UNCORRECTED PROOF ARTICLE IN PRESS. A performance-based approach to wheelchair accessible route analysis

ADVEI2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 A performance-based approach to wheelchair accessible route analysis Abstract Charles S. Han 1, Kincho H. Law*, Jean-Claude Latombe 2, John C. Kunz a Center for Integrated Facility Engineering, Stanford University, Stanford, CA 94305-4020, USA Received 7 September 2001; revised 29 October 2001; accepted 2 November 2001 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 computational 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 * Address: Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020, USA. E-mail addresses: chuck.han@autodesk.com (C.S. Han), law@ce. stanford.edu (K.H. Law), latombe@cs.stanford.edu (J.-C. Latombe), kunz@stanford.edu (J.C. Kunz). 1 Autodesk, Inc., San Rafael, CA 94903, USA. 2 Department of Computer Science, Stanford University, Stanford, CA 94305, USA. Advanced Engineering Informatics 00 (2002) 000±000 www.elsevier.com/locate/aei This paper develops a method to determine if a usable wheelchair accessible route in a facility exists using computer-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 objectives 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 highlevel 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 accessibility 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 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 1474-0346/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S1474-0346(01)00003-9 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:02 article wb Alden

2 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 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. 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 R N where R is the set of real numbers, and N ˆ 2 or 3 is the spatial dimension. The motion planner for the wheelchair assumes a two-dimensional space where N ˆ 2: The space W is populated with obstacles represented as B 1,B 2,¼, B q, and the motion planner parameters are de ned by the shape, position, and orientation of A, the B i s, 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 B i s. 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 B i s, 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 ˆ R 2 has three degrees of freedom: translations in the x and y directions and the orientation u. Working in the con guration 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 B i maps to the C-obstacle CB i by `growing' its shape based on the geometric parameters of A and B i as shown in Fig. 1. The basic algorithm establishes a reference point with respect to the robot A and tracing A around the obstacle B i. The path circumscribed by A describes the C-obstacle CB i. If A can freely rotate, the shape of CB i 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 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:02 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 3 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 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 R seg1 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. 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 parameters of A, the B i s, 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 accessible 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: R init the initial position (the starting point of an accessible route or segment of accessible route) R goal the goal position (the ending point of an accessible route or segment of accessible route) R seg a segment of the accessible route between the initial position R init and the nal position R goal within a space R open 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: R open nodes map to initial and goal points, R init nodes map to initial points, and R goal nodes map to goal points. The arcs of the graph (the R seg 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 interesting 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 accessible openings but the doorways at C and D are eliminated as potential R open node since they do not have suf cient clearance requirements. Also note that each opening R open and each route segment R seg can be evaluated independently. In the following, we rst discuss the application of a motion planner for determining the existence of an accessible route segment R seg. We then discuss the compliance checking of the component openings, R open. Finally, the determination of the initial and goal positions of various building elements is discussed. 4. The wheelchair motion planner and determination of an accessible route segment R seg 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 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

4 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 Fig. 3. The C 36 con guration space for a bathroom facility. White areas show spaces in which a 36 in. disk can move. 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 3 Note that ADAAG Fig. 7(a) and (b) are shown in this paper as Fig. 5. turn around will be discussed later for constructing the second pass. The general 36 in. (915 mm) width rule does not represent 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 A 36. Given the workspace W as determined by the oor space and the building components, the motion planner generates the con guration space C 36 given A 36 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 holonomic planner [7]. Fig. 3 illustrates the C 36 con guration space for a bathroom facility example. The white (nonshaped) areas represent legal positions for the A 36 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 between the entry door and the accessible toilet is discontinuous. For this pass, the motion planner does not actually generate the path. It simply generates the potential eld from the goal points to the initial points. If the potential- eld generation cannot reach the initial point, there is no 36 in. (915 mm) width path between the two points, and an accessible 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 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 5 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 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. 1 in. cell discretization and a 12-sided polygon with a 36 in. (915 mm) diameter for the A 36 robot. The contour lines illustrate the rectangular `Manhattan' nature of the generated 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)) referenced 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 C 36 con guration 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. 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

6 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 Fig. 6. Wheelchair dimensions as shown in the ADAAG. The wheelchair model represents these design speci cations explicitly. space generated in the rst pass, con guration spaces are also generated using the actual wheelchair robot denoted as A wc. 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 guration spaces generated by the planner are used as a guide to determine the path t for A wc. Since A wc 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 guration spaces C wc0 ¼C wcn where the angle (in radians) between two consecutive orientations A wc is equal to 2p/ n. Now, the motion planner can check the wheelchair position and orientation x; y; u against each appropriate con guration space C wci. The motion planner generates a nonholonomic path [8] by restricting A wc 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 A wc at the centerpoint of the halfdodecagon at the front of the robot. The displacement distance D from either turn (which is dependent on r) dictates the translation of A wc. 4.2.1. Determination of turning radii for the wheelchair The performance-based accessible route path planner employs two values r 1 and r 2 for the turning radius r to allow adjustment for maneuvering the wheelchair. The larger turning radius r 1 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 r 2. 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 r 2 to try to maneuver A wc 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 comfortable path t for the wheelchair user. The largest possible value for r 1 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 r 1 -value that works for both turning-around-an-obstruction con gurations produced by a trial-and-error process. Through this process, we selected 24 in. (610 mm) as the value of the larger turning radius r 1. As with the determination of r 1, a trial-and-error process was employed to determine the smaller turning radius r 2 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 r 2 is determined by nding the maximum turning radius that can make A wc perform the turning maneuver in a 60 in. (1525 mm) space. Fig. 11 illustrates the turning maneuver that satis es the 60 in. (1525 mm) width constraint (as shown by the dimension Fig. 7. Dimensions of the robot A wc. 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. 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 7 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 Fig. 8. The three movement behaviors (move left, right, and forward) for the A wc robot. Fig. 9. Determination of the large turning radius (r 1 ˆ 24 00 (610 mm)) for the exception in Provision 4.3.3 of the ADAAG. line) using a turning radius r 2 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 practice, 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 clearance 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 guration space C 36 to guide the wheelchair robot A wc as follows: starting from the initial position and orientation 5 Note that ADAAG Fig. A2 is shown in this paper as Fig. 12. 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

8 C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 q init, the motion planner examines the move options for left, right, and straight ahead (denoted as q left,q right, and q straight, respectively) using r 1 as the turning radius for the robot. 1. If q left resides in the C 36 and appropriate C wci con guration space, the motion planner compares the position Fig. 10. The prescribed turning circle and T-space from the ADAAG. x; y associated with q left with the position x; y associated with q goal. 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, q init ) in the node and marks q left in the appropriate C wci con guration space potential eld as having been already visited. The motion planner repeats this procedure for q right and q straight. 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 Fig. 11. Determination of the small turning radius (r 2 ˆ 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. 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:03 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 9 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 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 r 1 turning radius, and the last part of the path uses the smaller r 2 turning radius. three move options from the associated position and orientation q. The C wci con guration spaces include the visited as well as the free space information, and the motion planner treats a visited q init as an obstacle. When q is within an 18 in. (460 mm) locus of q goal, the planner starts generating new positions using the smaller turning radius r 2. 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 q goal for both position and the acceptable orientation range.fig. 13 illustrates a generated path from the entry door to the urinal in the bathroom facility. 5. Accessibility analysis of R open components ADAAG prescribes wheelchair clearances at doors and entrances along an accessible route. The R open node of an accessible route graph consists of three clearance components: 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 wheelchair clearances for doors. Note that the clearance geometries 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 dependent 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 6 Note that these gures are not shown in this paper. 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

10 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 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. 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 extending toward the hinge side (right picture of Fig. 14(b)). ² For the latch pull side approach, the clearance box extends 48 in. (1220 mm) from the wall (54 in. (1370 mm) if the door has a latch and closer) and covers 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 extends 42 in. (1065 mm) from the wall (48 in. (1220 mm) if the door has a latch and closer) and covers 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 11 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 Fig. 15. Initial and goal points for the R open 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). 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 R open component. Conversely, if at least one clearance box on either side passes the interference test, the potential R open component quali es as accessible and assigned as a node in the accessible route graph. 6. Determining the initial and goal points R init and R goal of an 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 necessary to determine the initial and goal positions of the building 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 R seg. 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 C 36 con guration space, the gure shows the circular A 36 robot as well as the A wc robot. The A wc 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 A wc 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 R goal 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 illustrates 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 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

12 C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 Fig. 16. Wheelchair transfer diagrams for water closets from ADAAG. The motion planner de nes both side and diagonal transfer behaviors. 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 wheelchair robot illustrated in Fig. 17(b) does not directly correspond 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 Fig. 17. Goal points for diagonal and side transfers. 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 13 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 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 pathplanner can determine that a path can be accessible, although non-compliant with the prescriptive code. planner positions the wheelchair robot such that it is possible to make the backup move to the nal side transfer position. 7. Prescriptive code analysis and performance-based usability analysis Because of the prescriptive nature of the disabled access code, it cannot address all possible building design con gurations 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 accessible. 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 parameters, 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 illustrated in Fig. 18 that falls under the U-turn-around-anobstacle 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 exception 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 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

14 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 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. radii established in the performance-based analysis, the motion planning simulation returns a successful path t around 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-obstruction 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 exception. The ambiguity of at what point the prescribed con guration 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 9081e to 908 or 9082e, the motion planner demonstrates the overly restrictive nature of the 908-turnaround-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 constitute a more dif cult accessible route. Furthermore, as illustrated 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 provisions 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 bathroom, and thus there is no accessible toilet in the building. 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:04 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 15 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 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. 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 Fig. 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. 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:05 article wb Alden

16 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 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). 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 performance-based analysis of wheelchair accessibility of a facility 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 practice 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 knowledge-intensive practices of practitioners, but their implementations 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 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:05 article wb Alden

C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 17 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 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. 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 wheelchair 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 represent their speci c situation. The detailed behavior model 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:05 article wb Alden

18 ARTICLE IN PRESS C.S. Han et al. / Advanced Engineering Informatics 00 (2002) 000±000 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 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. 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 explicitly 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 components 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 analysis, 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 performance 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 A wc robot parameters. The prescriptive nature of the code creates an indirect relationship between provision parameters and the wheelchair dimensions and behavior. 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 A 36 robot's diameter (and 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Advanced Engineering Informatics ± Model 5 ± Ref style 3 ± AUTOPAGINATION 2 05-12-2001 15:05 article wb Alden