TOWARDS A FLEXIBLE TRANSPORTATION IN DISTRIBUTION

CENTERS

Low-level Motion Control Approach

Sisdarmanto Adinandra, Dragan Kosti´c, Jurjen Caarls and Henk Nijmeijer

Dept. of Mechanical Engineering, Eindhoven University of Technology, PO Box 513 5600MB, Eindhoven, The Netherlands

Keywords:

Low-level motion control, Unicycle mobile robots, Collision avoidance, Priority rules, Distribution center.

Abstract:

In recent years autonomous mobile robots (AMR) have emerged as a means of transportation in distribution

centers. The complexity of transportation tasks requires efﬁcient high-level control planning and task schedul-

ing, as well as low-level motion control of the robots such that a more ﬂexible, and robust transport system

can be achieved. In this work we present a methodology to achieve coordination of a group of mobile robots

so that the objectives are met, focusing on low-level control approach. We use a reactive-to-dynamic-change

control concept. We consider an automated distribution center in a simulation case study. The transportation is

evaluated in terms of completion time and robustness to fault. In addition, the control strategies are validated

in a mock-up version of the automated distribution center.

1 INTRODUCTION

The transportation in a distribution center is typically

organized using conveyors systems. These systems

provide a good transport capacity and high availabil-

ity, but are sometimes very sensitive to conveyor fail-

ures. In the event of a conveyor breakdown, the

transport system of the distribution centers will likely

come to complete standstill. This is due to the fact

that the their relative high-cost in the warehousing

industry restrict having too much redundancy in the

transportation system. Another weakness is their

ﬁxed maximum capacity. If the business owner of the

distribution center changes, a larger capacity and lay-

out changes may be needed. Besides having a high

performance, an ideal distribution center transporta-

tion should be robust to system failures and ﬂexi-

ble to system changes. An autonomous mobile robot

(AMR) transport concept has these desired character-

istics (Wurman et al., 2007).

In such a concept, a large collection of AMR is re-

sponsible for transportation of goods in the distribu-

tion center. As the system has a large transport redun-

dancy, the breakdown of a single robot may lower the

system’s performance, but will not lead to a complete

system standstill. Flexibility can easily be achieved

by varying the number of robots in the system so that

the AMR is capable of handlingvariationsin transport

demands. However, to meet the requirements there

are needs for advanced control of individual robots as

well as inter-robots coordination.

In transportation system, planning, scheduling,

and control of tasks of the conveyors or robots are

done by a high-level control system. In a centralized

way, e.g. see (Gu et al., 2010) or decentralized way,

e.g see (Weyns et al., 2005), the high-level control

system allocates the tasks to the robots based on cus-

tomer orders and resource availability.

Recent developments in formation and coordina-

tion control of mobile robots by low-level motion

controllersshow promising results to realize the trans-

portation. In some techniques, e.g. leader-follower

and virtual structure, the motion controller achieves

tracking of individual robot trajectories and maintains

the desired spatial formation between the robots. See

for instances (Arai et al., 2002), (Chen and Wang,

2005), (Liu et al., 2010), and (Kosti´c et al., 2010) for

reviews and recent developmentsaround the low-level

motion coordination.

Some researches are devoted to performance anal-

ysis of different high-level strategies, see e.g. (Vis,

2004), (Le-Anh and Koster, 2006), (Gu et al., 2010),

and references therein. These articles discuss the

trends in high-level control of distribution centers and

propose different options to ﬁnd the optimal through-

put. It is to be pointed out that high-level control as-

sumes known operating conditions in the distribution

centers. If the system dynamics change rapidly, high-

155

Adinandra S., Kostic D., Caarls J. and Nijmeijer H..

TOWARDS A FLEXIBLE TRANSPORTATION IN DISTRIBUTION CENTERS - Low-level Motion Control Approach.

DOI: 10.5220/0003519801550160

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 155-160

ISBN: 978-989-8425-75-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

level control may fail in handling the system behav-

ior. This opens possibilities for more reactive and less

predictive control strategies.

As for the low-level motion controller, coordina-

tion controllers of mobile robots have been success-

fully simulated and validated in experiments. The ap-

plications are widely spread from cooperative clean-

ing (Jager and Nebel, 2002) to exploration (Burgard

et al., 2005). The ability to quickly react to dynamic

changes increases the robustness of the system as well

as speed of conducting the required tasks. However,

as indicated in (Arai et al., 2002) or (Buccieri et al.,

2009), there are needs to scale-up the demonstration,

and to demonstrate the advantages of cooperative mo-

bile robots in more complex tasks. Moreover, there is

a little information on how the coordination control of

AMR is applied in a distribution center.

In (Adinandra et al., 2010), it is investigated how a

group of AMR can execute one typical task in a distri-

bution center, i.e. transporting items from start to end

positions in a certain formation while avoiding colli-

sion. The performance of a high- and low-level co-

ordination control are analyzed. It is concluded that

the high-level has better throughput but is less robust

compared to the low-level control. However, further

generalization to more realistic transport tasks with a

larger number of AMR is needed.

There are two drivers for our research: (i) the

high-level control opens possibility for less predic-

tive and more reactive-to-dynamic-changes solutions,

and (i) the lack of information on how low-level con-

trol manage a group of AMR in a distribution center.

We conduct research on how ﬂexible and robust trans-

portation in a distribution center can be achieved us-

ing a group of AMR, focusing on low-level motion

control approach. Compared to the work in (Adi-

nandra et al., 2010), we investigate the transportation

in a more realistic simulation case study and using

more robots. We consider replacing part of the con-

veyor system of an automated distribution center with

AMR. We analyze the performance of the transport

system using relevant indicators, i.e. time to complete

tasks and robustness. To validate the control strate-

gies, we conduct experiments on a smaller scale of

the automated distribution center

The main contributions of this paper are: (i) pre-

sentation of a methodology to organize a group of

AMR in a distribution center, (ii) exploitation of low-

level motion controller for a group of AMR to achieve

ﬂexible, and robust transportation, (iii) simulation and

experimental validation of the control strategies in an

automated distribution center.

The paper is organized as follows. In Section 2 we

describe our control architecture, the kinematic model

of the mobile robot and its trajectory controller, as

well as the performance indicators used in this work.

Section 3 explains in details the low-level control

strategies. Section 4 highlights the automated distri-

bution center used in the case study. Section 5 reports

the simulation and experimental results and highlights

the main ﬁnding of this work. Conclusions and out-

look work are given in Section 6.

2 PRELIMINARIES

2.1 Control Architecture

As stated in references, control design and task plan-

ning in a distribution center are complex and difﬁ-

cult tasks, see e.g. (Gu et al., 2010). Narrowing the

problem to the transportation only does not reduce

the complexity. In some research, e.g. (Lacomme

et al., 2010), one tries to combine the problem of task

scheduling and robots dispatching in one optimization

problem. On the other hand, we can also keep the

problem of task scheduling and dispatching solved as

separate design problems.

In this work we choose to use the separation ap-

proach. We decompose the complexity of the task

into different control layers as shown in Figure 1. The

control layers give us convenience of having the con-

trol design isolated from the rest of the system and the

possibility to test different control algorithms. These

layers also allow shifting responsibilities in a given

transportation task. The main differences with re-

spect to typical control architectures for transport us-

ing conveyorsare the addition of trajectory generators

and controllers.

Figure 1: The proposed control architecture.

2.2 Unicycle Mobile Robots

There are various types of AMR. Some of them

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

156

belong to class of AMR with non-holonomic con-

straints. In practice, this constraint implies that no

sideways movement is allowed. Throughout this

work, we consider a group of m-AMR that are de-

scribed by the non-holonomic kinematic model of a

unicycle mobile robot (see e.g. (Kanayama et al.,

1990) and references therein):





˙x

˙y









cosθ

sinθ





. (1)

Here, v

and ω

are the forward and steering veloc-

ities respectively to control the AMR, x

and y

are

the Cartesian coordinates of the robot midpoint in

the world coordinate frame, θ

is the heading an-

gle relative to the x-axis of the world frame, and

i ∈ {1,2,3,...,m}.

2.3 Trajectory Tracking

In the most existing AMR-like systems the robots fol-

low ﬁxed lines, thus only controlling v

. The problem

is to ﬁnd paths that result in the optimal throughput,

see e.g. (Lacomme et al., 2010). This approach is

simple, but cannot easily accommodate changes in

transportation demands. Thus, we propose to use a

trajectory tracking controller. The idea is as follows.

The high-level control provides the reference tra-

jectory to each robot p

= [x

]

. Trajecto-

ries must fulﬁl the non-holonomic constraints, i.e.

− ˙x

sinθ

+ ˙y

cosθ

= 0. The low-level control is

responsible for accurate tracking of these reference

trajectories. In this work we use the following con-

troller (Jiang and Nijmeijer, 1997):

= v

cosθ

+ k

, (2a)

= w

+ k

sinθ

+ k

θi

, (2b)

where v

and ω

are the reference forward and steer-

ing velocities respectively, x

, y

, and θ

are the

tracking errors represented in robot local coordinate

frame, and k

θi

∈ R

are control gains.

2.3.1 Performance Indicators

We use the following indicators to evaluate the per-

formance of the proposed transportation system:

• Completion time, t

complete

, which is the time

needed to accomplish all transportation tasks and

is expressed as:

complete

= t

last,task

− t

ﬁrst,task

, (3)

where t

ﬁrst,task

and t

last,task

are the times for starting

the ﬁrst and completing the last task respectively.

• Robustness. We deﬁne robustness as the ability to

cope with exceptional situation, i.e. if uncertain-

ties and faults occur, and is quantiﬁed as follow:

complete,exceptional

− t

complete,normal

. (4)

3 LOW-LEVEL CONTROL

As shown in Figure 1, the low-level control is mainly

responsibilities of the trajectory controller given in

(2). Since in this work we put the ﬂexible layer into

low-level control, we implement collision avoidance

algorithms in the low-level control.

3.1 Assumptions on High-level Control

Since low-level control needs information from the

high-level control, the following assumptions are

used: (i) the high-level control provides the complete

orders, their allocations to the AMR, as well as the

robots’ dispatching rules; (ii) the high-level control

does not provide collision-free reference trajectories.

3.2 Slow-down using Penalty Function

Consider a situation where two robots almost collide

as shown in Figure 2(a).

a) b)

Figure 2: a) Situation in which robot j stops. Robot i has to

modify its path to avoid collision; b) Situation with 4 robots

at two junctions.

In this example robot j stops to pick items. Robot

i has to slow down or alter its path to avoid collision.

In our case study we choose to slow down using a

set P

of continuous, monotone, and bounded penalty

function concept (Kosti´c et al., 2009). An example of

a function in P

(x) =











0, x < γ

min



x−

γsin(2πx/γ)

2π



, γ

min

≤ x ≤ γ

max

1, x > γ

max

(5)

If q

= [x

]

and q

= [x

]

are the position

and orientation of robots i and j in Cartesian space,

TOWARDS A FLEXIBLE TRANSPORTATION IN DISTRIBUTION CENTERS - Low-level Motion Control Approach

157

we deﬁne a vector



− x

− y



, (6)

with its magnitude, representing the distance between

the centers of robots i and j:

|av

| =

− x

)

+ (y

− y

)

. (7)

Deﬁne the projection of the direction of robot i dir

[cosθ

sinθ

]

. The slowing down coefﬁcientof robot

i with respect to robot j is expressed as:



1, if dir

• av

≤ 0

γij

(|av

|) if dir

• av

> 0

, (8)

where the • sign represents the dot product of two

vectors, δ

γij

(|av

|) is a penalty function. The compu-

tation is repeated for all j 6= i, j ∈ {1,2,... , m} robots.

The reference forward velocity of each robot is penal-

ized as follows:

= v

des,i

∏

j=1, j6=i

, (9)

where v

des,i

is the desired forward velocity of each

robot.

The coefﬁcient computed in (8) indicates whether

robot j is behind or in front of robot i relative to the

direction of movement of robot i. According to ex-

pression (9), if robot i is behind j and the other robots,

then robot i will slow down to avoid collisions.

Furthermore, priority rules need to be applied if

situation shown in Figure 2(b) occurs, i.e. more

robots wait to enter the junctions. Applying only (9)

will result in deadlock, i.e. no robots move. This is

because robots that enter the junction assume they are

behind each other, i.e. σ

= σ

= 0.

Suppose we implement right-hand priority, i.e. at

the junction a robot that comes from the right side

of other robots has higher priority, σ

, σ

is adapted as follow: σ

= 1,σ

= 0, and σ

0,σ

= 1. Other priorities rules like low-number or

left-hand priority can also be applied.

Artiﬁcial Potential Field (APF) Concept. The col-

lision avoidance to coordinate the robots presented

above is used in a normal situation, i.e. there is no

fault in the system and all robots are operational.

To add robustness against faults, i.e. some robots

are subject to failures or unexpected obstacles block

the paths, we add collision avoidance using APF al-

gorithm presented in (Kosti´c et al., 2010). In the APF

algorithm a robot generates repulsive forces based on

other robots’ positions. In this way a robot can alter

its path and avoid collision with the failure robots.

4 AN AUTOMATED

DISTRIBUTION CENTER

For the simulation case study, we investigate the per-

formance of the transportation system of the auto-

mated distribution center shown in Figure 3 (Andrian-

syah et al., 2010). It consists of storage, conveyorsfor

transportation, and order picking workstations. The

overall system can be classiﬁed as product-to-picker

distribution center (van den Berg, 1999).

The main

conveyor

Storage

Workstation

(WS)

Figure 3: An automated distribution center.

4.1 Using AMR to Replace Conveyors

We deploy AMR to replace the main conveyor loop,

i.e. the conveyorthat transport the items from the stor-

age to the workstation. We choose two possible paths,

i.e. the single-path that resembles the conveyor ge-

ometry and multiple-paths that allows short-cuts. We

assume that the robot: (i) has a size of 0.8 m × 0.8

m, (ii) has nominal speed of 1 m/s, (iii) in each task

carries a product tote with one type of sku/item. For

comparison basis we use maximum conveyor capac-

ity, i.e. 1000 totes/hour.

Storage

WS3

single-path

multiple-paths

WS2

WS1

WS3

WS2

WS1

Storage

Figure 4: The geometric path options for the robots.

5 RESULTS AND DISCUSSION

Scenarios. We consider different scenarios, i.e.

different number of robots (n

robots

), priority rules,

and fault status. We choose n

robots

∈ { 2,4,...,20}.

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

158

The following abbreviations are used: SP: single-

path; MP-LN: multiple-paths, low number priority;

MP-LH: multiple-paths, left-hand priority; MP-RH:

multiple-paths, right-hand priority. The conveyor ca-

pacity is identiﬁed by CS.

5.1 Results and Analysis

Figure 5 shows how the low-level control performs

in different scenarios. We can observe that the AMR

concept, under the assumptions, can have similar,

even better performance as the conveyor systems.

By simulation, we can choose which combination of

robots

and priority rule that give us the desired perfor-

mance. The low-level control works with any num-

ber of AMR, i.e. we can easily add/remove robot to

increase/decrease the throughput. In this particular

case, the scenario SP with 16 robots give us the op-

timal throughput. Although adding more robots can

increase the capacity, if the space is kept constant, this

also means less space for movement. This results in

worse throughput or a deadlock if robots occupies all

spaces.

2 4 6 8 10 12 14 16 18 20

Number of Robots [−]

complete

[hour]

MP−LN

MP−LH

MP−RH

Figure 5: t

complete

in different scenarios.

Furthermore, Figure 6 show how robustness

against failures can be achieved using the APF con-

cept. In this example scenarios SP and MP-LH are

investigated. The ability of APF to generate alter-

native paths for the non-malfunctioned robot makes

the overall transport system still operate under fail-

ures, although with lower throughput. This means

that robustness against failure is achieved. This phe-

nomenon can be observed by the shifting of the orig-

inal solid-curves to the dashed-curves in Figure 6. In

each scenario the mean value of ρ

is 0.1066 and

0.1068 respectively.

Experimental Results. We conduct experiments us-

ing similar set-up to the one in (Adinandra et al.,

2010). We use similar distribution center layout as

in simulation but on a smaller scale.

In overallthe low-level control works well in prac-

2 4 6 8 10 12 14 16 18 20

Number of Robots [−]

complete

[hour]

SP, but with faults

MP−LH

MP−LH, but with faults

Figure 6: t

complete

of two scenarios in normal and fault

modes. In fault case two robots stops working and block

some paths (in different time) for 30 minutes.

tical situation. It can handle noise in measurement

and small time delays in sending the control signal.

Furthermore, Figure 7 shows a real-time situation

where 4 robots are in a threat of collision. In this ex-

ample robot 7 stops to collect an item. Thus, robot

8,9,10 has to slow down to avoid collision. This can

be seen in Figure 8 where the control signals of the

robots are zero. Once robot 7 starts to move again,

robot 8 will start moving. By, e.g. the left-hand pri-

ority, robot 10 gets higher priority than 9, so robot 10

will move forward followed by robot 9.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

dropping points

picking points

Figure 7: Threat of collisions at a junction.

115 120 125 130

0.02

0.04

0.06

0.08

time [s]

v [m/s]

robot 7

robot 8

robot 9

robot 10

Figure 8: Control signals of robots 7,8, 9,10.

6 CONCLUSIONS

In this work we have presented a methodology to ex-

TOWARDS A FLEXIBLE TRANSPORTATION IN DISTRIBUTION CENTERS - Low-level Motion Control Approach

159

tend ﬂexibility and robustness of transportation in dis-

tribution centers using a group of AMR. We show

how the low-level motion controller can achieve ﬂex-

ibility and robustness at the same time. This allows

us, by simulation, to ﬁnd the best solution according

to the requirements. Our experimental results show

that the control strategies work well in a real-time sit-

uation.

To reduce the dependencyfrom simulation results,

it is important to ﬁnd an analytical estimation or lower

bound of the system throughput. In addition, investi-

gation on optimal-low-level control algorithms need

to be done so better throughput can be gained.

ACKNOWLEDGEMENTS

This work has been carried out as part of the FALCON

project under the responsibility of the Embedded Systems

Institute with Vanderlande Industries as the industrial part-

ner. This project is partially supported by the Netherlands

Ministry of Economic Affairs under the Embedded Systems

Institute (BSIK03021) program.

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