Field and Service Robotics - Corke P. and Sukkarieh S.(Eds) Part 8 ppsx

The algorithm is implemented to adeveloped proto-type robot with limb mechanism, which has six limbs that can be used forboth locomotion and manipulation.. The proto-type robotwalks on t

Fig 1 Overview of the mechanism

Fig 2 Prototype Vehicle and Special wheel

r : radius of the wheel [mm]

ωi:rotation velocity of the wheel i [rad/s]

Vi:rotation velocity of the actuator i [rad/s]

k : gear ratio between the actuator and the wheel

Now, ˙X = ˙x ˙y ˙θ Tand V = V1· · · V7 Texpress the motion velocity vector

of the vehicle and the rotation velocity vector of the actuators, respectively V is alsoderived by using ˙X in equation (2)

Development of a Control System of an Omni-directional Vehicle

Thus, each wheel has to synchronize with the others when the vehicle runs onthe rough terrain In related works, some traction control methods for single wheelare already proposed However, they do not discuss synchronization of the wheelsfor running on rough terrain For our system, we must consider the synchronizationamong the wheels We explain our proposed method in next section.

3 Control System

3.1 Proposed method

In order to synchronize the wheels rotation during the vehicle passes over thestep, calculated torque reference value should not over the maximum torque of the

Fig 4 The vehicle losing the balance

motor If extraordinary load applies on the wheel(s) or the torque reference exceedsmaximum torque of the motor, the system cannot control the wheels, properly.Our proposed control system is shown in Figure 5 The control reference iscalculated by PID-based control system (equation (4))

Fig 5 Flow chart of the control system

The torque reference of i-motor is calculated by equation (4)

τi= kpe + ki e dt + kdde

where

e :Error value of the motor rotation velocity

kp:Proportional gain for PID controller

ki:Integral gain for PID controller

kd:Derivative gain for PID controller

Development of a Control System of an Omni-directional Vehicle

τmax :Maximum torque of the motor

τi :Calculated torque value

load A : 0.001[Nm/deg] from 37 to 60[sec]

load B : 0.004[Nm/deg] from 14 to 52[sec]

load C : 0.005[Nm/deg] from 22 to 57[sec]

In this case, we assume that the maximum torque of the motor is 30[N].The results of the simulation are shown in Figure 6 During the load applied

to the wheel (from 14 to 60[sec]), rotation velocity of the motor is reduced Usingproposed method, each controller adjusts control command to the wheel and recoverssynchronization among the wheel

3.3 Method of Sensing the Step

We utilized PID based control system, however it is difficult to determine theparameters of the controller when the control target has complex dynamics Thus, weswitch two parameter sets according to the situations The vehicle has the accuratecontrol mode for the flat floor and the posture stability control mode for the roughterrain The stability mode utilizes the proposed traction control method, too

Fig 6 Simulation result

In order to switch two parameter sets, the terrain estimation function is required.Thus, we proposed the estimation method using the body axes The angle of twoaxes of the body is changed passively by the ground surface The terrain can bemeasured by using the body kinematics information Two potentiometers measurethe angle of the axes (Figure 7) By this information, the controller can switch twoparameter sets according to the terrain condition

Fig 7 Two Potentiometers

4 Experiment

Here, we have the following two experiments

Development of a Control System of an Omni-directional Vehicle

252 D Chugo et al.

4.1 Measuring the Step

In first experiment, we verify the sensing ability of the vehicle when it passes overthe rough ground The vehicle climbs the step with 30[cm] depth and 1[cm] height.The experimental result is shown in Figure 8 and it indicates that the height ofthe step is 0.9[cm] and the depth is 32.5[cm] Our vehicle need to change the controlmode when the step is more than 3[cm] [7], it is enough step detection capability

Fig 8 The result of measuring the step

4.2 Passing Over the Step

Second experiment is for passing over the steps The vehicle moves forward at0.3[m/s] and passes over the 5[cm] height step Furthermore, we compare the result

by our proposed method with the one by general PID method

As the result of this experiment, the vehicle can climb up the step more smoothly

by our method (Figure 9) The white points indicate the trajectory of the joint point

on the middle wheel and they are plotted at every 0.3 [sec] on Figure 9

Figure 10 and 11 show the disturbed ratio which means the error ratio of therotation velocity (a), the slip ratio (b) [11] and the rotation velocity of each wheel(c) The disturbed rotation ratio and the slip ratio are defined by the equation (5) andthe equation (6), respectively

ˆ

ˆs = rω − vω

ω :Rotation speed of the actuator

ωref :Reference of rotation speed

r : The radius of the wheel

vω :The vehicle speed

As the result, the rotation velocity of the wheels is synchronized with the posed control method Furthermore, the disturbed rotation ratio and the slip ratio arereduced Thus, this control method is efficiency for step climbing

Fig 9 Step climbing with proposed controlling and general controlling

(a)The disturbed rotation ratio

(b)The slip ratio

(c)The rotation speed

Fig 10 Experimental Result of proposed method

(a)The disturbed rotation ratio

(b)The slip ratio

(c)The rotation speed

Fig 11 Experimental Result of old method

Development of a Control System of an Omni-directional Vehicle

254 D Chugo et al.

5 Conclusions

In this paper, we discuss the control method for omni-directional mobile vehiclewith step-climbing ability and the terrain estimation method using its body We alsodesigned new control system which realized the synchronization among the wheelswhen the vehicle passed over rough terrain

We implemented the system and verified its effectiveness by the simulations andexperiments For future works, we will consider the motion planning method based

on the environment information

References

1 G Campion, G Bastin and B.D Andrea-Novel, “Structual Properties and Classification

of Kinematic and Dynamic Models of Wheeled Mobile Robots,” IEEE Transactions on

Robotics and Automation, vol 12, No 1, pp 47–62, 1996.

2 G Endo and S Hirose, “Study on Roller-Walker: System Integration and Basic

Ex-periments,” IEEE Int Conf on Robotics & Automation, Detroit, Michigan, USA, pp.

2032–2037, 1999

3 M Wada and H Asada, “Design and Control of a Variable Footpoint Mechanism for

Holonomic Omnidirectional Vehicles and its Application to Wheelchairs,” IEEE

Trans-actions on Robotics and Automation, vol 15, No 6, pp 978–989, 1999.

4 S Hirose and S Amano, “The VUTON: High Payload, High Efficiency Holonomic

Omni-Directional Vehicle,” 6th Int Symposium on Robotics Research, Hidden Valley,

Pennsylvania, USA, pp 253–260, 1993

5 A Yamashita, et.al., “Development of a step-climbing omni-directional mobile robot,”

Int Conf on Field and Service Robotics, Helsinki, Finland, pp 327–332, 2001.

6 K.Iagnemma, et.al., “Experimental Validation of Physics-Based Planning and Control Algrithms for Planetary Robotic Rovers,” 6th Int Symposium on Experimental Robotics,

Sydney, Australia, pp 319–328, 1999

7 K.Yoshida and H.Hamano, “Motion Dynamic of a Rover With Slip-Based Traction

Model,” IEEE Int Conf on Robotics & Automation, Washington DC, USA, pp 3155–

3160, 2001

8 H Asama, et.al., “Development of an Omni-Directional Mobile Robot with 3 DOF Decoupling Drive Mechanism,” IEEE Int Conf on Robotics & Automation, Nagoya,

Japan, pp 1925–1930, 1995

9 T Estier, et.al., “An Innovative Space Rover with Extended Climbing Abilities,” Video

Proc of Space and Robotics 2000,, Albuquerque, New Mexico, USA, 2000.

10 http://mars.jpl.nasa.gov/MPF/ (as of Nov 2003)

11 D Chugo, et.al., “Development of Omni-Directional Vehicle with Step-Climbing ity,” IEEE Int Conf on Robotics & Automation, Taipei, Taiwan, pp 3849–3854, 2003.

Abil-S Yuta et al (Eds.): Field and Service Robotics, STAR 24, pp 255–264, 2006.

© Springer-Verlag Berlin Heidelberg 2006

Sensor-Based Walking on Rough Terrain

for Legged Robots

Yasushi Mae1, Tatsuhi Mure1, Kenji Inoue1, Tatsuo Arai1, and Noriho Koyachi2

1 Graduate School of Engineering Science, Osaka University

1-3 Machikaneyama, Toyonaka, Osaka,560-8531, JAPAN

Abstract A simple sensor-based walking on rough terrains for legged robots using an

acceleration sensor attached to the body is described The algorithm is implemented to adeveloped proto-type robot with limb mechanism, which has six limbs that can be used forboth locomotion and manipulation The six limbs are arranged on the body radially to haveuniform property in all directions This symmetrical structure allows the robot to generate agait trajectory for omnidirectional locomotion in a simple manner The trajectory of the sensor-based walking is obtained by a small conversion of this simple trajectory The proto-type robotwalks on the uneven ground while adjusting the pose of the body to keep high stability margin.Finally, adequate footholds of supporting limbs are examined for manipulation tasks by twoneighboring limbs of the robot

1 Introduction

Outdoor robots require high manipulability and mobility in the application of rescue,construction, agriculture, and space or ocean developments [1–6] Thus they shouldhave both handling and mobile mechanism Most of the conventional working robotshave been designed in such a manner that a manipulator is simply mounted on amobile platform [7,8] Legged robots suit for work in rough terrains because theycan select any landing points and keep stability of the pose during manipulation Inconsidering the advantage of legged robots, there may be many approaches to designlocomotion mechanism of robot may be taken

There are some animals or insects that can use their legs for their hands tomanipulate objects dexterously while walking on rough terrains If manipulationand locomotion functions can be integrated into one linkage called "limb", bothhigh terrain adaptability and manipulability are achieved Based on this notion, theconcept "Limb Mechanism" has been proposed that has integrated locomotion andmanipulation functions into one limb [9–14]

We call a robot with limb mechanism “limb mechanism robot” It is requiredfor a limb mechanism robot to walk in any directions quickly and smoothly while

256 Y Mae et al.

Fig 1 A limb mechanism robot Fig 2 Radial arrangement of limbs.

keeping its stability A limb mechanism robot has been designed and developedtaking such omnidirectional mobility into account [14]

As one of feasible structures of the limb mechanism a 6-limb mechanism hasbeen analyzed and evaluated in the aspects of omnidirectional mobility [15,16] In[15,16], two types of structures are compared with respect to their stroke, stability,and error of dead reckoning for six-legged locomotion The radial leg arrangementmodel will be proved to have higher omnidirectional mobility than the parallel legarrangement

In actual tasks it is essential for a limb mechanism robot to move on roughterrains quickly and smoothly Furthermore, in manipulation tasks, a limb mechanismrobot has to select adequate footholds of supporting limbs not to fall down due tomanipulation motions of limbs

In the present paper, first we introduce a limb mechanism robot, and describemainly following two topics one is a simple trajectory generation method in con-sidering gait control strategy on the uneven ground It can maintain the walkingspeed of the robot while keeping high stability, even when a transfer limb lands on abump The other is adjustment of footholds of four supporting limbs from the point

of view of static stability The footholds should be selected to keep higher stabilitymargin when two limbs are used as manipulation In the paper, we examine the casetwo neighboring limbs are used as arms, which makes the limb mechanism robotunstable the most

2 Limb Mechanism Robot

2.1 Configuration of Limb Mechanism Robot

First, we introduce a limb mechanism robot developed by Takahashi et al.[14,15](see Fig.1) In designing, the main concern is to fix the number of limbs A fourlimb mechanism will be feasible, but its mobility is extremely limited while one oflimbs will be employed for arm function Too many limbs, for example seven or

Sensor-Based Walking on Rough Terrain for Legged Robots 257

Fig 3 Configuration of a limb.

more, may cause difficulty in gait control A six limb mechanism seems the mostreasonable in the aspects of achieving high mobility and manipulability, since itenables four-legged locomotion with two arm manipulation in addition to six-leggedlocomotion

Arrangement of limbs are important parameter to determine property of a limbmechanism robot In most insects, two groups of three legs are arranged in parallel.This parallel arrangement has strong directivity in walking and working capabilities

No directivity, or omnidirectional mobility, may be preferable when the robot is plied in a narrow environment where posture and rotational motions are constrained.Especially in rough terrains, omnidirectional mobility is useful to obtain stable andquick change of walking directions If six legs are arranged equally or equilaterally,then the directivity and the interference among legs can be improved and a largeworking space can be assured for each limb

ap-Thus, the limb mechanism robot has been developed to have six limbs which arearranged radially (see Fig.2) Each limb has a 3 d.o.f serial linkage The structure is

a rotation-pivot-pivot articulation as shown in Fig.3 We call the joints first, second,and third joints in order from the body to the end

2.2 Overview of Control System

In outdoor working, remote control is desirable because control cables disturb arobot to work smoothly Since the developed limb mechanism robot has 18 d.o.f.,calculation of the amount of control of each actuator in the whole generation ofoperation becomes very complicated Although what has a highly efficient computerfor control is required, such a computer cannot be carried in a main part fromthe point of a size and weight, and sufficient calculation cannot be performed bycomputer which can be conversely put on a main part

Thus we adopt a radio control system Figure 4 shows the overview of the wholesystem This system consists of a transmitter, a receiver, and servomotors The trans-mitter is connected with the control computer We can drive the servomotors inproportion to the position commands which we input to the computer The servomo-tors of the robot are controlled in open loop The robot is equipped with the sensormodule It is constituted by an acceleration sensor, a PIC(a small CPU with A/Dconverter), and a transmitter The PIC processes the sensed gravity to obtain inclina-

Fig 4 Overview of the control system.

tion of the body and transmits it to the PC The PC generates the motion pattern ofthe robot and transmites the corresponding position commands to the servomotors

3 Basic Walking Trajectory

3.1 Simplified Trajectory Generation

As indicated in the previous discussion, it is rather complicated and tiresome tofind the trajectory of each leg for the generation of the gait pattern A more generaltreatment will be considered to find unique trajectory in any directions in each limb.The method is simple and easy to generate trajectories with the same stroke in anydirections

Figure 5 shows one example of the largest size of a circled area in the workingspace of the limb Any linear trajectories will be possible in any directions within it,therefore the trajectory generation for each limb might become much easier both infour and six-legged locomotion A control software is implemented in the controller

PC Actual omnidirectional walking motion has been confirmed in the developedrobot

The diameter of the circle is determined from the workspace of a limb Figure 6shows sectional view of the workspace of a limb The workspace is between outercurved line and inner curved line We assume a cylinder inscribed in the workspace

to generate basic trajectory of a limb (see Fig.6) Then observe two perimeters ofcircles and draw two perpendiculars from perimeters’ end to end These lines makethe basic trajectory

The method makes it possible to make the stroke of limbs the same length asevery direction The stroke is diameter of a circle Usually on regular terrains, the end

of limb passes on this trajectory The trajectory consists of four terms, lift up, forwardmotion, landing, and backward motion They are shown in Fig.7(a) As shown inFig.7(b), in case of changing moving direction of the robot, simple rotation of the

Sensor-Based Walking on Rough Terrain for Legged Robots 259

Fig 5 Stroke in omnidirectional locomotion.

Fig 6 Cylinder inscribed in workspace.

(a) Regular trajectory (b) Trajectory in changing

moving direction

Fig 7 Basic trajectory of a limb.

trajectory makes omnidirectional locomotion easy, whereby the limb mechanismrobot can change the moving direction without re-stepping

3.2 Simplified Gait Pattern by Phase Shift

Leg mechanisms like insects or animals have symmetry in longitudinal and lateraldirections, thus their stability margin and stroke varies in 90[deg.] phase, or itmay be called four axes symmetry In the gait control the trajectory of each legmay be generated only for this phase, and it can be repeatedly used in the otherdirections by taking this symmetry into account In our limb mechanism robot thetrajectories in 60[deg.] phase can be repeated due to its six axes symmetry This mayallows simpler control strategy even in four-legged gait as well as in six-legged Theomnidirectional gait may be generated simply by switching the basic gait patternssix times Furthermore, the patterns has symmetry centred in one limb, thus they areagain reduced to a half, that is, the trajectories in 30[deg.] phase are only requiredfor the gait control

260 Y Mae et al.

Fig 8 Trajectory on a bump Fig 9 Pose adjustment to reduce inclination of the body.

Fig 10 Limb mechanism robot on a bump with pose adjustment.

4 Sensor-Based Waling on Rough Terrain

On bumpy or rough terrains, it is difficult for the robot to continue walking by thebasic trajectory described in the previous section When some limbs land to bumps

or into hollows, the body inclines and it reduces stability margin In the worst case,the robot falls down Thus, it is necessary to adjust the pose of the body in walking

on the uneven ground

Easy conversion of the basic trajectory should make the robot possible to ing on the uneven ground while keeping omnidirectional mobility We describe atrajectory generation method for walking on the uneven ground, which uses an ac-celeration sensor attached to the body to measure the inclination of the body Inthe sensor-based trajectory generation, the following process is added to the basictrajectory generation process

walk-If the inclination is detected in "landing" term, the landing motion of the limb isstopped and the supporting limbs are moved to reduce the inclination After adjustinginclination, some ends of limbs may reach the end of working space and cannot moveany more Then, in order to bring the ends of the limb into the working space andkeep the height of the body constant, all landing limbs should be folded as shown

in Fig.9 After folding landing limbs, the landing limb performs backward motion.Though there are differences of levels between landing positions of limbs, the robotcan continue to move by adjusting verical trajectory length of the limbs

In this way, the robot walks on the uneven ground while keeping high stabilitymargin Figure 10 shows a scene where the robot moves over a bump in the tripodgait using six limbs The sensor-based pose adjustment algorithm is implemented

Sensor-Based Walking on Rough Terrain for Legged Robots 261

Fig 11 Change of stabilty marign while walking on the uneven ground.

in the walking algorithm We can see the pose of the body is kept horizontally byreducing inclination even a limb is on a bump

The left and right figures in Fig.11 show the changes of stability margin withoutand with the pose adjustment in walking, respectively The horizontal axes indicatethe walking distance of the robot The vertical axes indicate stability margin Thecircle in the left figure indicates the part where the limb lands on a bump and the sta-bility margin decreases In the right figure, the stability margin at the correspondingpart does not decrease From the figures, we can see the adjustment of the pose ofthe body makes stability margin almost constant even the robot moves over a bump

5 Adjustment of Footholds of Supporting Limbs

To keep static stability in manipulation tasks, the robot has to adjust footholds ofsupporting limbs in accordance with the pose of the manipulation limbs We discussadjusting footholds of supporing limbs in the case that the two neighboring limbsare used as arms This is the case that the mass center of the robot changes the most.The side of the manipulation limbs is called front or forward, temporarily Figure 12shows a limb mechanism adjusting footholds of supporting limbs; two neighboringlimbs are lifted up in parallel in front of the robot for simulation of manipulation

by two neighboring limbs When the robot moves the two neigboring limbs up, therobot falls down if it does not adjust the footholds of supporting legs

We examine the change of stability margin depending on the footholds of ing limbs In the examination, we fix the height of the body to 149[mm] horizontally

support-by fixing the joints of supporting limbs In that pose, the second joint is at 60 degreesdownward and the third joint is at 0 degrees Only the first joints of supporting limbsare rotated to change the footholds

Figure 13 shows the change of stability margin when the two first joints of thefront side supporting limbs are rotated from 0 degrees to 60 degrees in forward

262 Y Mae et al.

Fig 12 A limb mechainism robot supported by four limbs while two neighboring limbs are

lifted up

Fig 13 Change of stability margin for changing footholds by rotating the first joints of the

front side limbs

direction, while the two neighboring limbs are lifted up in parallel When the firstjoints are set at 0 degrees, the limbs are set at standard pose where the limbs arespread radially The horizontal axis indicates the sum of the rotational angles ofthe two joints The vertical axis indicates stability margin As the limbs are movedforward, stability margin is increased monotonously The maximum stability margin

is obtained at the limit of the rotational angles 60 degrees Thus, the two front sidesupporting limbs should be moved forward to obtain maximum stability marginbefore two neighboring limbs are moved up for manipulation

Figure 14 shows the change of stability margin when the two neighboring limbsare being up in parallel, while the two first joints of the front side supporting limbsare at 60 degrees in forward direction The two neighboring manipulation limbs aremoved up by actuating second and third joints The horizontal axis indicates the sum

Sensor-Based Walking on Rough Terrain for Legged Robots 263

Fig 14 Change of stability margin for moving two neighboring limbs after adjusting the

footholds to maximize stability margin

of the rotational angles of the two joints The vertical axis indicates stability margin

We examine two motion pattern of moving limbs In the first pattern, the third joint

is actuated first and the second joint is actuated next (motion A in Fig.14) In thesecond pattern, the second joint is actuated first and the third joint is actuated next(motion B in Fig.14) The second joint is rotated upward from −60 degrees to 45degrees The third joint is rotated upward from 0 degrees to 90 degrees

From Fig.14 we can see the high stability margin is hold for the two motionpatterns This is because the footholds of the front side supporting limbs are adjusted

to increase stability margin, before moving two neighboring manipulation limbs

6 Conclusions

In the paper, first we introduced a mobile robot with limb mechanism, and a basictrajectory generation for omnidirectional locomotion Second, we describe a sensor-based walking method on rough terrains using an acceleration sensor attached tothe body The experimental results of walking on the uneven ground show the pose

of the body is kept horizontally constant when a limb of the robot is on a bump inwalking Third, we describe adjustment of footholds of supporting limbs to keephigh stability margin while two neighboring limbs are used as arm The change ofstability margin is examined in accordance with the change of the footholds

Acknowledgement

This research was performed as a part of Special Project for Earthquake DisasterMitigation in Urban Areas in cooperation with International Rescue System Institute(IRS) and National Research Institute for Earth Science and Disaster Prevention(NIED)