilebasescanmoveinanydirectionornotat
all in response to a collision, whereas dynamically bal-
ancing mobile bases and humanoid robots must move
inthedirectionofthecollision.Thisabilitymakesstat-
icallystablemobilebasesmoreflexiblewhenmaneuver-
Fig. 1 Concept: unexpected collision between a robot and
ing in highly constrained environments.
apersononabicycle,as presentedinour supportingvideo.
To provide these capabilities, we take the follow-
ing steps: (1) we develop a floating base model with
contact and rolling constraints for an omnidirectional Another means of detecting external forces is phys-
mobile base; (2) we process torque sensor signals using ical force/torque sensors such as strain gauges or op-
thosemodelsandstatisticaltechniques;(3)weestimate toelectronics. This approach has been used in many
roller friction and incorporate it into the constrained mobile platform applications such as anticipating user
dynamics; (4) we implement a controller to quickly es- intention with a force-based joystick [21], developing a
cape from the collisions; (5) we present an experimen- handle with force/torque sensing capabilities [24], im-
tal testbed; and (6) we perform experiments including plementing an impedance control law based on force/
severalcalibratedcollisionswiththetestingapparatus, torque sensed on a handle [2], and quantifying user
and a proof of concept experiment in which the robot intent and responding with an admittance controller
movesthroughaclutteredenvironmentcontainingpeo- based on a force/torque sensor mounted on a stick [11,
ple against whom it must safely collide. 27]. However, all of these methods rely on detecting
Overall, our contributions are (1) developing the forces and torques at a specific location, such as on a
first full-body contact sensing scheme for omnidirec- handle, or joystick. When the user interacts or collides
tional mobile platforms that includes all of the robot’s with other parts of the robot’s body, such robots will
body and its wheels, (2) being the first to use floating not be able to respond to the applied forces safety.
basedynamicswithcontactconstraintstoestimatecon-
In [10], a force/torque sensor measures forces be-
tactforces,and(3)beingthefirsttoconductanexten-
tween the mobile robot’s body and an external pro-
sive experimental study on collisions with human-scale
tection cover, providing partial safety, but collisions
mobile bases.
against the wheels cannot be detected. In [7] they in-
troduce a quasi omni-directional mobile robot that is
compliant to external forces by measuring torques on
2 Related Work
the yaw joints of its caster wheels. This technique can
detectcollisionsonthewheelslikeours,butsuffersfrom
singularitieswhichlimitboththedirectionsinwhichit
2.1 Mobile Platforms with Contact Detection
can detect force and its freedom of motion. In [15] a
To be compliant to external forces, mobile robots have sensorized spring system is installed on the frame of
adopted various sensing techniques. One simple way a mobile base with caster wheels and is used for push
to detect external forces is by comparing actual and interactions. However, the base can respond to forces
desired positions [12] or velocities [4]. This method is only in limited directions and is once more insensitive
easy to implement because it can use the built-in en- to collisions against the wheels.
coders on the robot joints or wheels to detect external Othersensingpropertieshavebeenusedforcontact
forces.However,theabilitytodetectcontactsusingthis interactions, notably the tilt measured by an inertial
method depends largely on the closed-loop impedance measurement unit on ball-bot robots [18]. This type
chosen for the control law. of robot, and the associated inertial sensing, have been
TitleSuppressedDue toExcessive Length 3
usedeffectivelytohandlecontactinteractionswithpeo- HeadInjuryCriterionisnotwellsuitedforstudyingin-
ple[14]. However,themain drawback ofthis method is juries resulting from human-robot interaction. Instead,
thattherobotmustmoveinthedirectionofthedistur- the authors propose contact forces acting as a proxy to
bance or it will fall over. In contrast, non-inertial force bone fractures as their injury indicator. The low out-
sensing techniques like ours allow a robot to react in put inertia achievable with their torque control manip-
any direction upon collision or force interaction. This ulators is shown to be highly conducive to preventing
ability might be very useful when producing planned injury during collisions.
movements tailored to the external environment. Also relevant to our work is the study considering
child injury risks conducted in [8]. Extensive experi-
mental data is obtained from a 200Kg mobile robot
2.2 Contact Detection via Joint Torque Sensing moving at speeds of 2Km/h and 6Km/h and colliding
against a robot child dummy fixed to a wall. The head
Several existing studies use joint torque sensing to de-
injury and neck injury criteria are used to study the
tectcontact,likeus,butonlyaddressserialroboticma-
consequences of the impacts, and the severity of injury
nipulators.Notethatthistechniqueisdistinctfromthe
is expressed by the Abbreviated Injury Scale. Those
commonly used multi-axis force/torque sensor located
criteria are reinforced with analysis of chest deflection
at the end effector of a manipulator. Many researches
forseverityevaluation.Incontrastwithourwork,their
have investigated sensing external forces on all parts
mobile platform is uncontrolled and does not have the
of a manipulator’s body using distributed joint torque
ability to sense contact. This study is focused purely
sensors [28,17].
on impact analysis instead of contact sensing and safe
Like our method, this indirect external force sens-
control.
ing requires estimation that considers dynamic effects
suchaslinkageandmotormasses,inertias,momentum,
gravitationaleffects,andfriction.Statisticalestimation 2.4 Model-BasedControlofOmnidirectionalPlatforms
methods [6] are used to estimate external forces based
on joint torque sensing [16]. These methods have in- A mobile platform colliding or interacting with the en-
spired our research, but we note that we have taken vironment is not only affected by external forces, but
similar approaches for a mobile platform instead of for also by static and dynamic effects such as the robot’s
a robotic manipulator. A mobile platform has different inertia, its drivetrain and wheel friction, and other me-
dynamics because it has a non-stationary base and its chanical effects. [30] considers a simulated system con-
wheels are in contact with the terrain. Such differences sisting of a 6-DOF omni-directional mobile robot with
imply different dynamic models and modifications of caster wheels, and addresses the modeling and control
the estimation methods. of motion and internal forces in the wheels. [3] derives
the dynamic equation including the rolling kinematic
constraint for a mobile platform similar to ours, but
2.3 Safety Analysis in Robotics uses an oversimplified dynamic friction model with re-
specttotheeffectsofrollerfriction.Studiesthatincor-
Pioneering work on safety criteria for physical human-
porate static friction models include [26,1], but again
robot interaction are provided in [29]. In particular,
these use oversimplified models that ignore omniwheel
curvesofmaximumtolerablestaticforcesanddynamic
and roller dynamics. The studies above are mostly the-
impacts on various points of the human body are em-
oretical, with few experimental results.
pirically derived. A method to detect external forces
using motor current measurements and joint states is
proposed, and a viscoelastic skin is utilized to dampen 3 System Characterization
impacts.
In[31]thepositiveeffectsonsafetyofactuatorswith 3.1 Hardware Setup
aserieselasticcompliancearebroughtupbutlinkedto
lower performance. A double macro-mini actuation ap- To perform experimental studies on human-robot col-
proach is proposed to accomplish safe operation while lisions, we have built a series of capable mobile plat-
maintaining performance, and the automotive indus- forms. This study uses the most recent. We began de-
try’s Head Injury Criterion index is used to demon- signing mobile bases to provide omnidirectional rough
strate the benefits of this approach in terms of safety. terrain mobility to humanoid robot upper bodies [22].
Acomprehensiveexperimentalstudyonhuman-robot The newest iteration of our platform, produced in [12],
impactisconductedin[9].Thisstudysuggeststhatthe replaced the previous drivetrain with a compact design
4 Kwan SukKimetal.
an external force breaches our contact threshold, the
controller switches on an admittance controller. This
Trajectory PD Plant
admittance controller generates a trajectory that re-
Collision Ext Force
sponds to the sensed external force and rapidly leads
Detection Estimator
the robot away from the contact. We tested both an
Admittance
impedance and an admittance controller in this role
Controller
duringthecourseofourresearch,butfoundtheadmit-
Fig. 2 Control Diagram showing how estimated external
tance controller to be more responsive.
force, F , is fed through the collision detector and ulti-
ext
mately determines the position controller’s input. When the
robot detects a collision it uses an admittance controller in
place of its usual trajectory to escape the contact as fast as
itcansafely move. 3.3 Reaction to Collisions
The admittance controller is designed to provide com-
that minimized backlash by using belts and pulleys.
pliance with respect to the external force. The desired
Rotary torque sensors in the drivetrain and harmonic
dynamics can be expressed as
drivesontheactuatorswereincorporatedintothebase
in [13], enabling accurate force feedback control for
M x¨+B x˙ =F (t), (1)
des des ext,x
impedance behaviors. The electronics in the current
system improve over that of [13] in that the once cen-
whereM andB arethedesiredmassanddamping
tralized torque sensor signal processing is now divided des des
of a virtual compliant system, and F (t) is the time
into each actuator’s DSP in order to minimize electri- ext,x
dependentforcedisturbanceappliedtothesystem.As-
cal crosstalk. This paper is the first study that uses
suming the external force is close to a perfect impulse,
the torque sensors on the hardware base for full-body
i.e. a Dirac delta function, the above equation can be
model-based estimation of the contact forces.
solved to produce the desired trajectory,
Rotary torque sensors in the wheel drivetrains pro-
duce the unique feature of our base: full-body contact
F (cid:16) (cid:17)
estimation on all parts of its body, including any part x(t)=x0+ Bext,x 1−e−Bdes/Mdest , (2)
of the wheels. An alternative would have been to cover des
all of a robot’s body with a sensitive skin, but this op-
wherex isthepositionofthesystemwhenthecollision
tionwouldhaveleftthewheelsuncoveredandtherefore 0
happens. An identical admittance controller operates
unable to detect contact. We note that the wheels are
on the y degree of freedom.
often the first part of the base that collides with unex-
Our controller attempts to maintain constant yaw
pected objects. Therefore, our solution with three ro-
throughout the collision, i.e.
tary torque sensors in the wheel’s drivetrain is the first
andonlyoneofwhichweareawarethatcanrespondto
θ(t)=θ . (3)
collisionsonallpartsofthemobileplatform.Addition- 0
ally, the harmonic drives and belt-based drivetrain of
the base minimize backlash and therefore achieve more Combining the three degrees of freedom, we write the
accurate force sensing. robot’s full trajectory as
(cid:0) (cid:1)T
x (t)= x (t), y (t), θ (t) . (4)
des des des des
3.2 Safety Controller Design
Thistrajectoryisdifferentiatedandthenconvertedinto
Whenamobilebasecollideswithpeople,twocasescan a desired joint space trajectory using the constrained
bepreviouslydistinguished:Inunconstrainedcollisions Jacobian, J given in Eq. (19), i.e.
c,w
apersoncanbepushedaway,whereasinfixedcollisions
the person is pushed against a wall. In either scenario
q˙ (t)=J (t)x˙ (t), (5)
w,des c,w des
our robot moves away from the collision as quickly as
(cid:90) t
possible to mitigate injury.
q (t)=q (t )+ q˙ (τ)dτ, (6)
w,des w,des 0 w,des
Fig. 2 shows our proposed control architecture for
t0
detection of and reaction to collisions. Under normal
circumstances, the controller tracks a trajectory given and fed to the PD controller of Fig. 2 to achieve the
by a motion planner or sensor-based algorithm. When intended impedance behavior.
TitleSuppressedDue toExcessive Length 5
Neodymium
Magnet
Metal Spring PU
Housing
Fig. 3 Collision Testing Apparatus simulates human contact using a 10kg mass on a slider. This one degree of freedom
system is accelerated via a second weight hanging from an elaborate pulley system, and can also be used to apply a static
force.Motioncapturemarkersattachedtothesliderandthe PUbumperare usedtomeasuretheirposition.
3.4 Collision Testbed duceinjury,butisinsufficienttoeliminateit altogether.
Though it is impractical to fully pad a robot, some
To assess the safety of our mobile platform, we con- padding can drastically reduce the collision forces due
structed a calibrated collision testbed. Following the to collision with specific parts of the robot’s body. Yet
collisiontestprocedureusedintheautomotiveindustry reducing the forces makes the problem of detecting the
[5], we chose a 10kg mass as our leg-form test dummy. collision more difficult, and increases the amount of
The collision dummy is attached to a sliding system timebeforetherobotacknowledgesanimpact.Wehave
which provides a single degree of freedom for impact, designed a one DOF springloaded bumper with a rela-
and is accelerated by a free falling weight. In Fig. 3 tivelylongtraveltostudythedesignofsafepaddingfor
we illustrate details of the test environment. The abso- omnidirectionalrobots.Thisdesignfeaturesamagnetic
lute positions of the dummy and the mobile base are lock at peak bumper extension, which works to allow
measured by the Phase Space motion capture system earlier detection of a collision, while simultaneously re-
describedin[12].Fourmarkersonthemobilebasemea- ducing the overall maximum impact force. Details of
sure its position and two markers on the dummy mea- the bumper can be found in Fig. 3.
sure its linear motion.
4 Full-Body External Force Estimation
3.5 Stiction-Based Bumper
To estimate external forces based on drivetrain torque
The time requirement for our base to detect colli- sensing,werelyonamodeloftheactuators,andonthe
sion and reverse direction is roughly one hundred mil- robot’skinematicsanddynamics.Theconstrainedkine-
liseconds. Keeping the collision time brief works to re- matic mapping between the base’s motion and wheel
6 Kwan SukKimetal.
4.1 Torque Output Dynamics
To derive wheel and roller kinematics, we consider a
planar scenario where the wheel moves omnidirection-
ally on a flat floor. In [12] we developed the following
equations relating the contribution of the ith wheel’s
Torque angular velocity, q˙w,i, and their omniwheel roller’s an-
gularvelocity,q˙ ,totheCartesianvelocityoftherobot
Sensor r,i
with respect to a fixed inertial frame, x˙ and y˙:
Fig. 4 Actuator Modelincludingthetorquesensor,mod-
(cid:16) (cid:17)
eledasaspring.ThetwomassesmandM representthemo- x˙ =r q˙ cos(θ+φ )− r q˙ −Rθ˙ sin(θ+φ ),
r r,i i w w,i i
tor inertia, reflected through the gear system, and the load
mass.Motorsidefrictionandloadsidefrictionareexpressed (9)
(cid:16) (cid:17)
asthedampingterms B1 andB2,respectively. y˙ =rrq˙r,isin(θ+φi)+ rwq˙w,i−Rθ˙ cos(θ+φi).
(10)
motion is used to find the base and omniwheel roller
Where,θistheabsoluteorientationoftherobot’sbody,
velocities based on measured wheel velocities. The ac-
Risthedistancefromthecenteroftherobot’sbodyto
tuator model provides a mapping between motion and
the center of the wheel, r and r are the radii of the
expectedtorquesensorvaluesintheabsenceofexternal w r
wheels and their passive rollers, respectively, and φ is
forces. This model is trained empirically to better esti- i
the angle from a reference wheel to the i-th wheel in
mate the friction in the omni-wheel rollers. Ultimately
sequential order, i.e. 0◦, 120◦, or 240◦. The kinematics
the position, magnitude, and direction of the applied
of q˙ and q˙ are obtained from Eq. (9)
external forces is estimated based on the deviation of w,i r,i
theobservedwheeltorquesfromthosepredictedbythe r q˙ =−x˙sin(θ+φ )+y˙cos(θ+φ )+Rθ˙, (11)
w w,i i i
force free model, and the kinematics are again invoked
to transform this into the Cartesian frame. r q˙ =x˙cos(θ+φ )+y˙sin(θ+φ ). (12)
r r,i i i
To build an intuition of our method for estimat-
Expressing these equations in matrix form,
ing external forces, consider the single actuator system
shown in Fig. 4. In this system, the torque sensor is
q˙ =J x˙, (13)
w c,w
modeled as a torsional spring, with spring constant k,
and its displacement is proportional to the torque ap- q˙ =J x˙ (14)
r r,w
plied to the sensor. The spring is compressed or ex-
where
tended through the combined action of the motor, the
wheel’s inertia, and the external environment. Some of −sin(θ+φ ) cos(θ+φ ) R
1 0 0
tithseriomtopro’rstamnatsvs,araisabrleeflseicntceldudtehrtohuegmhomtoerc’hsatnoircqauleg,eτamr-, Jc,w (cid:44) rw −−ssiinn((θθ++φφ1)) ccooss((θθ++φφ1)) RR∈R3×3,
2 2
ing, m, the gear friction, B , the load’s mass (i.e. the
1 (15)
wheel, or the robot itself in the constrained case), M,
 
cos(θ+φ ) sin(θ+φ ) 0
the friction between the wheel and the external envi- 1 0 0
ronment, B2. But most importantly, the torque τenv Jc,r (cid:44) rr ccooss((θθ++φφ1)) ssiinn((θθ++φφ1)) 00∈R3×3,
includes the effect of the wheel traction on the floor 2 2
(16)
and any possible external collision with objects or peo-
ple,
are the Jacobian matrices, q (cid:44) (q , q , q )T,
w w,0 w,1 w,2
τenv =τtrac+τext. (7) qr (cid:44) (qr,0, qr,1, qr,2)T, and x (cid:44) (x, y, θ)T. The sys-
tem’s generalized coordinates combine the wheel and
Assumingthattheeffectofthewheeltraction,τ can Cartesian states
trac
be modeled, our goal is to estimate the external forces,
τext, based on observed sensor torque τs: q(cid:44)(cid:0)xT qTw qTr(cid:1)T . (17)
Notice that we not only include wheel rotations, q ,
τ =−τ +B +Mx¨−τ . (8) w
ext trac 2 s
but also side roller rotations, q . This representation
r
This method can then be applied to the estimation contrastspreviousworkonmodelingthatwedidin[23].
problem of the full base by using the kinematic con- The main advantage, is that the augmented model will
straintrelationshipsbetweenthewheelsandtheground. allow us to take into account roller friction which is
TitleSuppressedDue toExcessive Length 7
significant with respect to actuator friction. As such, Using the second and third equations above, we can
we will be able to estimate external interaction forces calculatetheconstraintforcesonthewheelsandrollers,
more precisely.
(cid:32) (cid:33)
I q¨ −T
The mappings given in Eqs. (13) and (14) can be w w
λ = . (25)
c
written as the constraint I q¨ +B
r r r
Jc q˙ =0, (18) Substituting this expression into the first equation of
the equation system (24) we get
with
(cid:18) (cid:19)
Jc (cid:44) JJc,w −0I −0I ∈R6×9. (19) Mx¨+JTc,w(Iwq¨w−T)+JTc,r(Irq¨r+Br)=0. (26)
c,r
Solving the above for the output torque, T, we get the
Usingtheabovekinematicconstraints,onecanexpress
nominal torque model
the coupled system dynamics in the familiar form
(cid:104) (cid:105)
Aq¨+B+JTcλc =UTT, (20) T=J−c,wT Mx¨+JTc,r(Irq¨r+Br) +Iwq¨w. (27)
where A is the mass/inertia generalized tensor, B is a Thismodelpredictstorquesensorvaluesintheabsence
vector containing the estimated wheel drivetrain fric- ofexternalforces.Bycomparingthetorquesensordata
tion and roller to floor friction, and λc is the vector against this estimate, as in Eq. (8), we will be able to
of Lagrangian multipliers associated with the traction infertheexternalforces.Butfirstwemustcalibratethe
forcesofthewheel,whereλc,w enforcestherelationship roller friction estimate.
between Cartesian robot position and wheel angle, and
λ enforces the relationship between Cartesian robot
c,r
position and omniwheel roller angle. In other words 4.2 Empirical Estimation of Roller Damping
(cid:16) (cid:17)T
λc = λTc,w, λTc,r . (21) AsweshowninEqs.(20)and(23),the damping terms
associated with the output dynamics correspond to
Additionally,Uisthevectormappingmotortorquesto
wheel output damping, B and roller damping, B .
generalized forces, and T ∈ R3 is the vector of output w r
Wheel output damping consists of the friction sources
torques on the wheels. As mentioned previously, these
between the torque sensor and the wheel, which corre-
areequivalenttothesensedtorques,T =T.Valuesfor
s spond to sensor bearings and the belt connecting the
the aforementioned matrices are
sensor to the wheel. Notice that gear friction is not in-
   
M 0 0 M 0 0 cluded, as the torque sensor is located after the gears.
A=0 IwI 0 ∈R9×9, M=0 M 0, (22) When we lift the robot of the ground and rotate the
0 0 IrI 0 0 Ib wheels, the mean value of the torque sensor signal is
close to zero, meaning that the drivetrain output fric-
B=(cid:0)0BT BT(cid:1)T ∈R9, U=(cid:0)0I0(cid:1)∈R3×9, (23) tion is negligible compared to roller friction. On the
w r
otherhand,rollerfrictionisrelativelylargeastherollers
where M, I , I , and I are the robot’s mass, body in-
b w r donothavebearingsandthereforeendurehighfriction
ertia, wheel inertia, and roller inertia respectively. The
when rotating in their shaft. In the next lines we will
dampingterm,B,consistsofthedampingatthewheel
explainourproceduretoestimaterollerdampingbased
output(i.e.torquesensorbearingsandbeltdrive),B ,
w on torque sensor data.
and the damping from the side rollers, B . We note
r Fig.5demonstratesthetwoexperimentsunderwhich
that the side rollers do not have bearings and consist
the roller friction model was calibrated. In these tests,
of a relatively high friction bushing mechanism. There-
joint position controllers for each wheel, simple high
fore, the wheel friction is negligible relative to that of
gain servos, push the robot through a nominal path,
the side rollers. Thus we estimate only roller friction in
and the resulting torque sensor values are measured in
our final controller. Eq. (20) can be decomposed into
the absence of any external force. In Subfig. 5 (a) we
separate equations expressing robot’s body, wheel and
showanexperimentinwhichwheel0movessinusoidally
roller dynamics as
with time while the other two wheels remain fixed, re-
 (cid:16) (cid:17) sulting in an arc motion of the entire robot. In Subfig.
Mx¨+ JTc,w JTc,r λc =0, 5 (b) we plot the sinusoidal joint trajectory of wheel 0
I q¨ −λ =T, (24) and the torque sensor readings from the three wheels.
w w c,w
I q¨ +B −λ =0. Thetorquesignalsonallwheelsshowanapproximately
r r r c,r squarewaveshiftingphaseaccordingtothedirectionof
8 Kwan SukKimetal.
3 3
M o vin g Dir e ctio n 2 WWWhhheeeJeeePlllo120s 2 WWWhhheeeJeeePlllo120s
1 d) 1 d)
Wheel 1 m) 2(ra m) 2(ra
N/ on N/ on
rque(0 Positi rque(0 Positi
To nt To nt
Wheel 0 -1 1Joi -1 1Joi
Wheel 2 Real Estimated
-2 -2
0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time(sec) Time(sec)
3 3
Wheel0 Wheel0
Moving Direction 2 WWhheeJeePllo12s 2 WWhheeJeePllo12s
Wheel 1 1 d) 1 d)
m) 2(ra m) 2(ra
N/ on N/ on
rque(0 Positi rque(0 Positi
Wheel 0 To nt To nt
-1 1Joi -1 1Joi
Wheel 2 Real
Estimated
-2 -2
0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time(sec) Time(sec)
Fig.5 TorqueSignalsfromSimpleMotionsareusedtocalibratetherollerfrictionmodel.Noexternalforcesareapplied
to the robot in this test. The JPos lines represent the motion along the two simple arc trajectories. Torque signals from the
calibrated model are shown to the right of the graphs representing the actual data on which they were trained. Subfigures
(a-c)representtherotationoftherobotaboutavirtualpivotoutsidethebaseofsupport,while(d-f)showapivotcenteredon
Wheel2.Grayarrowsinfigures(a)and(d)representthetorquesensedatthewheels,whiletheblackarrowsrepresentwheel
motion. By comparing (b) against (c) and (e) against (f), we can conclude that the expected roller friction torque model at
leastpartiallycaptures thegrossshapeof thedata.
wheel’s 0 motion. Because of this pattern, we assume perimental data. In that equation, the accelerations of
that most of the friction is due to Coulomb effects in- the wheels, the robot’s body and the side rollers must
stead of dynamic friction effects. We approximate this be known. We calculate them using the wheel trajecto-
Coulomb friction in our model using a tanh softening ries, q =3/2−3/2cos(2πωt), q =q =0, which
w,0 w,1 w,2
of the signum function, i.e. can be easily differentiated twice to obtain q¨ . To ob-
w
taintherobot’sbodyaccelerationweusetheinverseof
Br,i =Brtanh(αq˙r,i), (28) Eq. (13) and take the second derivative, yielding
where the magnitude Br and scaling factor α are tun- x¨ =J−c,w1q¨w+J˙−c,w1 q˙w. (29)
able parameters that we adjust based on the empirical
Eq. 14 then provides the roller accelerations
data. To do the tuning, we implemented Eq. (27) in a
softwaresimulationandcompareditsoutputtotheex- q¨ =J x¨+J˙ x˙. (30)
r r,w r,w
TitleSuppressedDue toExcessive Length 9
Plugging these values into the simulation of Eq. (27),
withB givenbythemodelofEq.(28)wesearchedover
r
B and α until the simulation matched the real data.
r
In Fig. 5 (c) we show the result of the simulation using
Eq.(27)whichcanbecomparedtotherealdataofFig.
5 (b). Our final model parameters were B = 0.2Nm
r
and α=0.4.
To further validate the procedure we conducted a
secondestimationprocess,shownintheFigs.5(d),(e)
and (f) in which two wheels of the mobile base track
a sinusoidal trajectory while one of them remains at
a fixed joint position. As we can see, the simulated
torques with the estimated roller friction model of Fig. Fig. 6 External Force Estimation is predicated on the
5 (f) has a good correspondence to the actual data of assumption that the external force is a purely translational
pushappliedtotherobot’ssurface,asapproximatedbyatri-
Fig. 5 (e).
angularprism.Thegreentriangleistheapproximatedrobot
body shape in a horizontal plane, and the perceived contact
point,aredcircle,occursatthefirstoftwointersectionsbe-
4.3 Model-Based Force Estimation tweenthistriangle andthelineofzeroexternal moment.
Following the simplified estimation of external torques
respect to the robot’s mass, and the effect of the wheel
from Eq. (8), we modified Eq. (20) to account for ex-
friction, B ≈ 0 with respect to the roller friction, we
ternal forces, yielding w
get a similar system of equations than that shown in
Aq¨+B+JTλ +JT F =UTT. (31) Eqs. (24), i.e.
c c ext ext
 (cid:16) (cid:17)
owfhtehreeJeexxtteirsntahlefoJracceosb,iaanndcoFrrespiosnadninegxttoertnhaellowcraetniochn Mx¨+ JTc,w JTc,r λc+JText,bFext =0,
ext −λ =T, (36)
containing a Cartesian force and a torque, i.e. c,w
F (cid:44)(cid:0)F F τ (cid:1)T . (32) Br−λc,r =0.
ext ext,x ext,y ext
Substitutingλ (cid:44)(λ ,λ )onthefirstequationabove
The differential kinematics of the point on the exterior c c,w c,r
bythevaluesofλ andλ obtainedfromthesecond
ofthebodyatwhichtheexternalforceisappliedcanbe c,w c,r
and third equations we get
expressedintermsoftherobot’sdifferentialcoordinates
as Mx¨−JT T +JT B +JT F =0. (37)
c,w c,r r ext,b ext
x˙ =x˙ +θ˙i ×d=J x˙ (33) In the absence of external forces, we can solve for the
ext z ext,b
torques
where x (cid:44) (cid:0)x y θ (cid:1)T, θ˙ is the angular veloc-
ity of theextbase, iezxtisetxhte uexntit vector in the vertical, z, T(cid:12)(cid:12)Fext=0 =J−c,wT(cid:104)Mx¨+JTc,rBr(cid:105). (38)
direction, × is the cross product, and d is a vector de-
The important point of the mapping above is that
scribingthedistancefromthecenteroftherobottothe
it can be numerically solved using the model and the
collisionpoint.Developingtheaboveequations,wecan
acceleration estimate of Eq. (29). On the other hand,
define
whentherobotcollideswiththeenvironment,thetorque
 
1 0 y−yext sensors read values according to the dynamics of Eq.
Jext,b (cid:44)0 1 xext−x∈R3×3. (34) (37). Assuming the output torque is equal to the value
0 0 1 givenbythetorquesensors,i.e.T =T,wecanusethe
s
previous two equations to solve for the external forces
Extending Eq. (33) with respect to the full generalized
coordinates yields (cid:16)T(cid:12)(cid:12)Fext=0−Ts(cid:17)=J−c,wTJText,bFext, (39)
x˙ =J q˙, with J (cid:44)(cid:0)J 0 (cid:1). (35)
ext ext ext ext,b 3×6 which can be written in the alternative form
UdysninagmitchseoafbEoqv.e(e3x1p),reasnsidonnefgolrecJteinxtg itnhetheeffeecxttoenfdthede JText,bFext =JTc,w(cid:16)T(cid:12)(cid:12)Fext=0−Ts(cid:17). (40)
wheel and roller inertias, I ≈ 0, and I ≈ 0 with We now make the following simplifying assumptions:
w r
10 Kwan SukKimetal.
– The external wrench has no net torque. 5 Experimental Results and Assessment
– The external wrench is applied at a point on the
triangular prism approximation of the body Throughout the previous sections we have established
– The external wrench is always of a pushing nature the following infrastructure: (1) full-body collision de-
tection capabilities using constrained models and in-
WiththosepremisesandtheexpressionofEq.(34),the
cluding wheel and side roller dynamics; (2) estimation
above equation becomes
of roller damping which is dominant in the behavior of
(cid:104) (cid:105)T the output robot dynamics; (3) fast collision response
F , F , (x −x)F −(y −y)F
ext,x ext,y ext ext,y ext ext,x capabilities by achieving desired impedances through
= JTc,w(cid:16)T(cid:12)(cid:12)Fext=0−Ts(cid:17). (41) atrnucatdumreititnacnlcuedicnogn,taromlleorb;i(le4)baasneewxiptehritmoreqnutaelsiennfsroarss-
This equation has four unknowns, {F ,F ,x , on the wheel drivetrains, a calibrated collision dummy,
ext,x ext,y ext
y } but only three entries. It is attempting to simul- and a motion capture system.
ext
taneously solve the external force and its location. Let The goal of this section is multi-objective: (1) to
us focus on the third entry of the above equation. The characterize the performance of our infrastructure in
third row can be written in the form terms of accuracy of force detection and the impact lo-
cation,(2)tomeasuretheamountoftimethattakesour
2
(x −x)F −(y −y)F =I θ¨− R (cid:88)τ . robottodetectcollisions,(3)tomeasuretheamountof
ext ext,y ext ext,x b r s,i time it takes our robot to respond to collisions once
w
i=0
they have been detected, (4) to poke the robot in var-
(42)
ious places to proof that we can detect collisions in all
This derivation comes from first comparing Eqs. (37) parts of the robot including its wheels, and (5) to give
and (40), which lead to anideaofwhataretheimplicationsofourmethodology
for providing safety in human-scale mobile bases.
JTc,w(cid:16)T(cid:12)(cid:12)Fext=0−Ts(cid:17)=Mx¨−JTc,wT +JTc,rBr, (43) To do so, we conduct five calibrated experiments
where we measure performance using a combination of
and then deriving the third row of the right hand side
the wheel torque sensor data, the wheel odometry and
of the above equation, yielding
the motion capture data on the robot and the collision
(cid:12) 2 dummy.Additionally,weconductaproofofconceptex-
JTc,w(cid:16)T(cid:12)(cid:12)Fext=0−Ts(cid:17)(cid:12)(cid:12)(cid:12)row3 =Ibθ¨− rRw (cid:88)i=0τs,i. (44) ppeeroipmleenintoanllsasfoerttys,wofhperoesttuhreersobanotdrcooalmlidsefsreweliythartohuenmd
The above results are obtained from the third rows of safely.
the transpose of Eqs. (19) and (16), i.e.
JcT,w(cid:12)(cid:12)row3 = r1 (cid:0)R R R(cid:1), (45) 5.1 Detection of External Force and Contact Location
w
JT (cid:12)(cid:12) =(cid:0)0 0 0(cid:1). (46)
c,r row3 In this experiment we evaluate our method’s ability to
Because Eq. (42) corresponds to a geometric line, the detect the point of contact on the robot’s body, the
location of the contact point can be solved using solely directionoftheexternalforce,andthemagnitudeofthe
Eq. (42) and our previously stated assumptions. The external force. In particular we will use only the wheel
line is parallel to the direction of the external force, drive-train torque sensors to identify those quantities
F ,andcanbeusedtofindthedistancefromthecen- withoutanyuseofexternalsensormechanisms.Inother
ext
ter of the robot to the intersection of the line with the words, the robot does not utilize motion capture data
robot’s body. The shape of our mobile base can be ap- or wheel odometry to detect those quantities.
proximatedasatriangularprism,anditsplanarsection To conduct these tests, we use the infrastructure
is a triangle, which is convex. Thus, there are only two depicted in Fig. 3. The horizontally sliding dummy is
points on its body where the line meets the premises. connected to a pulley system that runs to an overhead
Therefore, we solve for the location where the exter- systemwithaverticalweightof1Kg.Asaresultacon-
nal force is applied using those geometric constraints stant force of 10N is applied to the slider. In Fig. 7 we
as shown in Fig. 6. showimagesoftheexperimentalsetupwheretheslider
Once we find the location of the contact point, we isplacedincontactwiththebasebeforeconductingthe
now solve for the external force using the first and sec- estimationprocess.Therobot’swheelsarepoweredoff,
ond row of Eq. (41). andbecauseofthehighfrictionoftheharmonicdrives,