AnApproachtoStableWalkingoverUnevenTerrainUsing …downloads.hindawi.com/journals/jcse/2011/783741.pdfrobot leg inspired from a stick insect, the work presented in [25] has been reviewed

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2011, Article ID 783741, 12 pagesdoi:10.1155/2011/783741

Research Article

An Approach to Stable Walking over Uneven Terrain Usinga Reflex-Based Adaptive Gait

Umar Asif1, 2 and Javaid Iqbal1, 2

1 National University of Sciences and Technology, Islamabad 44000, Pakistan2 Mechatronics Engineering Department, College of Electrical & Mechanical Engineering, Peshawar Road, Rawalpindi 46000, Pakistan

Correspondence should be addressed to Umar Asif, [email protected]

Received 9 February 2011; Revised 25 April 2011; Accepted 25 May 2011

Academic Editor: Zhiyong Chen

Copyright © 2011 U. Asif and J. Iqbal. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper describes the implementation of an adaptive gait in a six-legged walking robot that is capable of generating reactivestepping actions with the same underlying control methodology as an insect for stable walking over uneven terrains. The proposedmethod of gait generation uses feedback data from onboard sensors to generate an adaptive gait in order to surmount obstacles,gaps and perform stable walking. The paper addresses its implementation through simulations in a visual dynamic simulationenvironment. Finally the paper draws conclusions about the significance and performance of the proposed gait in terms of trackingerrors while navigating in difficult terrains.

1. Introduction

In the field of motion planning for legged robots, a largebody of research work is inspired from insects due to the factthat they are responsive, adaptive and possess sensory sys-tems to generate reactive walking patterns [1]. In the field ofbiomimetic robots, a large volume of work [2–6] exists whichdeals with their modeling and design inspired from leggedcreatures found in nature.

It has been well understood through various researchstudies that mammals and walking insects posses inherentcapabilities to choose stable and secure walking patterns inresponse to external disturbances when the terrain becomesuneven to keep up a continuous gait. This walking patternis characterized by the sequential motion of legs and coor-dinated advancement of the body which makes them appro-priate and suitable for replicating in walking robots for thereal world. A wave gait is the typical gait which is consideredto possess intrinsic terrain adaptability. On the other hand, atripod gait [7] is well known for walking with high mobilitydue to its fast gait speed and greater static stability.

1.1. Literature Review and Related Work. In the field of navi-gation in difficult terrains, a large volume of research workdeals with the development of terrain adaptation control

algorithms to realize efficient and stable locomotion [8–10].Among few works, a motion planner based on a distributedneural network controller [11], gait generation methodsusing energy-based stability margins to understand reliablelocomotion [12], fault detection schemes [13], developmentof fault tolerant cyclic gaits [14], and gait planning basedupon kinematic control of hexapod robots [15] are someinvestigations with excellent results.

Earlier robot designs such as [16] focused on the devel-opment of behavior based strategies to formulate the robot-environment interactions in order to design adaptive walkingbehaviors using sensory information. Later on, studies suchas [17–19] investigated the design of robotic systems withtheir prime objective to realize the walking behaviors of in-sects in real walking machines. Thus, the objective of theseresearch studies has always been an effort to devise schemesto define leg movements which replicate those of actual in-sects in order to realize biologically inspired walking. Curseworked on such gait generation methodologies by investi-gating the walking behaviors of stick insects [20, 21]. Anappreciable contribution in this context was made by theresearchers Hess and Buschges [22] and Ekeberg et al. [1],who studied the insect neurobiology and investigated thatthe stick insects control their leg movements through sensoryoscillators in their joints and thoracic ganglia. Therefore,

2 Journal of Control Science and Engineering

x axis

y axis

Pitch (ψ)

Roll (ϕ)

Yaw (γ)

Heave

Surge

Sway

6

2

1

5

4

z axis

3

Figure 1: Pro engineer model of hexapod robot.

their joint movements in a particular leg are influenced bysensory signals from the brain as well as from the joints inother legs to generate reactive stepping patterns. Since, thepatterns are reactive the resulting locomotion is responsiveand adaptive that allows the insect to conform to its under-lying terrain. Such neurobiological-based gait generationmethodologies have been realized using computer simula-tions [1] with one and two legged robots [23]. A closelyrelated study [24] deals with an excellent implementationof such a neurobiological leg control system identified inthe thoracic ganglia of stick insects using a hexapod robotby modeling biologically plausible sensory pathways for pat-tern generation. The work [24] describes these pathways us-ing advanced algorithm like “Elevator Reflex” to surmountobstacles and “Searching Reflex” to surmount gaps and holesin order to improve navigation over rough terrains with ex-cellent results.

While these research investigations are sufficient to dem-onstrate the success of adaptive locomotion, most of thework deals with implementation on either smooth flat sur-faces or structured environments only. In natural terrains,the formation of impulsive forces during the impact (robot-ground interaction) giving rise to disturbances, affects thewalking gait and offers a great challenge to realize locomotionwith adequate stability and performance. Therefore, in con-trast, this paper aims to describe a biologically inspired gaitgeneration method for walking over uneven terrains with anability to traverse through obstacles and gaps with minimaltracking errors.

The first part of the paper describes our six-legged robotin terms of its modeling and design. The second part of thepaper describes our proposed foothold reflex control methodto generate a reactive and adaptive gait, able to plan footholdsand appropriate leg sequences to change support points andtransverse a rough terrain.

2. Robot Modeling and Design

2.1. Physical Model. The mechanical structure of our robotas shown in Figure 1, consists of six identical legs placed

Motionenvelope

Foothold

Coxa

Femur

TibiaLSF

Figure 2: Structure of an individual leg.

z-axis

1

3 6

4

52

Reachableworkspace

Dexterousworkspace

x-axis

Figure 3: Working envelopes of robot legs.

around the main body in a biologically inspired configura-tion to enable omni-directionability and enhance maneu-verability. In order to describe the kinematic model of therobot leg inspired from a stick insect, the work presented in[25] has been reviewed. There are four functional segmentsof the leg of a stick insect: the coxa (c), the femur ( f ), thetibia (t), and the foot. For simplicity, a stick insect leg can bemodelled as a serial manipulator with three hinge joints byneglecting the joint of the foot and the foot itself, resultingin three degrees of freedom as investigated in [25]. Thus, theleg of our robot consists of three links namely: coxa, femurand tibia, interconnected through three revolute joints. Fromthe body towards the foot, the joints are called body-coxajoint (θc), coxa-femur joint (θ f ), and femur-tibia joint (θt).Figure 2 portraits the kinematic configuration of the leg interms of its links and their motion envelope.

2.2. Reachable Workspace. If all the joints of a leg returnappropriate or desirable angles for a reference pose in agiven space, then that pose is considered to be a subset of

Journal of Control Science and Engineering 3

manipulator’s working space. In this context, analytic anddiagrammatizing methods are typically used to work out therobot’s working space. On the other hand, the numericalmethods have advantages such as fast speed, high precision,easy operation, large application range, and adaptability tovarious types of robotic structures. As a consequence, it iswidely used by researchers as investigated in [26, 28].

Figure 3 shows the working envelopes of all the legsattached to the main body as a reachable workspace repre-sented by solid annulus regions. Each leg has a reachable areain the form of a sector as defined in [29], where adjacent orneighboring areas cause overlap of each other’s region. Thus,

for avoiding the interference problem, a dexterous workspaceis determined contained inside the reachable workspace ofeach leg as shown in the Figures 2 and 3. The dexterousworkspace is an area on the plane mapped on the terrainwithin which a leg can be placed effectively anywhere whilesatisfying the static stability.

2.3. Kinematic Model. The kinematic model of our robotconsists of forward and inverse kinematic equations formu-lated using Denavit-Hartenberg convention as investigated in[30], further described by (1).

FootxGi = cos γ cosϕPx f t

Bi − cosγ sinϕPy f t

B

i+ sin γPz f t

Bi ,

FootyGi =

(cosψ sinϕ + sinψ sin γ cosϕ

)Px f t

Bi +

(cosψ cosϕ− sinψ sin γ sinϕ

)Py f t

B

i

− sinψ cos γPz f tBi ,

FootzGi =

(sinψ sinϕ− cosψ sin γ cosϕ

)Px f t

Bi +

(sinψ cosϕ + cosψ sin γ sinϕ

)Py f t

B

i

+ cosψ cos γPz f tBi ,

θci = ATAN2(

FootzGi , Footx

Gi

),

θ f i = ATAN2(ti,−Footy

Gi

)

+ ATAN2

⎛

⎜⎜⎝

⎛

⎜⎜⎝

√√√√√−FootyGi

2+ ti2 −

(t2i + l2f + Footy

Gi

2 − lt2)

2× l f

2⎞

⎟⎟⎠,

(ti2 + l f

2 + FootyGi

2 − lt2)

2× l f

⎞

⎠,

θti = ATAN2((−Footy

Gi cosθ f − sin θ f ti

),(ti cos θ f − l f − sin θ f Footy

Gi

)),

ti = FootxGi cos θc − lc + Footz

Gi sin θc,

CoMGi =

∑mi × pCoM

Gi∑

mi,

xiZMP =

n∑

i=1mi

(xi(yi + gy

)− xi yi

)

n∑

i=1mixi

(yi + gy

) ,

ziZMP =

n∑

i=1mi

(zi(yi + gy

)− ziyi

)

n∑

i=1mizi

(yi + gy

) ,

mi = mass of the link i;

xi, yi, zi = position vector of link i;

xi, yi, zi = accelerations of link i;

gy = gravity vector;

CoMGi = center of mass of link i;

[xiZMP ziZMP] = zero moment point position vector;[

FootxGi Footy

Gi Footz

Gi

]= foothold position vector;

[θci, θ f i, θti

]= qi = joints rotation angles.

(1)


Climbing up a step

Crossing a gap

Reflex-based foothold planningNormal walkingPerceived heights of the terrain

Figure 4: Climbing a step (top) and crossing gaps (bottom)scenarios to present the foothold planning using the proposedFoothold Reflex Control method. Normal walking behavior is mo-mentarily changed upon sensing an obstruction. Once the obstruc-tion is removed (e.g., loss of contact with the obstruction), thenormal motions are resumed.

In order to ensure the performance of a walking gait,the performance measures are typically evaluated in terms ofgait stability margins using zero moment point (ZMP) basedstability criterion. Therefore, it is necessary to consider anddefine the ZMP-based stability criterion. The definition ofZMP adopted in this paper is as described in [31, 32], whichis: ZMP is the projected point of the resultant forces of thegravity and the inertia forces acting on the robot to theground, to which the moments of the resultant forces equalto zero. To ensure dynamic stability, the ZMP must lie withinthe Support Polygon on Surface (SPOS) at all the times anddoes not lie on the edges of the SPOS. SPOS is the convexhull (polygon) of the footholds in contact with the ground.If the ZMP reaches the edge of the SPOS, the walking gait willdevelop a high tendency to become unstable and may resultin tumbling of the robot on the ground. The position of ZMPis derived from [31, 32], as described in (1).

3. Terrain Adaptation

Terrain exploration is considered to be an important aspectin motion planning of walking robots that has been previ-ously discussed in more detail in [33–40]. Once a terrainmap is available, a foothold selection method can be imple-mented. In this paper, the terrain knowledge is supplied tothe robot offline in form of terrain’s latitude, longitude, andaltitude information. The objective is to follow a referencepath on a known geographical location using its latitude,longitude, and altitude information. During walking, therobot uses sensor-based traction control to perform straightline walking.

3.1. Gait Generation. The gait modeled here constitutes threephases: swing, drop, and stance as described in (2). Each

phase is characterized by its unique combination of leg andjoint motions coordination. Swing is identified by protrac-tion of body-coxa joint, levation of the coxa-femur joint,and extension of the femur-tibia joint. This combinationserves to lift the foothold from FootyGi to FootyGi+1 and swayit in the direction of motion to acquire the next footholdposition (Footx

Gi+1, Footz

Gi+1) in air. Drop phase lowers the leg

until contact with ground is verified from foothold’s touchsensor notification. During stance phase, the involved legsboth support and propel the body in the direction of desiredmotion. Joint trajectories (qi, qi, qi) are computed usinglinear splines with parabolic blends as described in (2).

Swing = f(qi)(

leglift, legstroke),

0 < leglift ≤ 15 cm,

0 < legstroke ≤ 10 cm,

Stance = f(qi

)(duty factor

(β), legstroke

),

leglift = FootyGi

Δ−→ FootyGi+1,

legstroke =⎧⎪⎨

⎪⎩

FootxGi

Δ−→ FootxGi+1,

FootzGi

Δ−→ FootzGi+1,

Gait Speed = Si = δi+1 − δiti+1 − ti ,

β = tstance

tcycle,(βωswing + βωstance = 1

),

linear spline

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

qi = qi+1 +(qi+2 − qi+1

)ti,

qi = qi+2 − qi+1,

qi = 0,

parabolic blend

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

qi = qi+1

+(qi+2 − qi+1

)(ti − tblend)

+12qi+2tblend

2

qi = qi+2 − qi+1 + qi+2tblend

qi = qi+2

tblend = ti −(

12ti+1 + (ti+2 − ti+1)

)

ωswing = swing frequency;

ωstance = stance frequency;

tcycle = total cycle time;

tstance = stance time;

δi = distance travelled.

(2)


Leg sensorynetwork

Kinematics engineWalkingpattern

generation

Waypointnavigation

Foothold reflex control(FRC)

(1) Posture control(2) Traction control

Path generation Leg and joint trajectories Actuator commands

Jointactuators

Trackingerrors

Joint controlcommands

Sensors feedback

commandsBody attitude

Figure 5: Overall control system framework.

Figure 6: Pictorial representation of robot climbing steps of variable heights using Foothold Reflex Control (FRC) method.

As described earlier, a leg sensory network is establishedfor each leg that defines a reflex system to inform the maincontroller that a disturbance requiring a behavior otherthan normal walking has been encountered. Upon perceivingsuch an abnormal behavior, the controller generates sensoryinformation based upon disturbance estimation during theimpact (leg-environment interaction) that alters the normalsequential motion of joints to adaptive and emergent. Thisreflex-based gait generation method is termed as footholdreflex control (FRC), further explained in the followingSection 3.2.

3.2. Foothold Reflex Control (FRC). The Foothold ReflexControl (FRC) method aims to step over surmountable ob-stacles, sizeable gaps and holes using online traction control.The method makes an estimate of the terrain by using thefoot contact point information from the leg sensory network.If all the contact points are at the same height, the robot isconsidered to be walking on a flat terrain. In such a case, therobot uses a short leglift and a large legstroke to increase itstravel speed.

Upon detecting a step or a surmountable obstacle usingthe sensor information, the FRC initiates the behavior otherthan normal walking that alters the motions of the involvedleg to retraction to a safe zone (an attempt to minimize the

risk of snagging on the obstacle), levation in air (an effortto acquire a position higher than the perceived height of theobstacle), and swing to its next foothold planned within thedexterous workspace of the involved leg. In parallel, FRCuses an independent attitude controller to keep the robot’sbody leveled above the terrain with online adjustments whileclimbing and traversing over the gaps using a sensor-basedtraction control. This phenomenon is further illustrated inFigure 4 using dynamic simulation results in order to validatethe success of the proposed method.

Foot interaction with the ground is modeled here basedon a general coulomb friction model [41, 42], further de-scribed in (3).

⎡

⎣FootxGi+1

FootzGi+1

⎤

⎦ =⎡

⎣FootxGi

FootzGi

⎤

⎦ +

⎡

⎢⎢⎢⎣

∫∫ i+1i

fx i +miximi

∫∫ i+1i

fz i +mizimi

⎤

⎥⎥⎥⎦

,

Fti ≤ μNi,

√fx

2i + fz

2i − μNi < 0,

(3)

where Fti is the total tangential force between the contactpoint and the terrain, μ is the combined coefficient of ground


Figure 7: Pictorial representation of robot descending steps of variable depths using Foothold Reflex Control (FRC) method.

Figure 8: Pictorial representation of robot traversing through gaps of variable gap lengths using Foothold Reflex Control (FRC) method.

1

3

2

7 m

7 m

7 m

7 m

Reference path

S

Figure 9: Terrain created using heightfield maps in a dynamic sim-ulation environment.

static and dynamic friction, and Ni is the total normalreaction force to prevent the penetration of the contact point.The coefficients of static and dynamic friction are takenas a combined coefficient of ground friction for simplicity,calculated online using the tangential and normal reactionforces estimated using leg sensors data. The overall controlframework is further illustrated in Figure 5.

3

21

Waypoint 2 Waypoint 1

Start

Waypoint

point

3S

Figure 10: Pictorial representation of the path traced by the robotwithout using the FRC method.

3.3. Gait Performance Measures. To be able to generate anoptimal gait, it is necessary to determine the performance ofthe proposed gait generation. In this paper, the performanceof the gait is chosen to be measured on the traction of therobot and its stability. As described earlier, the stability of therobot is determined online by evaluating the position of theCoM and ZMP relative to the SPOS.


0 200 400 600

−100

0

100

200

300

400

500

600

700

Distance Z (cm)

Dis

tan

ceX

(cm

)

Center of massZero moment point

WaypointsSupport polygon on surface

Plot of CoM and ZMP with support polygon on surface

Average speed: 0.33 m/s, time taken: 238.73 s

(a)

−500 −500

0 0

500500

10001000

−50

0

50

100

150

Distance Z (cm)

Distance X (cm)

Dis

tan

ceY

(cm

)

Center of mass

Zero moment point



(b)

Figure 11: Plot of CoM and ZMP with SPOS without using the Foothold Reflex Control method.

0 200 400 600 800 1000 1200

Plot of tracking errors without reflex control

−5

0

5

Iteration (i)

Heading error profile

Rot

atio

nal

erro

r(d

eg)

(a)

0 200 400 600 800 1000 1200−100

−50

0

50

Iteration (i)

Displacement error profile

Tran

slat

ion

aler

ror

(cm

)

(b)

Figure 12: Tracking errors of robot locomotion without using the FRC method.

700

600

500

400

300

200

100

0

0 200 400 600

−20

0

20

40

60

80

Distance Z (cm)

Footholds mapping on terrain without reflect control

Dis

tan

ceX

(cm

)

800

Figure 13: Terrain intercepted by the robot without using the FRCmethod.

4. Simulation Results

Initial simulation tests were performed to realize the successof the FRC method to traverse through steps and gaps as

3

2 1

Waypoint 3

Waypoint 2 Waypoint 1

Start point

S

Figure 14: Pictorial representation of the path traced by the robotusing the proposed FRC method.

illustrated in Figure 4. Pictorial representation of the robotclimbing and descending steps is further shown in Figures 6and 7 while traversing over gaps is pictorially illustrated inFigure 8.

4.1. Obstacle Crossing Testing. During these tests, the robotwas able to walk with a maximum speed of 5 cm/sec.


0 200 400 600−100

0

100

200

300

400

500

600

700

Distance Z (cm)

Dis

tan

ceX

(cm

)




Average Speed: 0.32 m/s, time taken: 214.59 s

(a)

−500 −500

0 0

500500

10001000

−50

0

50

100

150

Distance Z (cm)

Distance X (cm)

Dis

tan

ceY

(cm

)




(b)

Figure 15: Plot of CoM and ZMP with SPOS using the proposed Foothold Reflex Control method.

700

600

500

400

300

200

100

0

0 200 400 600

−20

0

20

40

60

80

Distance Z (cm)

Dis

tan

ceX

(cm

)

Footholds mapping on terrain with reflect control

Figure 16: Terrain intercepted by the robot using the FRC method.

The robot started with control inputs (leg-lift: 9 cm and leg-stroke: 5 cm) and easily surmounted the initial steps (stepheights: 3 cm, 5 cm, 2 cm, 6 cm, 7 cm) without much modifi-cation to the planned control variables. Upon perceiving ob-struction (step height: 10 cm), the leg retracted 2 cm, levated6 cm, and extended with a leg-stroke of 7 cm as a conse-quence of the Foothold Reflex Control method intervention.As this leg-lift of 6 cm was still insufficient to clear the ob-stacle, the contact switch again detected the surface andthe FRC sequential loop re-executed. The robot surpassedthe obstruction eventually with a leg-lift of 12 cm and leg-stroke of 7 cm. Similarly, upon detecting obstruction (stepheight: 15 cm), the leg was elevated 20 cm which was themaximum achievable leg-lift within its dexterous workspaceto surmount obstacle. The robot successfully steered throughthe rest of the descending steps using the same methodology.Raised surfaces of variable widths and variable heights wereplaced over an uneven terrain perpendicular to the robot’spath of motion in order to test the ability of the controller innavigating through gaps and holes. The first gap was approx-

imately 5 cm deep and 7 cm across, while the second gap was7 cm deep and 9 cm across. Success was observed in most ofthe simulation trials.

4.2. Walking over Uneven Terrain Testing. In order to evaluatethe performance of the proposed FRC method for navigationin irregular terrains, a terrain is setup using dynamic simu-lation environment provided by Microsoft Robotics Devel-oper Studio. The terrain constitutes an uneven surface-meshcreated using heightfield maps to model elevations and de-pressions which can offer significant disturbances whilewalking, as shown in Figure 9. This terrain offers a big chal-lenge in comparison to flat surfaces in terms of stable loco-motion because the elevations and depressions subject therobot to a large deal of disturbances in both lateral and an-gular directions.

In the first simulation test, the FRC method was not used.Figure 11 shows the locomotion of the robot in terms of itscenter of mass (CoM) and zero moment point (ZMP) pro-files with the support polygons on surface. As apparent fromthe figures, when the FRC method was not used, the robottends to diverge from the straight line paths between thedesired waypoints, further illustrated pictorially in Figure 10.The heading and displacement errors are shown in Figure 12,where positive error corresponds to a divergence along theleft side of the reference track while the negative portioncorresponds to a divergence along the right side of the refer-ence track. The results show a maximum translational errorof ±52 cm and a maximum rotational error of ±3 degreesapproximately. The terrain negotiated by the robot duringwalking is shown in Figure 13 as a surface mesh gener-ated using the contact point information. The color bar inFigure 13 represents the height of the terrain along the y axis.

A total of 25 simulation tests were conducted using theproposed FRC method. The simulation results are plotted inFigure 15 which represents the path traced by the robot. Asapparent from Figure 15, both the CoM and ZMP profiles lie


0 1000 2000 3000 4000 5000 60000

1

2

3

4×10−3

Plot of ground reaction forces with reflex control

Iteration (i)

Forc

e(N

)

μNTotal tangential force (Ft)

(a)

0

0.01

Plot of ground reaction forces without reflex control

0 1000 2000 3000 4000 5000 6000

Iteration (i)

0.005

μN

Forc

e(N

)

Total tangential force (Ft)

(b)

Figure 17: A Representation of ground forces in the two simulation tests.

0 1000 2000 3000 4000 5000 6000−15

−10

−5

0

5×10−4 No-slip condition with reflex control

Zero

Ft − μN

Iteration (i)

(a)

0 1000 2000 3000 4000 5000 6000

10

Zero

×10−3 No-slip condition without reflex control

Iteration (i)

−5

0

5

Ft − μN

(b)

Figure 18: Plots of No-Slip condition in the two simulation tests.

inside the Support Polygons on Surface satisfying the dynam-ic stability constraints and the path traced by the robot close-ly matches with the reference track as shown pictorially inFigure 14. The terrain explored by the robot is shown inFigure 16.

Figures 17, 18, and 19 demonstrate a comparative evalu-ation of the locomotion of the robot with and without usingthe proposed foothold reflex control method represented by

Distance

(cm

)

0 200 400 600 800 1000 1200

−0.5

0

0.5

Iteration (i)

(a)

0 200 400 600 800 1000 1200−6−4−2

02

Velocity

(cm

/s)

Iteration (i)

(b)

−500

50

0 200 400 600 800 1000 1200

−1

Acceleration

(cm

/s)2

With reflex controlWithout reflex control

Iteration (i)

(c)

Figure 19: A comparative representation of disturbance estimationwith and without using the proposed FRC method.

blue and red plots respectively. Figure 17 shows a compar-ative representation of the estimated ground reaction forces.A close inspection of Figure 17(a) reveals that the total tan-gential force remains lesser than the normal reaction forcetimes the combined coefficient of ground friction whichvalidates the satisfaction of stability criterion throughoutthe robot’s locomotion, further verified by the blue plot inFigure 18(a). Further evaluation of the simulation resultsreveals that the disturbances have significantly reduced whenusing the FRC method as shown in Figure 19. The attitude


1400−5

0

5Plot of tracking errors with reflex control

Rot

atio

nal

erro

r(d

eg)

Heading error profile

0 200 400 600 800 1000 1200

Iteration (i)

(a)

−10

−5

0

5

Tran

slat

ion

aler

ror

(cm

)

Displacement error profile

14000 200 400 600 800 1000 1200

Iteration (i)

(b)

Figure 20: Tracking Errors using the proposed FRC method.

controller efficiently tracked the robot posture while walkingas shown in Figure 21. Average speed of the robot was re-duced from 0.33 m/sec to 0.32 m/sec using the proposed re-flex control method however, the robot completed the coursein relatively lesser time (3.5 mins as compared to 4 minswhen not using the FRC method) with minimal trackingerrors. The results reported in Figures 19 and 20 are consid-ered satisfactory given the quality of the kinematic model andthe precision of software sensors provided by the open dy-namics engine.

5. Conclusion

The robot presented here is a hexapod to walk using a bio-logically inspired leg control system over an uneven terrainusing a sensor-based traction control. Sensory network in aleg is responsible for influencing the direction and motion ofeach joint such that an evolving, adaptive, and reactive step-ping pattern is realized through leg-environment interaction.Simulation tests that evaluated this gait model showed thatthe robot could clear raised and lowered obstructions overuneven surface which were within and beyond the nominalgait control variables (leg-lift and leg-stroke), as shown bythe obstacle crossing testing results. The simulation testingof the proposed foothold reflex control method showed sig-nificant improvement in the robot’s ability to track a refer-ence path over an uneven terrain. The gait stability was en-sured using the center of mass and zero moment point stabil-ity criterion. The novelty of the proposed navigation methodthus lies in the successful implementation of a reflex-basedgait generation with an ability to perform obstacle crossingand path following in irregular terrains with adequate

1

12

23

3

Waypoint 1

Waypoint 1

Waypoint 2

Waypoint 2

Waypoint 3

Waypoint 3 Start

Start

point

S

S

Figure 21: Locomotion of robot in visual simulation environmentto show the body attitude control.

stability and minimal tracking errors. Future work in thisarea will involve improving fusion of sensor data through ad-vanced filtering and disturbance rejection techniques.

References

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AnApproachtoStableWalkingoverUnevenTerrainUsing …downloads.hindawi.com/journals/jcse/2011/783741.pdfrobot leg inspired from a stick insect, the work presented in [25] has been reviewed