Quick slip-turn of HRP-4C on its toes

Abstract

We present the realization of quick turning motion of a humanoid robot on its toes via slipping between its feet and the floor. A rotation model is described on the basis of our hypothesis that turning via slip occurs as a result of minimizing the power caused by floor friction. Using the model, the trajectory of the center of the foot can be generated to realize the desired rotational angle. Toe joints are used to realize quicker turningmotion, while avoiding excessive motor load due to frictional torque. Quick slip-turn motion with toe support is successfully demonstrated using a humanoid robot HRP-4C.

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Quick Slip-TurnofHRP-4C onits Toes
KanakoMiura, FumioKanehiro, KenjiKaneko, ShuujiKajita, and KazuhitoYokoi
Abstract— Wepresent the realizationofquickturning motion
of ahumanoidrobot on itstoes viaslippingbetween itsfeet
and the floor.Arotationmodel isdescribedonthe basisof
ourhypothesisthat turning viaslip occursasaresult of
minimizing the power causedby floorfriction.Using the model,
thetrajectory of thecenter of thefoot can begenerated to
realizethe desiredrotationalangle.Toejoints are usedtorealize
quicker turning motion, while avoiding excessivemotorloaddue
to frictionaltorque.Quickslip-turnmotionwith toesupportis
successfullydemonstrated using a humanoidrobot HRP-4C.
I. INTRODUCTION
In general,current humanoidrobot locomotion assumes
no slipcontacts.Asaresult,robotstend totakemanysmall
steps when turning in one place; thus,aconsiderable amount
of timeisrequired tocompletethe turning motion. Taking
these small stepsresults in inefficientenergy consumption
andinadequate stability.Therefore,webelievethat theuse
of slipisimportant for realizing quick and smoothturning
motion.
Issues regarding the proactiveuseof slipfor humanoid
motion havebeen addressedinsome studies.The first
publishedreporton rotation usingslip may be attributed to
Takahashi[1],who filed aJapanesepatent application in
Honda during the secret development ofhumanoids.Itwas
claimed that aquick turn is realized when arobot places all
its legson thefloorandmovesthemwhile maintaininga
uniform ground reaction force. Subsequently,Nishikawa[2]
proposed amechanical system using slipfor enabling biped
robotstoturn. Koeda etal.[3] studied the application ofslip
totheturning motion ofasmallhumanoidrobot HOAP-2.
Ahuman-sized humanoid robot WABIAN-2R successfully
demonstrated quick slip-turn motion through 80 degrees in
1.5 s supported by the toe and theheel [4]. Some studies [2]
[4]havereportedthat robotscan consume up to 60 percent
less energy by turning using slip,ascompared toturning in
steps.However,thephysical model ofturn viasliphas not
been developed thus far.
The slipphenomenon has already been discussed, and
our hypothesishas been demonstrated using humanoidrobot
platforms HRP-2 [5]and HRP-4C [6] [7].However,the
demonstrated motions were slow; therefore, wepresent a
video showing therealization ofquick and highlysophis-
ticated slip-turn motion by humanoidrobots.
All authors are with Humanoid Research Group, Intelligent
SystemsResearch Institute, National Institute of Advanced
Industrial Science and Technology,Tsukuba 305-8568,
Japan. {kanako.miura, f-kanehiro, k.kaneko,
s.kajita, kazuhito.yokoi }@aist.go.jp
II. SLIP MODEL
First,wehypothesize that turning viaslipoccurs as aresult
of minimizing thepower caused by floor friction.
ω=argmin
˜ω{P(˜ω)}(1)
where ωdenotes the angular velocityof therobot,and Pis
the total power generated on both soles.
Ahumanoidrobot can be modeledasasetof rigidbodies;
wedefinethe robot’sbaseframe ΣBon thepelvis, with the
orientation parallel tothe frontal direction ofthe pelvislink.
The origin ofthe worldframe ΣWis its projection on the
floor at thebeginning of therobot’smotion. It isassumed that
thecenter ofmass iscoincidentwith theorigin ofthebase
frame soas tosimplifythe model.Weconstrainthe left-foot
motion to besymmetrical withtheright-foot motion about
theorigin ofthe baseframe. Inaddition, wedo not change
thefoot direction.
Onthebasisof our hypothesis,weobtainthe following
expression of the angular velocityω.Notethat the detailed
explanation isprovided in[6].
ω=12(YBvx−XBvy)
12(X2
B+Y2
B)+l2
x+l2
y
(2)
where XBand YBdenotetheposition ofthecenter ofthe
sole,vxand vyrepresent the velocitycomponentsofv,and
lxand lydenotethe lengthand width ofthe sole,along the
x-andy-axesofthe baseframe, respectively,as shownin
Fig.1.This equationrelates thegiven velocity v(vx,v
y)to
the angular velocityω.
Bycalculating the timeintegral of (2) through themotion,
thetotal rotation angleisobtained. However,theinverse
problem cannot be solved using this model becausethere are
severaldifferenttrajectories for realizingthesamerotational
W
v
X
Y
B
B
BB
r
Fig. 1. Definitions of variables inthe equations.Left: position of robot’s
foot for (2). Right: arc trajectory ofboth feet for (3).
2012 IEEE International Conference on Robotics and Automation
RiverCentre, Saint Paul, Minnesota, USA
May 14-18, 2012
978-1-4673-1404-6/12/$31.00 ©2012 IEEE 3527

angle. It isadvisablefor arobot toselect themosteffective
motion torealize the desired rotational angle, whichmaxi-
mizes the angular velocitywiththesame magnitude as the
given velocity.The velocity vector of thefoot that maximizes
ωhas been found to be perpendicular tothe position vector
ofthecenter ofthefoot[7].Thevelocity that satisfies this
condition yieldstoanarctrajectory,thecenter ofwhich is
coincidentwith thecenter ofpressureassumedto be exactly
thesame asthe midpoint of right and left feet.
The slip-turn motion for realizing the desired rotational
angleθcan be generated by the equation
ξ=12|r|2+l2
x+l2
y
12|r|2θ(3)
where ξdenotes the anglebetween theinitial and final
position vectorsofthearctrajectory,andrrepresents the
current position vector of the center ofthe robot’s sole, which
isequal tothe radius of the arc, as showninFig. 1.
III. MOTION ACCELERATION BYTOE SUPPORT
When afoot turns withfloor slip,the frictional torque
occurs as areactiveforce. It is determined by integrating
theproduct ofthe frictional force and the moment arm over
therobot’s sole.Thus,the powerPrequired by the robot to
twirlits footon theflooris expressed as
P=τω =µNf(lx,l
y)ω(4)
f(lx,l
y)=g(α)ld(5)
g(α)=1+α2
12√1−α2log√1−α2+1
α+1−α2
12αlogα+1
√1−α2(6)
where τisthefrictional torque, ωisthe angular velocityas
in(1), µisthefriction coefficient between therobot’s sole
and the floor,Nisthenormal force, ld=l2
x+l2
y,lx=αld,
and ly=√1−α2ld.Notethat the valueofPis notthesame
as the power Prequired torotatethe entirebody in(1).
The function ofthe lengthand width ofthe solef(lx,l
y),
givenin(5) and (6), isdetermined by the diagonal lengthld
andtheratio α; the former is the dominant factor affecting
f(lx,l
y).
From (4), it can be inferred that the quicker arobot turns,
thegreater is thepower requiredagainst τω.However,the
motorpower of arobot islimited. Therefore, thefrictional
torque τhas to bereduced; this can be achieved by decreas-
ingµ,N,orld.
Weadopt thethird solution, i.e., decreasing ldby using
thetoejoints ofHRP-4C[8].Themotion ofthetoelink
is generated on the basisofcubic polynomials; the initial,
maximum, and final angles of thetoe jointsare connected
during the toesupport period. The maximum angleofthe
toejoint is setat the middleofthe period.
IV.DEMONSTRATION WITH HRP-4C
Slip-turn motion withtoesupport was demonstrated using
humanoid robot HRP-4C.Inaddition, we used our latest
controller [9] [10]to allowmotionwith an extremely small
stability margin.Theparametersforthefoottrajectorywere
Fig. 2. HRP-4C turning on its toes.Total motion period: 3.0[s],toe support
period: 1.2[s],turning period: 1.05[s],and maximumangle oftoe joint:
30.0[deg].
|r|=0.143[m], ξ=90.0[deg], and expected θ=84.7[deg].
Snapshots ofHRP-4C taken every 0.3sareshowninFig.
2. The resultant rotational anglewas 93.1[deg], and it was
larger than the expected angle. This may attributed to alarge
velocityof motion, whichinduces non-negligibleinertial
force.
V.CONCLUSIONS
Wedemonstrated quick turning motion ofHRP-4C using
slipbetween itsfeet and the ground. The foot trajectory was
generatedunder the hypothesisthat turning viaslipoccurs
as aresultofminimizing the powercaused by floor friction.
Torealize quicker motion, thetoe jointsof therobot were
utilized to reduce thefrictional torque.
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