Indoor Platoon Driving of Electric Wheelchair with Model Error
Compensator along Wheel Track of Preceding Vehicle
Tatsuya SUGANO1 , Yusuke DAN1 , Hiroshi OKAJIMA1 , Nobutomo MATSUNAGA1 and Zhencheng HU1
Abstract— As one of the leading method of electric
wheelchairs, platoon driving using Adaptive Cruise Control(ACC) has been proposed to keep constant time-headway.
The platoon driving system has been widely used assuming
straight roads that has good visibility, but has not been used in
narrow corridor. While, the gross weight of wheelchair changes
drastically depending on passenger’s weight. In this paper, anovel platoon driving system is proposed for narrow corridor
driving. The platoon controller is constructed with the intervehicle distance control based on ACC and precise lateralcontrol based on target point following along wheel track ofpreceding wheelchair. The effectiveness of the proposed method
is verified by the driving experiments at the corner in narrowcorridor.

I. INTRODUCTION
In aging societies, the electric wheelchairs have been
widely used. An electric wheelchair STAVi has been developed for elderly and handicapped persons [1]. STAVi has aunique piggybacking design that allows the user to climb
into the wheelchair in a comfortable manner.
In hospitals and care facilities, the care worker have totake care of many patients who use wheelchair at the sametime. As one of the leading method of many wheelchairs, theplatoon driving using Adaptive Cruise Control (ACC) has
been proposed [2] [3]. The platoon driving is assumed to be
used at a straight road that has good visibility. Because ofnarrow corridor without good visibility, it is difficult to guidemany wheelchairs in single file by common ACC technology.
There are two important issues in indoor platoon drivingof electric wheelchairs. First, the dynamic characteristic ofa wheelchair is affected by the passenger’s weight or otherdriving conditions, because a wheelchair is lighter than acar. As the modeling error makes the platoon unstable, therobust controller which suppresses modeling error is required. Second, in order to avoid collision against a wall, thefollowing vehicle must precisely track along the trajectoryof preceding vehicle. Therefore, we must design a precise
following controller in stable platoon driving.
In this paper, a novel platoon driving system is proposedin narrow corridor based on ACC with Modeling Error
Compensator (MEC) [4]. The platoon controller is constructed for each wheelchair considering precise and stable
driving. At first, the inter-vehicle distance control based on
ACC is designed, and the modeling error depending on
passenger’s weight is suppressed by MEC. Next, the lateralcontrol based on target point following algorithm using
1 Department of Computer Science and Electrical Engineering, Kumamoto University, 2-39-1, Kuroami, Chuo-ku, Kumamoto 860-8555, Japan

matunaga@cs.kumamoto-u.ac.jp219

way point is designed [5], and the precise following along
wheel track of the preceding vehicle is achieved. Finally, theeffectiveness of proposed method is evaluated by a platoon
driving experimented at a corner of narrow corridor in thebuilding.
II. I SSUES OF PLATOON DRIVING IN NARROW SPACE
Piggyback type personal wheelchair STAVi was developedfor elderly and handicapped persons [1]. STAVi has a uniquepiggybacking design that allows the user to climb into thewheelchair in a comfortable manner. The seat height can be
adjusted based on user preferences and then be raised backto the driving position to maintain the user’s eye line as theirstanding position.
Here, we consider the driving scene of STAVi in the hospital or the care facility. The care worker often leads patientsto rehabilitation or exercise area by electric wheelchairs. The
care worker must pay attention to all patients whose recovery
level or driving ability are different. If the care worker leads
some patients by platoon, patients’ and care person’s burden
will be reduced. However, there are few platoon control
systems of wheelchair to drive in narrow space, and thecontrol method suitable for practical use has been studied.
Fig.1 shows a demonstration with STAVi at outdoor. Here,simple ACC algorithm was applied. In this demonstration,
the 1st carriage (STAVi♯2) is driven by a conductor. 2nd
one (STAVi♯3) is electric wheelchair, and 3rd one is acarrier. A conductor sometimes leads wheelchairs withoutpassengers. The difficulty of platoon driving is attributableto time constant and/or center of gravity changes according
to passenger’s or baggage weight. Also, it is difficult for
simple ACC to realize a precise driving for narrow corridor.

Fig. 1.

Driving demonstration with electrical wheelchair STAVi

The objective of our research is to design indoor platoon
driving controller which suppresses parameter variations bypassenger’s weight and follows the preceding wheelchair innarrow corridor precisely.
III. P LATOON D RIVING USING ACC

where Kj (j = 1, 2, 3) are feedback gain of ACC calculatedby the optimal servo [6].
Fig.3 shows block diagram of ACC. Gi (s) represents thetransfer function of wheelchair in eq.(1). H represents the
spacing policy shown in eq.(2). And K(s) represents ACC
controller.

A. Adaptive Cruise Control
There are two methods for platoon driving; one is theConstant Inter-vehicle Distance (CID) control, the otheris the Constant Time-Headway (CTH) control. The CID
control keeps constant inter-vehicle distance even though
the preceding wheelchair changes its velocity. On the other
hand, the CTH control keeps the time-headway. Therefore,
inter-vehicle distance changes according to driving velocity.
If the leading wheelchair drives fast, inter-vehicle distancebecomes large. In contrast, the CID control has an advantagethat inter-vehicle distance becomes shorter. However, it isdifficult to satisfy string stability conditions in case thatdesired inter-vehicle distance is short. By using the CTH
control, it becomes easy to satisfy string stability condition
with simple velocity feedback using own vehicle information. Therefore, we apply the CTH control called ACC tothe platoon driving system.
Here, the ACC systems will be outlined. The relationshipbetween the preceding and the following wheelchair is shownin Fig.2. vi is a wheelchair velocity and di is an intervehicle distance. Suffix i and i − 1 are the following andthe preceding wheelchair number, and i = 1 indicates theleading wheelchair.
The dynamics from control input ui to wheelchair velocity
vi is assumed as follows;vi
1
Gi (s) ==,(1)
ui
τi s + 1
where τi represents the time constant.
The desired inter-vehicle distance dri is represented by
the multiplication of wheelchair velocity vi and desired
time-headway T . The time-headway is arrival time of thefollowing to the preceding wheelchair. The desired intervehicle distance is defined as follows;
dri = T vi + d0 ,(2)

where d0 is standstill distance. εi , zi and d˙i represent
distance error εi = di − dri , integral of distance error andderivative of distance error d˙i = vi−1 − vi . The control input
for Gi (s) is designed as follows;ui = K1 d˙i + K2 εi + K3 zi ,Fig. 2.

(3)

Relation between the preceding and the following wheelchair

220

Fig. 3.

Block diagram of ACC

B. Modeling Error Compensator
It is well known that STAVi’s dynamic model is nonlinear [7]. Therefore, the acceleration and deceleration model
represented as eq.(1) is strictly different from the plant. Besides, STAVi’s parameters are changed according to driving
situation. In particular, the STAVi’s body weight is about
80[kg], also maximum driver’s weight is assumed to be
80[kg]. Fluctuation of weight has a significant influence on
the longitudinal control, because the driver’s weight ratio
against STAVi is larger than the ratio against car.
To design the platoon controller, it is difficult to obtain not
only the STAVi’s parameter but also precise bodily weight
for every vehicle and patient. If the modeling error can be
minimized, we design ACC parameters for nominal model
regardless of various parameter changes. In this paper, aModeling Error Compensator (MEC) is used to suppress theerror of ACC [4].
Fig.4 shows the block diagram of MEC. In this figure, P
and PM represent the dynamics of STAVi and the reference
model. The vehicle velocity vi is the output of P , and vmi
is the output of PM , where i denotes i − th vehicle. C is thecontroller compensating the model error between P and PM .
In case the same characteristic between P and PM is given,
the feedback becomes invalid. On the other hand, in case of
the different characteristic between P and PM , control input
works to minimize vmi − vi . By proposed compensator, it isexpected that the input-output relation of P becomes close
to that of PM .
Here, the longitudinal reference model PM is represented
as follows;
1
vmi
=
,
(4)
PM =
ui
τmi s + 1
where τmi is time constant of reference model. C is PD typecontroller to compensate the model error.

wheelchair disappears at the corner by the wall as shown in
Fig.6(a). In case of T = 1.0[s], as the wheelchair does notdisappear, the distance can be measured easily as shown in
Fig.6(b). By preliminary experiments, we define the desired
time-headway T = 1.0[s] and d0 = 1.0[m], where thefollowing vehicle’s velocity is assumed 0.5[m/s] (2.0[km/h]).
B. Longitudinal reference model with MEC
Block diagram of Modeling Error Compensator

IV. D ESIGN OF LONGITUDINAL CONTROL

velocity[m/s]Fig.5 shows block diagram of longitudinal control systemof platoon driving. Left-side block is feedback gain of
ACC for nominal model, and right-side block is STAVi
compensated by MEC. In this section, the design method ofdesired time-headway T , reference model PM , and feedback
gain K are discussed.

We show some simulation results to confirm the effectiveness of MEC for the variation of driver’s weight [7]. STAVi’s
gross weight range is M ∈ [80 160][kg]. To show theeffectiveness of MEC, we examine the open loop responseof STAVi, at first.
The wheelchair velocity without MEC under variation ofgross weight is shown in Fig.7(a). The nominal model’s
weight is M = 80[kg] that means no passenger. The heavier
the weight becomes, the larger the time constant will be.
Fig.7(b) shows the velocity with MEC. Even thought theweight is changed, the model error is suppressed by MEC.
As STAVi is regarded as the reference model PM , ACC
controller can be designed for the reference model.
0.7

0.7

0.6

0.6

0.5

0.5

velocity[m/s]Fig. 4.

0.4

0.3

0.2

Fig. 5.

00

A. The desired inter-vehicle distance
It is easy to be string stable for platoon system if large
desired time-headway T is given in eq.(2). As the large T
gives long inter-vehicle distance, large T is not permitted fornarrow indoor driving.
In the case of the platoon driving system, the preceding
wheelchair disappears at the corner by the wall. This implies
that inter-vehicle distance cannot be measured. Therefore, we
determine appropriate time-headway T not to lose sight ofpreceding wheelchairs. The vision from following wheelchairis shown in Fig.6, when the following wheelchair is driven at
about 2[km/h]. Fig.6(a) and (b) indicate inter-vehicle distanceat T = 3.0[s] and 1.0[s]. In case of T = 3.0[s], the timeheadway is sufficient large for stable driving, but preceding

Fig. 6.

0.1

nominalvariable
5

10

15

20

25

30

0
0

nominalvariable
5

10

15

20

time[s]time[s](a) Without MEC(b) With MEC

Fig. 7.

2530

Velocity of STAVi perturbed by the weight change

C. Design of ACC controller
Platoon driving system is generally designed to satisfy
string stability [8]. The string stable denotes that oscillationof inter-vehicle distance is not amplified upstream fromdi−1 to di . When the following wheelchairs repeat acceleration/deceleration, the drivers feel uncomfortable due to theoscillations. For the reason, we should design the ACC gain
not only to be string stable, but also to be oscillations-free.
The criterion of string stable is given as follows;||SS(s)||∞ ≤ 1 ∀ω .

(5)

In case that ||SS(s)||∞ ≤ 1 for all frequency, the platoon
satisfy string stable. Here, SS(s) is a transfer function fromdi−1 to di assuming all time constant τ is identical.
SS(s) =(a) T = 3.0[s]

0.3

0.2

0.1

Block diagram of platoon driving system

0.4

K1 s2 + K2 s + K3
di
= 3
di−1
τ s + Ka s2 + Kb s + K3

(6)

where Ka = 1 + T K2 + K1 , Kb = T K3 + K2 .
The ACC feedback gains are characterized by root locus.
The weight matrix is Q = diag[1 300 470], where statevector x = [d˙i εi zi ]T . The weight r of input matrix ischanged from 100 to 0.001. The root locus is shown in Fig.8.
From eq.(6), SS(s) has three poles and two zero points. If
r is smaller, the poles are moved to arrow direction.

(b) T = 1.0[s]Setting of time-headway T

221system by the simulation. The leading wheelchair starts
driving at 5.0[s], after then the leading wheelchair drives
at constant velocity 0.52[m/s]. The gross weight is changed
as M ∈ [80 160][kg]. Fig.9 (a) and (b) show inter-vehicle
distance without and with MEC, respectively. Solid line anddash line are nominal and fluctuation of responses, respectively. When the weight is changed, inter-vehicle distance isamplified than nominal one. When the proposed controller isused, the overshoot is suppressed even though driver’s weightchanges. As a result, the inter-vehicle distance converges
without oscillation.
V. D ESIGN OF LATERAL CONTROL
Fig. 8.

In this section, a practical CTH control along wheel trackof preceding wheelchair is proposed to achieve a precise
platoon driving.

Root locus of SS(s)Platoon driving characteristics is changed according topoles location. When r is large value, poles are located onarea O − A. Then, the wheelchairs are string unstable. Whenr is small value, poles are located on area A − C. Then, thewheelchairs become string stable. In particular, when r issmaller than 0.013, the oscillation of inter-vehicle distancedoesn’t arise because poles are located on real axis B−C. So,
it is better to set r as smaller than 0.013 to be string stable.
In this paper, we define r = 0.01 to suppress oscillation andobtain the feedback gain [K1 K2 K3 ] = [73.27 241.6 151.9].
We confirm effectiveness of the proposed platoon driving

1.6inter−vehicle distance[m]1.5

nominalvariable

1.4

1.3

1.2

2nd−3rd
1st−2nd

1.1

5

10

15

20

25

20

25

Generally, way points have been used at inflection pointof the trajectory for automatic drive system [5]. In thispaper, precise CTH control along wheel track of preceding
wheelchair using way point generation is proposed. The
concept of way point generation along wheel track is shownin Fig.13. The way point data detected by LRF are marked

time[s](a) without MEC
1.6

inter−vehicle distance[m]1.5

The target point following (TPF) is major method forlateral control [5] [9]. Fig.10 show a schematic diagramof TPF algorithm. When target point (xp , yp ) is given, thedesired trajectory (heavy line) is generated using third-order
curve to drive smoothly.
It is well known that the platoon following error will belarger if the number of vehicles increases. Fig.11 and Fig.12
show experimental results of traditional TPF with ACC at
corridor corner. In Fig.11, the maximum following error was
0.36[m] in corridor corner. Also the inter-vehicle distance
between preceding and following wheelchairs is shown in
Fig.12. Maximum inter-vehicle distance error was about
0.18[m] (dr = 1.55[m]). However, inter-vehicle distance is
not precise at the corner because the distance is measured bydirect distance using Laser Range Finder (LRF). The issue
is lack of accuracy for narrow indoor platoon driving. In thiscase, only one patient can be lead using traditional controller
when corridor width is 2.0[m].
B. CTH control algorithm along wheel track

1

0.9
0

A. Traditional control based on target point following

nominalvariable

1.4

1.3

1.2

2nd−3rd
1st−2nd

1.1

1

0.9
0

5

10

15

time[s](b)with MEC
Fig. 9.

Simulation result of inter-vehicle distanceFig. 10.

222

Schematic diagram of TPF algorithmTABLE I
8

E XPERIMENTAL PARAMETERS

Preceding vehicle
Following vehicle

7

Name
Sampling time
Time constant of PM
Desired time-headway
Standstill distanceGain of ACC
Gain of MEC

6
5

y[m]

4
3
2
1

Symbol∆t
τM
Td0[K1 K2 K3 ][CP CD ]Value
0.1[s]
0.5
1.0 [s]1.0 [m][73.27 241.6 151.9][240 35]

0
−1
−2
0

1

2

3

4

5

6

7

8

9

25[s]. And the preceding one decelerates to about 0.1[m/s].
Table I shows control parameters.
Fig.14 shows inter-vehicle distance. The desired intervehicle distance was 1.3 [m]. In Fig.14(a), when the preceding wheelchair accelerated or decelerated, the overshootwas observed and following wheelchair velocity converges
with oscillation. In this case, the string stability was notguaranteed. In Fig.14(b), the oscillation of inter-vehicle distance was suppressed stably using proposed method. Here,ACC gain was adjusted for M = 80[kg] without passenger.
From the experiment, the parameter variation by passenger’s
weight was suppressed by MEC.

10

x[m]

Fig. 11.

Vehicle trajectory using traditional TPF algorithm
1.7inter−vehicle distance[m]

1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0

5

10

15

20

25

30

35

40

time[s]1.4
1.35

Inter-vehicle distance using traditional ACC

by following wheelchair. The detail algorithm is omitted inthis paper, but the way points are rotated according to yaw
angle of following wheelchair. As the way points are marked
within certain period (100[ms]), the target wheel track will
be more precise in slow speed.

inter−vehicle distance[m]Fig. 12.

1.3
1.25
1.2
1.15
1.1
1.05
1

measured distancereference distance

0.95
0.9
0

5

10

15

20

25

30

35

40

45

time[s](a) Inter-vehicle distance without MEC
1.4

Fig. 13.

inter−vehicle distance[m]1.35

Proposed time-headway tracking along wheel track

1.3
1.25
1.2
1.15
1.1
1.05
1

measured distancereference distance

0.95
0.9
0

VI. E XPERIMENT OF PLATOON DRIVING USING STAV I
In this section, we show some experiments using STAVi.
STAVi♯3 is the preceding wheelchair and STAVi♯2 is thefollowing one. LRF (UTM-30LX) is mounted on following
wheelchair to measure the relative position. The relative position among wheelchairs are estimated by odometry method
obtained by encoders [6].
A. Experiment of driving straight corridor
The effectiveness of proposed control system is confirmedby driving experiment. The preceding wheelchair starts driving at 5[s], and keeps the constant velocity 0.3[m/s] until
223

5

10

15

20

25

30

35

40

45

time[s](b) Inter-vehicle distance with MEC
Fig. 14.

Experimental evaluation on straight corridor

B. Experiment of following error at corridor corner
We show the driving experiment to turn off at the corner of corridor. The preceding wheelchair accelerated until
0.5[m/s]. The corridor width is 2.0[m] and STAVi width is
0.7[m]. The preceding wheelchair turns off at the 90[deg]corner with constant velocity.
The following wheelchair’s velocity is controlled by ACC
with MEC. Also, the inter-vehicular distance is controlled by

TABLE II
L ARGEST ERROR IN EXPERIMENT ( CORRIDOR WIDTH :2.0[ M ])Type
Traditional
Proposed

Fig. 15.

Error of inter-vehicle distance
0.18 [m]0.05 [m]Numberof party
2-vehicles
6-vehicles

was improved to 13.52 (12.8%) although the IAE of traditional TPF was 105.6.
Fig.17 shows experimental inter-vehicle distance. Theinter-vehicle distance error was improved from 0.18[m] to
0.05[m] where time-headway set as T = 1.0[s] (inter-vehicle
distance 1.57[m]). Table II summarized maximum errors at
corner of corridor.

Driving experiment at corridor corner

8

Preceding vehicle
Following vehicle

7

Max error
at corner
0.36[m]0.11[m]6
5

VII. C ONCLUSION

y[m]

4

In this paper, we proposed indoor platoon driving ofelectric wheelchair with MEC along wheel track of preceding vehicle. In this experiment, the leading number ofwheelchairs was six vehicles included leader. The advantage
of our method is implemented easily for parameter variationof the platoon system even though this system uses odometry
method. By suppressing the model error using MEC, comfortable control system can be realized without oscillationof velocity. Also, the lateral controller was based on CTH
control along wheel track of preceding wheelchair. The way
points were generated considering the relative position ofwheelchairs. The effectiveness of proposed control system
was evaluated by experiments at narrow corridor.
We designed the MEC for longitudinal controller, however,the MEC for lateral motion has not been considered yet. For
precise following, the design of nominal model considering
longitudinal and lateral controllers, application of corporative
ACC and localization of platoon are future works.
R EFERENCES

3
2
1
0
−1
−2
0

1

2

3

4

5

6

7

8

9

10

x[m]

Fig. 16.

Experiment of vehicle trajectory

1.7

inter−vehicle distance[m]

1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0

5

10

15

20

25

30

35

40

time[s]Fig. 17.

Experiment of Inter-vehicle distanceproposed method along wheel track of preceding wheelchair.
The wheelchair can follow measured way point by proposed
algorithm. Fig.15 is the condition of a driving experiment at
corridor corner. The curvature radius of reference trajectoryat corridor corner is 1.0[m].
Fig.16 is an experimental trajectory. Maximum trajectory
error between preceding and following wheelchair was suppressed 30.5% comparing one of traditional TPF method.
By using proposed controller, it is expected that five patientscan be led by platoon leader. Integral Absolute Error (IAE)
is evaluated for precise platoon driving at the corner. IAE is
defined as∫ t2 √(xp − xf )2 + (yp − yf )2 dt
(7)
IAE =
t1

where (xp , yp ) and (xf , yf ) are position of preceding andone of following wheelchair. For evaluation, we set [t1 , t2 ] =[11, 34][s], which is defined as constant velocity interval.
Comparing Fig.11 and Fig.16, the error of proposed method
was smaller than one of TPF. The IAE of proposed method
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