Contact forces applied on the robot The revolute joints between the legs and the upper plate sustain only axialforce - Faacting along the leg, and tangential force – Ftacting parallel t
Trang 1Motion Analysis of a Parallel Mobile Robot
Shraga Shoval1and Moshe Shoham2
1
Department of Industrial Engineering & Management,
Academic College of Judea and Samaria, Ariel, Israel
shraga@yosh.ac.il
2
Faculty of Mechanical Engineering,
Technion, Haifa, Israel,
shoham@tx.technion.ac.il
Abstract This paper presents a kinematic and force analysis of a mobile robot built on the
principle of parallel mechanisms The robot consists of an upper plate connected to 3 legs,each equipped with an asynchronous driving unit A kinematic model for the robot provides data for accurate position estimate, even in rough and slippery terrains whereconventional odometry fails The paper presents an analysis of the forces acting on therobot under various surface conditions and robot configurations This analysis providesuseful data to determine whether a specific motion can be completed given the limitations
on stability, the geometry and friction of the surface, and the required motion direction.The paper presents simulation results that are verified by experiments using our prototypemodel
1 Introduction
Parallel mechanisms consist of an upper platform that is maneuvered by several(3-6) legs connected to a lower stationary platform The maneuverability, rigidityand accuracy are functions of the number of legs and the type of joints betweenthe plates and the legs The basic conceptual mechanics is known as the Stewartplatform [Stewart, 1965] even though earlier versions are known, and since thenmany manipulators were developed based on this mechanism [Hunt 1983, Tsaiand Tahmasebi 1983 and others]
Ben Horin and Shoham [1997] have suggested using mobile joints betweenthe legs and the stationary platform, turning the mechanism into a semi-mobilerobot The mechanism consists of the following components: three links of fixedlength, having a spherical joint on one end and a revolute joint on the other end,three actuators which move plenary on a stationary platform and an outputplatform having six degrees-of-freedom (DOF) To further increase mobility, BenHorin and Shoham [1999, 2000] suggest a more flexible design This mechanism,shown in Fig 1, is based on 3 inflatable legs, an upper platform and 3asynchronous driving units for the three legs The upper joint of each leg is arevolute joint, while the lower joint, which connects the leg to the driving unit, is
a spherical joint This configuration offers six DOF for the upper plate where thecontrol parameters are the positions (X,Y,Z) of the three driving units Themechanism is designed for applications that require a light weight and easy
S Yuta et al (Eds.): Field and Service Robotics, STAR 24, pp 323–331, 2006.
© Springer-Verlag Berlin Heidelberg 2006
Trang 2324 S Shoval and M Shoham
deployable robot Given the required trajectory for the end effecter (6 parameters)the inverse kinematics model can generate the required path of each driving unit,subject to its non-holonomic constraints
Fig.1 The inflatable mobile robot [Ben Horin and Shoham, 2000]
In this paper we present a kinematic and force analysis for the parallelmobile robot The kinematic analysis, shown in section 2, enables an improvedposition estimate based on additional encoders attached to the upper platform.Section 3 details the force analysis for the robot, and section 4 shows simulationresults for motions in various configurations and constraints Section 5 verifies the simulation results with experiments conducted with our prototype platformand section 6 provides concluding remarks
2 Kinematic Analysis
Figure 2 is a schematic description of the parallel mobile mechanism The upper plate is connected to each of the three legs with revolute joints The three legs aredriven by three asynchronous units that are connected to the legs with sphericaljoints Controlled motion of the three driving units determines the pose (positionand orientation) of the upper plate
Trang 3Motion Analysis of a Parallel Mobile Robot 325
Fig.2 Schematic description of the mobile parallel mechanism
To determine the accurate configuration of the upper plate, both the absoluteposition of each driving unit (Xi,Yi,Zi) and the direct kinematics model arerequired The position of the driving units is determined by Odometry usingencoders attached to the driving wheels Tahmasebi and Tsai [1994] show that for the above parallel mechanism there are 16 possible direct kinematics solutions,which require extensive computational effort Furthermore, determining theabsolute position of each driving unit is subjected to odometric errors and cannotprovide a reliable position estimate To improve the accuracy and to simplify thedirect kinematics model Shoval and Shoham [2001] use additional measurementstaken from on board encoders attached to the upper revolute joints The additionalencoders measure the rotation angle between the upper plate and the legs Based
on these measurements, the positions of the three driving units are derived in theU-V-W coordinate system (attached to the center of the upper plate) Based onthe position of the drive units as determined in the U-V-W system, the Euclidean
distances between the drive units l 1 , l 2 and l 3are given by Eq 1:
2 1 2 1 2
If the odometric system is accurate, the distances derived in the upper plate
coordinate system (l i) are equal to the distances derived in the world coordinate
system (m i) If, however, these distances are different, the odometric calculation
is faulty An odometric error in one drive unit affects two distances according to
Eq 2 Assuming a single odometric error at each interval time, the accurate
Driving Units + SphericalJoints
RevoluteJoints +Encoders
(X1,Y1,Z1)
(X3,Y3,Z3
)
(X2,Y2,Z2)
Trang 4326 S Shoval and M Shoham
position of three driving units is continuously updated In the unlikely event thattwo (or three) driving units are subjected to odometric errors simultaneously, theproposed procedure cannot be implemented and additional measures must betaken (i.e re-calibration of the robot’s position)
3 Force Analyses
Fig 3 shows the contact forces applied on the robot by the ground Do and Yang[1988] suggest a solution based on the Newton-Euler method, resulting in 36linear equations Other researchers use the principle of virtual work to reduce thecomplexity of the solution Ben Horin [1999] uses the Kane method to determinethe dynamic equations, solving it with numerical procedures To simplify thesolution we assume that the robot’s mass is concentrated at the upper plate, whilethe legs have negligible mass We also assume that internal changes in the robotinternal configuration are quasistatic (dynamic forces associated with changes ofinternal configuration are negligible compared with other)
Fig.3 Contact forces applied on the robot
The revolute joints between the legs and the upper plate sustain only axialforce - Faacting along the leg, and tangential force – Ftacting parallel to the axis
of the revolute joint Reducing the problem to 6 unknown forces simplifies thesolution to the following equations:
x i
i i t i i
i i
1
cos cos cos
y i
i i t i i
i i
1
sinsin
i
z i t i i
i a
−
− +
=
i i t a i z b i i i t i i a
i
3
(6)
Trang 5Motion Analysis of a Parallel Mobile Robot 327
•
=
=
− +
+
− +
−
b i i t a i z b i i
i i t i i
+
− +
−
b i i i t i i a i x b i i
i i t i i a
F - the tangential force in leg i.
θi- the angle between leg i and the X-Y plane (therefore the angle between the
axial force and the X-Y plane)
µi- the angle between leg i and the positive X axes.
δi- the angle between the tangential force of leg i and the X-Y.
γi- the angle between the tangential forces of leg i and the positive X axes.
b
i
r - the position vector of the bottom of leg i.
c
r - the position vector of center of the upper plate
a x ,a y ,a z– accelerations along the X,Y and Z
θ,ω,ξ - Euler orientation angles
J- Moment of inertia of the upper plate
m – Mass of the upper plate
Let us assume a friction coefficient µ between the driving wheels and the surface
We transform the axial -Fi aand tangential -Fi t forces (derived by Eq 3-8) to anew coordinate set defined by:u)d- in the direction of the required motion,u)l- inthe lateral direction, and u)n - normal to the surface The lateral force F lacting onthe driving unit is given by:
)
i l
•
•+
•
)(
)(
l t
u
F
u F
u
F
))
))
(11)Given a specific moment Mdgenerated by the driving motor and r - the radius of
the driving wheel, the friction driving force – F d generating the motion of thedriving unit in the required direction is limited by:
)( i a n i t n
d
d M r F u F u
Given a specific terrain topography and friction, the actual driving forces applied
on each leg can be determined both along the longitudinal and lateral directions
Furthermore, based on these forces the accurate dynamic reaction of the robot
can be calculated
Trang 6328 S Shoval and M Shoham
4 Simulation Results
We first examine the forces applied on the robot when traveling at a constantspeed on a horizontal surface, with an identical inclination angles (η) between thelegs and the upper plate The robot is traveling in the positive Y direction with aconfiguration is shown in Fig 5a We start the experiment withη=90o
(legs areperpendicular to the surface and the upper plate), while gradually andsimultaneously reducing the inclination angles for all legs The weight of theupper plate is 100N As expected, the axial forces - Fi aon all three legs areidentical, starting with 33.33N when the legs are perpendicular (η=90o
), andincreasing as η decreases (Figure 5b) Since all driving units are in the traveldirection, the tangential forces -Fi t are close to zero in all legs, and therefore arenot shown in the graphs
0 100 200 300 400 500 600
0 20 40 60 80 100
Fig.5 Axial forces for constant motion over a horizontal surface.
Next, we transform the axial and tangential forces to the corresponding
components in the longitudinal (F d ), lateral (F l), and normal to the surface
directions (F n) Due to the symmetry, the normal components in all legs remainconstant (33.3N) The friction coefficient is 0.7, generating a maximal frictionforce of 23.33N for all legs Fig 6a shows the lateral and longitudinal forces for legs 1 and 2 These forces are identical due to the symmetry of the two legsrelative to the driving direction Fig 6b shows the same forces for leg 3 Asshown, the lateral forces on legs 1 and 2 pass the maximal friction force atη=53o
.The longitudinal force of leg 3 passes the friction force limit at η=55o
The robotcan therefore travel at a constant speed on a horizontal surface with a frictioncoefficient of 0.7 as long as the inclination angle of the legs is larger than 55o At that angle, longitudinal slippage occurs at leg 3 Further decrease of theinclination angle to 53ocauses additional lateral slippage in legs 1 and 2
Travel
Direction
3
2 1
X Y
Trang 7Motion Analysis of a Parallel Mobile Robot 329
L e g 1 a n d le g 2
0 5 10 15 20 25 30
0 20 40 60
Fu L e g 3
-10 0 10 20 30 40
0 20 40 60 80 100
Fig.6 Forces on legs 1 and 2 (a) and 3 (b) for constant speed.
In the next set of simulations, the robot travels along a horizontal surface in
a straight line with constant acceleration along the Y+ axis (equivalent totraveling at a constant speed on an inclined surface) In addition to frictionconstraints, external stability must also be considered Fig 7 shows the forces onlegs 1 and 2 as a function of the inclination angleη during a 5m/sec2
(equivalent
to traveling on an inclined surface of 30o) The results indicate that legs 1 and 2lose contact at inclination angles larger than 78o (shown as a negative frictionforce) However, the lateral force is larger than the friction limit for all inclinationangles, resulting in lateral slippage for any internal configuration In order tocomplete a stable motion at a 5m/sec2 the inclination of the “front” leg (leg3)must be reduced, as shown in Fig 7b This change adjusts the force distribution,similar to humans climbing a steep hill The new internal configuration enables stable motion as long as inclination angle for leg 3 is in the range of 68o-53o, andlegs 1 and 2 are larger than 78o
L e g s 1 a n d 2
-40 -20 0 20 40 60 80 100
0 20 40 60 80
Fig.7 Accelerated motion of 5m/sec2
Similar results are obtained for circular motion Again, symmetric internalconfiguration results either in tipover or immediate slippage in one or more legs.Asymmetric internal configuration enables the robot to safely complete therequired motion even for sharp curvatures with relatively high speeds
TravelDirection
Trang 8330 S Shoval and M Shoham
To verify the simulation results we have conducted field experiments using ourinflatable mobile platform shown in Fig 1 In these experiments we measured thestability limits for various internal The results indicate close match between thetheoretical simulations and the field experiments For example, stability limit for horizontal surface with symmetric configuration (shown in Figs 5-6) is obtainedfor inclination angle of 60o, compared with 53o determined in the simulation.Motion over inclined surface of 30ois stable when inclination angle for leg3 is inthe range of 65o-55ocompared with 68o-53odetermined in the simulation
5 Field Experiments
6 Conclusions
A new design for a parallel mobile robot is presented The robot consists of threelegs, each driven by an asynchronous mechanism connected to the legs with aspherical joint Each leg is connected to an upper platform with revolute joint andadditional encoders, measuring the revolute angle of the upper joints Theseencoders provide data used by the kinematic model for early detection andcorrection of positioning errors generated by odometry Early detection andcorrection of odometric errors in each leg prevent accumulation of significant errors of the upper plate, and can identify irregularities on the surface
A simplified dynamic model provides a solution for the forces applied on therobot The model determines whether a specific task can be reliably performed,given a specific surface topography and friction The model can also detect instabilities either by loosing contact with the ground (tipover), or by slippage(longitudinal or lateral) An unstable configuration can be avoided by changingthe inclination angles between the legs and the upper plate This feature allowsthe robot to complete motions in complex terrains where conventional robots cannot maintain stability due to inertial forces, surface topography, or frictionconstraints
References
1 Ben Horin (Dombiak) P., 1999, Analysis and Synthesis of an Inflatable Parallel
Robot”, M.Sc Thesis, Technion, Haifa.
2 Ben Horin (Dombiak) P., Shoham, M., and Grossman, G., “ A Parallel Six Degrees
of-Freedom Inflatable Robot,” ASME 2000 Mechanism and Robotics Conference,
Washington, 2000
3 Ben Horin R., “Criteria for Analysis of Parallel Robots”, D.Sc Thesis, Technion, Haifa,
1997
4 Do W Q D., Yang D C H., “Inverse Dynamics Analysis and simulation of a
Platform Type of Robot”, Journal of Robotic Systems, Vol 5, No 3, pp 209-227, 1998.
5 Hunt K H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot Arm”, ASME Journal of Mechanisms Transmissions and automation in Design, Vol 105, pp 705-
712
Trang 9Motion Analysis of a Parallel Mobile Robot 331
6 Shoval S and Shoham M “A Redundant Parallel Mobile Mechanism”, Proceedings of IEEE International Conference for Robotics and Automation, May 2001, Seoul, Korea,
pp 2273-2279
7 Stewart D., 1965, “A platform with six Degrees of Freedom”, Proceedings of Instittute
of Mechanical Engineering, London England, Vol 180, pp 371-386.
8 Tahmsebi F., Tsai L W., 1994, “Closed-Form Direct Kinematics Solution of a New
Parallel Minimanipulator”, Transactions of the ASME, Vol 116, pp 1141-1147.
9 Tsai L W., Tahmasebi F., 1983, “Synthesis and Analysis of a New Class of Six
Degree-of-Freedom Parallel Minimanipulators”, Journal of Robotic Research, Vol 10,
pp 561-580
Trang 10S Yuta et al (Eds.): Field and Service Robotics, STAR 24, pp 333–342, 2006.
© Springer-Verlag Berlin Heidelberg 2006
Teleoperation System for Two Tracked Mobile Robots Transporting a Single Object in Coordination Based
on Function Allocation Concept
1 Dept of Machine Intelligence and Systems Engineering,
Abstract In this paper, we propose a collision avoidance algorithm for two nonholonomic
tracked mobile robots transporting a single object based on a function-allocation concept
In this algorithm, a leader robot is controlled manually A follower robot estimates thedesired trajectory of the leader along its own heading direction and generates the motion fortransporting the object and for avoiding obstacles by using an omni-directional vision sensor
We experimentally implement the proposed algorithm in a tracked mobile robots system, andillustrate the validity of the proposed control algorithm
1 Introduction
A trailer, which is transporting a large size container, has steering mechanisms inboth the front wheel and the rear wheel to advance the motility of the trailer Usuallytwo operators drive this type of the trailer and each operator controls each steering.However, long experiences are needed to drive such a trailer efficiently especiallywhen the trailer circles In this paper, we consider this trailer system as the twomobile-robot system that transports a single object in coordination We will discussthe motion control method of this system In general, we control directly one ofthe robots and the other robots are controlled autonomously to maneuver a multiplerobot system by an operator If we control this system by this way, the operatorhas to determine the control input not only for the controlling robot itself but alsofor the whole system This makes the controllability be declined In the proposedsystem, the effective task could be realized by allocating the functions which arenecessary to realize the task Based on different concept on function distributed andinformation management, many researchers have proposed various motion controlalgorithms for the multiple mobile robots to handle a single object in coordination[1]-[6] etc We briefly review some of the multi-robot systems which execute thecoordinate task
N.Miyata et al have proposed the control algorithm transporting a single object
by multiple nonholonomic car-like robots based on the function allocation cept [4] In this algorithm, several functions for achieving tasks are allocated to
Trang 11con-334 H Takeda, Z.D Wang, and K Kosuge
each robot and multiple mobile robots realize the tasks effectively To realize thissystem, however, each robot is controlled in the centralized control system to sharethe information of other robots
Kosuge et al proposed a leader-follower type of motion control algorithm fornonholonomic tracked mobile robots to transport a single object[8] In this algorithm,
a motion command of the object is given to one of the robots referred to as aleader The rest of the robots referred to as followers estimate the motion of theleader through the motion of the object and transport it together with the leader incoordination Because the robots do not use explicit communication, the execution
of more reliable transport task is expected In addition, authors proposed a collisionavoidance algorithm for two-tracked mobile robots[9] In this system, the motioncommand of the leader is given in advance in this control algorithm Then we have
to design the whole trajectory in advance when we apply this control algorithm Inthis paper, we expand the method of [9] and apply to dynamic environment such asthe slip of wheels could not be neglected
2 Basic Leader-Follower Algorithm
In this section, we briefly explain the decentralized control algorithm proposed in [8]
In case of the mobile robots under a nonholonomic constraint, we assume that eachrobot holds the object through a free rotational joint, which is located on the axis ofboth wheels, as shown in Fig 1 In this case, the motion of the robot is characterized
by two kinds of motion One is the translational motion along the heading direction
of the robot, and the other is the rotational motion around the free rotational joint
In the algorithm proposed in [8], each robot was controlled to have a followingdynamics along the heading direction
where D is a positive definite damping coefficient and K is a positive definite
desired trajectory of the object is given to the leader and the follower estimates its
Fig 1 Holding mechanism applied to both
leader and follower robot, which has nomic constraints, to transport a single object incoordination
Trang 12nonholo-Teleoperation System for Two Tracked Mobile Robots 335
Fig 2 (a)General view of the real caster
model which has fixed Coff, (b)Proposeddual-caster model The direction of the off-set of the caster Coff is changed to mini-mize the rotational angle((b-1)(b-2))
motion along the heading direction of the follower by using the estimation algorithmproposed in [8] For the rotational motion of the robot, each robot is controlled as if
it has a caster-like dynamics as shown in Fig 2 The follower makes its orientationrotate to the heading direction of the object based on the caster-like dynamics Let
us briefly review this dynamics
rotational joint as shown in Fig 2(a) The caster turns to the direction of the forceapplied to the caster by this offset If the robot is controlled to imitate the motion ofthe real caster directly, the robot will rotate more than 90 degrees, when the robot
is pulled backward In the cooperative object transportation, the excessive forcewill be generated between robots during rotational motion more than 90 degrees
of the follower To avoid this problem, we propose that the follower is controlled
to have two different caster dynamics as shown in Fig 2(b) That is, we considerchanging the position of the free rotational joint according to the force directionapplied to the robot When the robot is pushed forward, the offset is set equal to
action
3 Function Allocation
In this research, the task is to control two tracked mobile robots which is transporting
a relative large object in an environment with obstacles from a remote site Therobots system should have two functions, transporting the object in coordination andavoiding collision between obstacles and the transportation system including robotsand the object In this research, we allocate the two types of function to each robot.One is to control the position of the object and the other is to control the orientation
of the object and to transport the object in coordination We allocate the positioncontrol function of the object to the leader, so that the leader transport the object
Trang 13336 H Takeda, Z.D Wang, and K Kosuge
Fig 3 Avoidance velocity vector of the follower
V is calculated based on h , the minimal dis-avd i
tance between the obstacle and the object toavoid the obstacle i
based on the joystick control of the leader We also allocate the orientation controlfunction of the object and the transport function with the other robot to the follower,
so that the follower transports a single object with the leader
The collision avoidance problem here is similar with the case of a multi-trailerssystem In a relatively simple environment, it may be possible to avoid collisionbetween an obstacle and transported object by only controlling path of the leader ifthe operator has enough knowledge of both the obstacle and characteristics of thefollower’s motion However, it becomes very hard if the environment is complicatedand the operator does not have enough information of the follower’s motion Actually,
in the proposed leader-follower system, the orientation of the follower depends onthe force applied to the follower and it is difficult to estimate the motion of thefollower in advance
In this research, we solve the problem by controlling the leader on its collisionfree path and allocating the obstacle avoidance function of both the transportedobject and the follower to the follower When the leader is moving on a collision freepath, the collision between the object and obstacles could be avoided by controllingthe orientation of the object, which is depending on the follower’s motion This can
be realized by introducing an avoidance velocity vector to the follower’s motioncontrol (Fig 3) In [9], we proposed a control system for achieving the cooperativetransporting task in a static environment based on this function allocation concept
In the proposed system, a fixed trajectory is given to the leader in advance andthe follower’s collision motion is based on a static map of the environment, whichinvolves the position and the geometrical information of the obstacles However,when we apply this system to more general environment, we have to construct themap each time Furthermore, static maps information is not enough if there has largeslips of the wheels of the robots or the position of the obstacles are changed duringthe execution of the transportation task In this paper, we use the camera installed onthe leader to provide environment information in front of the leader to the operator
We also utilize an omni-directional vision sensor to get the information of theenvironment not only around the robot but also around the object for the avoidancemotion of both the object and the follower in the dynamic environment The omni-directional vision sensor is installed on the top of the follower’s rotational center
Trang 14Teleoperation System for Two Tracked Mobile Robots 337
Fig 4 Omni-directional image of the follower
dur-ing object transportation The object is projected as
a dark trapezoid sharp area from the image center.The leader is supporting the front part of the objectwhich is indicated by two white marks on the object
Fig 5. Processed directional image shown inFig 4: (a) detected marks of theleader (b) detected obstacles
omni-Processed data of the omni-directional image, which are including the position ofthe obstacles and the orientation of the object, are utilized for the motion control
of the follower In this system, the operator only needs to take care of the leader’sobstacle avoidance, which is a reasonable easy task for the operator from the remotesite
4 Control of Robots
4.1 Control of Leader
The operator controls the leader’s motion based on the information from a camerainstalled on the front side of the leader The leader is controlled by a 2-DOF joystick.This joystick has the translational velocity input and the angular velocity input.The control commands of the joystick are sent through the wireless Ethernet in ourlaboratory
4.2 Control of Follower
Detecting of object In [9], the object is modeled as the line |P Q|, which consists of
the free rotational joint of the robots, as shown in Fig 3 In addition, the orientation
of the object is decided by utilizing the data of the force sensor which is mounted
Trang 15338 H Takeda, Z.D Wang, and K Kosuge
Fig 6 determination of the nearest point
on each obstacle by referring the pixel data
of the obstacle’s area
minimum distance between the i-th obstacle and the object which is described as
obstacles In this paper, we model the object and get the orientation of the object byprocessing the two white marks on the object, one of which is on the position of thefree joint of the leader as shown in Fig 4 This image is digitized to distinguish themarks as shown in Fig 5(a) This makes the sensing more stable comparing to theprevious method based on the output of the force sensor
Detecting obstacles In the digitized image from the omni-directional vision sensor,
the area of the obstacle is extracted by utilizing the area filter(Fig 5(b)) Each
Next the value of the pixels on perpendicular line of the object from the point
area of the obstacle can be decided The follower refers the value of the pixel along
Avoidance motion of follower The avoidance velocity vector Vavd is generated asfollows[9]
constant From eqs.(3) and (4), the follower could avoid obstacles by specifying the
For the rotational motion around the free rotational joint of the follower, we considerthat how the follower generates the angular velocity of the follower around its freerotational joint by using the velocity along the heading direction of the follower and
Trang 16Teleoperation System for Two Tracked Mobile Robots 339
Fig 7 The motion direction of the follower is derived
by the velocity vector of the object, which is lated by estimation of the leader’s motion Vf, and theavoidance velocity vector Vavd, which is generatedbased on the minimum distance among the obstaclesand the object
the follower is also calculated as follows
θV f−avd= tan−1 Vavd
Let us consider how the follower aligns its orientation to the direction calculated
magnitude of the force f applied to the follower as shown in Fig 2
dual caster as shown in Fig 2 By specifying the velocity along the heading direction
of the follower calculated by the estimation algorithm expressed in section 3 andthe angular velocity of the follower around its free rotational joint expressed in thissection, the follower could transport a single object in coordination without collidingwith obstacles
Trang 17340 H Takeda, Z.D Wang, and K Kosuge
Fig 8 Experimental system: View of the
coordi-is sent by the wireless Ethernet The follower was controlled by using the proposedalgorithm in the previous section
The results are shown in Figs 10– 11 Fig 10 shows the pathes of the leadercontrolled by the human operator and the follower using the proposed algorithmrespectively and the snap shot of the experiments Fig 11 shows the translationaland angular velocity of the leader It is evident that the leader realizes the motioninstructed by the joystick input As shown in Figs 10– 11, the transportation taskwas successfully done without colliding with the obstacles In this experiment, thefollower detects the obstacles which are coming close to the object or itself andgenerates the avoidance motion Then we can see that the leader and the followercould execute the transportation task successfully