Improved control and simulation models of a ... - Semantic Scholar

J Intell Manuf (2008) 19:715–722 DOI 10.1007/s10845-008-0122-4

Improved control and simulation models of a tricycle collaborative robot Z. M. Bi · Sherman Y. T. Lang · Lihui Wang

Published online: 22 June 2008 © Springer Science+Business Media, LLC 2008

Abstract The objective of collaborative manufacturing is to create the synergism from the collaboration of manufacturing resources. Most of the studied collaborations are made among intelligent machines; however, the collaboration can be realized even between machines and human being, and a collaborative robot (Cobot) belongs to the latter. A cobot is a robot designed to assist human beings as a guide or assistor in a constrained motion. Various prototypes have been developed and the potentials of these robots have been demonstrated. The research presented in this paper focuses on the control and simulation models of a tricycle cobot with three steered wheels, with the following two contributions: (i) A concise model for the closed-loop control is developed. Existing closed-loop control has been implemented in an intuitive way, and some control parameters have to be determined by a trial-and-error method. (ii) A simulation model is proposed to validate the control algorithms. No simulation model is available and the control models of other existing systems have to be validated experimentally. The developed control and simulation models have been implemented. Graphic simulation is also developed. Case studies are provided and the simulation results are analyzed. Keywords Collaborative manufacturing · Collaborative robots · Cobot · Passive robots · Mobile robots · Open-loop control · Closed-loop control · Simulation Z. M. Bi (B) Northern Ireland Technology Centre, Queen’s University at Belfast, Belfast BT9 5HN, Northern Ireland, UK e-mail: [email protected] S. Y. T. Lang · L. Wang Integrated Manufacturing Technologies Institute, National Research Council of Canada, London, ON, Canada N6G4X8 L. Wang e-mail: [email protected]

Introduction Collaborative manufacturing fosters the most cost-effective methods to design, source, make, deliver, and service standard, mass-customized or to-order products. Collaborative manufacturing allows various resources to act together to generate the mutual gain (MESA 2004). Most of the studied collaborations are made among the intelligent machines; however, the collaboration can be achieved between machines and human being, and a collaborative robot (Cobot) belongs to the latter. The cobot was first invented at the Northwestern University by Peshkin and Colgate (1996). A cobot is a robot designed to assist human beings as a guide or assistor in a constrained motion. Different from traditional robots, the cobots provide the guidance rather than raw power. They are passive in the sense that the power for fulfilling a task is provided by operators. However, cobots are motorized to restrict their motions when an external force is applied to drive them from planned trajectories. Unlike robots that perform specialized tasks only in restricted areas, cobots have been designed to work with human operators in a shared workspace (Paula 1997). Cobots allow human operators use their muscle power more safely and effectively (Peshkin et al. 2001; Jabre et al. 2002). Most of the cobots are developed for two primary purposes: (i) to assist operators in moving heavy objects under some physical constraints, and (ii) to assist patients or people with disabilities in navigation or rehabilitation. For purpose (i), Peshkin et al. (2000) have proposed a variety of cobots for materials handling. Some cobots for assembly are actually commercially available (Stanley 2002). Besides, Hodgson and Emrich (2002) and Townsend et al. (2004) have developed and patented a prototype cobot for the surgeons to move C-arm X-ray machines, where the surgeon prefers not to

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hand over control of a procedure to an autonomous robot. For purpose (ii), Ulrich and Borestein (2001) have developed a guide-cane to navigate visually impaired patients, and Nejatbakhsh et al. (2005) have developed a passive walker for rehabilitation. The operating principle of cobots is to use Continuously Variable Transmissions (CVTs) to produce high quality rolling constraints (Peshkin and Colgate 1996). In many cases, cobots use steered rolling wheels as the CVTs, and their appearances are similar to a mobile robot with the steered wheels. However, the rolls of the wheels of a cobot are free rather than controlled in a mobile robot, and the control mechanisms are significantly different from that of a mobile robot. A few researchers have studied the control of cobots. Nejatbakhsh et al. (2005) and Ulrich and Borestein (2001) have developed a control model for the cobots; the differences of their systems are that the latter used omni-wheels instead of steered wheels, and the omni-wheels are actually controlled by braking instead of steering. Peshkin and his collaborators have established the most extensive control models for tricycle cobots. In their model, the planned trajectory is parameterized in terms of the arc length, and the rotational velocities of the steered wheels have to be detected to calculate control variables (Peshkin and Colgate 1996; Wannasuphoprasit et al. 1997; Wannasuphoprasit 1999; Gillespie et al. 2001; Peshkin et al. 2001). This, however, brought a technical problem to mount the encoders on steered wheels, since the electrical wires of the encoders could be twisted when the wheels are steered freely. To overcome the problem, the developers installed another set of glide wheels to measure the rolling velocities (Mills 1998). In this paper, the extensive works include: (i) a concise model for closed-loop control (in literatures, the closed-loop control of a cobot has been implemented in an intuitive way); (ii) a simulation model for validation of the control algorithms. So far, no simulation model is available and the control algorithms have to be validated experimentally (Boy et al. 2003). Both of control and simulation models have been implemented. Case studies are also provided and the simulation results are analyzed. The remainder of the paper is organized as follows. In section “Description of cobot”, the

Fig. 1 Geometric description and parameters of a cobot. (a) Geometric description; (b) Structural parameters

(a)

parametric description of a tricycle cobot is presented. In sections “Open-loop control” and “Closed-loop control”, forward and closed-loop control models are developed, respectively. In section “Simulation model”, simulation model is developed for the validation of the control models. In “Implementation and case studies”, case studies are illustrated and conclusions are drawn from the simulation results. Finally, section “Summary and furture work” summarizes our works. Description of cobot The tricycle cobot has a motion with three degrees-offreedom (DOF), i.e., x- and y-translations and z-rotation. The motion trajectory is specified based on the given task; but the cobot is moved by a human operator, and the wheels are controlled to steer the cobot to the desired moving direction. A laser tracking system is needed to acquire the posture and velocity of the cobot continuously. The tricycle cobot consists of a platform and three steered wheels. As shown in Fig. 1a, the posture of the cobot is defined with respect to the reference point Oc . To describe the motion of the cobot, the world coordinate system is denoted as {O-XYZ}. The cobot is represented by a local coordinate system {Oc -X c Yc Z c } with the origin of Oc . The structural parameters are listed in Fig. 1b. Without losing the generality, the world coordinate system is chosen to be consistent with the local coordinate system {Oc -X c Yc Z c } at its origin. Open-loop control As shown in Fig. 2, open-loop control is to decide the controllable variables ωi (i = 1, 2, 3) merely based on a specified trajectory and measured velocities of the cobot. Open-loop control does not require the feedback to determine the values of the controlled variables at the next time step. The goal of open-loop control is to achieve the planned cobot motion (rc , θc ) by manipulating steering velocities ωi (i = 1, 2, 3). The control system has two inputs: (i) the planned motion trajectory, and (ii) the detected linear speed and acceleration

(b)

r2 (x2, y2) Wheel 2

L2

Reflectors for sensors Yc

α3 xc

Wheel 3 Y

L3

Platform

α2

θc

α1 yc

Xc L1

Wheel 1

r3 (x3, y3) r1 (x1, y1) O

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X

Li The normal of the vector Li from a wheel center to reference point Oc αi The angle between Xc and Li ri (xi, yi) The position of wheel center i rc (xc, yc) The position of reference point Oc of the cobot θc The rotation of the cobot with respect to X

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717

vc dq = 

2 2 dt dyc d xc + dq dq 
d2q dt 2

=

d xc dq

 2
2 d xc d 2 xc dyc c + dy a − c dq dq dq 2 + dq
2
2 d xc c + dy dq dq

(2)

d 2 yc dq 2




 dq 2 dt

(3)

2

Fig. 2 Open-loop and closed-loop controls

of the motion along the trajectory. The latter relies on the external force applied to the robot, and it is measured by the laser tracking system mounted on the platform of the cobot. The control system has the output of the required rotating speeds of the steering wheels. In the next section, the relationship between the inputs and outputs is discussed. Description of the motion of the cobot platform As shown in Fig. 1a, the motion of the platform is denoted as (rc , θc ), where rc = [xc , yc ]T is the position of Oc , and θc is the z-axis rotation of the cobot under the world coordinate system {O-XYZ}. Many researchers used arc length s as the parameter of a trajectory (Wannasuphoprasit et al. 1997; Wannasuphoprasit 1999; Gillespie et al. 2001; Peshkin et al. 2001). However, it is common that an explicit description of a trajectory requires a curve parameter other than the arc length. The conversion between different descriptions has to be determined. Assume an arbitrary curve parameter q has to be used to describe a trajectory explicitly, xc = xc (q) ,

yc = yc (q) , θc = θc (q)


(1) 

c dθc and Deviating with respect to time q gets ddqxc , dy dq , dq
2  2 2 d xc d yc d θc , which are obtained from the specified tra, , dq 2 dq 2 dq 2 jectory in Eq. 1.

Determination of cobot motion based on detected vc and ac The actual linear speed vc and acceleration ac along the trajectory depend on the external forces applied by a human operator. However, they have to be detected to implement the control. One has,

d q where dq dt , dt 2 are the derivations of q with respect to time t, respectively. The motion velocity and acceleration of the cobot platform are finally calculated as dyc dq ˙ dθc dq ⎫ x˙c = ddqxc dq dt , y˙c = dq dt , θc = dq dt ⎪ ⎪ ⎪
2 ⎪ ⎪ d 2 xc dq d xc d 2 q ⎪ x¨c = dq 2 dt + dq dt 2 , ⎬
 2 (4) 2 2 c d q ⎪ y¨c = ddqy2c dq + dy ⎪ dt dq dt 2 , ⎪ ⎪
2 ⎪ 2 2 ⎪ ⎭ θ¨c = d θ2c dq + dθc d q2 dq

dt

dq dt

The control of the steered wheels The position ri of the center of a steered wheel is calculated from the known motion of the reference point Oc in Eq. 1 



xc + L i cos (θc + αi ) xi = (i = 1, 2, 3) . (5) ri = yc + L i sin (θc + αi ) yi Taking the derivation of Eq. 5 with the time gives the velocity of ri as



 x˙i x˙c − L i sin (θc + αi ) θ˙c dri = dt = y˙ ˙ y˙c + L i cos (θ⎡c + α i ⎤i ) θc

 x˙c (i = 1, 2, 3) 1 0 −L i sin (θc + αi ) ⎣ ⎦ = y˙c 0 1 L i cos (θc + αi ) θ˙c (6)   where x˙c , y˙c , θ˙c have been calculated from Eq. 4. Similarly, the acceleration of ri is obtained as ⎡ ⎤  x¨c

2 d ri 1 0 −L i sin (θc + αi ) ⎣ ⎦ = y¨c 0 1 L i cos (θc + αi ) dt 2 θ¨c ⎡ ⎤  x˙

0 0 −L i θ˙c cos (θc + αi ) ⎣ c ⎦ + y˙c (7) 0 0 −L i θ˙c sin (θc + αi ) θ˙c   where x¨c , y¨c , θ¨c have been calculated from Eq. 4. Note that the linear velocity and acceleration of the cobot along the planned trajectory have to be calculated to determine the controlled steering. The linear velocity is expressed as 

2 dsi 2 dyi d xi = + dt dt dt

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Finally, the steering velocity of a wheel has to satisfy ωi = κi u i = κi

ni

ti

dϕ κ ( s) = ds

dsi dt

(14)

By applying the developed model, the steering velocities of three wheels can be determined from the given motion profile Eq. 1 of the reference point Oc of the cobot.

ri Closed-loop control

ϕ

In the open-loop control described in the previous section, the steering velocities of the wheels are determined under the condition that the cobot follows the planned trajectory perfectly. However, it is unrealistic due to the factors such as the slips of wheels. As shown in Fig. 2, closed-loop control takes into considerations of the discrepancy of the actual trajectory from the planned trajectory, so that the steers of the wheels can compensate this discrepancy. As shown in Fig. 4, the motion within time duration (t, t + t) is considered. Assume that the discrepancy of motion

Fig. 3 Relation of the tangent vector on the curvature normal vector on a trajectory

 = x˙c2 + y˙c2 +L i2 θ˙c2 +2L i θ˙c (−x˙c sin(θc +αi )+ y˙c cos(θc +αi )) (8) where si is the parameter for arc length on the trajectory of the center of a steered wheel. Taking the derivation of Eq. 8 with the time gives

x˙c x¨c + y˙c y¨c + L i2 θ˙c θ¨c − [L i θ¨c x˙c + L i θ˙c (x¨c + y˙c θ˙c )] sin(θc + αi ) + [L i θ¨c y˙c + L i θ˙c ( y¨c − x˙c θ˙c )] cos(θc + αi ) d 2 si  = dt 2 x˙ 2 + y˙ 2 + L 2 θ˙ 2 + 2L θ˙ (−x˙ sin(θ + α ) + y˙ cos(θ + α )) c

c

i c

i c

The center of each steered wheel has its own motion trajectory of ri under {O-XYZ}. The tangent vector ti of this trajectory becomes ti =

dri = dsi

dri dt dsi dt

(10)

where ti is the tangent vector of the motion trajectory ri , and dsi i it is proven to be a unit vector (Belyaev 2006). dr dt and dt are defined in Eqs. 6 and 8, respectively. Taking the derivation of Eq. 10 with time gives dti = dsi where

dti dt dsi dt dri dt

=

·

dsi dt




− dsi dt

dri dt 3

·

d 2 ri are defined dt 2 d 2 si are defined in dt 2

and

dsi dt

d 2 ri dt 2

d 2 si dt 2

(11)

in Eqs. 6 and 7, respectively,

and and Eqs. 8 and 10, respectively. As a result, the curvature of the trajectory of ri can be determined from κi ni =

dti dsi

(12)

dti where ds has been calculated in Eq. 11, and ni can be found i from its relation with ti illustrated in Fig. 3 as 

cos( π2 ) sin( π2 ) t (13) ni = − sin( π2 ) cos( π2 ) i

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c

c

i

c

c

(9)

i

trajectory is detected at the time t, and t is the time duration required to correct the discrepancy. At the time t, the reference point Oc of the cobot is supposed to be at r0,e ; however, the actual position is at r0,a under a discrepancy r. The actual trajectory should be corrected after time duration t. Considering both of the discrepancy and the planned trajectory, an interpolated function is used to replace the planned trajectory during this time period. This replaced trajectory starts from r0,e , and return to r1,e on the planned trajectory after time duration t. To maintain the smoothness of the motion, the tangent vectors of the beginning and ending points on the interpolated equation are consistent with those on the corresponding points of the planned trajectory. Assume the interpolated trajectory has the continuation of its derivation, one has r ≈ r0 + r˙0 t +

r¨0 t 2 2

(15)

Equation 15 will be adjusted due to the discrepancy of the trajectory, i.e. r ≈ (r0 + r0 ) + (˙r0 + ˙r0 ) t +

(¨r0 + ¨r0 ) t 2 2

(16)

To maintain the continuation, the following conditions must be satisfied,

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Fig. 4 Planned and actual trajectories. (a) Translation; (b) Rotation

(b)

(a)

θ c1,a ( θ c1,e)

t1,a (t1,e) t0,a r0,a

r1,a (r1,e)

θc

θ c0,a

t0,e θc0,a

∆r

∆s

r0,e Acutal trajectory

∆θc Acutal trajectory

Expected trajectory

θ c0,e

θc0,e Expected trajectory

t

  2 r t=t − r1,e = r0 + ˙r0 t + ¨r02t = 0  r˙ t=t − r˙1,e = ˙r0 + ¨r0 t = 0

(17)

Therefore, ¨r0 = ˙r0 =

2r0 t 2 −2r0 t

θc0,a (θc0,e)

 (18)

In the same way, the compensations of the θc motion profile can be calculated. After the compensations for position r, velocity ˙r0 , and acceleration ¨r0 of the motion profile of the cobot are determined, and Eqs. 6–14 can be applied again to determine the controlled variables ωi (i = 1, 2, 3) at this time step.

t+∆t

Time

is needed. As shown in Fig. 5, a simulation model is to tackle the dual problem of system control, i.e., to determine the posture of cobot at certain time step when the steered velocities of three wheels are given. The inputs and output of the simulation model are illustrated in Fig. 5; the inputs include (i) the posture of the cobot at time t, (ii) the measured linear velocity and acceleration of the cobot at the time t, and (iii) the steered variables ωi (i = 1, 2, 3). The output is the posture of the cobot after time duration t.

Simulation model It is ideal to validate the control models before the physical system is actually developed. Therefore, a simulation model

rc 0 ω i (i =1,2,3)

vc,ac

α i ,L i (i =1,2,3)

rc

Fe

Fig. 5 The inputs and output of the simulation model

Fig. 6 Determination of the posture of cobot when the steered velocities ωi (i = 1, 2, 3) are given

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As shown in Fig. 6, the simulation model include two steps: (i) to determine the new positions ri (i = 1, 2, 3) of the centers of three steered wheels from the known original positions and the steered velocities ωi (i = 1, 2, 3) of the wheels, and (ii) to calculate the posture of the reference points Oc from ri . As shown in Fig. 6, taking into considerations of the change of tangent vector on the motion trajectory of a wheel center, one has 

cos (ωi t) sin (ωi t) r˙ (19) r˙i = − sin (ωi t) cos (ωi t) i0

velocity along the trajectory that is simulated by a random function with the time. The system output is the actual trajectory of the cobot based on controllable variables ωi (i = 1, 2, 3). The performance of the control is evaluated by comparing the planned trajectory and the actual trajectory determined by the simulation model. In the case studies, both of straight and circle motions are considered, and the planned trajectory is assumed to be ⎫ xc = vx φ + r cos φ ⎬ yc = v y φ + r sin φ (24) ⎭ θc = kφ

Correspondingly, the change of the position ri is represented by  t (20) r˙i dt ri1 = ri0 +

where vx = 125.0 mm/s, v y = 0.0, r = 500.0 mm, k = 0.1. The simulated linear speed vc along the trajectory is assumed to be evenly distributed within (0.0, 1000.0),

t=0

Substituting Eq. 19 into Eq. 20 gives

 1 sin (ωi t) ri0x + (1 − cos (ωi t)) ri0y ri1 = ri0 + ωi sin (ωi t) ri0y − (1 − cos (ωi t)) ri0x (21) Once ri (i = 1, 2, 3) is calculated from Eq. 21, the orientation of the cobot can be determined as   (r11 − r01 ) · (r10 − r00 ) (22) θc1 = θc0 + a cos r11 − r01  · r10 − r00  The position of the cobot platform is determined as rc1

 3  1 cos (θc1 + αi ) ri1 − L i = sin (θc1 + αi ) 3

(23)

i=1

Implementation and case studies The control and simulation models are programmed and implemented in the Java environment. The system inputs include a planned trajectory that can be arbitrary and the (b) 7

Max/Average Errors (arc)

Max/Average Errors (mm)

(a) 6 5 4 3 2 Max

1

Average

0 0

0.002

0.004

0.006

0.008

Time step (second)

vc = 1000.0 ∗ random() (mm/s) The linear acceleration ac can be determined from the differential of vc accordingly. Random() is a function to represent an even distribution within (0.0, 1.0). Case study 1: open-loop control Control accuracy vs. size of time step Under the open-loop control, the maximum and average position errors with respect to time step have been simulated in Fig. 7a. The maximum position error is the high peak of the position error along the trajectory from the origin to the current position at the measured time. The average position error is the mean value of the position errors of all points on the trajectory from the origin to the current position at the measured time. It is shown that the position error is closely related to the size of time step. It is reduced dramatically when the size of time step is reduced. The similar result can be observed for the discrepancy of orientation of the cobot from Fig. 7b.

2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04

Max Average

0.00E+00 0.01

0

0.002

0.004

0.006

0.008

0.01

Time step (second)

Fig. 7 The position and orientation errors vs. the time step of open-loop control. (a) Max and average position errors; (b) Max and average orientation errors

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(a) 1.60E+02

(b) 7.00E-02

1.40E+02 1.20E+02 1.00E+02 8.00E+01 6.00E+01 4.00E+01 Max Average

2.00E+01 0.00E+00 0.00E+00

1.00E-01

2.00E-01

Max/Average Errors (arc)

Max/Average Errors (mm)

Fig. 8 The positional and orientational errors vs. trajectory parameter φ. (a) Max and average position errors; (b) Max and average orientation errors

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3.00E-01

6.00E-02 5.00E-02 4.00E-02 3.00E-02 2.00E-02

0.00E+00 0.00E+00

phi (arc)

1.00E-01

2.00E-01

3.00E-01

phi (arc)

(b) 4.00E-05

0.12 0.1 0.08 0.06 0.04 Max

0.02

Average 0 0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01 3.00E+01

Max/Average Errors (arc)

(a) 0.14 Max/Average Errors (mm)

Fig. 9 The position and orientation errors vs. trajectory parameter t in closed-loop control. (a) Max and average position errors; (b) Max and average orientation errors

Max Average

1.00E-02

3.50E-05 3.00E-05 2.50E-05 2.00E-05 1.50E-05 Max

1.00E-05

Average

5.00E-06 0.00E+00 6.00E+00 1.20E+01 1.80E+01 2.40E+01 3.00E+01

phi (arc)

phi (arc)

Control performance under motion discrepancy Assume that a random discrepancy within 1% of the total values of controllable variables happens in the open-loop control. In Fig. 8a and b, both the discrepancies of the position and orientation are accumulated with the time rapidly and the result of the open-loop control becomes unacceptable. It is obvious that the pure open-loop control is impractical. Case study 2: closed-loop control Control accuracy vs. size of time step Closed-loop control takes advantages of the feedback of the actual trajectory, and the controllable variables are compensated by combining the requirements of the planned trajectory and the discrepancy of the actual trajectory. The size of time step has the similar influence on the control accuracy. Both the discrepancies of the position and orientation of the cobot can be reduced in the same way when the size of time step is reduced.

Fig. 10 Simulation of the cobot controls in Java3D

of the time, and the result of the closed-loop control is acceptable.

Control performance under motion discrepancy

Graphic simulation

Similarly, assume that a random discrepancy within 1% of the total values of controllable variables happens in the closedloop control. In Fig. 9a and b, both the discrepancies of the position and orientation become stable after a certain period

As shown in Fig. 10, a Java3D model of the cobot has been created. The control and simulation models are also implemented. The calculated results are used to drive the graphic simulation. Fig. 10 has illustrated the motion on the trajectory

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segment (φ = 0.0 ∼ 4π ) under the forward and closed-loop controls.

Summary and future work A tricycle cobot with three steered wheels have been investigated. Some issues of available control and simulation models have been discussed. The works presented in this paper is motivated to address these issues. The contributions of this paper have three aspects: (i) the control model has been developed based on a generalized description of the motion trajectory of the cobot. The advantage of the improved model is that only the motion of the reference point of the cobot is needed to be measured and this eliminates the technical challenge of mounting rolling encoders on the steered wheels; (ii) the closed-loop control is implemented by an interpolated function. The trial and error method for the determination of the intuitive gains can thus be avoided; (iii) the simulation model is developed so that the control algorithms and models can be validated cost-effectively. Our future work is to develop a physical system and to validate the developed theoretical models through experiments.

References Belyaev, A. (2006). Plane and space curves, curvature, curvature-based features, http://www.mpi-sb.mpg.de/~belyaev/gm06. Boy, E. S., Burdet, E., Teo, C. L., & Colgate, J. E. (2003). Motion guidance experiments with scooter cobot. In Proceedings of the 11th Symposium on Haptic Interfaces for Virtual Environment and Teleoperators Systems, HAPTICS 2003 (pp. 63–69). Gillespie, R. B., Colgate, J. E., & Peshkin, M. A. (2001). A general framework for cobot control. IEEE Transactions on Robotics and Automation, 17(4), 391–401.

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J Intell Manuf (2008) 19:715–722 Hodgson, A. J., & Emrich, R. (2002). Control of a minimally constrained cobot. Journal of Robotic Systems, special section on robot and human integration, 19(7), 299–314. Jabre, L., McGrew, R., Gillespie, R. B., & Goleski, P. (2002). An assistive cobot for aid in self care activities. 2nd IFAC Conference on Mechatronic Systems, Berkeley, CA, December, 2002. MESA. (2004). Collaborative manufacturing explained. http://www. automationworld.com/images/sponsored_content/wp_mesa_cme. pdf. Mills, A. L. (1998). An analysis of position and velocity sensor systems for a 3 degree-of-freedom planar collaborative robot. MS thesis, Northwestern University, USA. Nejatbakhsh, N., Hirata, Y., & Kosuge, K. (2005). Passive omnidirectional walker—design and control. In 12th International Conference on Advanced Robotics, ICAR ’05, July 18–20, 2005, pp. 518–523. Paula, G. (1997). Cobots for the assembly line. http://www.memagazine. org/backissues/october97/features/cobots/cobots.html. Peshkin, M., & Colgate, J. E. (1996). ‘Cobots’ work with people. IEEE Robotics & Automation Magazine, 3(4), 8–9. Peshkin, M., Colgate, J. E., Akella, P., & Wannasuphoprasit, W. (2000). Cobots in materials handling. http://www.mech.northwestern.edu/ colgate/Website_Articles/Book_Chapters/Peshkin_2000_CobotsIn MaterialsHandling.pdf. Peshkin, M. A., Colgate, J. E., Wannasuphoprasit, W., Moore, C. A., Gillespie, R. B., & Akella, P. (2001). Cobot architecture. IEEE Transactions on Robotics and Automation, 17(4), 377–390. Stanley. (2002). Intelligent assist devices: Revolutionary technology for material handling. http://www.stanleyassembly.com/documents/en/ Cobotics%20IAD%20White%20Paper.pdf. Townsend, B., Radford, M., & Groves, A. (2004). Collaborative robotics with medical applications. Project report 0401, ENPH 459, University of British Columbia, Canada. Ulrich, I., & Borestein, J. (2001). The guidecane—applying mobile robot technologies to assist the visually impaired. IEEE Transactions on Systems, Man, Cybernetics—Part A: Systems and Humans, 31(2), 131–136. Wannasuphoprasit, W. (1999). Cobots: Collaborative robots. Ph.D. Thesis, Northwestern University, USA. Wannasuphoprasit, W., Gillespie, W., Colgate, J., & Peshikin, M. (1997). Cobot control. In Proceedings of the 1997 IEEE International Conference on Robotics and Automation (pp. 3571–3576).