The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS13.050

Autonomous Gait Planning for a Hexapod Robot in Unstructured Environmentsbased on 3D Terrain Perception

Xun Chai∗ Feng Gao† Yang Pan‡ Yi-lin Xu§

Shanghai Jiao Tong University Shanghai Jiao Tong University Shanghai Jiao Tong University Shanghai Jiao Tong UniversityShanghai,P.R. China Shanghai,P.R. China Shanghai,P.R. China Shanghai,P.R. China

Abstract— Legged robots have extremely important ap-plications in unstructured environments, e.g. accomplish-ing rescuing and detecting tasks in the earthquake and nu-clear accidents instead of human beings. In such environ-ments, legged robots must have the potential to plan gait-s autonomously based on the site environment without de-tailed instructions from a human operator. In this paper, wepresent an autonomous gait planning method for the hexa-pod robot “Octopus”, which will be applied in unstructuredenvironments. The method is based on the terrain map per-ceived by a 3D vision system. Further, two indices are de-fined to describe terrain conditions. An important part ofthe method is a foothold selection function, which consid-ers the influence of terrain conditions. The detailed walk-ing process of Octopus on the rough terrain is discussedtoo. At last, we apply our method to Octopus, and showthat it allows Octopus to pass through the uneven terrainautonomously.

Keywords: Autonomous gait planning, Hexapod robot, Unstruc-tured environments, 3D terrain map

I. Introduction

Legged robots have excellent terrain adaptability and areable to accomplish tasks, such as opening valves, clearingobstacles, carrying heavy equipment, detecting dangeroussituations in harsh environments instead of human beings.A human operator in a safe place can send simple task in-structions to the legged robot in the field, while it is im-possible to send detailed data to the robot because of therestriction of remote transmission. For this the legged robotmust have the ability to adjust its feet and body to adapt tocomplex terrains autonomously. Some studies have madesignificant progresses in the issue of terrain adaption forlegged robots. The famous quadruped robot Big Dog [1],developed by Boston Dynamics, can pass through roughterrains using the trot gait based on the dynamics balance al-gorithm. RHex [2], [3] is a compliant-legged hexapod robotwhich can traverse rough terrains without complex controlalgorithms. The compliant legs can reduce the impact ofexternal force on RHex and provide it with impressive ter-

∗chaixun@sjtu.edu.cn†fengg@sjtu.edu.cn‡py0330@sjtu.edu.cn§xuyilin@sjtu.edu.cn

rain adaptability. Yasuhiro Fukuoka, Hiroshi Kimura andAvis H. Cohen [4] used a PD controller at the joints of aquadruped robot. The PD controller could construct the vir-tual spring-damper system as the visco-elasticity model ofa muscle, which played an important role in the body stabi-lization and system energy storage. Apart from the bionicsdesign in the mechanism, some researchers have also devel-oped a novel control algorithm the central pattern generator(CPG) [5] inspired by the principal of the biological con-trol scheme. The quadruped robot Tekken[6] can walk witha medium walking speed on the irregular terrain based onthe neural system model consisting of a CPG and reflexes.

Most of the related studies satisfy the requirement ofadaption to complex terrains by using the balance controlalgorithms and the special design concept of legs. In re-cent years, due to the vast developments of vision sensorsand force sensors, control methods combined with thesesensors have been developed, which provide legged robotswith the sensing ability. After having a good knowledge ofthe site environment, legged robots can select a safe pathand a set of appropriate footholds initially, then plan thefeet and body motions effectively in order to traverse roughterrains with high stability, velocity and low energy con-sumption. The use of sensors especially vision sensors andforce sensors plays an important role in the robotics field,and is a higher level application of the biological engineer-ing. There has been some work concerning the motion plan-ning for legged robots based on vision sensors. The Little-Dog [7], [8] uses the laser scanning system and the externalmotion capture system to model a high resolution terrainmap around the robot, then the terrain map is processed inquantity. The control strategy of LittleDog includes threeparts, a system that learns optimal footholds choices, a bodytrajectory optimizer and a floating-base inverse dynamic-s controller, which allows the LittleDog to perform a fastlocomotion over the rough terrain. Stephane Bazeille etal. [9] proposed a control scheme for the quadruped robotHyQ, which performed the goal-oriented navigation on theunknown rough terrain by using the inertial measuremen-t data and the stereo vision. The six-legged walking robotDLR [10], [11], [12] can navigate in rough terrains. Thecontrol system of DLR uses the SGM method to build thedigital elevation map, then defines the traversal index andplans the path concerning about the information of legs di-

mension sizes, the body posture and the obstacles distances.In this paper, we propose an autonomous gait planning

method for the hexapod robot Octopus, shown in Fig. 1,based on the site terrain detected by a 3D vision system.The structure of the paper is organized as follows. In sec-tion 2, we present a description of the robot system, includ-ing the mechanism structure of Octopus and the terrain mapmodeling. The detailed gait planning method is proposed insection 3. Section 4 describes the processes and results ofthe experiment. The paper is concluded in section 5.

Fig. 1. The Octopus robot

II. Description of the Robot System

A. PrototypeThe hexapod robot is a six DOFS parallel-parallel mov-

ing platform integrated walking and manipulating, which ismainly designed for handling emergency tasks in hash en-vironments. We call it Octopus, for its moving movementsare like those of a real octopus. Octopus has a hexagonalbody with six symmetrically distributed legs. All the legshave the same mechanism structure and dimension size, soOctopus is isotropic on six leg directions. Every leg hasthree chains, which is a parallel mechanism, shown in Fig.2. The U2P2S2 chain and the U3P3S3 chain have the samemechanism structure and dimension size, each one is con-structed by a universal joint, a prismatic joint and a spher-ical joint. Another chain, the U1P1 chain, which is con-structed by a universal joint and a prismatic joint, is mainlyused to endure the external force. All the prismatic jointsare actuated by motors, the linear movement of the pris-matic joint is achieved by the ball-bearing screw. Every legof Octopus has 3 DOFS in space. In order to perform so-phisticated terrain adaption, a spherical joint Sf surroundedby a spring is proposed, which connects the foot with theleg and allows the foot to rotate ±35◦ along the leg. Thespecial parallel-parallel mechanism design concept not on-ly fulfills the DOF requirement but also provides Octopus

with outstanding walking stability, load capacity and terrainadaption.

U1 Universal joint

U2 Universal joint

U3 Universal joint

P1 Prismatic joint

P2 Prismatic joint

P3 Prismatic joint

S2 Spherical joint

S3 Spherical joint

Sf Spherical joint

Motor

Fig. 2. The leg structure

Octopus will be applied in environments inaccessibleto human beings to perform rescuing and detecting tasks.Considering the restriction of remote transmission, a certaindegree of intelligence is necessary for Octopus to chooseappropriate footholds and plan the gait trajectory. A 3D vi-sion system as a first step towards providing Octopus withthe visual perception is equipped as shown in Fig. 3. In thereal application environment, a human operator sends thetask instruction to the host computer using a remote controlequipment. The remote control equipment communicateswith the host computer via Wi-Fi which is created by thehost computer. The 3D vision system (i.e. a MS Kinect) ismounted at the top of Octopus, which can provide the ob-jects’ distances in the range of the detection area. The 3Dvision system is connected with the host computer via US-B. The host computer sends command instructions to theslave computer, which runs a real-time Linux OS, via Wi-Fi too. The slave computer sends planned data to driversvia EtherCAT, after planning the gait.

Host Computer

3D Vision

System

Ball-bearing

Screw

Ankle

Spring

Foot

Slave Computer

Fig. 3. Octopus with the 3D vision system

B. Modeling of the Grid Terrain MapAccurate 3D coordinates of the terrain around Octopus,

which can be transferred from the depth image captured bythe 3D vision system, are essential for the autonomous gaitplanning. The original 3D coordinates with respect to the3D vision sensor coordinate system need to be transferredin the Octopus coordinate system before planning the gait.For this the relative mounted position and orientation of the3D vision system should be identified. The origins of theOctopus coordinate system and the 3D vision sensor co-ordinate system are both difficult to be measured. So thegeometric relationship between these two coordinate sys-tems, which is represented by an identification matrix R

VT,can hardly be obtained by direct measurements. An indirectmethod is used to solve the identification problem instead.We use the absolute ground as a reference target as Fig. 4shows. The ground position and orientation with respectto Octopus can be computed using the kinematics model-s, and the ground position and orientation with respect tothe 3D vision system can be computed by processing thepoint cloud too. The ground with respect to Octopus canbe transferred in the 3D vision sensor coordinate system bymatrix R

VT, and the transferred ground is called the theoret-ical ground. The ground detected by the 3D vision systemis the measured ground. R

VT can be calculated based on thecoinciding relationship between the theoretical ground andthe measured ground.

Fig. 4. The identification method

The raw terrain map is constituted by large amounts ofpoint cloud data (have been transformed into the Octopuscoordinate system by R

VT), which takes a long time for thecomputer to restore and process. For this reason, a gridterrain map is used to decrease the amount of data and in-crease the speed of map updating and processing. The gridterrain map is structured by a set of regular 3-dimensionalgrids. The underside of the grid is a square, and the gridheight denotes the real height of the terrain. Consideringthe performance of Octopus, we regulate the dimension sizeof the square is 0.025m× 0.025m, and the whole map sizeis 120 × 120, so the real dimension size of the grid terrainmap is 3m× 3m. All the point cloud data, whose x coordi-nates are less than 3m and z coordinates are in the range of

-1.5m∼+1.5m, should be mapped into corresponding grid-s correctly. The grid height is obtained by calculating theaverage of the y coordinates of all the point cloud locatedin the same grid. Two kinds of unreasonable grids may exitand influence the precision of the gait planning. One kindis the wrong data due to the environments noise and defectsof the 3D vision system itself, the other kind is the missingportions caused by inevitable effect of occlusions in the sen-sors line of sight. The grid terrain map has to be processedfurther in order to exclude unreasonable grids. The refreshrate of the grid map is about 20 FPS. Fig. 5 shows the realterrain around Octopus and the grid terrain map modeledby the above method.

Real Terrain

Point cloud

Grid terrain

map

Grid terrain map

after processing

Transferring

Grid terrain

map building

Processing

Fig. 5. Modeling of the grid terrain map

III. Autonomous Gait Planning MethodOctopus uses the tripod gait when it walks as Fig. 6

shows, which is quite advantageous to hexapod robots. Thetripod walking gait enables Octopus to have three nonadja-cent feet touching with the ground all the time, the center ofmass (COM) can be located in the support triangle easily.

Fig. 6. The tripod walking gait

The gait trajectory is very important for the walking sta-bility and speed. The rectangular trajectory is typical butquite useful, as shows in Fig. 7. The determination of therectangular trajectory only needs three parameters, the steplength a, the height of lifting foot b and the height of fallingfoot c, which facilitates the planning process.

Grid Terrain Map

Gait Trajectory

Current

FootHold

Next

FootHold

Leg

Foot

Step Length a

Height of

falling foot c

Height of

lifting foot b

Fig. 7. The rectangular gait trajectory

The step length a is attempted to be long enough to in-crease the walking speed. The maximum step length Smax

of Octopus is restricted by the working space of the foot.The index LR in formula 1 is defined to describe the influ-ence of Smax on a.

LR =

√(x(i, j)− x(i0, j0))2 + (y(i, j)− y(i0, j0))2

Smax(1)

where x(i, j) and y(i, j) are coordinates of the nex-t foothold, x(i0, j0) and y(i0, j0) are coordinates of the cur-rent foothold. LR must be less than 1 according to formula1, otherwise it is an error value.

On the other side, terrain conditions should be consid-ered when selecting the appropriate foothold in order toavoid the foot slippage and maintain high stability. Twoindices, the terrain inclination θ in formula 2 and the terrainroughness R in formula 3, are employed to describe terrainconditions.

θ = max(|y(i,j)-y(m,n)|

∆)

m = i− 1, i, i+ 1;n = j − 1, j, j + 1(2)

where m, n are not equal to i, j at the same time. As Fig. 8shows, y(i,j) is the height of the next foothold grid, y(m,n)is the height of the grid which is around the next footholdgrid, and ∆ is the distance between the two adjacent grids.There are 8 other grids around the next foothold grid, so 8inclinations can be computed, the maximum one is chosenas the terrain inclination of the next foothold grid.

As Fig. 8 shows, the terrain roughness R of the nextfoothold grid can be calculated from formula (3).

R =

√1

8

∑[y(i, j)− y(m,n)]2

m = i− 1, i, i+ 1;n = j − 1, j, j + 1

(3)

where m, n are not equal to i, j at the same time too.

Fig. 8. Description of the terrain condition

The selection function of the next foothold is defined bythe following equation 4. The foot is attempted to be placedat a further possible foothold in order to enable Octopus towalk at a high speed, and bigger LR results in a long steplength. Minimum inclination and roughness are desired forthe next foothold, which can avoid the foot slippage. So thegrid (i, j) is chosen as the next foothold by calculating themaximum value of E(i, j) from formula 4.

E(i, j) = LR +θmax

θ+Rmax

R(4)

where θmax and Rmax are the max value of the inclinationand roughness of the terrain. Then the step length a can becomputed using formula 5.

a = |x(i, j)− x(i0, j0)| (5)

The height of lifting foot b can be calculated from for-mula 6, ymax is the height of the highest grid between thecurrent foothold and the next foothold as Fig. 9 shows. δs isadded to ymax in order to avoid interfering with the terraincaused by some random errors. The height of falling foot cis determined in formula 7, y(i, j) is the height of the nextfoothold.

b = ymax + δs (6)

c = |ymax − y(i, j)| (7)

After obtaining the gait trajectory, positions of leg actua-tors (prismatic joints) should be computed to control Octo-pus to walk according to the planned trajectory. The inversekinematics is needed, and our previous work [13], [14], [15]have finished the kinematics model of Octopus.

Fig. 10 shows the kinematic model of single leg, theposition of the spherical joint Sf can be calculated fromthe gait trajectory. l1, l2 and l3 are the lengths of prismaticjoints P1, P2 and P3. The geometric constraint equation ofthe inverse kinematics is as equation (8) shows

[x y z 1]T

= LA[Sfx Sfy Sfz 1

]T(8)

Fig. 9. Model of the trajectory planning

x

z

y

L(U1)

A

x

y

z

U2

U3

P1

P2P3

Sf (x,y,z)

α1

β1

l2l3

l1

S2

S3

Fig. 10. Kinematic model of single leg

where LA is the transformation matrix from the ankle coor-dinate system (A-CS) to the leg coordinate system (L-CS),Sfx , Sfy and Sfz are coordinates of Sf with respect to A-CS, (x, y, z) denotes the position of Sf with respect to L-CS.LA =

cosα1cosβ1 −cosα1sinβ1 sinα1 l1cosα1cosβ1sinβ1 cosβ1 0 l1sinβ1

−sinα1cosβ1 sinα1sinβ1 cosα1 −l1sinα1cosβ10 0 0 1

(9)

Formula 9 shows the detailed expression of LA, α1, β1are rotation angles of U1 along two vertical directions. Thesolutions of the inverse kinematics in formula 10 can beobtained by solving equation 8.

l1 =√x2 + y2 + z2 − Sfy

2 − Sfz2 − Sfx

β1 = arcsin

y√(l1 + Sfx)2 + Sfy

2

− arcsin

Sfy√(l1 + Sfx)2 + Sfy

2

α1 = arctan

[Sfzx−

[(l1 + Sfx) cosβ1 − Sfy cosβ1

]z[

(l1 + Sfx) cosβ1 − Sfy sinβ1]x+ Sfzz

](10)

LA can be calculated by substituting α1, β1 and l1 intoequation 9. l2 and l3 can be obtained from the following

equations.

l2 =

∣∣∣∣−−−−−→LU2LS2

∣∣∣∣ =∣∣LAAS2 − LU2

∣∣l3 =

∣∣∣∣−−−−−→LU3LS3

∣∣∣∣ =∣∣LAAS3 − LU3

∣∣ (11)

where LU2, LU3, LS2, LS3 are positions of joints U2, U3,S2 and S3 with respect to L-CS respectively, and AS2, AS3

are positions of joints S2 and S3 with respect to A-CS re-spectively.

The following equation 12 is used to transform the gaittrajectory from the ground coordinate system (G-CS) to theL-CS.

LΓ = LRTR

GTGΓ (12)

where GΓ represents the gait trajectory in the G-CS, andLΓ represents the gait trajectory in the L-CS. R

GT is thetransformation matrix from the G-CS to the robot coordi-nate system (R-CS), and L

RT is the transformation matrixfrom the R-CS to the L-CS. R

GT is related to the body tra-jectory, and L

RT is a constant matrix which can be calculat-ed based on the dimension size of Octopus.

As Fig. 6 shows, a whole walking gait of Octopus con-sists of two stages. In stage one, it moves feet 1, 3, 5, feet 2,4, 6, are fixed on the ground. In this stage, prismatic jointsof legs 2, 4, 6 are actuated to enable the body of Octopus tomove forward, GΓ of feet 2, 4, 6 are fixed and R

GT can becomputed based on the body trajectory, then LΓ is obtainedfrom the equation 12. Positions of prismatic joints of legs2, 4, 6 can be obtained from equations 10 and 11. In stageone, GΓ of feet 1, 3, 5 are determined from formulas 5, 6,and 7, LΓ is obtained from the equation 12, and positionsof prismatic joints of legs 1, 3, 5 can be calculated from e-quations 10 and 11. In stage two, Octopus moves feet 2, 4,6, and feet 1, 3, 5 are fixed on the ground in turn. Positionsof prismatic joints of all the legs can be computed in thesame way as stage one.

IV. ExperimentIn this section, experimental results of the proposed

method are presented. Figure 11 shows the experimentalenvironment, the obstacle in front of Octopus is construct-ed by three bricks, whose dimension size is 1800mm ×300mm×100mm (length×width×height). The grid terrainmap is as figure 5 shows.

Fig. 11 shows the whole process of passing over the ob-stacle, the body of Octopus is regulated to move forwardhorizontally. During the whole process, all the feet areplaced at the planned footholds calculated based on the pro-posed method, so its body maintains nearly horizontal whenwalking on the obstacle. The results show a successful ap-plication of the method to the autonomous gait planning forOctopus in unstructured environments, which validates ourtheory.

Fig. 11. Snapshots of Octopus passing through obstacles

V. ConclusionIn this paper we present an autonomous gait planning

method for the Octopus hexapod robot, which enables it towalk in unstructured environments with a high walking sta-bility. The method is based on the terrain map detected by a3D vision system. And the terrain map is processed in orderto facilitate the gait planning. We also define two indices,the terrain inclination and the terrain roughness, to describeterrain conditions. The foothold selection function concern-ing about the terrain conditions and Octopus’ own perfor-mance can provide Octopus with appropriate footholds. Ex-perimental results show that the autonomous gait planningmethod works well in reality, Octopus can pass through thecomplex terrain consisting of obstacles steadily.

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