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A performance-based approach to wheelchair accessible route analysis

Charles S. Han1, Kincho H. Law*, Jean-Claude Latombe2, John C. KunzaCenter for Integrated Facility Engineering, Stanford University, Stanford, CA 94305-4020, USA

Received 7 September 2001; revised 29 October 2001; accepted 2 November 2001

Abstract

This paper presents a method to determine if a usable wheelchair accessible route in a facility exists using motion-planning techniques. We

use a `performance-based' approach to predict the performance of a facility design against requirements of a building code. This approach

has advantages over the traditional `prescriptive' code-based approach for assessing acceptability of designs, which is normal practice today

for assessing wheelchair accessibility. The prescriptive method can be ambiguous, contradictory, complex, and unduly restrictive in practice,

and it can be ad hoc and dif®cult to implement as a computer application. The performance-based approach directly models the actual

possible behaviors of an artifact (in this case, wheelchair motion) that are related to the functional intent of the designed system (a building)

and (hopefully) to the speci®cation of a prescriptive building code. This paper presents example cases from architectural practice to illustrate

the use of robot motion-planning techniques for wheelchair accessibility analysis. This application is an example of using modern computa-

tional methods in support of knowledge-intensive engineering. The simulation method has broad applicability within engineering design. We

illustrate and discuss how to analyze virtual simulations of the detailed behavior of a designed artifact in order to assess its use by intended

users. q 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Motion planning; Disabled access; Wheelchair accessibility; Performance-based analysis

1. Introduction

This paper develops a method to determine if a usable

wheelchair accessible route in a facility exists using compu-

ter-based motion-planning techniques. One concern for

designing a facility is the extent to which it satis®es a set

of usability objectives. In the US, wheelchair access in

private facilities is often an important objective, and certain

wheelchair accessibility is a constraint that is mandated

by law for most public facilities. The Americans with

Disabilities Act Accessibility Guidelines (ADAAG) contain

`prescriptive' speci®cations for determining the existence of

a valid wheelchair accessible route as well as other objec-

tives for disabled access

Advantages of using prescriptive provisions include

straightforward evaluation of a design using the prescribed

parameters, and such evaluation often does not need high-

level engineering knowledge about the speci®c analysis.

However, prescriptive-based codes can be ambiguous,

contradictory, complex, and restrictive [6]. Solutions

constrained by prescriptive-based codes such as the

ADAAG address only a fraction of the possible solutions

that meet the design intent or objectives of these codes.

Since it often is implicit, it is often dif®cult for both

designers and code checkers to discern the design intent

and objectives of a building code or code provision.

However, in the case of the ADAAG, the intent is clearly

stated as ª¼scoping and technical requirements for acces-

sibility to buildings and facilities by individuals with

disabilities¼º

Furthermore, instances exist in which adhering to these

prescriptive provisions produces a design that may not be

usable.

As a partial solution to the problems of prescriptive-based

building codes, many jurisdictions have adopted or are

moving toward the adoption of `performance-based'

codes. We use the term `performance-based' to imply the

performance computed by simulating behavior of models

(in this case, a wheelchair in the con®guration of a facility).

For example, California provides a performance-based

alternative to its prescriptive-based energy codes [2]. As

opposed to prescriptive-based codes that provide solutions

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Advanced Engineering Informatics 00 (2002) 000±000

ADVEI2

1474-0346/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.

PII: S1474-0346(01)00003-9

www.elsevier.com/locate/aei

* Address: Department of Civil and Environmental Engineering, Stanford

University, Stanford, CA 94305-4020, USA.

E-mail addresses: [email protected] (C.S. Han), law@ce.

stanford.edu (K.H. Law), [email protected] (J.-C. Latombe),

[email protected] (J.C. Kunz).1 Autodesk, Inc., San Rafael, CA 94903, USA.2 Department of Computer Science, Stanford University, Stanford, CA

94305, USA.

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Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:02 article wb Alden

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abstracted from the design intent or objective of a building

code, performance-based codes attempt to directly capture

the behaviors that conform to the intent of the design codes

or regulations. This direct performance-based approach

accepts design solutions that satisfy the usability

constraints, including those solutions that do not comply

with the prescriptive-based constraints speci®ed by a design

code. When a performance-based approach accurately

models usability, this approach will identify and reject

design solutions that are not usableÐsome unusable

designs may be accepted using the prescriptive-based

constraints speci®ed by a design code.

This paper presents the methods developed for accessible

route analysis using motion-planning simulation to capture

the behavior of a moving wheelchair. First, we give a brief

overview of motion planning and the technique adopted in

this work. We then provide a de®nition of an accessible

route and its components. Methodologies for the analysis

of accessible components are then discussed. Application

examples are provided to demonstrate the bene®ts of the

performance-based approach. Application of the approach

for the analysis of a ¯oor plan is also given. Finally, this

paper concludes with a short summary and discussion for

future considerations.

2. Basics of motion planning

In basic motion-planning, a robot A moves through a

Euclidean space W (the workspace) represented as RN

where R is the set of real numbers, and N � 2 or 3 is the

spatial dimension. The motion planner for the wheelchair

assumes a two-dimensional space where N � 2: The space

W is populated with obstacles represented as B1, B2,¼, Bq,

and the motion planner parameters are de®ned by the shape,

position, and orientation of A, the Bis, and W. Given the

initial and goal positions and their orientations, the objective

of the motion planner is to determine if a path exists from

the initial to the goal positions and, if so, to generate a

continuous path t through the workspace W for the robot

A avoiding the obstacles Bis. To ®nd a path in a space, the

method ®rst approximates the wheelchair by a disc. Then, it

grows the obstacles isotropically by the radius of this disc.

Finally, the motion planner computes paths between given

points of the resulting free space. The remainder of this

section elaborates the way we applied the approach for the

wheelchair problem.

The motion planner generates a con®guration space C

from the geometric properties of A, the Bis, and W, and it

attempts to construct a path in this con®guration space. In

the new space C, the motion planner transforms robot A to a

point object, and the motion-planning problem becomes one

of generating the path t in C. For a 2-dimensional space W,

the dimension m of the con®guration space C is 3. For

example, a robot A restricted to move in the xy-plane �W �R2� has three degrees of freedom: translations in the x and y

directions and the orientation u . Working in the con®gura-

tion space C instead of the workspace W, the constraints

become more explicit. If the motion planner works directly

with the workspace W, it would have to perform operations

such as collision checking at each proposed path position in

C, the collision-checking operation has already been

addressed for all possible robot positions.

As the motion-planner maps or `shrinks' A to a point

object, an obstacle Bi maps to the C-obstacle CBi by

`growing' its shape based on the geometric parameters

of A and Bi as shown in Fig. 1. The basic algorithm

establishes a reference point with respect to the robot A

and tracing A around the obstacle Bi. The path circum-

scribed by A describes the C-obstacle CBi. If A can freely

rotate, the shape of CBi depends on A's orientation. Fig. 1

illustrates the transformation of an obstacle to a C-obstacle,

given a ®xed orientation of A.

By generating the con®guration space C, the motion

planner transforms the path-planning problem into the

problem of ®nding a smooth curve within C. Now, the

motion planner must guide the robot from the initial point

to the goal point through C. Latombe [7] notes that using

some type of `potential ®eld' is the most successful method

for guiding the robot A. The generated potential ®eld guides

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Fig. 1. Generation of con®guration space. A robot (A) and an obstacle (B) exist in a workspace. The motion planner grows the obstacle in con®guration space

C by adding to B the shadow of A as it moves about the perimeter of B. The planner then reduces the robot to a reference point.

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A by forcing it down the gradient from the initial point to the

goal point. The motion planner discretizes C by de®ning a

grid over the space and generates the potential ®eld values

for each grid cell.

Since the motion planner knows the geometric para-

meters of A, the Bis, and W a priori, it can generate potential

®elds free of local minima. The accessible route analysis

developed in this paper uses a potential-®eld-generating

algorithm NF1 as described by Ref. [7], which can be

shown to be free of local minima. The algorithm creates a

potential ®eld that guides the robot A from the initial point

to the goal point on a path t that grazes the C-obstacles.

3. De®nition of the accessible route

The ADAAG de®nes an accessible route as:

Provision 3.5 De®nitions. Accessible Route. A continuous

unobstructed path connecting all accessible elements and

spaces of a building or facility¼

In addition to the above de®nition, the ADAAG

prescribes measurements that de®ne accessibility for

various building elements (such as doors and toilets) along

an accessible route. An accessible route can thus be

described as a sequence of accessible route segments and,

if needed, adequate clearance at the openings of critical

components of a space.

Our motion planning technique determines accessible

route segments in a space between building elements

(such as doors and toilets). In addition, individual elements

are checked for geometric clearances. A complete accessi-

ble route includes many accessible components (including

openings and route segments). The route is considered

accessible if all components in the route are accessible.

The following de®nitions de®ne the terms that we use in

the performance based accessibility analysis:

Rinit the initial position (the starting point of an acces-

sible route or segment of accessible route)

Rgoal the goal position (the ending point of an accessible

route or segment of accessible route)

Rseg a segment of the accessible route between the

initial position Rinit and the ®nal position Rgoal

within a space

Ropen the clearance area at an opening of building

elements

The motion planner generates a path between an initial

point and a goal point. Building components along the

accessible route graph map to the R nodes: Ropen nodes

map to initial and goal points, Rinit nodes map to initial

points, and Rgoal nodes map to goal points. The arcs of the

graph (the Rseg components) map to the generated path

between the R nodes. Fig. 2 shows the potential accessible

route segments and components of a bathroom facility and

the associated accessible graph. Route segments (arcs) are

established between adjacent building elements. It is inter-

esting to note that there are two established goal nodes (and

two route segments) for the toilet at K because the algorithm

models access to the toilet using either a side or a diagonal

transfer. Furthermore, nodes A and B are potential accessi-

ble openings but the doorways at C and D are eliminated as

potential Ropen node since they do not have suf®cient clear-

ance requirements. Also note that each opening Ropen and

each route segment Rseg can be evaluated independently.

In the following, we ®rst discuss the application of a

motion planner for determining the existence of an acces-

sible route segment Rseg. We then discuss the compliance

checking of the component openings, Ropen. Finally, the

determination of the initial and goal positions of various

building elements is discussed.

4. The wheelchair motion planner and determination ofan accessible route segment Rseg

Although the goal of this study is to directly model the

motion of a wheelchair through a space using the actual

wheelchair geometry, the motion planner ®rst tries to verify

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Fig. 2. Potential accessible route components and accessible graph of a bathroom facility. The left ®gure shows the components (A±K) of a multi-occupant

bathroom. The bold nodes and arcs in the access graph on the right show the path from the entry door to the accessible toilet. The graph shows one accessible

route segment Rseg1 from A to B and two accessible route segments from B to K. Note that the path planner found that G and H are inaccessible from A.

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the existence of a `comfortable' width along the route. To

determine an accessible route segment within a space, the

motion planner performs two basic tasks:

1. Verify the existence of adequate clearance width along

the route.

2. Determine if a wheelchair user can negotiate this route

given the assumed geometric and behavioral constraints

of the wheelchair.

4.1. Pass one: determining the clearance width of the

accessible route

The existence of an accessible route is intended to ensure the

usability of a facility for wheelchair-bound users, and in most

cases, the wheelchair user should be able to negotiate the

accessible route using only forward motion. The ADAAG

provision below prescribes the width parameters of the route.

Provision 4.3.3 Width. The minimum clear width of an

accessible route shall be 36 in. (915 mm) except at doors

(see 4.13.5 and 4.13.6). If a person in a wheelchair must

make a turn around an obstruction, the minimum clear

width of the accessible route shall be as shown in Fig.

7(a) and (b).3

For the ®rst pass, we focus on the general 36 in. (915 mm)

requirement on the accessible route. The exception rule for

turn around will be discussed later for constructing the second

pass. The general 36 in. (915 mm) width rule does not repre-

sent the width of a wheelchair but prescribes a `comfortable'

width for the wheelchair user to negotiate. To satisfy the

provision, the motion planner uses a 36 in. (915 mm) disc to

describe the geometry of the robot A36. Given the workspace

W as determined by the ¯oor space and the building compo-

nents, the motion planner generates the con®guration space

C36 given A36 and W. The path generated by this planner is not

subject to geometric and physical constraints (such as turning

radius) of a robotÐthe robot simply slips and slides down the

potential gradient. This type of planner is known as a holo-

nomic planner [7]. Fig. 3 illustrates the C36 con®guration

space for a bathroom facility example. The white (non-

shaped) areas represent legal positions for the A36 disc robot

and are ensured to provide a 36 in. (915 mm) clearance. Note

that the motion planner treats a doorway with the door in the

closed position, and, hence, in the con®guration space be-

tween the entry door and the accessible toilet is discontinuous.

For this pass, the motion planner does not actually gener-

ate the path. It simply generates the potential ®eld from the

goal points to the initial points. If the potential-®eld genera-

tion cannot reach the initial point, there is no 36 in.

(915 mm) width path between the two points, and an acces-

sible wheelchair route between the points does not exist. If,

however, the potential-®eld generation does reach the initial

point signifying that a 36 in. (915 mm) wide path does exist

between the two points, the motion planner proceeds to the

second pass. Fig. 4 illustrates the actual potential ®eld

generated between the entry door and a urinal using a


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4483 Note that ADAAG Fig. 7(a) and (b) are shown in this paper as Fig. 5.

Fig. 3. The C36 con®guration space for a bathroom facility. White areas show spaces in which a 36 in. disk can move.

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UNCORRECTED PROOF1 in. cell discretization and a 12-sided polygon with a 36 in.

(915 mm) diameter for the A36 robot. The contour lines

illustrate the rectangular `Manhattan' nature of the gener-

ated potential ®eld [7].

4.2. Pass two: capturing the characteristics of wheelchair

motion

To closely examine exceptional rules, e.g. the clear width

of an accessible route around an obstruction, we need to be

able to capture the behavior of wheelchair motion. Fig. 5

illustrates the two ADAAG ®gures (Fig. 7(a) and (b)) refer-

enced by Provision 4.3.3 of the ADAAG. Note that in the

prescriptive width de®nition, the exceptional rules and the

associated ®gures do not address all possible turn-around

con®gurations. In order to provide accessibility check on

all possible con®gurations, the route planner models, as

closely as possible, the behavior of wheelchair motion as

to the level of detail set by the guidelines.

In the second pass, in addition to the C36 con®guration


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Fig. 4. The potential ®eld between the initial entry door and the goal right urinal of the bathroom design of Fig. 2. The robot path-planner ®nds the potential

®eld and ®nds any routes within the ®eld.

Fig. 5. Minimum accessible route turning clearances de®ned in Provision 4.3.3 of the ADAAG. These exceptional provisions are examples of the many

exceptional rules that prescriptive code speci®cations represent explicitly.

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space generated in the ®rst pass, con®guration spaces are

also generated using the actual wheelchair robot denoted as

Awc. Fig. 6 shows the reference wheelchair dimensions as

given in the ADAAG, and Fig. 7 illustrates the geometry of

the wheelchair robot which has its width less than 36 in.

(915 mm) wide. The potential ®elds within the con®gura-

tion spaces generated by the planner are used as a guide to

determine the path t for Awc.

Since Awc is not a disc, the motion planner must keep

track of the robot's orientation while generating a path,

and the motion planner must check each wheelchair position

and orientation against the obstacles in the space. The

motion planner discretizes the rotation space into n con®g-

uration spaces Cwc0¼Cwcn where the angle (in radians)

between two consecutive orientations Awc is equal to 2p/

n. Now, the motion planner can check the wheelchair posi-

tion and orientation �x; y; u� against each appropriate con®g-

uration space Cwci. The motion planner generates a non-

holonomic path [8] by restricting Awc to three moves: a

left turn, a right turn, and a straight-ahead move. Fig. 8

illustrates these three options. For the left and right turns,

the motion planner describes the vertex of the turning angle

as the perpendicular length r from the centerpoint between

the major wheelchair wheels. The motion planner records

the actual position of Awc at the centerpoint of the half-

dodecagon at the front of the robot. The displacement

distance D from either turn (which is dependent on r)

dictates the translation of Awc.

4.2.1. Determination of turning radii for the wheelchair

The performance-based accessible route path planner

employs two values r1 and r2 for the turning radius r to

allow adjustment for maneuvering the wheelchair. The

larger turning radius r1 is employed to move the wheelchair

robot to the goal point. As the wheelchair user nears a goal,

the user naturally slows down allowing ®ner maneuvering

with a smaller turning radius r2. In this study, when the

wheelchair has moved within an 18 in. (460 mm) locus of

the goal point, the motion planner switches to the smaller

turning radius r2 to try to maneuver Awc to the goal point

with an acceptable orientation.

In determining the value for the turning radius, a larger

value represents a larger turning circle and a more comfor-

table path t for the wheelchair user. The largest possible

value for r1 was determined using a trial and error process

using the two turning-around-an-obstruction con®gurations

based the ADAAG Provision 4.3.3 shown in Fig. 5. Figs. 9

and 10 illustrate the ®rst legal paths with an r1-value that

works for both turning-around-an-obstruction con®gura-

tions produced by a trial-and-error process. Through this

process, we selected 24 in. (610 mm) as the value of the

larger turning radius r1.

As with the determination of r1, a trial-and-error process

was employed to determine the smaller turning radius r2

based on Provision 4.2.3 of the ADAAG:

Provision 4.2.3 Wheelchair Turning Space. The space

required for a wheelchair to make a 1808 turn is a clear

space of 60 in (1525 mm) diameter (see Fig. 3(a)) or a T-

shaped space (see Fig. 3(b)).4

Fig. 10 shows the ADAAG ®gures associated with this

provision. The turning radius r2 is determined by ®nding the

maximum turning radius that can make Awc perform the

turning maneuver in a 60 in. (1525 mm) space. Fig. 11 illus-

trates the turning maneuver that satis®es the 60 in.

(1525 mm) width constraint (as shown by the dimension


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Fig. 6. Wheelchair dimensions as shown in the ADAAG. The wheelchair model represents these design speci®cations explicitly.

Fig. 7. Dimensions of the robot Awc. The robot path-planner represents the

dimensions shown in this ®gure in its model of a wheelchair. 4 Note that ADAAG Fig. 3(a) and (b) are shown in this paper as Fig. 10.

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line) using a turning radius r2 of 9 in. (230 mm). It should be

noted that while this clearance width of 60 in. (1525 mm) is

suf®cient, the necessary clearance width orthogonal to the

dimensioned clearance exceeds the 60 in. (1525 mm)

diameter requirement. Indeed, this clearance width, in prac-

tice, should exceed the 60 in. (1525 mm) as discussed in the

Appendix of the ADAAG:

Provision A4.2.3 Wheelchair Turning Space. These

guidelines specify a minimum space of 60 in.

(1525 mm) diameter or a 60 in. by 60 in. (1525 mm by

1525 mm) T-shaped space for a pivoting 1808 turn of a

wheelchair. This space is usually satisfactory for turning

around, but many people will not be able to turn without

repeated tries and bumping into surrounding objects. The

space shown in Fig. A2 will allow most wheelchair users

to complete U-turns without dif®culty.5

Fig. 12 (ADAAG Fig. A2) illustrates an acceptable clear-

ance oval, and the turning movement as shown in Fig. 11 ®ts

into the suggested oval geometry.

4.2.2. Wheelchair motion planner and path generation

The motion planner uses the potential ®eld in the con®g-

uration space C36 to guide the wheelchair robot Awc as

follows: starting from the initial position and orientation


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Fig. 8. The three movement behaviors (move left, right, and forward) for the Awc robot.

Fig. 9. Determination of the large turning radius (r1 � 24 00 (610 mm)) for the exception in Provision 4.3.3 of the ADAAG.

5 Note that ADAAG Fig. A2 is shown in this paper as Fig. 12.

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qinit, the motion planner examines the move options for left,

right, and straight ahead (denoted as qleft, qright, and qstraight,

respectively) using r1 as the turning radius for the robot.

1. If qleft resides in the C36 and appropriate Cwci con®gura-

tion space, the motion planner compares the position

�x; y� associated with qleft with the position �x; y� asso-

ciated with qgoal.

2. If the two positions are not the same, the motion planner

looks up the potential ®eld of the position and inserts the

node into a priority queue, which prioritizes the nodes by

their potential ®eld value (the lower the value, the higher

the priority).

3. Finally, the motion planner inserts a pointer to the

previous position (in this case, qinit) in the node and

marks qleft in the appropriate Cwci con®guration space

potential ®eld as having been already visited.

The motion planner repeats this procedure for qright and

qstraight.

The motion planner continues the iterative process by

removing the highest priority node (the node with the lowest

potential value) from the priority queue and examining the


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Fig. 10. The prescribed turning circle and T-space from the ADAAG.

Fig. 11. Determination of the small turning radius (r2 � 9 00 (230 mm)) for

use by the motion planner to address the issue of Provision 4.2.3 of the

ADAAG. Fig. 12. The ADAAG turning clearance geometry.

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three move options from the associated position and orien-

tation q. The Cwci con®guration spaces include the visited as

well as the free space information, and the motion planner

treats a visited qinit as an obstacle. When q is within an 18 in.

(460 mm) locus of qgoal, the planner starts generating new

positions using the smaller turning radius r2. When the robot

reaches the goal position, the motion planner examines

whether the orientation u associated with the current q is

within the allowable range of u goal and, if so, it records the

path t . The iterative process continues until either the

motion planner empties the priority queue (indicating no

path t exists) or the position �x; y� associated with the

current q matches with qgoal for both position and the accep-

table orientation range.Fig. 13 illustrates a generated path

from the entry door to the urinal in the bathroom facility.

5. Accessibility analysis of Ropen components

ADAAG prescribes wheelchair clearances at doors and

entrances along an accessible route. The Ropen node of an

accessible route graph consists of three clearance compo-

nents: the clearance of the opening and clearances on either

side of the opening. For the opening, the analysis applies a

geometric test with the parameters of the required clearance

box taken directly from the following provision:

Provision 4.13.5 Clear Width. Doorways shall have a

minimum clear opening of 32 in. (815 mm) with the

door open 908, measured between the face of the door

and the opposite stop (see Fig. 24(a)±(d)). Openings

more than 24 in. (610 mm) in depth shall comply with

Provisions 4.2.1 and 4.3.3 (see Fig. 24(e)).6

EXCEPTION: Doors not requiring full user passage, such

as shallow closets, may have the clear opening reduced to

20 in. (510 mm) minimum.

Fig. 14 shows the ADAAG ®gure that prescribes wheel-

chair clearances for doors. Note that the clearance geome-

tries are dependent on the approach of the wheelchair and

additional parameters speci®c to the building element. For

example, for doors, the clearance geometry may be depen-

dent on the direction of the swing. For a single swinging

door, the ADAAG de®nes the side from which the user pulls

the door to open it as the pull side and the side from which

the user pushes the door to open it as the push side. From

each side, the user can approach the opening from the front,

hinge side, or latch side of the door:

² For the front pull side approach, the clearance box

extends 60 in. (1525 mm) from the wall that contains

the opening and the door and covers the width of the

opening plus 18 in. (460 mm) on the latch side of the

door (left picture of Fig. 14(a)).

² For the front push side approach, the clearance box

extends 48 in. (1220 mm) from the wall and covers the


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Fig. 13. The generated path from the initial doorway entry to the goal right urinal in the bathroom facility. The ®rst part of the path uses the larger r1 turning

radius, and the last part of the path uses the smaller r2 turning radius.

6 Note that these ®gures are not shown in this paper.

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width of the opening plus 12 in. (305 mm) on the latch

side if the door has a closer and a latch (right picture of

Fig. 14(a)).

² For the hinge pull side approach, the clearance box extends

60 in. (1525 mm) from the wall and covers the width of the

opening plus 36 in. (915 mm) on the latch side. Or the

clearance box extends at least 54 in. (1370 mm) from the

wall and covers the width of the opening plus 42 in.

(1065 mm) on the latch side (left picture of Fig. 14(b)).

² For the hinge push side approach, the clearance box

extends 42 in. (1065 mm) from the wall (48 in.

(1220 mm) if the door has a latch and closer) and covers

the width of 54 in. (1370 mm) from the latch side extend-

ing toward the hinge side (right picture of Fig. 14(b)).

² For the latch pull side approach, the clearance box



the width of the opening plus 24 in. (610 mm) on the

latch side (left picture of Fig. 14(c)).

² For the latch push side approach, the clearance box




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Fig. 14. Door approaches and wheelchair clearance. The motion planner models the different door approaches and clearances, based on the de®nitions of the

ADAAG.

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the width of the opening plus 24 in. (610 mm) on the

latch side (right picture of Fig. 14(c)).

The accessible route analysis examines all possible

approaches by performing geometry interference tests on

the associated clearance boxes. Failure of all interference

tests for either the pull or push side disquali®es the potential

Ropen component. Conversely, if at least one clearance box

on either side passes the interference test, the potential Ropen

component quali®es as accessible and assigned as a node in

the accessible route graph.

6. Determining the initial and goal points Rinit and Rgoal ofan accessible segment

Each accessible route segment starts from an initial point

and ends at a goal point. To automatically generate and

check a route segment using the motion planner, it is neces-

sary to determine the initial and goal positions of the build-

ing elements. The following describes the determination of

the initial and goal points for certain building elements, such

as doors and openings and the toilet.

6.1. Doors and openings

Since the potential opening component is a node in the

accessible route graph, the component provides the initial/

goal point for a route segment Rseg. Fig. 15 illustrates the

positions of the initial and goal points associated with the

opening. Since the motion planner uses the initial and goal

points to generate the potential ®eld in the C36 con®guration

space, the ®gure shows the circular A36 robot as well as the

Awc robot. The Awc robot shown in the ®gure has a ®xed

orientation associated with the initial points. However, the

motion planner accepts any orientation within a 908 range

for the orientation of the Awc robot at the goal position. Note

that when passing through a door opening, the wheelchair

goes from the goal point of a path segment on one side of the

door opening to the initial point of another path segment on

the opposite side of the door opening. The goal point±initial

point sequence through a door opening is either (b)±(c) or

(d)±(a) from the ®gures shown in Fig. 15. The door opening

goal point and initial point parameters as shown in Fig. 15

guarantee that a path exists from the goal point±initial point

pair.

6.2. Water closet

In general, an Rgoal node maps to one goal point. However,

for certain accessible building elements such as toilet, the

motion planner needs to establish more than one goal point

to check whether a component is accessible. Fig. 16 illus-

trates water closet usage by a wheelchair user, an action

known as wheelchair transfer. As shown in the ®gure, the

wheelchair user can transfer from the wheelchair to the

toilet via two fundamentally different methods: diagonal

transfer and side transfer. Thus, the motion planner speci®es


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Fig. 15. Initial and goal points for the Ropen node. The wheelchair moves forward, i.e. up in ®gures (a) and (c) and down in ®gures (b) and (d). The goal of one

segment, e.g. (b) becomes the initial point of a connected segment, e.g. (c).

ARTICLE IN PRESS


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two different goal points and orientations to re¯ect the

different methods.

Fig. 17 illustrates the two goal points and orientations

associated with the two transfer options. Note that for the

side transfer, the goal point and orientation of the wheel-

chair robot illustrated in Fig. 17(b) does not directly corre-

spond to the side transfer position illustrated in Fig. 16(b).

Currently, the motion planner restricts the wheelchair to

only forward motion, and the ADAAG assumes backing

up to the ®nal side transfer position. Therefore, the motion


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Fig. 16. Wheelchair transfer diagrams for water closets from ADAAG. The motion planner de®nes both side and diagonal transfer behaviors.

Fig. 17. Goal points for diagonal and side transfers.

ARTICLE IN PRESS


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planner positions the wheelchair robot such that it is possi-

ble to make the backup move to the ®nal side transfer

position.

7. Prescriptive code analysis and performance-basedusability analysis

Because of the prescriptive nature of the disabled access

code, it cannot address all possible building design con®g-

urations or wheelchair use patterns; the code limits the

special cases it addresses to the turn-around-an-obstruction

exceptions. In practice, wheelchair users can comfortably

use a large number of design con®gurations that do not

comply with the prescriptive accessible route provisions

from the ADAAG. On the other hand, a design con®guration

which is code complied does not necessarily imply acces-

sible. Here, we analyze design con®gurations against the

prescriptive parameters as given in the ADAAG and

compare the results to the performance-based analysis

based on the motion planner.

For a given con®guration, the following four scenarios for

accessibility are possible:

² Code-compliant and usable.

² Not code-compliant and usable (Section 7.1).

² Code-compliant and unusable (Section 7.2).

² Not code-compliant and unusable.

The performance-based analysis uses speci®c provisions

from the ADAAG to instantiate the turning radius para-

meters, and by default, the tested con®gurations were both

code-compliant and usable. Providing examples that are

both non-compliant and unusable can also be trivially

demonstrated, for example, with a less-than 36 in. wide

(915 mm wide) corridor. The following examples illustrate

a non-compliant route that a wheelchair user can actually

negotiate and a code-compliant route that a wheelchair user

cannot negotiate.

7.1. Example 1

The ®rst example presents a design con®guration illu-

strated in Fig. 18 that falls under the U-turn-around-an-

obstacle exception category: the width of the obstruction

is less than 48 in. (1220 mm), and the con®guration cannot

be transformed into the 908-turn-around-an-obstacle excep-

tion by making the obstruction wider than 48 in. (1220 mm).

Following the parameters of the ADAAG Provision 4.3.3,

the con®guration fails to comply with the exception that:

² The widths of the ®rst and third legs are less than 42 in.

(1065 mm).

² The width of the second leg is less than 48 in. (1220 mm).

Using the performance-based parameters for the turning


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Fig. 18. Example of an U-turn-around an obstacle exception. This trace of a wheelchair path around an obstruction illustrates that the performance-based path-

planner can determine that a path can be accessible, although non-compliant with the prescriptive code.

ARTICLE IN PRESS


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radii established in the performance-based analysis, the

motion planning simulation returns a successful path taround the obstruction for the non-compliant con®guration

as illustrated in the ®gure. Thus, from the performance

perspective, the motion planner deems that the con®guration

is usable by a wheelchair user.

This example demonstrates that the wheelchair model

constructed from the constraints of the two ADAAG U-

turn con®gurations can successfully navigate through a

non-compliant U-turn con®gurationÐhowever, such a

demonstration simply points out that the code might be

too conservative.

7.2. Example 2

Fig. 19 shows a con®guration that is a code-complied but

unusable situation. Following the parameters given in the

ADAAG Provision 4.3.3, the design complies with the code

in that:

² The accessible route is equal to or greater than 36 in.

wide.

² Since it is not a 1808 U-turn, the turn-around-an-obstruc-

tion exception does not apply.

Using the performance-based parameters, the motion

planning simulation fails to return a path t around the

obstruction for the code-compliant con®guration. By trial

and error, one can extend the length of the second leg to

®nd a usable design con®guration shown in Fig. 20.

This example illustrates ambiguities that exist in current

prescriptive code. First, note that if the angle between the

second and third leg equals 908 instead of exceeding 908, the

®rst turn-around-an-obstruction exception from Provision

4.3.3 might apply. The building of®cial may contend that

the exception applies with a small angular increment e , but

as e grows, the con®guration does not qualify for the excep-

tion. The ambiguity of at what point the prescribed con®g-

uration applies illustrates the dif®culty of applying a

prescriptive-based code directly. On the other hand, by

changing the angle between the second and third legs of

the route from 908 1 e to 908 or 908 2 e , the motion planner

demonstrates the overly restrictive nature of the 908-turn-

around-an-obstruction exception from Provision 4.3.3.

While not explicitly stated, the exception should apply to

angles less than 908 since this con®guration would consti-

tute a more dif®cult accessible route. Furthermore, as illu-

strated in Fig. 20, the second and third leg dimensions

provide a viable path t around the obstruction, and these

lengths are clearly less than the required 48 in./42 in.

(1220 mm/1065 mm) exception requirement, as in the

provision.

8. Accessibility analysis of ¯oor layout

We applied the methodology to analyze the accessibility

of the ¯oor plan for an existing building as shown in Fig. 21.

Fig. 22 shows the analysis report with a view of the modeled

¯oor plan [3]. The comments associated with inaccessible

building components have links to the prescriptive provi-

sions of the ADAAG document as an informative guide.

The analysis reports shown in Fig. 22 reports that there is

no accessible route to the water closet in the men's bath-

room, and thus there is no accessible toilet in the building.


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Fig. 19. Example of a code-compliant but unusable con®guration. This design example is accessibility-compliant, but the motion planner shows that it is

unusable.

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Fig. 23 con®rms the inaccessibility of the water closet. Here,

the wheelchair user is not able to pass through the stall's

doorway. It is interesting to note that the partition walls

were added to the original plan to ensure privacy for the

toilet user. Ironically, the addition of these walls made the

toilet inaccessible to wheelchair users. With the removal of

the partitions, the men's bathroom would revert back to a

single-occupancy from a multiple-occupancy. As shown in

Fig. 24, without the partition walls, the motion planner

generates an accessible route to the toilet. Note that the


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1680Fig. 21. Floor plan of an actual facility. As shown in Fig. 22, the motion planner found that it lacked wheelchair accessibility to the men's toilet. As shown in

Fig. 23, the men's toilet is indeed inaccessible to a wheelchair user.

Fig. 20. Example of a viable but non-compliant path around an obstruction. With the motion planner incorporated into a design system, a designer could

recognize a problem such as that of Fig. 19, change the building design model, and immediately use the path planner to assess usability of design variants, such

as this one.

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path is discontinuous between adjacent spaces since the

route segments are generated between building elements

and the openings and entrances are checked independently.

We performed similar analyses to check access to other

facilities such as the bookshelf, the women's bathroom

and the interview room, etc. [4].

9. Summary and discussion

This paper discusses the nature and bene®ts of perfor-

mance-based analysis of wheelchair accessibility of a facil-

ity using motion planning techniques developed in robotics

research. In the practices of architects, wheelchair designers

and wheelchair users and in its computer implementation,

wheelchair accessibility is a knowledge-intensive activity.

This paper discusses one approach to implementation of

knowledge-intensive engineering analysis in the computer

and our results in applying this approach. Built on the prac-

tice of architecture, the design of building codes, theory of

robotic motion planning and building product models, this

work is an example of the multidisciplinary engineering

informatics methods that have started to demonstrate high

performance in applications of computers in engineering.

Traditional expert systems have tried to replicate the knowl-

edge-intensive practices of practitioners, but their imple-

mentations have often proved to be ad hoc in design and

brittle in performance [9].

The performance-based motion-planning techniques

developed directly capture motion and behavior given the


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Fig. 22. Accessibility analysis report. This automatically generated report circles the inaccessible men's toilet (left pane) and identi®es the relevant section of

the ADAAG code (right pane).

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wheelchair's parameters as described in the ADAAG. This

direct performance analysis obviates the need for the

complicated exception analysis associated with the

ADAAG accessible route parameters, an artifact that is a

consequence of the prescriptive nature of the ADAAG.

Furthermore, the performance-based analysis method can

ensure the usability of an accessible route. The ADAAG

prescribes minimal legal requirements. This general

prescription necessarily ignores details of individual wheel-

chair designs and the abilities and preferences of individual

users. Thus, the prescriptive ADAAG can inform the design

of wheelchairs by manufacturers, and it can inform the

design of individual buildings by clients, but it cannot repre-

sent their speci®c situation. The detailed behavior model


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Fig. 23. Inaccessible water closet. The photo shows that a wheelchair user is unable to access the men's toilet in the facility diagrammed in Fig. 21 and

referenced in Fig. 22.

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UNCORRECTED PROOF

and simulation can readily accommodate the behavior

details of different wheelchair designs, and designers can

also use this method to analyze the performance of different

wheelchairs in different building designs while considering

the detailed abilities and preferences of different users.

The development method created a number of speci®c

instances of very general system design components,

including:

² Explicit symbolic (non-numeric) representation of the

physical components of the (building) design and some

component attributes and relationships. The model expli-

citly represents fundamental concepts of the engineering

problem: geometric forms (of both the building and

wheelchairs), the design functional intent (of building

components, i.e. that certain kinds of building compo-

nents are to be wheelchair accessible, and wheelchairs,

i.e. the assumption that motion is always forward and that

turning radii are constrained), and computable behaviors

(of a wheelchair and a building, i.e. paths and wheelchair

accessibility). The simulator model uses this model of the

user and its functional behaviors.

² Both to aid development and understanding of the analy-

sis, the simulation system has an associated graphical

user interface that shows 3D views of the designed

system and time-varying animations of the behavior of

the physical system user, as well as helpful explanations

of the ®ndings of the analysis system.

² Interactive in system use, enabling system users (both

designers and, potentially, code checkers) to interpret

the behavior of any design version and change the

product and process models, exploring predicted perfor-

mance of designs using criteria that are dif®cult to model

explicitly.

The performance-based accessible route analysis uses the

dimension for a wheelchair as given by the ADAAG to

develop the Awc robot parameters. The prescriptive nature

of the code creates an indirect relationship between provi-

sion parameters and the wheelchair dimensions and beha-

vior. In fact, the relationship between the actual wheelchair

constraints and the prescriptive route usability analysis is

not explicitly de®ned. In contrast, the approach described

can model more accurately the desired performance and

usability of space.

A designer can vary the parameters used by the motion

planner that is developed in this paper. Varying speci®c

parameters allows wheelchair manufacturers and users to

test the behavior of a speci®c wheelchair model or assign

personal preferences. Varying the A36 robot's diameter (and


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Fig. 24. Wheelchair route to men's toilet with the stall partitions removed. Integrated into a design system, the designer can make what-if changes to the design

and invoke the motion-planner to analyze wheelchair accessibility of each design option.

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in¯uencing the C36 con®guration space) allows the user to

choose a preferred comfort level for the path width indepen-

dent of the actual wheelchair parameters. Of course, the

diameter should exceed the wheelchair width. Manufac-

turers make wheelchairs with various physical dimensions,

and the performance-based analysis can easily capture these

dimensions to model the Awc robot. In addition, the turning

radii and the centerpoint of the turn depend on the wheel-

chair's mechanical constraints. Finally, independent of

these mechanical constraints, users have their own comfort

level associated with the possible turning radii r1 and r2.

In short, the performance-based approach allows wheel-

chair manufacturers and users to specify custom wheelchair

parameters. Once these parameters are determined, the

motion planner can simulate wheelchair movement through

a space that has been deemed usable by a `model' or

`general-purpose' wheelchair to con®rm the custom wheel-

chair's usability.

This paper has illustrated the use of the performance

prediction method using both small illustrative examples

and a real commercial example. Code specifying bodies

have started to use performance-based methods for some

aspects of building performance, e.g. energy. For example,

the US Department of Energy Building Standards and

Guidelines Program (BSGP) is a software tool that checks

compliance with the commercial building energy code using

whole-building performance simulation methods.

In this work, the non-holonomic path-planning analysis

developed limits the wheelchair motion to three options:

left, right, and forward. The motion planner imposes this

restriction in an attempt to capture the intent of the

prescribed code and match the compliance results of the

ADAAG accessible route provisions. However, the techni-

que can be extended to accommodate a number of options of

forward motion to include various (left or right) and forward

turns. In general, we implemented a simple motion planner:

it demonstrates that the performance-based simulation

approach is interesting and may lead to a change how

designers and code checkers specify and check access

requirements.

The motion planner described in this paper focuses on

forward motion alone. However, the motion planner can

be extended to support backward motion. Reeds [10]

describes optimal paths for a car-like robot that can reverse

its direction. Indeed several ADAAG provisions assume

backward motion. The motion planner would limit the

number of backups for a given path t according to the

speci®cations of the building code or the user.

While this study has illustrated the bene®ts for a perfor-

mance-based analysis of accessible route, further possible

extensions of current works warrant. First, while the motion

planner guarantees the discovery of the 36 in. (915 mm)

wide path if one exists, the non-holonomic planner devel-

oped for the actual wheelchair motion for the second pass

might not ®nd a path even if one exists. The problem

concerns the discretization of the con®guration space.

Determining the necessary discretization granularity for

the non-holonomic con®guration space is not straightfor-

ward since the location of the wheelchair robot's next possi-

ble position (using trigonometric functions) may not

correspond to the exact grid discretization. A promising

alternative is the randomized motion planner for robots

developed under kinematic and dynamic constraints in

which the probability that the planner fails to ®nd a path

when one exists converges toward zero [5].

10. Conclusions

This work is an example of the kind of automated analysis

of the predicted performance of a design that modern auto-

mated simulation now enables. The particular performance

analysis is complicated, highly knowledge-intensive, and

dif®cult both in theory and in practice. There are very

general components to the development method described

in this paper and summarized in the discussion. These

components build on carefully identi®ed and selected and

represented engineering knowledge. The computer imple-

mentation of this model-based simulation provides a new

way to predict the performance of designed systems, one

that appears to be signi®cantly more powerful than either

manual or static heuristic analyses of predicted system beha-

vior. The system components seem general in the sense that

they potentially enable many kinds of high-performance

predictions of system behavior. Although the analysis

system of this paper stores the design model in an applica-

tion-speci®c database, a more general implementation could

store both the design and the user (wheelchair) models in

shared, reusable and potentially changing databases.

10. Uncited references

[1]. [2].

Acknowledgements

This research is supported by the National Science Foun-

dation under Grant No. EIA-9983368 and by the Center for

Integrated Facility Engineering at Stanford University. Any

opinions, ®ndings, and conclusions or recommendations

expressed in this paper are those of the authors and do not

necessarily re¯ect the views of the sponsoring agencies. The

authors would like to thank Mr Joe Cavanaugh for his parti-

cipation in this research and the thoughtful anonymous

reviewers.

References

[1] ADAAG. Americans with disabilities act accessibility guide.

Washington, DC: Access Board, US Architectural and Transportation

Barriers Compliance Board, 1997.


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[2] CSC. Energy ef®ciency standards for residential and nonresidential

buildings. Sacramento, CA: California Energy Commission, 1999

title 24, section 6.

[3] Han CS, Kunz JC, Law KH. A client/server framework for on-line

building code checking. J Comput Civil Engng, ASCE 1998;12(4):

181±94.

[4] Han CS. Computer models and methods for a disabled access analysis

design environment. PhD Thesis, Department of Civil and Environ-

mental Engineering, Stanford University, Stanford, CA, 2000.

[5] Hsu D, Kindel R, Latombe JC, Rock S. Randomized kinodynamic

motion planning with moving obstacles. Workshop on Algorithmic

Foundations of Robotics, 2000.

[6] Kiliccote H. A standards processing framework. PhD Thesis, Depart-

ment of Civil and Environmental Engineering, Carnegie Mellon

University, Pittsburgh, PA, 1996.

[7] Latombe JC. Robot motion planning. Norwell, Mass: Kluwer

Academic Publishers, 1991.

[8] Latombe JC. A fast planner for a car-like indoor mobile robot.

Proceedings of the Ninth National Conference on Arti®cial Intelli-

gence, Anaheim, CA, 1991b. p. 659±65.

[9] Partridge D. The scope and limitations of future generation expert

systems. Future Generations Computer Systems 1987;3:1±10.

[10] Reeds JA, Shepp RA. Optimal paths for a car that goes both forward

and backward. Paci®c J Math 1991;145(2):367±93.


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