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Transporting an Object by aPassive Mobile Robot with ServoBrakes in Cooperation with aHumanYasuhisa Hirata a , Zhidong Wang b , Kenta Fukaya c &Kazuhiro Kosuge da Department of Bioengineering and Robotics, TohokuUniversity, 6-6-01, Aoba, Aramaki, Aoba-ku, Sendai980-8579, Japan;, Email: [email protected] Department of Advanced Robotics, Chiba Institute ofTechnology, Narashino, Chiba 275-0016, Japanc Department of Bioengineering and Robotics, TohokuUniversity, 6-6-01, Aoba, Aramaki, Aoba-ku, Sendai980-8579, Japand Department of Bioengineering and Robotics, TohokuUniversity, 6-6-01, Aoba, Aramaki, Aoba-ku, Sendai980-8579, JapanPublished online: 02 Apr 2012.

To cite this article: Yasuhisa Hirata , Zhidong Wang , Kenta Fukaya & Kazuhiro Kosuge(2009) Transporting an Object by a Passive Mobile Robot with Servo Brakes in Cooperationwith a Human, Advanced Robotics, 23:4, 387-404, DOI: 10.1163/156855309X408745

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Advanced Robotics 23 (2009) 387–404www.brill.nl/ar

Full paper

Transporting an Object by a Passive Mobile Robot withServo Brakes in Cooperation with a Human

Yasuhisa Hirata a,∗, Zhidong Wang b, Kenta Fukaya a and Kazuhiro Kosuge a

a Department of Bioengineering and Robotics, Tohoku University, 6-6-01, Aoba, Aramaki,Aoba-ku, Sendai 980-8579, Japan

b Department of Advanced Robotics, Chiba Institute of Technology, Narashino,Chiba 275-0016, Japan

Received 2 May 2008; accepted 7 August 2008

AbstractIn this paper, we introduce a passive mobile robot called PRP (Passive Robot Porter) to realize transportationof an object in cooperation with human, which is developed based on a concept of passive robotics. PRPconsists of three omni-directional wheels with servo brakes and a controller. It can manipulate an objectby controlling an external force/moment applied by a human based on the control of the servo brakes. Weconsider the characteristics of the servo brakes and control the brake torque of each wheel based on thebrake force/moment constraint so that several motion functions of PRP are realized based on the appliedforce. This allows PRP to track a path which includes motion perpendicular to the pushing direction of thehuman without using servo motors. The impedance-based motion control is also realized with respect to theperpendicular to the pushing direction. These functions are implemented on PRP experimentally, and theexperimental results illustrate the validity of PRP and its control method.© Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2009

KeywordsPassive mobile robot, passive robotics, object handling, human–robot interaction, brake control

1. Introduction

Most robots have been used as industrial robots in factories to replace humans do-ing tasks that humans do not want to do or could not do, and have been isolatedfrom humans. Recently, however, we expect to utilize robot systems not only in theindustrial fields, but also fields such as the home, office and hospital in cooperationwith humans. For realizing physical support for a human being using robot systems,we have to consider two main points: achieving high performance and user safety.

* To whom correspondence should be addressed. E-mail: [email protected]

© Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2009 DOI:10.1163/156855309X408745

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388 Y. Hirata et al. / Advanced Robotics 23 (2009) 387–404

To achieve high performance, human–robot cooperation issues have been stud-ied by many researchers [1–5] for augmenting human performance. Most of theseconventional intelligent robot systems have servo motors that are controlled basedon the sensory information from sensors such as force/torque sensors, ultrasonicsensors and laser range finders. The high performance for intelligent systems is re-alized in the form of functions such as power assist, collision avoidance, navigation,variable motion characteristics, etc.

However, if we cannot appropriately control the servo motors of the intelligentsystems, they can move unintentionally and might be dangerous for human beings.In particular, in Japan, the legislation has to be formulated for using them in a liv-ing environment practically. In addition, these systems with servo motors tend tobe heavy and complex, because of the servo motors, reduction gears, sensors, con-troller, batteries, etc. The battery problem is also very severe for long time working,as the servo motors need much electricity to work.

On the other hand, Goswami et al. have proposed concept of passive robotics [6],in which the system moves passively based on the external force/moment withoutusing the actuators, and have dealt with the passive wrist, whose components aresprings, hydraulic cylinders, dampers, etc. The passive wrist responds to an appliedforce by computing a particular motion and changing the physical parameters ofthe components to realize the desired motion. Peshkin et al. have also developeda handling system of an object called Cobot [7] based on passive robotics, whichconsists of the caster and the servo motor for steering its caster.

The concept of the passive robot has been extended to many fields. Wasson etal. [8] and Rentschler et al. [9] proposed a passive intelligent walkers. In most ofthese walkers, a servo motor is attached to the steering wheel, similar to the Cobotsystem [7], and the steering angle is controlled based on environmental informationfor navigating the user. We have also proposed a passive intelligent walker calledRT Walker (Robot Technology Walker) [10]. It differs from other passive intelligentwalkers in that it controls servo brakes appropriately to realize several functionswithout using any servo motors.

In addition, PADyC (Passive Arm with Dynamic Constraints) has been proposedas an assistant tool for surgeons [11]. Other applications for surgical robots are seenin Ref. [12]. Applications to rehabilitation have also been considered by many re-searchers. One example is shown in Ref. [13]. Applications of the concept to hapticdisplays have been proposed in Refs [14, 15]. These passive systems are intrinsi-cally safe because they cannot move unintentionally with a driving force. Thus,passive robotics will prove useful in many types of intelligent systems throughphysical interaction between the systems and humans.

In this research, we develop a new passive-type mobile robot system for han-dling a single object in cooperation with a human. The passive object handlingrobot called PRP (Passive Robot Porter) consists of three omni-directional wheelswith servo brakes, which can realize omni-directional motion, and its motion iscontrolled based on the servo brakes similar to RT Walker proposed by us [10].

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Y. Hirata et al. / Advanced Robotics 23 (2009) 387–404 389

Different from the object handling robot called Cobot [7], PRP does not utilize anyservo motors for realizing the passive robotics concept; it utilizes the servo brakes,which have some unique characteristics. The constraints based on the characteris-tics of the servo brake make the control of a passive robot difficult compared torobot with servo motors. In this paper, we especially address the characteristicsof the servo brake and derive the servo brake condition for controlling the omni-directional passive mobile robot. Finally, experimental results on the path trackingmotion control and the impedance-based motion control for transporting an objectin cooperation with a human illustrate the validity of the proposed system.

2. PRP

We have developed a passive object handling robot called PRP as shown in Fig. 1based on the concept of passive robotics [6]. PRP consists of three omni-directionalwheels with servo brakes and a controller. The omni-directional wheel consists ofseveral small free rollers so that the wheel can move in all directions. Each omni-directional wheel is directly connected to a servo brake and the three wheels areequally spaced with axes sets spaced apart by 2π/3 radi. Three encoders are alsoinstalled on three wheels for odometry. The brake systems of the whole wheels arepowered by batteries.

The control performance of PRP depends on the characteristics of the servobrakes. In the first prototype of PRP, we used the MR Brake (Magneto-Rheologicalfluid Brake: Load Corp., MRB-2107-3, maximum on-state torque: 5.6 N m) as thepassive actuator. The braking torque of the MR Brake is generated by chain mech-anisms of iron powder from the free-flow state which are reacting to the appliedmagnetic field. This provides high response and good linearity for controlling thebraking torque of wheels. In addition, it consumes a relatively small amount ofpower compared to servo motors and its weight is similar to a motor–gear compo-nent with the same output torque.

Figure 1. PRP.

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3. Characteristics of the Servo Brake

In this section, we first explain the characteristics of the servo brake and de-rive the servo brake condition for controlling PRP. The servo brakes have someunique characteristics. PRP with servo brakes can only move based on the exter-nal force/moment applied to it, because it does not have any active actuators suchas servo motors. This is a very important feature in realizing safety actions. Also,some constraints make the control of the passive robot difficult compared to therobot with servo motors. Let us consider how the output torque of an actuator isapplied to a mobile robot in the case of active and passive actuators such as a servomotor and a servo brake, respectively.

• Output torque of servo motor. It is well known that the torque applied to thewheel τw will be equal to the output torque of the servo motor as:

τw = kmIm, (1)

where Im denotes the input current of a motor and is expressed as −Im_max �Im � Im_max. km denotes the torque constant of the motor. Without losing gen-erality, the gear ratio is assumed as 1.

• Output torque of servo brake. To control the motion of PRP based on the ex-ternal force few applied to the wheel with the servo brake, we can derive thefollowing relationships with the respect to the angular velocity of the wheelwith servo brakes φw:(i) For φw �= 0

τw = −kbIb sgn(φw). (2)

(ii) For φw = 0:

τw ={−fewRw |few|Rw � kbIb

−kbIb sgn(few) |few|Rw > kbIb,(3)

where sgn(∗) is the function to have sign of a parameter. τw is the brake torqueapplied to the wheel which is generated by the servo brake of PRP. Ib is theinput current for the servo brakes and is expressed as 0 � Ib � Ib_max. kb is thepositive coefficient expressed as the relationship between the brake torque andthe input current, and Rw is the radius of the wheel.

Different from the control of the robot with servo motors, we can only controlthe motion of PRP under the relationships of the servo brake. It is obvious thatthe characteristics of the brake system of wheels are complicated compared to amotor–wheel system. The characteristics of the brake system depend on the wheelrotational direction. The sign of the output torque of the wheel is decided by thedirection of the wheel rotation and the magnitude of the torque is proportional to theinput current of the brake. From (2), we can have the following condition betweenthe angular velocity of the wheel and the braking torque of a brake–wheel system:

τwφw � 0. (4)

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This condition is the servo brake control constraint of the system and indicates thatthe system cannot have arbitrary torque from a servo brake. Therefore, we need toconsider the feasible brake torque τw during motion control of a robot.

4. Control Method of a Passive Mobile Robot with a Servo Brake

4.1. Kinematics and Motion Type of PRP

As mentioned in the previous section, PRP consists of three omni-directionalwheels and the axes of the three wheels intersect on a single point. The kinematicsrelation between the motion vector of PRP rq = [rx ry rθ ]T and angular velocityvector of wheels � = [φw1 φw2 φw3]T can be expressed as the following equationwith Jacobian J:

rq = J�, (5)

where:

J =

⎡⎢⎢⎢⎢⎢⎣

0 −Rw√3

Rw√3

−2Rw

3

Rw

3

Rw

3

−Rw

3L−Rw

3L−Rw

3L

⎤⎥⎥⎥⎥⎥⎦

. (6)

Here, Rw denotes the radius of the wheel and L denotes the distance between thecenter of the wheel and intersection point of three axes of wheels in the horizontalplane. The robot coordinate system r� is set as shown in Fig. 2.

Since the brake torque of each wheel depends on the direction of the wheel rota-tion, we classify the motion of PRP into eight different cases based on the signs ofthe angular velocities of the three wheels (sgn(φwi

), i ∈ 1,2,3) as shown in Table 1.

Figure 2. Configuration and robot coordinates of PRP (top view).

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Table 1.Motion types based on brake conditions of PRP

Sign of angular wheel velocity

Wheel 1 + + + + − − − −Wheel 2 + + − − + + − −Wheel 3 + − + − + − + −Motion type no. 1 2 3 4 5 6 7 8

In each motion type, the signs of the angular velocities of the three wheels will notchange. Therefore, the feasible braking torque on each wheel will follow the samerelationship with the input current on the servo brake.

Note that the motion types of PRP can be classified by 27 different cases exactly,if we consider that the velocity of a wheel equal to zero as expressed by (3). Thesecases are the singularities of the braking torque of PRP, which is explained in Sec-tion 4.3 in detail. For simplicity, in this paper, we only consider that each wheelrotates with a velocity during the transportation as shown in (2).

4.2. Feasible Braking Force and Moment Based on Servo Brake Constraint

We can express the relation between braking torque τw = [τw1, τw2, τw3]T gen-erated by wheels and resultant braking force and moment rFw = [rfx,

rfy,rnz]T

applied to the robot as follows:

τw = JT rFw. (7)

This relation is exactly the same with robots with servo motors, which has a linearmapping in the case that J is full rank because of the wheel arrangement of PRP.However, we have to consider that the servo brakes will apply several kinds oftorques to the robot according to the motion types of PRP as shown in Table 1.With the possible torques for all motion types, the braking torque set V will be thesame as for the robot with active actuators:

V = {τw1e1 + τw2e2 + τw3e3 | |τvi| � τmax

}(i = 1,2,3), (8)

where:

[e1 e2 e3] = diag(1,1,1). (9)

This is shown in Fig. 3a as a closed cube in the configuration space of the brakingtorque. Note that each axis of the coordinate system in Fig. 3a expresses the possibletorque of each wheel of PRP. However, it does not mean that all torques in thisset will be feasible by setting a proper control input, since the robot motion onlybelongs to a particular motion type in a moment as shown in Table 1. The servobrake control constraint in (4) should be considered in the derivation of the feasiblebraking torques. Here, we discuss the feasible braking torque in each motion type.Uk denotes the set of feasible braking torque when PRP is in kth motion type (k =

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(a) (b)

(c)

Figure 3. Derivation of feasible force and moment for control of PRP. (a) Total set of braking torque V .(b) Wheel braking torque set U1. (c) Feasible force and moment set A(U1).

1,2, . . . ,8) and A(Uk) denotes the resultant feasible force and moment set of therobot from the feasible braking torque set Uk :

Uk = {τw1e1 + τw2e2 + τw3e3 | τwiφwi

� 0, |τwi| � τmax} (i = 1,2,3) (10)

A(Uk) = {τw1v1 + τw2v2 + τw3v3 | τwi∈ Uk} (i = 1,2,3), (11)

where:

[v1 v2 v3] = JT−1[e1 e2 e3]. (12)

Since PRP has eight different motion types, eight sets of Uk exist as the subsetof set V and, correspondingly, eight A(Uk) sets also exist. It is easy to know thatV = ∑8

k=1 Uk . We note that Uj ∩Uk = φ (j, k = 1,2, . . . ,8, j �= k) and also A(Uk)

have the same propositions.Figure 3b and 3c shows the sets of Uk and A(Uk), respectively, when PRP is in

Case 1. Uk is a subset of V just in one quadrant of the braking torque configurationspace with six plane constraints. The three constraint planes connected to the originof the coordinates are the braking torque constraints. The other three constraintplanes are from the maximum torque limitation of each servo brake.

Since the resultant feasible force and moment set A(Uk) is the set projectedfrom Uk , each constraint surface of A(Uk) set has the same meaning. Note thateach axis of the coordinate system shown in Fig. 3c expresses the possible forces

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and moment derived by PRP, respectively. Based on the motion which belongs toone motion type in Case 1–8, the resultant feasible generalized force rFw and itscorresponding braking torque τw could be determined uniquely.

4.3. Singularity of Braking Torque of PRP

Since the omni-directional wheel incorporated in this system rotates freely on theaxis direction of the wheel, the velocity vwi

of wheel i have two independent com-ponents: the velocity along the braking direction vwi_bra and the velocity on passivedirection vwi_pas . It is well known that the motion of PRP will have an instanta-neous center of rotation xICOR and the velocity of any point on the robot will beperpendicular to the line connected to xICOR as shown in Fig. 4a.

According to the discussion in the previous section, the singular point of thebraking torque exists in the case that vwi_bra = 0 and at this moment, vwi

is equal tovwi_pas . The singular point of the braking torque is not unique in this kind of system.Here, we denote the set of points lsig_wi

that the wheel i is braking singular wherethe instantaneous center of rotation xICOR is located. In PRP shown in Fig. 4b,

(a) (b)

(c)

Figure 4. Instantaneous center of rotation of PRP and singular positions. (a) Normal state. (b) Singu-larity of wheel 1. (c) Singularity of wheels 1 and 3.

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lsig_wiis a line parallel to the rotational direction of the wheel i, and passing through

the intersecting point of the wheel and wheel axis. In addition, from the geometricanalysis, we can understand that there exist points that two wheels are in singularson braking torques as shown in Fig. 4c. In this moment, only the braking torqueof one wheel can be controlled by (2). The other two wheels cannot be controlleddirectly. Torques from those two wheels are governed by (3).

Note that from the viewpoint of control, the singularity of PRP and many otherpassive systems is different from the singularity of manipulator or leg mechanisms.In general serial manipulator and leg systems, the motion degrees of freedom of therobots are degenerated so that the control of the robot becomes unstable if we do notapply another control method here and the robot might move unintentionally. On theother hand, the singular points of the passive robot are led from the servo brake con-dition as shown (3). This means that the singular configuration only happens whilethe velocity of one or more servo brakes is zero. In this case, the braking torque hastwo characteristics: (i) it has both upper and lower bounds which are determined bycommand current to the brake, and (ii) it always balances with the external force onthe wheel with passive behavior in cases where it does not reach the upper or lowerbound. Different from the singularity in an active manipulator or leg systems, thesetwo characteristics make the passive system convenient for motion control in/nearsingular points and are great advantages to the physical human–robot cooperationsystem. The motion control method in the singular points should be considered inmore detail in future work.

4.4. Motion Control of PRP Based on Feasible Braking Force and Moment

During object transportation by utilizing a mobile robot, the force and moment rFdshould be generated in real-time, which are determined by the control law appliedto the system such as motion control for path tracking, obstacle collision avoidance,impedance control, etc. For an active-type robot using servo motors, we just simplycommand the servo motors of the robot to generate torques for realizing this de-sired force and moment rFd. However, in the control of a passive robot system, thefeasible force and moment always depend on the current motion of the system.

If the desired force and moment rFd is within the feasible force and moment set inthe current motion of PRP, which is determined by the sign of the angular velocitiesof the wheels explained in the previous section, we can command the brake torquesof the wheels directly as rFw = rFd. On the other hand, of course, many cases existwhere the desired force and moment rFd is located out of the feasible set of theforce and moment, and cannot be generated by servo brakes. One typical exampleis that a passive robot cannot generate force or moment for accelerating the motionof the object by itself.

The system considered here is that a human operator is always pushing PRP andthe system dynamics can be represented as:

(MPRP + Mobj)rq + D rq = rFh + rFw, (13)

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where MPRP and Mobj denote the inertia matrices of the robot and the object, D de-notes the damping coefficient matrix. rFh is the force and moment applied by thehuman operator, and rFw is the feasible braking force and moment generated by theservo brakes of PRP. In addition, the force/moment applied by the human rFh canbe divided into two elements. One is the driving force/moment rFt utilized for thetransportation of the object along the pushing direction of the human and the otheris the assistive force/moment rFa for realizing the several functions such as pathtracking. This relationship is illustrated by:

rFh = rFt + rFa. (14)

We discuss a motion control algorithm of PRP for realizing several functions.The dynamics of PRP are expressed by (13) and we consider an apparent dynamicsof PRP expressed as follows:

(MPRP + Mobj)rq + D rq = rFt + rFd. (15)

This equation means that PRP is moved based on the driving force/moment rFt andthe desired force/moment rFd for realizing several functions such as path tracking,obstacle collision avoidance, impedance control, etc.

From (13)–(15), we derive the following equation with respect to the brakingforce and moment rFw:

rFw = rFd − rFa. (16)

If we can specify the feasible brake force/moment rFw based on the above equa-tion, the apparent dynamics of PRP expressed by (15) is realized. In other words,(16) means that the desired force/moment rFd is generated by the composition ofthe feasible brake force/moment rFw and the assistive force/moment rFa, which is apart of the force/moment applied by the human as shown in Fig. 5 when rFd is outof the feasible brake force/moment set A(U).

Under the relationship expressed by (16), the feasible brake force/moment rFwshould be derived within the feasible brake force/moment set A(U) so that themagnitude of the assistive force/moment rFa is as small as possible, because if the

Figure 5. Control of PRP based on feasible braking force and moment.

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assistive force/moment rFa is large, the total force/moment of the human rFh in (14)for realizing the transportation task is large and the burden of the human increases.

5. Experiments

In this research, we conducted two experiments to illustrate the validity of the pro-posed passive robot system and its control algorithm. The first is the experiment ofthe path tracking function and the other is the impedance-based motion control. Inboth experiments, we consider that a human operator is always pushing the object.This is important for the passive robot, because this could not only let the objecttransportation task be achieved without losing speed, but also guarantee the con-trollability of PRP based on the feasible brake force and moment.

5.1. Path Tracking Control

For illustrating the validity of the passive object handling robot, we experimentedwith PRP. PRP carries the object rigidly and is controlled to keep its orientationconstant. In this experiment, a human applies a force along the x-axis of the globalcoordinate system as shown in Fig. 6 and PRP is controlled based on the desiredbrake force rfdy along the y-axis of the global coordinate system to follow a linewhich is designed as follows:

Gydes = B cos

(Gxπ

A

)− B (17)

Gydes = −Gxπ

AB sin

(Gxπ

A

), (18)

where Gydes and Gydes are express the desired position and the velocity of PRPalong the y-axis of the global coordinate system, and Gx and Gx are the real positionand the velocity along the x-axis of the global coordinate system. Here, A = 2 m

Figure 6. Transportation of an object using the path following function.

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and B = 0.3 m. From these equations, we can design the desired brake force rfdy asper the following equation for the path tracking control:

rfdy = kdy (Gydes − Gy) + kpy (

Gydes − Gy), (19)

where Gy and Gy are the real position and the real velocity along the y-axis of theglobal coordinate system, and kdy and kpy are the derivative and proportional gains,respectively.

To keep the orientation of PRP, we also design a desired brake moment rnd asfollows:

rnd = kdθ (Gθdes − Gθ ) + kpθ (

Gθdes − Gθ), (20)

where Gθdes and Gθdes express the desired orientation and the desired angular ve-locity of PRP, Gθ and Gθ are the real orientation and the real angular velocity ofPRP, and kdθ and kpθ are the derivative and proportional gains, respectively.

Since we assume that the direction of the force/moment applied by the humanis the x-axis as shown in Fig. 6, the desired brake force rfdy for realizing the pathtracking along the y-axis is obviously located out of the feasible set of the brak-ing force and moment, and cannot be generated by servo brakes only. In this case,the desired force/moment rfdy and rnd are specified by using the feasible brakeforce/moment rFw and the assistive force rfax applied by the human along thex-axis.

As the result, PRP realizes the transportation task based on the driving forcerftx and the desired force/moment rfdy and rnd. Note that this path following func-tion is realized without using the force/torque sensor, because the desired brakeforce/moment in this experiment expressed by (19) and (20) can calculate by onlyusing the position and orientation information of PRP.

The experimental results are shown in Figs 7 and 8. Figure 7 expresses the posi-tion and the orientation of PRP with respect to the x–y plane, and Fig. 8 expressesthe position and the orientation of PRP with respect to the time during the ex-periments of the object transportation. We experimented with PRP with the pathtracking function to avoid the collision with the obstacle as shown in Fig. 9.

Figure 7. Experimental result showing the path of PRP.

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(a) (b)

(c)

Figure 8. Experimental results showing the trajectory of PRP. (a) Position (Gx). (b) Position (Gy).(c) Orientation (Gθ ).

Figure 9. Example of collision avoidance motion based on path tracking control.

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5.2. Impedance-Based Motion Control

In this experiment, we focus on how to realize the desired apparent dynamics ofPRP. This is more challenging than tracking a path since it needs to have a de-tailed design of the interaction with the human being or environment. We considerimpedance-based apparent dynamics because it not only is useful when consid-ering safety issues while the system is directly interaction with human being orenvironment, but also contributes to realizing the cooperative object handling withmultiple PRPs.

We consider realizing the following apparent dynamics of PRP:

Mdrq + Dd

rq + Kd�q = F (21)

�q = rq − rqd, (22)

where rqd is the desired position and orientation of PRP, and Md, Dd and Kd arethe apparent inertia, damping and stiffness matrices, respectively. F is an externalforce applied by humans or the environment. F is measured by the force/torquesensor which is specially attached to PRP for realizing the impedance-based motioncontrol.

For satisfying the above apparent dynamics, we can derive the following equationbased on the actual dynamics of PRP shown in (13) and the apparent impedancedynamics shown in (21):

rFd = (MPRP + Mobj − Md)rq + (D − Dd)

rq − Kd�q + F − rFt. (23)

In this experiment, we consider the impedance-based motion control along they-axis, which is perpendicular to the object transport direction and around the ro-tational direction, under the assumption that the human always pushes the objectalong the x-axis (rFt = [rftx 0 0]T). In addition, the prototype PRP developed inthis research could not provide accurate acceleration feedback because it has onlya low-resolution encoder for each wheel to calculate its acceleration. Therefore, weassume that Md is equal to MPRP + Mobj. From these conditions, we modify (23)as the following equation with respect to the y-axis and the rotational direction:

rFd = (D − Dd)rq − Kd�q + F. (24)

From this equation, we can specify the desired force/moment rFd by using the fea-sible brake force/moment rFw and the assistive force/moment rfax applied by thehuman for realizing the impedance dynamics. Different from the previous experi-ment for path following, the force information is required for calculating the desiredforce rFd in the experiment of the impedance control, i.e., the force/torque sensorhas to be attached to PRP for realizing the impedance dynamics.

For illustrating the validity of the impedance-based motion control, in this ex-periment, a human operator pushes the object along the x-axis and it is pushed byanother one perpendicular to the original path during the transportation. In addition,the orientation of the object is controlled to keep a desired orientation (90◦). Exper-imental results are shown in Figs 10–12. Figure 10 shows the path of PRP on thex–y plane and Fig. 11 shows the force applied to PRP and the position/orientation

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Figure 10. Experimental results of impedance-based control showing the path of PRP.

(a) (b)

(c) (d)

Figure 11. Experimental results of impedance-based control. (a) Force applied to PRP along they-axis. (b) Trajectory of PRP along the y-axis. (c) Trajectory of PRP along the x-axis. (d) Orien-tation of PRP.

of PRP. Figure 12 also shows an example of experiments where PRP is pushedby other person during object transportation. In Fig. 11b and 11d, the actual posi-tion/orientation PRP is compared with the position/orientation calculated from theapparent impedance dynamics.

The experiment results show that with only braking torque, PRP performs goodimpedance-based motion characteristics as shown in Fig. 11b in the direction per-pendicular to the moving direction. When the other person pushes PRP (5.5–8.5 s),PRP is moving to have compliance along the push direction. After the human beingstops pushing (8.5 s), PRP moves back to its original path.

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Figure 12. Example of the experiment on impedance-based motion control.

6. Conclusions

In this paper, we introduced a passive mobile robot called PRP to realize trans-portation of an object in cooperation with a human based on the concept of passiverobotics. It can manipulate an object by controlling the external force/moment ap-plied by the human based on the control of the servo brakes. The analysis of thefeasible braking force/moment set, which depends on the motion of the system, andsingularity of the system are provided. A basic strategy for controlling PRP withassistance force from the human operator was proposed. Finally, we have demon-strated the concept and control strategy by the prototype PRP and illustrated thevalidity of the proposed concept.

How large an assistance force we need to have depends on two points. One is themagnitude of the resultant force that we need to generate for handling the object.Another is the relation between the direction of the assistance force and the geo-metric configuration of the passive wheels. This is the problem of manipulability ofpassive-type systems with the push of the human operator. Some basic investiga-tions on this issue have been done using our prototype PRP. Systematic analysis ofmanipulability and design of interaction force will be our future works.

References

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About the Authors

Yasuhisa Hirata received his BE, ME and PhD degrees in Mechanical Engineer-ing from Tohoku University, Sendai, Japan, in 1998, 2000 and 2004, respectively.From 2000 to 2006, he worked as a Research Associate in the Department ofBioengineering and Robotics, Tohoku University. From 2002 to 2004, he wasa Researcher at Precursory Research for Embryonic Science and Technology(PRESTO), Japan Science and Technology Agency. Since 2006, he has been work-ing as an Associate Professor in the Department of Bioengineering and Robotics,Tohoku University. He received the Young Investigator Excellence Award of the

Robotics Society of Japan in 2001, the Best Paper in Robotics Award of ROBIO in 2004, the ResearchPromotion Award of the Aoba Foundation for the Promotion of Engineering in 2004, the JSME Award

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for Best Paper from the Japan Society of Mechanical Engineers in 2005, the Best Paper Award ofthe Robotics Society of Japan in 2005, and the Original Paper Award of the FANUC FA and RobotFoundation in 2006. His research interests include intelligent control of multiple mobile robots in co-ordination, human–robot cooperation systems, power assist systems and walking support systems. Heis a member of the IEEE, Robotics Society of Japan and Japan Society of Mechanical Engineers.

Zhidong Wang received the BS degree from Beijing University of Aeronauticsand Astronautics, Beijing, China, in 1987, and the MSc and PhD degrees in En-gineering from the Graduate School of Engineering, Tohoku University, Sendai,Japan, in 1992 and 1995, respectively. In 1995, he joined the Advanced RoboticsLaboratory, Tohoku University, where he joined the Intelligent Robotics Labora-tory, Department of Bioengineering and Robotics, in 2001. During 2000–2001,he was a Visiting Scholar of the GRASP Laboratory, University of Pennsylvania.Since 2006, he has been a Professor of Advanced Robotics and the Head of the

Biomimetic Systems Laboratory, Department of Advance Robotics, Chiba Institute of Technology,Chiba, Japan. His current research interests include human–robot systems, distributed autonomousrobot systems and application of intelligent robot technologies for the disabled. He has served atseveral academic meetings, and was the Program Chair of the 2006 IEEE International Conferenceon Mechatronics and Automation, in June 2006, and Program Chair of the 2007 IEEE InternationalConference on Robotics and Biomimetics, in December 2007.

Kenta Fukaya received his BE degree in Mechanical Engineering from WasedaUniversity and ME degree in Mechanical Engineering from Tohoku University,in 2004 and 2006, respectively. Currently, he is working as a Design Engineerin Mitsubishi Heavy Industries, Ltd. In Tohoku University, his research topic wasdevelopment of passive mobile robots with omni-directional wheels and establish-ment of the basis of a motion control method for them.

Kazuhiro Kosuge received the BS, MS and PhD degrees in Control Engineer-ing from the Tokyo Institute of Technology, in 1978, 1980 and 1988, respectively.From 1980 to 1982, he was a Research Staff in the Production Engineering De-partment, DENSO Co., Ltd. From 1982 to 1990, he was a Research Associatein the Department of Control Engineering, Tokyo Institute of Technology. From1989 to 1990, he was a Visiting Scientist at the Department of Mechanical En-gineering, Massachusetts Institute of Technology. From 1990 to 1995, he was anAssociate Professor at Nagoya University. From 1995, he has been a Professor

in the Department of Bioengineering and Robotics, Tohoku University. For more than 20 years, hehas been doing research on various robot control problems. He has over 150 technical publicationsin the area of robotics and its applications to the real world. He received the JSME Awards for theBest Papers in 2002 and 2005, the Excellent Paper Award from FANUC FA and Robot Foundation in2003 and 2006, and the Best Paper Award of IROS’97. He is an IEEE Fellow, a JSME Fellow, a SICEFellow and a RSJ Fellow.

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Download - Transporting an Object by a Passive Mobile Robot with Servo Brakes in Cooperation with a Human

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