Feedforward and feedback dynamic trot gait control
for a quadruped walking vehicle
Ryo Kurazume

Shigeo Hirose

University of Tokyo

Tokyo Institute of Technology

7-22-1, Roppongi, Minato-ku, Tokyo, Japan

2-12-1, Ookayama, Meguro-ku, Tokyo, Japan

Abstract

To realize dynamically stable walking for a quadrupedwalking robot, the combination of the trajectory planning of the body and leg position (feedforward control)
and the adaptive attitude control using sensory information (feedback control) is indispensable. In this paper, we initially propose a new trajectory planning forthe stable trot gait named 3D sway compensation trajectory, and show that this trajectory has lower energy consumption than the conventional sway trajectory that the authors have proposed. Next, as theadaptive attitude control method used during the 2leg supporting phase of the trot gait, we consider four
methods: a) rotation of body along the diagonal line
between supporting feet, b) translation of body along
the perpendicular line between supporting feet, c) vertical swing motion of recovering legs, and d) horizontal swing motion of recovering legs. The stabilization eÆciency of each method is veri ed through computer simulation and the damping experiment using aquadruped walking robot, TITAN-VIII. Furthermore,
the dynamic trot gait control that combines the feedforward control based on the proposed 3D sway compensation trajectory and the adaptive feedback control
using body translation and vertical motion of swing
legs is developed, and the walking experiment on roughterrain using TITAN-VIII is carried out.
1

Introduction

To increase the walking speed and the energy eÆciency
of a quadruped walking vehicle, it is indispensable torealize dynamically stable walking that has a phasewhen the vehicle body is supported by less than 2 legs
and the body attitude becomes unstable.
Within a trot [2],[3],[4],[7], pace[12], and bound[13],[14],[15] gaits that are fundamental dynamicallystable gaits, the authors have studied the trot gaitin paticular. This gait is attractive because it has aclose aÆnity to the crawl gait, which is one of thestandard statically stable gaits, and can be classi ed

Kan Yoneda

as a \safety gait" [1] that avoids complete tumblingby touching a swing leg to ground. Then, the authors
have proposed a generalized trot gait [2],[3] that cansmoothly shift from the crawl gait to the trot gait inproportion to walking speed, and an intermittent trot
gait [4] that makes the diagonal legs as swing and support legs simultaneously to reduce dynamic e ect of
the recovering swing legs on the body.
Furthermore, the sway compensation trajectory of thevehicle body [2], which uses lateral body motion tokeep a zero momentum point (ZMP) on a diagonalline between the support legs, was proposed and thee ectiveness of this trajectory control to realize a dynamically stable walk was veri ed through walking experiments using TITAN-IV and TITAN-VI.
In the environment where the unknown roughness or
inclination exists, however, dynamically stable walking is diÆcult using feedforward gait control such as
the sway compensation trajectory only, and the adaptive feedback control system that stabilizes the body
attitude using mounted attitude sensors, gyroscope
sensors, etc. is requisite.
In this regard, for the realization of the practical dynamically stable trot gait for a quadruped walking vehicle, authors believe that the combination of feedforward control based on the sway compensation trajectory and feedback control based on the adaptive attitude control is one possible e ective control method.
The basic ideas underlying this feedforward and feedback dynamic trot gait control are as follows: First,
the state of the system is generously transferred adjacent to the unstable equilibrium point by o -line,
feedforward gait planning such as the sway compensation trajectory. Then, the remaining small deviationfrom the equilibrium point is adaptively compensatedby a simple, linear feedback control system.
In this paper, rst, we propose the new sway trajectory of the vehicle body named 3D sway compensation
trajectory that uses lateral, longitudinal, and verticalmotion of the vehicle body to keep ZMP on the diag-onal line of the support legs. With the proposed trajectory, it is possible to improve the energy eÆciency
against the conventional sway compensation trajectory that controls the position of ZMP by the lateralmotion only.
Next, as the adaptive feedback control method, several attitude control methods using the body translation and swing leg waving motion are proposed.
The control performance of each method is examinedthrough computer simulation and damping control experiments in the two-leg supporting phase using thequadruped walking vehicle named TITAN-VIII [11].
Furthermore, the feedforward and feedback dynamic
trot gait control system that combines the 3D sway
compensation trajectory and the adaptive body position and swing leg motion control is developed and thewalking experiment on rough terrain using TITANVIII is carried out.
2

3D sway compensation trajectory

2.1 Conventional sway compensation
trajectoryFirst, we show the formulation of the conventionalsway compensation trajectory. Here, we consider avehicle as a mass point at (xg ; yg ; zg ). If the ground is
at and the height of the body from the ground, z , isconstant, the position of ZMP (xz ; yz ; 0) is given as



xz
yz

 
=

xg
yg





xg
yg

A



(1)

where, A = zgg . Next, the diagonal line of the support
legs is de ned ascos  x + sin  y = d(2)Then, in order for ZMP to keep on this line, the centerof gravity has to be satis edcos (xgAxg ) + sin (ygAyg ) = d(3)

Assuming that the position of the body along the xaxis is expressed as
xg = x0 + vt +

1 2
at
2

(4)

By substituting this equation into Eq.(3), we getcos (x0

Aa + vt +1 2at ) + sin (yg2Ayg ) = d (5)The solution of this di erential equation, yg , is given
as
t
ptA
y
y p
+ ay2 t2 + ay1 t + ay0 (6)yg = C1 e A + C2 e
From the boundary condition for the continuity of the
trajectory (y_g;t=0 = y_g;t= T2 = 0; yg;t=0 = yg;t= T2 ),each coeÆcient is determined aspTp
T a2 + (1 e 2 A )vy
C1 =A cot (7)
pT
pT
(e 2 A e 2 A )pTap
T 2 + (1 e 2 A )v
y
(8)
C2 =
A cot pT
pT
(e 2 A e 2 A )ya2 =a cot (9)ya1 =v cot (10)ya0 =x0 cot  + d csc 
(11)
p
T
T
p
p
d
1 AT (e 2 A + e 2 A + 2) T 2
T
x0 =
+ (
)a
v
T
T
p
p
cos  44
4(e 2 A e 2 A )(12)Where, T is a walking cycle. This trajectory of thecenter of gravity, which is given as Eqs.(4) and (6), isde ned as the (conventional) sway compensation trajectory [2].

2.2 Expansion for longitudinal motion
The conventional sway compensation trajectory mentioned above can be expanded to include a sway toward the longitudinal direction.
First, Eq.(3) is decomposed into two equations for thex and y directions, and each solution trajectory is assumed to be given as Eq.(6) andpt
ptA
xg = C1x e A + C2xe
+ ax2 t2 + ax1 t + ax0 (13)
By substituting the boundary condition about thecontinuity of the trajectory, the following equations
with two parameters ax2 and ax1 are derived.
p(T 2 + 4 AT )ax2 + 2T ax1 2L
x
(14)
C1 =
T
8(e 2pA 1)
C2 =
x

(T 2

p

4

AT )ax2 + 2T ax1

8(e

pT
2 A

2L

1)

pT
C1 = A cot TT(e 2pA e 2pA )Tp
T ax+ (1 e 2pA )ax1
y2
C2 = A cot TT(e 2pA e 2pA )
y

p

T ax
2 + (1e 2 A )ax
1

(15)
(16)
(17)

a2 =
y

a1 =
y

a0 =

1
+ (
cos  2
d

p

(18)
(19)
(20)

x

a1 cot xa0 cot  + d csc 

y

a0 =

a2 cot x

pT
pT(e 2 A

pT
pT
e 2 A)

AT (e 2 A + e 2 A + 2)

T2

)ax2

T

4 1
(21)
Where, L is the body stroke in one walking cycle.
x

4

ax

2.3 Expansion for vertical motion

pt
ptA
+A g
zg = C1 e A + C2z elaterallateral andlateral,only

longitudinallongitudinal,


ax
1

0.623

0.334

0.2

0.107

0.107

A

0.02040.02040.0207and vertical

0.1 ygfoot position

Ag

C1 =

H

foot position

Trajectories

-0.05

pT
(Ag H )e 2 A
(24)
C2 =
pT
1 + e2 A
Where, H is the body height at t = 0; T2 .
We de ne these expansions of conventional sway compensation trajectory toward longitudinal and verticaldirection as \the 3D sway compensation trajectory".

0.05

0.1

0.15

xg

with longitudinal motion
andwith vertical motion-0.05

lateral motion only
(conventional trajectory)

(22)

(23)

T
1 + e 2pA

moving direction

0.05

-0.1

Where, A is an arbitrary constant. By substituting theboundary condition about the continuity of trajectory,coeÆcients with the parameter A are derived as
z

0.331

diagonal line

Moreover, the above equations can be expanded to theform including a sway in the vertical direction.
Considering A = g+zgzg , we assume the trajectory to
the vertical direction, zg , is given asz

Table 1: Minimum of squared accelerationfoot positions
moving direction
zgwith vertical motion

0.202

-0.05

0.201
0.2
0

0.05

0.1

xg
0.15

lateral motion only
(conventional trajectory)
andwith longitudinal motionz

2.4 Energy eÆciency of the 3D sway
compensation trajectory
The energy consumption of a walking vehicle is affected by many factors such as the mass of body andlegs, the con guration of the degrees of freedom, thetrajectory of body and legs, the negative power at eachactuator, etc [9],[10]. In this paper, however, the trajectory that minimizes the sum of squared acceleration
through the entire trajectory is considered.

Z T2(x 2 + y 2 + z 2 )dt(25)0Here, a regular walk (a2 = 0) is considered for simplicity.
Simulation results that minimize the sum of squared
acceleration are shown in Table 1. Here, T =
=

g

x

g

g

Figure 1: Trajectories of vehicle body1[s]; H = 0:2[m]; L = 0:2[m];  = 30[deg], and d = 0.
Figure 1 shows the obtained body trajectories forthe conventional sway compensation trajectory, theexpansion in the longitudinal direction, and the longitudinal and vertical direction, respectively. In Fig.1,
the upper gure shows the trajectories projected on
the ground (x-y plane), and the lower gure shows
the trajectories projected on the x-z plane from thelateral direction in which the vertical axis is magnied 20 times.
From these gures, it is veri ed that the sum of thesquared acceleration can be reduced by swaying not
only in the lateral direction but also in the longitudinal
and vertical directions.

2.5 Computer simulation using the dynamic motion simulator, ADAMS
To verify the energy eÆciency of the 3D sway compensation trajectory derived in section 2.4 in the actual
robot system, the computer simulation using the dynamic motion simulator, ADAMS, is carried out.
The con guration of degrees of freedom, weight, etc.

Leg 2(a) Rotation of body(b) Translation of body(c) Vertical motion of swing legs(d) Horizontal motion of swing legs

Leg 1
Joint 2
Leg 3

Joint 1
Joint 3

Leg 4

Figure 3: Four attitude control methods

Figure 2: Simulation model for ADAMS
Table 2: Comparison of energy consumption
laterallateral andlateral,only

longitudinallongitudinal,

straight

E [J]

142.0

114.6

108.6

96.8



2.35

1.90

1.80

1.60

and verticalof a quadruped walking vehicle model for computer
simulation is the same as the TITAN-VIII [11] developed in our laboratory.
Figure 2 show the simulation model. The sum of
power consumption at each joint, E, and speci c resistance, , [6] are shown in Table 2. In the simulation,
the walking cycle is 1 [s], walking speed is 0.2 [m/s]and duty factor is 0.5. The columns show the resultsof the conventional sway compensation trajectory, thetrajectory including lateral and longitudinal sway, thetrajectory including lateral, longitudinal, and verticalsway, and straight line with no sway control. The
trajectories that minimize the sum of squared acceleration derived in section 2.4 are used for the 3D sway
compensation trajectories. Note that in case that the
body moves on a straight line with no sway control,
the body attitude cannot be maintained to be parallelto the ground, and the swing leg touches the groundunexpectedly.
From these results, power consumption and speci cresistance can be improved by the 3D sway compensation trajectory that minimizes the sum of squared
acceleration.
3

Adaptive attitude control

As mentioned above, in the environment where theunknown roughness or inclination exists, dynamicallystable walking is diÆcult using only the feedforward
gait control such as the 3D sway compensation trajec-

tory. In addition, for example, when an extended trot
gait is applied, the body attitude sometimes becomes
unstable and oscillates due to the dynamic e ect of
the recovering motion of the swing legs [4]. Therefore,
a feedback control system using mounted attitude sensors, gyroscope sensors, etc. which adaptively corrects
body attitude are required. In this section, we propose
the attitude control method during 2-leg supporting
phase using the body translation and rotation, andswing leg waving motion.

3.1 Attitude control methods andcomputer simulation
To produce the required moment for attitude recovery
in the two-leg supporting phase, the method using rotation of the body along the diagonal line between the
support legs as shown in Fig.3(a) has been proposed[16]. The required moment for attitude recovery, however, can be produced by the translation of body position as shown in Fig.3(b). Furthermore, though therecovery motion of swing legs has been considered as
disturbance that induces the oscillation of body [4], by
controlling the recovery path appropriately, swing legs
can be used for the damping control of body attitude.
From the above discussion, four attitude control methods as shown in Fig.3 are considered in this paper.
(a) Rotation of body along the diagonal line between
the support legs.
(b) Translation of body along the direction perpendicular to the diagonal line between the support legs.
(c) Vertical motion of swing legs during recovery.
(d) Horizontal motion of swing legs during recovery.
First, each method is simpli ed as a three-link model
corresponding to a support leg, a body, and a swing
leg as shown in Fig.4, and motion equations of eachmodel and optimum linear regulators are designed torepress the oscillation of the body. Fig.5 shows ex-

Link 3

φ1 φ
2Link 2

φ1

Table 3: Comparison of power consumption for attitude control

x

Joint 2
Link 3

Joint 1

Joint 2
Joint 1

Link 1(a) Rotation of bodymethodabcdsum of power [w]

0.74

12.02

1.22

1.44

(b) Translation of body

φ1

φ1

Joint 2
φ2

φ2

Joint 2

Attitude sensor

Joint 1
φ2φ2(c) Vertical motion of swing legs

Joint 1(d) Horizontal motion of swing legs

Figure 4: Analysis models
40

φ 1 [deg.]

0

-20

0

2

4
6
Time [sec.]

8

-40

10

80

20

60

10

x [mm]

φ 2 [deg.]

Gyrosensors

20

φ 1 [deg.]

10
8
6
4
2
0
-2

40
20

4
6
Time [sec.]

8

10

0

-20
2

4
6
Time [sec.]

8

0

10

(a) Rotation of body2

4
6Time [sec.]

810(b) Translation of body
10
8
6
4
2
0
-2

φ 1 [deg.]

φ 1 [deg.]

10
8
6
4
2
0
-2

2

-10

0
0

0

0

2

4
6
Time [sec.]

8

10

0

2

80

60

60

φ 2 [deg.]

φ 2 [deg.]

80

40
20
0

4
6
Time [sec.]

8

10

40
20
0

0

2

4
6
Time [sec.]

810(c) Vertical motion of swing legs

0

2

4
6
Time [sec.]

810(d) Horizontal motion of swing legs

Figure 5: Simulation results
amples of computer simulation of the designed optimum linear regulators when the initial conditions are1 = 5[deg:],2 = 0[deg:], and x = 0[deg:]
From Fig.5(a) using the rotation of body, the bodyhas to be inclined up to 40 [deg.] toward the inclination direction to recover the inclination of the support
leg. Fig.5(b) using the translation of body shows thatmaximum body movement to recover the inclinationof the support leg is 0.2 [m] Though this body motion
can be executed by TITAN-VIII, the inclination of the
support leg becomes vibrational. Next, in Fig.5(c)and (d), the maximum angles of the swing legs become 80 [deg.] and 70 [deg.], respectively. Thus, it isdiÆcult to stabilize the body attitude using the e ectof vertical and horizontal motion of the swing legs only
because of the limitation of the actual movable joint
angles.

Figure 6: 4-legged walking robot, TITAN-VIII
To compare the energy eÆciency for these methods,
the sum of power consumption was calculated. Table 3 shows the comparison of power consumption foreach method. The method (a) was the least power
consumption. On the other hand, the method (b) was
the worst and it needed ten times larger power consumption than method (a).

3.2 Damping control experiment in
two-leg supporting phase
The damping control experiment using four attitudecontrol methods proposed in Section 3.1 was carriedout with the quadruped walking robot named TITANVIII shown in Fig.6. This robot is equipped with acomputer board (Pentium 200MHz, Japan Data System), AD/DA boards, Ethernet card, silicon disk, 3axes attitude sensor, (Maxcube, Japan Aviation Electronics), and two gyrosensors (Gyrostar, Murata).
In the experiment, the body of TITAN-VIII standing
with two support legs was tilted by an external force
applied to the body by pushing by hand. The body's
attitude return to the stable state was measured foreach control method after the hand is released.
The ankle of TITAN-VIII is restricted mechanicallyto let the sole be parallel to the body. Thus, as shownin Fig.7, the body attitude returns to the stable state
without an attitude control if the inclination angle issmaller than about 8 [deg.]. The moment for the recovery of body inclination is produced by the soles.
For the purpose of increasing the dynamic e ect of the

6

15
10
5
0
-5
-10
-15
0

6

15
10
5
0
-5
-10
-15
0

20

φ 1 [deg.]

10

φ 1 [deg.]

φ 1 [deg.]

0

-10
-20
0

4
6
Time [sec.]

8

10

6
4
2
0
-2
-4
-6

φ 2 [deg.]2

Figure 7: Experimental result (no sensor)

1

2

3
4
Time [sec.]

5x [mm]

15
10
5
0
-5
-10
-15
0

0

1

2

3
4
Time [sec.]

5(a) Rotation of body

Figure 8: Recovering path of swing legs
swing legs to the body, the swing legs are stretchedlaterally in the middle of the return path as shown in
Fig.8(b) and the inertia of the legs is increased.
Inclination angle of the support leg along the diagonalline between the support legs, 1, and control variables 2 and x for each control method are shown in
Fig.9. Here, 2 in Fig.9(a) is the body rotation angle, x in Fig.9(b) is the body displacement, and 2
in Figs.9(c) and Fig.9(d) is the angle of joint 2 inFig.4 calculated from the amount of swing motion.
Fig.10 shows the damping control experiment using
the vertical motion of the swing legs. In this experiment, the swing legs are swung up during the recovery of body attitude. From the experimental resultsin Fig.9(a) using the rotation of body, the swing legof the leaning side contacted the ground because thebody was tilted more and more, and large body vibration was generated by the reaction force. Next, forthe method using the translation of the body shown in
Fig.9(b), though the body attitude was vibrational, it
nally converged to horizontal. From the comparisonof Fig.9(c) and Fig.7, which are the results for thecontrol method using vertical motion of the swing legs
and without an attitude control, performance of convergence was clearly improved by the dynamic e ectof swinging. However, the swing width of the swing
leg is limited in the joint movable area, and thus, recovery from a large tilt angle to horizontal is diÆcult
using only this method. On the other hand, Fig.9(d)which shows using the horizontal motion of the swing
legs indicates the convergence performance is hardly
improved. This is because the displacement of actual246Time [sec.]

8

10

10

2

4
6
Time [sec.]

8

10

10

15
10
5
0
-5
-10
-15
0

2

4
6
Time [sec.]

810

φ 1 [deg.]2

46Time [sec.]

8

5
0
-5

-10

10

φ 2 [deg.]

φ 2 [deg.](a) Recovering path is perpendicular (b) Recovering path is inclinedwith respect to ground.
to ground

8

15
10
5
0
-5
-10
-15
0

10

34[deg.]4
6Time [sec.](b) Translation of bodyφ 1 [deg.]

15
10
5
0
-5
-10
-15
0

2

0

2

4
6
Time [sec.]

8(c) Vertical motion of swing legs(d) Horizontal motion of swing legs

Figure 9: Experimental results of attitude control forslow trot gait

Figure 10: Experiment of attitude control using swing
legs
links was smaller than the case using vertical motionof the swing legs, and the dynamic e ect is small.
These results suggest that the attitude stabilization
performance might be the highest by combining thevertical motion of the swing legs and translation of
the body. Fig.11 shows the experimental result whenthese two methods are simply superimposed. In comparison with Fig.11, Fig.7 and Fig.9(b), both convergence performance and stability are improved.
4

Dynamicallystablewalkingexperiment with TITAN-VIII

The dynamic trot gait control method, which employs
feedforward control using the 3D sway compensation
trajectory and feedback control using vertical motion

20
10x [mm]

φ [deg.]
1

15
10
5
0
-5
-10
-15
0

0

-10
2

4
6
Time [sec.]

8

10

4

8

10

-20
0

2

4
6
Time [sec.]

8

10

φ [deg.]
2

10
5
0

-5

-10

0

2

6

Time [sec.]

Figure 11: Experimental result (Combination of translation of body and vertical motion of swing legs)of the swing legs and translation of body, was applied
to TITAN-VIII, and the walking experiment on roughterrain was carried out.
In the experiment, TITAN-VIII walked with the dynamically stable trot gait in an environment wherean unknown and leaning step exists, and the attitude
stabilization performance was examined. Fig.12 is aseries of photos of the experiment, and Fig.13 shows
the inclination angle of the support leg around the
diagonal line between the support legs. In this experiment, the duty factor is 0.5, the walking cycle is 10[s],and the walking velocity is 0.02 [m/s]. The photos
on the left in Fig.12 show the results using the 3Dsway compensation trajectory and the proposed attitude stabilization control. The photos on the rightshow the results using the 3D sway compensation trajectory only. Fig.14 shows the return path of theswing legs. The horizontal axis is the walking direction, and the vertical axis is the vertical direction. By
using swing leg control only in the region where theheight of the swing leg from the ground is larger thana speci c height (5 [cm]), the body vibration causedby the contact of the swing leg to the ground is prevented.
From Fig.13, dynamically stable walking with small
attitude uctuation can be performed by the 3D sway
compensation trajectory on a at surface in 0  12[s].
In 1225[s], one of the right legs runs on the step. For
the case without attitude control, the body gradually
inclined and the swing leg contacted the ground unexpectedly as shown in the fourth photo of the rightcolumn in Fig.12. However, for the case with theproposed attitude stabilization control, maximum inclination of the body was about 8 degrees. As shownin Fig.11, if the inclination of the body is smaller thanabout 10 degrees, the body attitude can be recoveredby the proposed attitude control method. Thus, dynamically stable walking was realized even in an en-(a) attitude control(b) no sensor

Figure 12: Dynamically stable walking experiment onrough terrain
vironment where an unknown and leaning step exists,
and the e ectiveness of the proposed attitude stabilization control was con rmed.
5Conclusion

In this paper, the 3D sway compensation trajectory,
an expansion of the conventional sway compensation
trajectory toward longitudinal and vertical motion, is
proposed. The 3D sway compensation trajectory enables keeping ZMP on the diagonal line of the support
legs more eÆciently with less energy consumption.
Next, four adaptive attitude control methods using the body position and swing leg motion control
are proposed, and the damping performance of eachmethod was compared through computer simulationand damping control experiments with TITAN-VIII.
Furthermore, the feedforward and feedback dynamic
trot gait control system that combines the 3D sway
compensation trajectory and the adaptive body position and swing leg motion control is developed and thewalking experiment on rough terrain using TITAN-

[5] S. Hirose,A Study of Design and Control ofa Quadruped Walking Vehicle,Int. J. Robotics
Research,Vol.3,No.2,pp.113-133,1984

4

Inclination [deg.]

0[6] G.
GabrielliandI. von Karman,What price speed?,MechanicalEngineering,Vol.72,No.10,pp.775-781,1950-4
3D sway compensation
trajectory
and attitude control-8-12

3D sway compensation
trajectory only

-16
0

5

10

15
20
Time [sec.]

25

30

35

Figure 13: Body inclination of robot walking dynamically on rough terrain
with vertical motion of swing leg
0.1[7] K. Yoneda, H. Iiyama, and S. Hirose,Skyhook suspention control of a quadruped walking vehicle,Proc. Int. Conf. on Robotics andAutomation,,,pp.999-1004,1994[8] H.Kimura, I.Shimoyama and H.Miura, Dynamics
in the dynamic walk of a quadruped robot, RSJ.
Advanced Robotics, vol.4, no.3, pp.283-301, 1990z [m][9] D. W. Marhefka and D. E. Orin,Gait Planning forEnergy EÆciency in Walking Machines,Proc. Int.
Conf. on Robotics and Automation, pp.474-480,(1997).

Figure 14: Recovering path of swing leg[10] K. Arikawa and S. Hirose, Study of Walking Robot for 3 Dimensional Terrain,Proc. ofIEEE/RSJ Int. Conf. on Intelligent Robots andSystems '95, pp.703-708, (1995).

VIII is carried out. Results of the experiment showedthat this control methodology was very e ective forpractical use and could make dynamically stable walking of walking vehicle possible on rough terrain.

[11] K. Arikawa and S. Hirose,Development of
Quadruped Walking Robot TITAN-VIII,Proc. ofIEEE/RSJ Int. Conf. on Intelligent Robots andSystems '96,,,pp.208-214,1996

00

0.1
x [m]

0.2

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