Computer-Aided Design 42 (2010) 1095–1107

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Computer-Aided Design

journal homepage: www.elsevier.com/locate/cad

A dynamic priority-based approach to concurrent toolpath planning formulti-material layered manufacturingS.H. Choi ∗, W.K. ZhuDepartment of Industrial and Manufacturing Systems Engineering, Faculty of Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

a r t i c l e i n f o

Article history:Received 9 October 2009Accepted 19 July 2010

Keywords:Layered manufacturingMulti-materialsToolpath planningMulti-object motion planningDynamic priority

a b s t r a c t

This paper presents an approach to concurrent toolpath planning for multi-material layered manufactur-ing (MMLM) to improve the fabrication efficiency of relatively complex prototypes. The approach is basedon decoupled motion planning for multiple moving objects, in which the toolpaths of a set of tools are in-dependently planned and then coordinated to deposit materials concurrently. Relative tool positions aremonitored and potential tool collisions detected at a predefined rate. When a potential collision betweena pair of tools is detected, a dynamic priority scheme is applied to assign motion priorities of tools. Thetraverse speeds of tools along the x-axis are compared, and a higher priority is assigned to the tool at ahigher traverse speed. A tool with a higher priority continues to deposit material along its original path,while the one with a lower priority gives way by pausing at a suitable point until the potential collision iseliminated. Moreover, the deposition speeds of tools can be adjusted to suit different material propertiesand fabrication requirements. The proposed approach has been incorporated in a multi-material virtualprototyping (MMVP) system. Digital fabrication of prototypes shows that it can substantially shorten thefabrication time of relatively complex multi-material objects. The approach can be adapted for processcontrol of MMLM when appropriate hardware becomes available. It is expected to benefit various appli-cations, such as advanced product manufacturing and biomedical fabrication.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Layered manufacturing

Layered manufacturing (LM), or rapid prototyping (RP), is anadditive process that fabricates a physical prototype from a CADmodel layer by layer, more rapidly than conventional manufactur-ing processes [1]. LM technology is now seen in a wide range of ap-plications, such as product development, biomedical engineering,and architecture, etc. It offers huge potential to reduce or eliminatesome stages of the traditional supply chain. The global market forLM products and services grew to an estimated USD1.183 billion in2008, and the LM industry is expected to more than double in sizeby 2015, according to Wohlers Report 2009 [2].

LM processes can be roughly categorised as vector-based orraster-based. While a vector-based LM process drives a tool alonga predefined path to deposit fabrication material, a raster-basedprocess selectively generates specific contours out of an entirelayer ofmaterial. Each of these LMprocesses offers distinctive traitsfor some specific types of prototypes [3].

∗ Corresponding author. Tel.: +852 2859 7054; fax: +852 28586535.E-mail addresses: shchoi@hku.hk (S.H. Choi), h0795413@hkusua.hku.hk

(W.K. Zhu).

0010-4485/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2010.07.004

Although LM can shorten prototyping cycles, the process is notas rapid as desired.Wohlers [2] pointed out that applications of LMare increasing, yet current LM systems are becoming unacceptablyslow in respect of the increasing size and complexity of prototypesbeing made. Kochan [4] claimed that one of the main limitationsof rapid prototyping was the low speed at which a part wasfabricated. Bellini [5] presented that Fused Deposition Modelling(FDM) was fast enough for small parts of a few cubic inches, orthose of tall, thin features, but it could be very time-consuming forparts with wide cross-sections. Hauser et al. [6] also pointed outthat the methodology of LM was essentially a start–stop processbecause each layer was processed and deposited sequentially. Thebreaks in the build cycles, for example the positioning of hardware,often slowed down the build rate.

Some efforts have been devoted to enhancing the fabricationefficiency of LM. Sintermask Technologies [7] developed amachinewith a SelectiveMask Sintering (SMS) process capable of projectinginfrared radiation through masks to sinter a whole layer ofpolyamide powder in ten seconds. Voxeljet [8] introduced a plasticpowder binding system capable of building 400 cubic inches perhour. Hauser et al. [6] developed a software system to controla process called spiral growth manufacturing (SGM), capable ofbuilding ten layers per minute. Despite these developments, mostcommercial LM machines are still slow for relatively large andcomplex prototypes.

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1.2. Multi-material layered manufacturing

Another major problem is that most LM machines to date canonly fabricate homogeneous prototypes of a single material. How-ever, recent trends in various industries, particularly advancedproduct development [9] and biomedical engineering [10], havewarranted heterogeneous objects which offer superior propertiesunparalleled by homogeneous ones [1]. Heterogeneous objectsmay be classified into two major types, namely discrete multi-material (DMM) objects with a collection of distinct materials di-vided by clear boundaries, and functionally graded multi-material(FGM) objects with materials that change gradually from one typeto another [11]. There is indeed an imminent need to developmulti-material layered manufacturing (MMLM) for fabrication ofheterogeneous objects, and some pioneering works have been re-ported in recent years.

Qiu et al. [12] developed a virtual simulation system for fabri-cation of parts consisting of discretematerials; a toolpath planningmethod for twomaterials was reported to reduce defects and voidsof a virtual part. Jepson [13] developed an experimental MMLMmachine, which could blend two types ofmetallic powders to forma layer of some material gradients and subsequently sinter it tobuild an FGM part. Cho et al. [14] extended their patent ‘‘3D print-ing’’ to fabricate FGM parts; twomaterials were dispersed throughtheir respective inkjet tools and printed into the powder bed. Khalilet al. [10] developed amulti-nozzle biopolymer deposition system,which was capable of extruding biopolymer solutions and livingcells for freeform construction of tissue scaffolds. Cesarano III [15]developed a so-called Robocasting technology which was able tofabricate either single material or multi-material ceramic parts. Byturning the blender on or off, fabrication of graded alumina/metalcomposites, and discrete placement of fugitive materials could beachieved. Inamdar et al. [16] developed a multiple material stere-olithography machine. The mechanism consisted of three vats,each of which contained a specific material, and a customised Lab-VIEW system was used to control the rotating multiple vat systemto fabricate a multi-material model. Wang and Shaw [17] intro-duced a method for fabricating functionally graded materials viainkjet colour printing. The print heads dispatched Al2O3 and ZrO2aqueous suspensions in different quantities to form a particularcomposition. Malone et al. [18] developed the Fab@Home multi-material 3D printer for fabrication of electro-mechanical systems.Typical materials included polypropylene and ABS thermoplas-tics, and low melting-point metal alloys such as lead and tin. AZn–air cell battery of about the size of a coin, composed of fivelayers of different materials in a plastic case, was fabricated. ObjetGeometries Ltd. [19] claimed that its Connex350 offered the abil-ity to fabricate assemblies made of two types of photopolymermaterials, with different mechanical properties. The photopoly-mer materials were cured by ultra-violet light immediately afterjetting.

These systems have made significant contributions to thedevelopment of MMLM, although they were mostly experimentaland could onlymake simple prototypes of a few types of materials.However, practical and viable MMLM systems for relatively large,complex objects have yet to be developed.

It can be said that development of MMLM is mainly concernedwith three major research issues, namely (1) fabrication materials,(2) hardware mechanism for deposition of materials, and (3) com-puter software for planning the toolpaths and subsequent processcontrol of multiple tools for prototype fabrication. These three is-sues are generally studied by researchers of specialised expertise.Nevertheless, the software issue of toolpath planning is particu-larly important as it has a significant impact on the overall effi-ciency and quality of fabrication, especially of large and complexprototypes.

1.3. Issues of toolpath planning

Toolpath planning for LM is mainly concerned with (i) contourfilling strategy, and (ii) tool sequencing strategy [20]. Contourfilling strategy concerns mainly with how to fill up the internalarea of a contour. This issue has been well-studied and standardcontour filling patterns have been developed for LM [21]. On theother hand, tool sequencing strategy is more about coordinatingthe motions of a set of tools, each of which deposits a materialon specific contours, to fabricate a multi-material prototype safelyand effectively. Tool collisions and fabrication efficiency are mainconsiderations, which may be exacerbated by the need to varythe tool deposition speeds to suit different material propertiesand fabrication requirements [22]. Tools can be planned to depositmaterials either sequentially to avoid collisions at the expenseof fabrication efficiency, or concurrently to enhance fabricationefficiency with risks of collisions. This is a difficult problem ofMMLM.

Few research works on toolpath planning for MMLM have beenreported. Qiu et al. [12] developed a simulation system for toolpathanalysis of MMLM. In the system, a toolpath file per materialwas generated first and then integrated into one multi-materialtoolpath file. A toolpath planning method for two materials wasreported to reduce the defects and voids of a virtual part. Thismethod could process relatively simple objects, such as cylinderand cube. Zhu and Yu [23] proposed a collision detection andtool sequencing method for simple multi-material assemblies.Zhou [24] proposed a toolpath planning algorithm for fabricationof functionally graded multi-material (FGM) objects. First, thegradual material distribution in each layer was discretised intostep-wise sub-regions, in each of which the material could beassumed homogeneous. Then, sequential toolpath for each sub-region was generated separately.

The experimental MMLM systems described in the previoussection also involved some basic toolpath planning algorithmswhich were either sequential or could only handle relatively sim-ple prototypes. Choi and Cheung [25] developed a multi-mate-rial virtual prototyping system integrated with a topologicalhierarchy-based approach to toolpath planning for MMLM. Thisapproach was later improved with an entire envelope-based ap-proach [20] and with a separate envelope-based approach [26].These approaches were characterised by the construction ofbounding envelopes around slice contours by offsetting outwarda distance of the tool radius. Overlap test was executed for theseenvelopes. Tools in the non-overlapped envelopes could deposittheir specific materials concurrently without any collisions. Nev-ertheless, they did not allow tools to move concurrently when theassociated envelopes of the contours overlapped, incurring someidle time of tools.

1.4. Research objective

It can be concluded that toolpath planning for MMLM remainsa vital but difficult research issue, which has yet to be fully tack-led. This paper therefore proposes a new approach to concurrenttoolpath planning for MMLM to further improve the fabricationefficiency of relatively large, complex prototypes. This approacheradicates the associated constraints of the previous approaches[20,25,26] to further improve the fabrication efficiency. It is char-acterised by the construction of envelopes around individual toolsdirectly, rather than around the slice contours of each layer. Rela-tive tool positions are monitored to detect potential collisions at apredefined rate. A dynamic priority assignment scheme is appliedto assignmotion priorities of the tools to avoid collisions and to co-ordinate the tool motions accordingly. Deposition speeds of toolscan also be adjusted to suit different material properties and fabri-cation requirements. This concurrent toolpath planning approachcan substantially shorten the build-time of MMLM, in comparisonwith the previous approaches.

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2. Related works

2.1. Collision detection

Tool collision is a major obstacle of multi-toolpath planning.Collision detection, also knownas interference detection or contactdetermination, is an interdisciplinary issue which is particularlyimportant in motion planning, robotics, CAD/CAM, etc., [27].Detection accuracy and computation cost are two inherentlycontradictory factors. The rate of collision detection is quiteapplication-specific. For instance, haptic interfaces require updaterates of about one thousand hertz, while about twenty to thirtyupdates per second would be sufficient for real-time graphicalapplications [28]. A number of application-specific and practicalcollision detection algorithms have been proposed, and each ofthem has its own merits and deficiencies [29].

2.2. Multi-object motion planning

In an MMLM process, a number of tools deposit materials onspecific contours to fabricate a prototype, preferably in concurrentmotion to increase efficiency. It can be regarded as a more gen-eral control problem of multiple mobile objects sharing a commonworkspace to complete their individual tasks without collision.This problemhas received a great deal of attention in other applica-tions, such as mobile robots [30], manipulation of robot arms [31],route planning for vehicles in a warehouse [32], etc.

A variety of methods have been proposed to solve the multi-object motion planning problem, in which avoidance of collisionsis paramount for safety and effectiveness. In general, potential col-lisions are first detected, and the object motions are subsequentlycoordinated to avoid collisions and to improve optimality. Optimi-sation objectives include the minimisation of energy, path length,and motion time. Indeed, practicality often demands a good bal-ance between optimality (solution quality) and complexity (com-putation cost). A broad review ofmulti-objectmotion planning canbe found in Lavalle’s work [33], and this problem may be roughlycategorised into coupled and decoupled [34], as follows.

2.2.1. Coupled methodsA coupled method for multi-object motion planning combines

the configuration spaces of all the objects into a compositeconfiguration space in which a feasible path is searched for [32].In general, it can achieve completeness and optimality. However,the composite configuration space grows exponentially with thenumber of objects [35], rendering the problem PSPACE-hard [36].Lavalle and Hutchinson [37] worked on simultaneous optimisationof the motions of three robots from the start points to the goals.Li and Latombe [31] presented an approach to concurrent mani-pulation of two robot arms to grab parts of various types ona conveyor and transfer them to their respective goals whileavoiding collisions with obstacles. These works were among earlyapplications of coupled multi-object motion planning techniqueson relatively simple systems. Indeed, coupled methods are oftenused in systemswith only a few objects, or for off-line applications.

2.2.2. Decoupled methodsIn a decoupled method, on the other hand, the path of each

object is separately generated and subsequently coordinated toavoid collision [32]. Different decoupled methods have beenapplied to coordinate the motion of multiple objects, includingadjustment of geometric paths,modification of velocities, and timedelay [34]. Wagner et al. [30] demonstrated an efficient approachto coordinating a group of cooperative cleaner robots to clean acommon dirty floor. Lee and Kim [38] developed a multi-robot

printing system, in which the host computer commanded a set ofclient printer–robots to cooperatively draw a picture on a sheetof paper. In the work of Peng and Akella [39], the path of eachrobot was first generated irrespective of other robots, while thevelocities were subsequently altered along their paths to avoidcollision. Rekleitis et al. [40] presented an algorithm to control ateam of robots, moving in zigzags, to complete the coverage of a2D plane. Lee et al. [41] used potential functions to guide objectsto their destinations. Chang et al. [42] used a time delay methodto avoid collisions between two robot arms. The minimum delaytime needed for collision avoidance was obtained by a collisionmap scheme.

In essence, decoupled methods involve assigning priorities toobjects to determine the order in which the paths are to be coordi-nated [43]. Erdmann and Perez [44] assigned static priority to eachrobot and sequentially computed paths in a time-varying config-uration space. Ferrari et al. [45] used a fixed priority scheme andchose random detours for the robots with lower priorities. Thesestatic priority schemes were suitable for predefined applications.On the other hand, dynamic priority schemes are more flexible tohandle different situations. Azarm and Schmidt [46] proposed anapproach that considered all possible priority assignments for upto three robots. Clark et al. [47] presented a motion planning sys-tem that could construct collision-free paths for groups of robotsin dynamic environments. They introduced a priority scheme thatgave way to the robot whose local workspace was most crowded.Bennewitz et al. [35] optimised different possible priority schemesfor teams of mobile robots. Unfortunately, searching different se-quences of priorities was computation-intensive, and might fail tofind solutions to complex planning problems. van den Berg andOvermars [43] proposed a heuristic for assigning priorities to ateam of robots, in which a higher priority was assigned to a robotwith a longer moving distance. Decoupled methods often adoptpriority-based approaches due to its prioritisation essence [35].They are computationally simpler and can response faster in real-time applications, in comparison with coupled methods, althoughthey cannot guarantee optimal solutions. Moreover, they are scal-able for handling more mobile objects [32].

Based on the review above, a dynamic priority-based decoupledmethod is proposed to generate concurrent toolpaths for MMLM.However, MMLM has its distinct characteristics with respect tomulti-object motion planning. First, the tools do not have self-control and sensing capabilities, and they cannot communicatewith each other. They are coordinated by a central controller.Second, the tools are normally constrained to move along fixedpaths of zigzags or spirals, at constant deposition speeds. Andthird, the toolpath planning approach for MMLM should take intoaccount the mechanical and thermal properties of the fabricationmaterials. Hence, the multi-object motion planning technique hasto be suitably adapted for concurrent toolpath planning forMMLM.

3. Thedynamicpriority-based approach to concurrent toolpathplanning for MMLM

In a general scenario of multi-objects, the object motions maybe omni-directional and erratic with multiple intersections, asshown in Fig. 1. But tools in MMLM are normally constrained tomove along fixed paths of zigzags or spirals at constant depositionspeeds inside specific contours that do not overlap, as shown inFig. 2. The material deposition mechanism of MMLM may consistof a set of tools, each of which deposits a specific material on therelated slice contours. The tools do not invade other unrelatedcontours, and there may be collisions of tools only when they getin close vicinity, like the purple tool and the yellow tool. Indeed,some hardware constraints may hinder concurrent depositionof materials and consideration of collisions between tools and

1098 S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107

Fig. 1. A general motion scenario of multiple objects.

support mechanisms, in addition to tool collisions, would furthercomplicate the control problem. But as pointed out previously,hardware mechanism is another research issue of MMLM. Wetherefore assume appropriate deposition hardware without tool-support interferences would be available, and we limit the scopeof this paper to consider collisions between tools only.

The proposed concurrent toolpath planning approach firstgenerates the toolpath (hatch lines) of each tool for depositinga specific material on the related contours of a layer. The toolsare then coordinated to fabricate the layer concurrently. Collisiondetection of tools is executed at a predefined rate.When a potentialcollision between a pair of tools is detected, their traverse speedsalong the x-axis are compared, and a higher priority is assignedto the tool travelling at a higher traverse speed. The tool witha higher priority continues to deposit material along its originalpath, while the one with a lower priority gives way by pausingat a suitable point until the potential collision is eliminated. Assuch, the level of concurrent tool motions, and hence the overallfabrication efficiency, can be significantly improved.Moreover, thedeposition speeds of tools can be adjusted to suit differentmaterialproperties and fabrication requirements. The following sectionspresent the details of traverse speed, collision detection, andmotion priority assignment for implementation of the proposedconcurrent toolpath planning approach.

3.1. Analysis of traverse speed: Vx

There are two commonmodes inwhich a tool fills up a contour:(1) the zigzag mode where the toolpaths are hatch lines whichcan be either horizontal, or at 45° slope, or vertical [12] and,(2) the spiral mode where the toolpaths are offset inwards fromthe contours. The proposed approach adopts the zigzagmode withvertical hatch lines. As shown in Fig. 3(a), a tool moves in up-and-down zigzags at deposition speed V to deposit material to fill upa circular contour. As a whole, the tool moves from the left to theright at a traverse speed Vx. The deposition speed V is bidirectional,while the traverse speed Vx is unidirectional. V can be varied tosuit differentmaterial properties and fabrication requirements, butit is constant for a specific material during the whole fabricationprocess of a prototype. Vx, on the other hand, depends on the hatch

lines. Fig. 3(b) shows the lengths and the widths of two adjacenthatch lines. While the width w remains constant, the length hvaries across the contours during the fabrication process. Assumethat a tool traverses a distance of thehatchwidthw along the x-axisin a time it takes to complete depositing material along the hatchlength h. The time that a tool spends on a hatch line is T = h/V , andtherefore the tool’s traverse speed is given by Vx = w/T = wV/h.It can be seen in Fig. 3(a) that the hatch length increases from theleftmost to the centre of the circle and decreases from the centreto the rightmost of the circle afterwards. Accordingly, the traversespeed Vx of a tool decreases first and increases afterwards. Thecurve of tool displacement along X-axis versus time is shown inthe X–t graph in Fig. 3(c), whose varying gradient is Vx.

It can be said that the traverse speed Vx of a tool is instan-taneous, varying across a contour during the fabrication process.Motion priorities are dynamically assigned to the tools accordingto their traverse speeds to avoid collisions.

3.2. Collision detection

Collision detection plays an important role in avoiding colli-sions to ensure the safety and effectiveness of an MMLM process.Since the tools deposit specific materials at related slice contoursconcurrently, there may be collisions between a pair of tools whenthey get in close vicinity. In multi-object planning, object motionsmay be omni-directional and erratic with multiple intersections,rendering the relative velocities and the motion directions of ob-jects’ complex factors in collision detection. It may be necessary toiterate detection of the instantaneous relative velocities and centredistances of tools, which is computationally intensive if the detec-tion rate is high.

However, as we adopt up-and-down zigzags as the contourfilling strategy, detection of tool collisions for MMLM can besimplified considerably. It would only be necessary to considerthe distance between the ends of the hatch lines being depositedby the tools in question. In general, collisions between a pair oftools would not happen if either the horizontal or the verticaldistance between the ends of two hatch lines is greater than thesum of the tool radii, regardless of the deposition speeds anddirections of the tools. Hence, collision detection is only neededat a predefined rate of the completion of a number of hatch lines,making the algorithm relatively simple yet effective. The principleof the proposed collision detection is outlined as follows.

A cylinder is constructed around each tool as the boundingenvelope and hence a circle projected on the X–Y plane representsa tool. In Fig. 4(a), a red tool and a blue tool are depositingmaterialsalong hatch lines AB and CD, respectively. The tools are of the sameradius R. Let dx be the horizontal distance between the ends of twohatch lines which are currently being deposited by the associated

Fig. 2. Schematic of the proposed MMLMmechanism.

S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107 1099

(a) A simple layer of a circular contour. (b) Hatch length and hatch width.

(c) X–t graph of the circular contour.

Fig. 3. Analysis of traverse speed.

(a) Tools likely to collide. (b) Safety margin. (c) Tools not likely to collide.

(d) Tools not likely to collide.

Fig. 4. Tool collision detection for MMLM. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

1100 S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107

tools respectively, and dy the closest vertical distance between theends of the two hatch lines. Since dx < 2R and dy < 2R, the toolsare about to collide when the red tool is near point B and the bluetool is close to C .

Condition of potential collision:Any two tools moving along their respective hatch lines are

considered as about to collide if the following condition holds:

dx ⩽ 2R + safety margin = 2R + R = 3R AND dy ⩽ 2R.

The proposed algorithm incorporates a safety margin of R in thex-axis direction, which may be changed if necessary, for furthersafeguard against potential collisions as shown in Fig. 4(b). Fig. 4(c)and (d) show two cases in which the tools would not collide whendx > 3R, and when dx < 3R but dy > 2R, respectively.

The rate of collision detection should be well chosen to strikea good balance between detection accuracy and computation cost.A high detection rate improves accuracy with more computationresources, while a low detection rate reduces computation costat the expense of accuracy. For the MMLM process, the highestrate is to detect collision after fabrication of a hatch line. Onthe other hand, we adopt the lowest allowable rate of collisiondetection, which is derived as follows. In Fig. 4(b), imagine anextreme situation in which the traverse speed VxB of the blue toolapproaches zero, the red tool will catch up with the blue tool afterthe completion of n = R/w hatch lines, where R is the safetymargin andw is the hatchwidth. Hence, an interval of n hatch linesis the lowest allowable rate of collision detection. Whenever a toolfirst completes n hatch lines, the collision detection is executed.

3.3. Dynamic assignment of priorities for tool motion coordination

When potential collision between a pair of tools is detected,a higher motion priority is assigned to the tool that travels at ahigher traverse speed for it to continue to depositmaterial along itsoriginal path. The tool with a lower priority gives way by waitingat a suitable point until the potential collision is eliminated. Thispriority scheme ensures that a potential collision is resolved asquickly as possible so that the paused tool can resume fabricationtominimise uneven cooling thatmay impair the prototype quality.The procedure of dynamic assignment of tool motion priorities isas follows:

Step 1: Read in a new layer, initialise the speeds of tools, and startfabrication;

Step 2: Perform collision detection between all pairs of the tools;Step 3: If no potential collision is detected, go to Step 8;Step 4: Find the pair of tools which is likely to collide;Step 5: Calculate the traverse speeds Vx = wV/h of tools which

are likely to collide;Step 6: Assign priorities to the tools according to their traverse

speeds. A higher priority is assigned to a tool at a higherVx;

Step 7: A tool with a higher priority continues deposition along itsoriginal path, while the one with a lower priority waits ata suitable point to give way until the potential collision iseliminated;

Step 8: Tools without potential collision deposit materials concur-rently;

Step 9: If a layer is not completed, repeat from Step 2. Otherwise,repeat from Step 1 until all the layers are completed.

3.4. A simple prototype to illustrate the proposed approach

The following section illustrates how the proposed dynamicpriority-based approach to concurrent toolpath planning forMMLM works.

Fig. 5. A simple prototype of three discrete materials.

3.4.1. Workflow of the proposed concurrent toolpath planningapproach

Fig. 5 shows a simple prototype, of dimensions 230 mm ×

100 m × 6 mm, to be made of three discrete materials. Theprototype is sliced into 30 layers. In Fig. 6, three tools, Tred, Tgreen,and Tblue, of the same radiusR = 10mm,deposit the red, green, andblue materials respectively on a selected layer. For simplicity, thedeposition speeds of the three tools are set to be VR = VB = VG =

10 mm s−1, and the hatch width w is 1 mm. The effect of adjustingthe deposition speeds will be presented in the next section.

To start fabricating this layer, the three tools are initialisedwiththeir deposition speeds and they move from their datum positionsaround O to the bottom point of the leftmost hatch line of theirrespective contours. The proposed collision detection algorithmis executed on all pairs of the tools. At first, there is no potentialcollision as dx between all pairs of current hatch lines are greaterthan 3R, so all the three tools can start to deposit specific materialsconcurrently. The traverse speed of each tool is VxR = VxG = VxB =

wV/h, wherew and h are thewidth and length of the current hatchline being deposited by each tool.

As shown in Fig. 6, the length of each red hatch line is at firstshorter than that of the blue one; the traverse speed of the redtool is thus higher than that of the blue one, i.e., VxR > VxB.The red tool will catch up with the blue one some time later.As shown in Fig. 7, collision detection indicates that there is apotential collision between the red tool and the blue tool at timet1, because the condition of dx < 3R and dy < 2R holds. Thedynamic priority assignment algorithm is executed here to adjustthe motion priorities of the red tool and the blue tool accordingly.It calculates and compares the traverse speeds of the tools attheir respective current hatch lines, and assigns priorities to thesetools according to their traverse speeds. Here, a higher priority isassigned to the red tool, for it is at a higher traverse speed. The redtool continues its original path, while the blue tool with a lowerpriority waits at a suitable point to give way until the potentialcollision is eliminated. As to the blue tool, waiting at a suitablepoint means that the blue tool waits at the far end of its currenthatch line after completing deposition (shown as the solid bluecircle in Fig. 6) in order not to hamper the quality of the resultingprototype.

Now, while the blue tool is paused, the red tool and thegreen tool deposit materials concurrently, because no potentialcollision between them is detected. Some time after t1, the collisiondetection algorithm finds that the potential collision between thered tool and the blue tool has been eliminated. Subsequently, allthe three tools are commanded to fabricate concurrently.

Some time after the tools gradually traverse to the right side ofthe respective contours, the length of the blue hatch line becomesshorter than that of the red one. Thus, the traverse speed of the bluetool becomes higher than that of the red tool and the blue tool iscatching upwith the red tool. At time t2, as shown in dashed circlesin Fig. 6 and time t2 in Fig. 7, collision detection finds that there isa potential collision between the red tool and the blue tool again.

Now, the traverse speed of the blue tool overtakes that ofthe red tool. The priorities of these two tools are reversed, i.e., ahigher priority is assigned to the blue tool. Thus, the blue toolcontinues its original path while the red tool with a lower priority

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Fig. 6. Three tools fabricating the selected layer.

200

150

100

50

0Dis

plac

emen

t alo

ng X

-axi

s (m

m)

0.5 1 1.5Time (minutes)

2 2.5 3

Fig. 7. X–t graph of the selected layer. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

waits at a suitable point to give way until the potential collisionis eliminated. At this moment, the blue tool and the green tool,without potential collision, deposit concurrently while the red toolis waiting. Some time after t2, the collision detection algorithmfinds that the potential collision between the red tool and the bluetool has been eliminated. All the three tools can again fabricateconcurrently until the layer is completed. Digital fabrication of theselected layer with VR = VB = VG = 10 mm s−1 is shown fromFig. 8(a)–(e).

3.4.2. Adjustment of deposition speedsTo suit different material properties and fabrication require-

ments, it may be necessary to adjust the deposition speed of a tool.In this section, the deposition speeds of the red, green, and bluetools are varied to be VR = 15 mm s−1, VG = 10 mm s−1, VB =

8 mm s−1, respectively. Fig. 9 shows the X–t graph with these ad-justed deposition speeds.

Like in the previous example, the three tools first move con-currently to deposit their specific materials as shown in Fig. 10(a).Then, due to the higher deposition speed of the red tool and theshorter length of red hatch lines, the traverse speed of the red toolis much higher than that of the blue one. Hence, the red tool willquickly catch up with the blue one at time t1, as shown the X–tgraph in Fig. 9. The dynamic priority assignment algorithm is exe-cuted for the red tool and the blue tool accordingly. A higher pri-ority is assigned to the red tool which is at a higher traverse speed.The red tool continues fabrication along its original path, while theblue tool with a lower priority waits at a suitable point to give wayuntil the potential collision is eliminated, as shown in Fig. 10(b).

Now, the red tool and the green tool, which are not likelyto collide, deposit materials concurrently while the blue tool is

waiting. Some time after t1, the collision detection algorithm findsthat the potential collision between the red tool and the blue toolhas been eliminated. The three tools can again deposit materialsconcurrently, as shown in Fig. 10(c). Hence, in comparisonwith theprevious example of uniform deposition speed, the red tool travelsa lot faster and it will never be caught upwith by the blue tool aftert1. All the three tools continue to deposit materials concurrentlyuntil the layer is completed.

4. Implementation and case studies

The proposed dynamic priority-based approach has been incor-porated with other major in-house modules for STL model manip-ulation, slicing, hierarchical contour sorting, contour hatching, anddigital fabrication, to form an integrated system for multi-materialvirtual prototyping (MMVP) [48]. The system was implementedin C/C++, and integrated with WorldToolKit Release 9 for fabrica-tion simulation in a semi-immersive virtual reality (VR) environ-ment, and with Virtools Dev toolkits for a full-immersive CAVEVR environment. It can digitally fabricate relatively complex ob-jects for biomedical applications and advanced product develop-ment. The following presents two case studies, a human ear modeland a toy tank, to demonstrate some possible applications of theMMVP system and to verify the effectiveness of the proposed dy-namic priority-based approach to concurrent toolpath planning forMMLM.

4.1. A human ear model

In recent years, doctors and surgeons have often used biomed-ical prototypes to help visualise the anatomy of human organsand design prostheses for surgical planning and implantations.Indeed, multi-material prototypes would be particularly useful forstudy and planning of delicate surgeries, in that they can differ-entiate clearly one part from another, or tissues from blood ves-sels of a human organ. A model of a human ear with dimensionsof 175 mm × 186 mm × 190 mm, as shown in Fig. 11, is slicedinto 800 layers with layer thickness of 0.2 mm. Fig. 12 shows thecontours of a layer to bemade of fourmaterials coloured in orange,pink, blue, and grey,with four tools of the same radius R = 10mm.

The deposition speeds are set to be VP = 20 mm s−1, VO =

15 mm s−1, VB = 5 mm s−1, and VG = 5 mm s−1 for the toolsthat deposit pink, orange, blue, and grey materials, respectively.Adjusted deposition speeds will be presented later.

At first, the pink, orange, blue, and grey toolsmove concurrentlyto deposit their specific materials. When t = t1, as shown in solidcircles in Fig. 12 and the time t1 in Fig. 13, collision detection finds

1102 S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107

Fig. 8. Digital fabrication of the selected layer.

Dis

plac

emen

t alo

ng X

-axi

s (m

m)

Time (minutes)

200

150

100

50

00.5 1 1.5 2 2.5 3.53

Fig. 9. X–t graph of the selected layer with adjusted deposition speeds. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

that there is a potential collision between the pink tool and theorange tool. The dynamic priority assignment is executed for thepink tool and the orange tool according to their traverse speeds.A higher priority is therefore assigned to the pink tool which isat a higher traverse speed. This allows the pink tool to continuedeposition along its original path, while the orange tool with alower priority waits at the far end of its current hatch line until thepotential collision is eliminated. As collision detection is executedat the predefined rate, the potential collision between the pink tooland the orange tool has been eliminated some time after t1. Hence,they can again deposit materials concurrently, as shown in Fig. 13some time after t1. Meanwhile, it can be noticed that the blue tooland the grey tool have already completed their respective tasks.

At time t2, as shown in dashed circles in Fig. 12 and time t2in Fig. 13, a potential collision is detected between the pink tooland the orange tool again. Contrary to the case at t1, the pink toolnow traverses at a lower speed than the orange tool, because thelengths of hatch lines of the pink contour aremuch longer than thatof the orange one. The dynamic priority assignment is executedagain for the pink tool and the orange tool in the order of theirtraverse speeds. Thus a higher priority is assigned to the orangetool which is at a higher traverse speed. The orange tool continuesto deposit material along its original path, while the pink tool witha lower priority waits until the potential collision is eliminated.Some time after t2, the potential collision between the pink tooland the orange tool is found to have been eliminated. This paircan again deposit materials concurrently, as shown in Fig. 13 sometime after t2. When the pink tool finishes its task, this layer iscompleted. The digital fabrication process of the selected layer ofthe ear model is shown in Fig. 14.

To suit different material properties and fabrication require-ments, it is assumed that the deposition speed of the orange toolis increased from 15 mm s−1 to 20 mm s−1. Fig. 15 shows X–tgraph of the ear model layer with increased deposition speed forthe orange tool. In this case, the pink tool can never catch upwith the orange tool. Hence, four tools can deposit concurrentlyto complete the layer. Fig. 16 compares the build times of thehuman ear model by different toolpath planning approaches. Forconsistency, the deposition speeds of tools in all the approachesare VP = 20 mm s−1, VO = 15 mm s−1, VB = 5 mm s−1,and VG = 5 mm s−1. It can be seen that the proposed dynamicpriority-based approach improves the efficiency by 32%, 19%, and18% respectively, in comparison with the sequential approach, theentire envelope-based approach [20], and the separate envelope-based approach [26]. The entire envelope-based and the separate

S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107 1103

Fig. 10. Digital fabrication of the selected layer at adjusted deposition speeds.

Fig. 11. Anatomical model of a human ear.

Fig. 12. A selected layer of the human ear model. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web versionof this article.)

18016014012010080604020

Dis

plac

emen

t alo

ng X

-axi

s (m

m)

Time (minutes)0.5 1 1.5 2 2.5 3.53

Fig. 13. X–t graph of the selected layer of the human earmodel. (For interpretationof the references to colour in this figure legend, the reader is referred to the webversion of this article.)

envelope-based approaches are characterised by the constructionof bounding envelopes around slice contours by offsetting outwarda distance of the tool radius. Overlap test is executed for these en-velopes, and tools are not allowed to move concurrently when theassociated contour envelopes overlapped. For example, the orangetool in Fig. 12 cannot move until the pink tool completes the pinkpart.

The proposed dynamic priority-based approach eliminates thisconstraint. It constructs envelopes around the tools directly, ratherthan around the slice contours. Relative positions of tools aremonitored at a predefined rate. It enhances concurrency of toolmotions by assigning tool motion priorities to avoid collision. Thishighlights the effectiveness of the proposed approach in improvingthe fabrication efficiency of biomedical objects.

4.2. A toy tank

A tank model with dimensions of 225 mm × 78mm × 96mm,as shown in Fig. 17, is processed below to demonstrate possibleapplications of the proposed work in development of complex toyproducts. The model is sliced into 480 layers. Fig. 18 shows a layerof the tank to be made of four materials, represented in black,green, red, and orange. The deposition speeds of the four tools,of the same radius R = 10 mm, are set to be VB = 20 mm s−1,

1104 S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107

Fig. 14. Digital fabrication of the selected layer of the human ear model.

180

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-axi

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m)

80

60

40

20

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Fig. 15. X–t graph of the ear model layer with increased deposition speed of theorange tool. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

1800

1600

1400

1200

1000

800

800

400

200

2000

0

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ld T

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utes

)

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1225.59Sequential

Entire envelope - basedconcurrent

Dynamic priority - basedconcurrent

Separate envelope - basedconcurrent

Fig. 16. Comparison of build times of the human ear model by different toolpathplanning approaches.

S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107 1105

Fig. 17. A toy tank model.

Fig. 18. A selected layer of the tank model. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

150

100

50

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m)

0.2 0.4 0.6 0.8Time (minutes)

1 1.2 1.4

Fig. 19. X–t graph of the selected layer of tank model. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web versionof this article.)

VG = 15 mm s−1, VO = 15 mm s−1, and VR = 10 mm s−1, for theblack, green, orange, and red tools, respectively.

At the beginning, since the collision detection algorithm findsthat the orange tool will collide with the black tool, the orange toolwith lower traverse speed is commanded to start deposition afterthe potential collision is eliminated. So, at first, the black, red, andgreen tools move concurrently to deposit their specific materials.Some time later at t1, a potential collision is detected between theblack tool and the green tool, as shown in solid circles in Fig. 18and time t1 in Fig. 19. The motion priorities of the black tool andthe green tool are assigned according to their traverse speeds. Theblack tool, which is at a higher traverse speed, is assigned with a

higher priority and thus continues material deposition along itsoriginal path together with the orange tool, while the green toolwith a lower priority pauses to givewayuntil the potential collisionis eliminated. Some time after t1, the green tool, the black tool,and the orange tool can again deposit materials concurrently tocomplete this layer. The digital fabrication process of the selectedlayer of the tank model is shown in Fig. 20.

Fig. 21 compares the build times of the tank model by differenttoolpath planning approaches. It can be seen that the proposeddynamic priority-based approach improves the efficiency by 62%,51%, and 43% respectively, in comparison with the previousapproaches. This highlights that the effectiveness of the proposedapproach to improve the fabrication efficiency of relatively com-plex objects and to shorten the product development cycleaccordingly.

5. Conclusion and future work

This paper presents an approach to concurrent toolpath plan-ning to improve the fabrication efficiency of MMLM. The approachincorporates decoupled motion planning technique for multiplemoving objects with a collision detection algorithm and a dynamicpriority assignment scheme. It is characterised by the constructionof envelopes directly around individual tools, which are treated asmultiple moving objects, while the dynamic priority assignmentscheme coordinates the tool motions to avoid collisions. The pro-posed approach has been integrated with a multi-material vir-tual prototyping system, and digital fabrication of prototypes forbiomedical applications and product development shows that itcan substantially shorten the fabrication time of relatively complexmulti-material objects. The approach can be adapted for processcontrol of MMLM when appropriate hardware becomes available.

Nevertheless, some further developments are deemed benefi-cial. Firstly, as the proposed approach now adopts only up-and-down zigzags for internal contour filling, it would be useful toinclude the spiral contour filling mode, which is also a commoncontour filling strategy in LM. This may require modifying thealgorithms for tool collision detection and motion coordinationaccordingly.

Secondly, tool collision detection in the proposed approach isa real-time process being executed at a predefined rate. It seemsthat pausing a tool to avoid collision may possibly impair thesmoothness of the fabrication process. Although attempt has beenmade to reduce such effect by holding the tool only at the far end ofthe current hatch line after it is completed, it may be worthwhileto further improve the fabrication process. In this connection, itwould perhaps be beneficial to take advantage of the X–t graph(tool displacements versus time), which shows the locations andtimes of possible tool collisions during the complete fabricationprocess of a layer, to eliminate tool pauses. X–t graphs for alllayers would first be generated off-line, from which the locationsand times of possible tool collisions could be pre-loaded into thecomputer for prior coordination of tool motions. For example, thestart time of a tool could be suitably adjusted to avoid potentialcollisions, instead of halting the tools during fabrication. Indeed,this off-line planningwould reduce the computation requirementsduring digital or physical fabrication, particularly for large andcomplex objects.

Thirdly, the impact of the proposed toolpath planning approachon fabrication quality needs further investigation. Shrinkage andwarpage of prototypes may be affected by the adopted toolpathplanning strategy. It would be desirable to study the relationshipbetween the toolpath planning strategy and the prototype quality.

1106 S.H. Choi, W.K. Zhu / Computer-Aided Design 42 (2010) 1095–1107

Fig. 20. Digital fabrication of the selected layer of the tank model.

953.36

743.62

646.95

366.17

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Dynamic priority - basedconcurrent

Separate envelope - basedconcurrent

1000

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utes

)

1200

0

Fig. 21. Comparison of build times of the tankmodel by different toolpath planningapproaches.

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S.H. Choi is associate professor in the IMSE Departmentat the University of Hong Kong. He obtained both hisB.Sc. and Ph.D. degrees at the University of Birmingham.He worked in computer industry as CADCAM consultantbefore joining the University of Hong Kong. His current re-search interests include CADCAM, advanced manufactur-ing systems and virtual prototyping technology.

W.K. Zhu gained his M.Phil degree from the IMSE Depart-ment at the University of Hong Kong. He continued hisPh.D. research study in the Department, and his researchinterest is in virtual prototyping technology and motionplanning.