GAO Zhan , LECUYER Anatole, and ZHANG Shuyou

1 State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China

2 School of Computer Science and Technology, Nantong University, Nantong 226019, China

3 BUNRAKU Group, INRIA, Campus University de Beaulieu, Rennes 35042, France

1 Introduction

Nano-electro-mechanical systems(NEMS) typically integrate nano-electronics with mechanical actuators,pumps, or motors to form physical, biological, and chemical sensors. The nanometer range of device dimension leads to low mass, high mechanical resonance frequencies, potentially large quantum mechanical effects such as zero point motion, and a high surface to volume ratio, which are potentially useful for surface-based sensing mechanisms[1]. NEMS opens a new realm, where mechanical, fluidic and biological phenomena at the level of molecule or cluster of molecules are being explored[2].NEMS devices have already demonstrated superior features such as having resonant frequency up to 10 GHz and detecting mass as small as zeptogram (10?21g)[3].

Nano structures are the backbone of any NEMS.Realization of such nanostructures depends on the development of nano-assembly technologies, which will lead to potential breakthroughs in manufacturing new revolutionary industrial products. Nano-assembly techniques can be categorized into “bottom-up” and“top-down” methods[4]. One of the most promising“bottom-up” techniques is nanoscale self-assembly, which is good at making regular, symmetric patterns of nano structures. However, this technique is not capable to build asymmetric nano structures. On the other hand, “top-down”methods, such as lithography, are matured in the fabrication of semiconductor. However, “top-down” methods may fail to build nanostructures due to limitations of the lithography,where the smallest feature that can be made must be larger than half the wavelength of the light used in the lithography[5]. Nano-manipulation, or positional control at nanoscale, is a key enabling technology for nano assembly by filling the gap between “top-down” and “bottom-up”strategies[4]. Nano-manipulations were enabled by the invention of atomic force microscope(AFM). AFM,introduced by Binnig, is a widely used imaging technique at nanoscale[6]. In AFM, a micro cantilever shaped probe with a sharp downward tip underneath is used to scan samples on substrate surface. The interaction forces(attractive and repulsive) between the tip and the substrate cause the free end of the probe to deflect. Through the measurement of the height field of the substrate, 3D topographic map of the sample and the substrate surface can be obtained. Besides its microscopic function, AFM is also capable to manipulate nano-scale objects. For example,AFM is utilized for positioning nano particles[7]or carbon nanotubes[8]on a substrate by contact pushing or pulling operations. Although AFM is widely used in direct nano manipulation, it does not mean that the manipulation using AFM is easy. Since the scanning and manipulation are done in sequences with the same AFM tip, operators are blind during manipulation because they cannot see the real-time environment changing. In this study, we researched how to use virtual reality technologies to simulate and facilitate using AFM to assemble NEMS.

At present, available building blocks of NEMS include nano particles, nano rods and nanotubes. Nanotubes distinguish themselves from the others by the well-defined geometry, superb mechanical and electronic properties. The flexibility of nanotubes also makes it more convenient to build desired shapes, as compared to other nano objects.However, also because of the flexibility and deformation during the manipulation process, nanotubes may be more difficult to manipulate than the others. Reasons mainly include our limited knowledge of nano mechanics and the deformation of nanotubes as compared to the rigidity of nano particles or nano rods. Furthermore, direct manipulation of nanotubes is difficult using an AFM system since the scanning and manipulation are done in sequences using the same probe. Operators are blind during manipulation because they cannot see the real-time environment changing. A typical nanotube manipulation strategy is a scan-manipulate-scan cycle: firstly, the AFM scans the nanotube locally to obtain the shape of the nanotube; then, an AFM tip manipulation trajectory is given by the operator to move the nanotube; after the manipulation, a new local scan is needed to update the form and position of the nanotube. In general, the scan-manipulate-scan cycle makes nanotube manipulation an unintuitive, time-consuming and tedious task.

One of the potential solutions is virtual reality(VR)technologies, which enable scientists to extend their eyes and hands into the nano world and also enable new types of exploration[9]. In fact, VR technologies have been used to help manipulate other nano-objects, such as nano particles and nano rods. Taylor introduced virtual reality graphics and force feedback for touching the nano-world[10]. SITTI,et al[11], developed nano-contact models in order to simulate tip-object-surface interactions and to provide visual and haptic feedback to a user. VR technology can also help to facilitate manipulation by the means of novel interaction techniques and metaphors. For example, in Refs. [12?13],interaction metaphors, such as force field and virtual fixture in order to find optimal manipulation paths for nano particles, are discussed. In our previous research[14], a haptic VR simulator with visual and haptic feedback for training and prototyping of tele-manipulation of nanotubes has been proposed.

According to our best knowledge, there is few previous research work focused on using VR tools to facilitate the assembly of nanotubes-based NEMS. Also, most previous researches on virtual nano-assembly dedicate to manipulating nano particles or nano rods. This study is focused on the assembly of nanotube-based NEMS by the means of AFM manipulation. The objective of this study is to develop strategies and virtual tools to enhance the efficiency and accuracy of nanotube-based NEMS assembly. A virtual nano-assembly simulator is also built to test and justify the proposed methods of NEMS assembly.The contributions of this paper include: an automated nanotube-based NEMS assembly path generation, a four-step nanotube manipulation procedure and virtual fixtures for safe and accurate manipulation. This paper is organized as follows. Physical simulation of nanotube manipulation and the virtual nano-assembly simulator are described in section 2. The general framework of the NEMS assembly using nanotubes is presented in section 3.Section 4 introduces an automated path planning algorithm and the virtual tools to facilitate the nano-assembly. The experimental results are presented in section 5. The conclusions are reported in section 6.

2 Virtual Simulator of NEMS Assembly and Nanotube Manipulation

This section discusses the principles of nanoscale mechanics and the implementation of the virtual simulator of NEMS assembly. The virtual simulator is used for offline planning and testing of nano-assembly strategies.The VR tools and nano-assembly methods proposed in this paper are all tested and justified in this virtual simulator.

2.1 Nanoscale physics

Nano objects show different mechanics from macro sized objects. For example, adhesive surface forces dominate over inertial forces at nano-scale. In addition, there are non-contact forces such as Van der Waals, capillary, and electrostatic forces. There are three major categories of interaction forces in the physics of nano-manipulation:tip-nanotube, nanotube-substrate and tip-substrate interactions.

(1) Tip-nanotube interactions: non-contact force models are considered in addition to the contact force models.

(2) Nanotube-substrate interactions: during the manipulation, the nanotube is in continuous contact with substrate surface. Therefore, contact and friction forces must be considered here.

(3) Tip-substrate interactions: both contact and non-contact models are used to calculate the interaction forces.Tip-substrate interaction in nano scale is particularly different from one’s experience in macro scale. When the tip is approaching the substrate surface, it will suddenly be pulled down to the surface because of the long range adhesive Van der Waals force. During the manipulation, the tip is always attached to the substrate surface. When the tip is to be detached from the substrate surface, upward force which is greater than adhesive force has to be applied to the tip until it bounces back away from the substrate.According to JKR (Johnson, Kendal and Roberts) theory,the pull-off force is 75% of the adhesive force[15].

2.2 Tip-substrate-nanotube interaction model

Based on the tip-substrate-nanotube interaction model in Ref. [16], a simplified force model is introduced. Because the lateral direction stiffness of the tip is much higher than that of normal direction, we believe that the tilting of the probe tip is rather minute. Therefore, the tip is assumed to be vertical. Also, the tip is modeled with a cylinder since the taper angle of the tip is also very small. The force variables are labeled in a way similar to those in Ref. [16],such that the superscript can be: a—adhesive, f—frictional,or r—repulsive. The subscripts are a combination of two letters (t—tip, n—nanotube, s—substrate) that indicate the force between the two objects. For example,means the adhesive force between tip and substrate.

Fig. 1(a) shows the forces applied on the nanotube.According to the equilibrium condition of the nanotube both in horizontal and vertical direction, we have

The forces applied to the tip as shown in Fig. 1(b) should be balanced by the normal force Fz, and the lateral force Flfrom the cantilever. The equilibrium condition of the tip in the normal and lateral direction is as follows:

According to Newton's third law,andThe equation for the friction between the nanotube and substrate is

where μnsis the sliding frictional coefficient between object and substrate surface and υ is the shear coefficient. The adhesive force between the tip and the substratecan be measured by using AFM in force calibration mode. The adhesive forces, such asandcan be assumed to be proportional to the contact area[16]. Therefore, the adhesive forceandcan be estimated by relating tip-substrate contact area and the nanotube-substrate contact area as follows:

Fig. 1. Tip-substrate-nanotube interaction model

More details about the interaction model can be found in Ref. [14].

2.3 Nanotube deformation simulation

There are two major categories of methods for simulation of nanotubes: one is atomic mechanics approaches and the other is the continuum mechanics approaches. The atomic mechanics method is precise but it would be too slow for real-time simulation. The simulation of nanotubes deformation is based on the method in Ref.[17], which treats nanotubes as solid beams at a global level. In this research, deformation of nanotubes is simulated based on beam theory in order to achieve real-time updating rate. It is assumed that the bending stiffness, EI, of a nanotube is given by the classic formula:

where E is Young’s module, R is the radius of nanotube,and h is the wall thickness of nanotube.

Based on beam theory, nanotube is modeled with a mass-spring system. Particles are connected by linear springs and torsion springs.

The length and deflection angle of the ith element are denoted as liand γi, respectively. The force applied with the tip is F and the friction forces applied on each element is Fi.The moment caused is M. For each element, we have

where the torsion spring stiffness is

2.4 Haptic rendering of nanotubes

With our current AFM platform, the manipulation of nanoobjects is mainly 2D, i.e., nanotubes are always adhered on a planar substrate due to the Van der Waals force. In addition, the manipulation movements are also constrained on the substrate surface. The substrate is represented with a horizontal plane and nanotubes are represented with 2D line segment chains formed by the skeleton of mass-spring deformable model which locates on the substrate plane. Before the tip touches the substrate,forces applied to the tip are non-contact attraction forces from the substrate. To manipulate a nanotube, the probe tip has to be put on the substrate firstly. The tip is then attracted by Van der Waals force and remains adhered to the substrate. From this moment, the collision detection module starts to detect the collision between the tip and the nanotubes. The collision detection algorithm is similar to the 3D point to mesh “god-object” haptic rendering approach[18]but only in 2D space. The task is to find the proxy point on the line segments according to the current position of the probe tip. When the tip is approaching to a line segment, the sidedness of the tip respecting to the line segment is computed. When the sidedness of the tip is found changing to the opposite side, meaning the tip is crossing the line segment, a collision is detected and the proxy point is found as the closest point on the current line segment. Fig. 2 shows the nanotube model of segments for deformation simulation and collision detection.

Fig. 2. Nanotube model for deformation and collision detection

2.5 Implementation of virtual simulator

The virtual simulator has been developed in C/C++ by using HOOPS for graphics rendering. The virtual simulator utilizes a Virtuose 6DOF device from Haption for controlling the tip position of an AFM and for reflecting interaction forces back to a user. Besides the haptic feedback, a stereoscopic immersive visual display, similar to that in Ref. [19], is provided to obtain the better depth cue and eye-hand coordination. The system is illustrated in Fig. 3. The stereoscopic display image is reflected by a horizontal mirror to the operator. The visual coordinate system is coincident with the haptic device coordinate system. Liquid crystal shutter glasses are used to provide a stereoscopic display with a refresh rate at 150 Hz. After proper calibration, the virtual AFM tip and operator’s hand remain co-registered from the viewpoint of the operator.The visual display is designed in a way similar to the microscopic view field. We expect that this metaphoric similarity is helpful for the operator. Fig. 4 shows the virtual scene of nanotube manipulation.

Fig. 3. System at work

Fig. 4. Virtual scene of nanotube manipulation

3 General Framework of NEMS assembly

The NEMS assembly process can be divided into two stages: assembly planning and nanotube manipulation. The tasks of assembly planning include: designating nanotubes to specific targets and determining the assembly sequence.Nanotube manipulation is to move nanotubes from their initial positions to destinations and to shape the nanotubes according to the definitions of the CAD models of NEMS.The general framework of NEMS assembly is illustrated in Fig. 5.

Fig. 5. General framework of NEMS assembly

NEMS assembly process starts by identifying nanotubes,which are randomly distributed on a substrate, from an AFM image. The available nanotubes are then examined against the CAD model of NEMS, in order to find the most appropriate nanotubes for specific components of NEMS design. The criteria include nanotube’s size, electronic and mechanical properties, etc. The most matched nanotubes are then designated to specific destinations.

The sequence of assembly is mainly determined by the structure of NEMS. Unlike macro world assembly design problems, planning assembly sequence for NEMS is trivial.Three facts make the assembly sequence problem easy to handle. Firstly, the NEMS assembly is 2D, which greatly reduces the complexity of the problem. Secondly, the rule governing the sequence planning is straightforward?inner destinations have priority while outer destinations should be left for the later stages of assembly process. Another reason is that the number of nanotube components of NEMS is often limited, as compared to the macro-world assembly problem. All these factors bring down the complexity and make it possible to solve the assembly sequence problem totally manually. In this study, we let the operator decide the assembly sequence. Once the plan for assembly is obtained, nanotubes can be manipulated to their destinations, one by one.

The aim of nanotube manipulation is to maneuver nanotubes from their initial position to destinations, with shape requirements fulfilled at the end of manipulation.

We subdivide the process of nanotube manipulation into four stages.

(1) Path planning. The purpose is to find a collision free path leading from the initial position roughly to its destination.

(2) Preparation. The purpose is to prepare the nanotube for long distance travel in the next step.

(3) Long range maneuver, in which the AFM tip moves along the predefined path to bring the nanotube to its destination.

(4) Finalization, in which the nanotube is finely adjusted according to the target shape. Since this step determines the final shape and position of the nanotube, accuracy is the most important issue for this step.

In some special cases, nanotubes could be close to their destinations. In this situation, there is no need for the preparation and long distance maneuver. Instead,finalization should be performed directly.

Automatic manipulation is very difficult to implement for the preparation and finalization steps. Therefore,interactive manipulation techniques should be used in these two steps. On the other hand, the path planning step and long range maneuver step should be automated in order to reduce the fatigue of operators and hence decrease the chance of operational errors.

4 Strategies and Virtual Tools for Nanotube Manipulation

Nanotubes have both translation and deformation during the manipulation process, whilst a nano particle or a nano rod has only rigid motions. Accordingly, nanotube manipulation strategies are often more complicated than those of other nano objects. We put forward several methods and virtual tools to facilitate nanotube manipulation.

4.1 Automated path planning

The purpose of path-planning is to generate a path from initial position to destination while respecting maximization of the distance from obstacles in order to avoid collision or attraction forces due to nano physics[13].Most previous researches on path planning for nano-manipulation focus on the manipulation of nano particles. The manipulation paths are obtained either manually using haptic devices[11,20]or in an interactive way based on the AFM images[21]. CAD-guided path generation and automated nano assembly of both nano particles and nano rods using AFM are developed in Ref.[5]. In our previous research, a two-step path planning method for nanotube manipulation was developed[22]. We have further optimized the method in this study. Fig. 6 shows the framework of path planning.

The initial position of nanotube can be obtained from AFM images. The destination of nanotube is determined by the CAD model of NEMS. Obstacles include other nanotubes or even nano particles on substrate. Fig. 7 illustrates an example of path generation. Fig. 7(a) shows the initial situation of a nanotube manipulation task. The ultimate task is to push the nanotube in the lower-left corner to the target on the top.

Fig. 6. Framework of path planning

Fig. 7. An example of path planning

Safe distances must be kept between the moving nanotube and obstacles. Due to the van der Waals force between nano objects, nano particles may be attracted to the nanotube if the distance between them is too small.Therefore, a safe distance D1has to be determined first to avoid the attraction between the nanotube and particles. D1can be found by the method introduced in Ref. [5]. On the other hand, the attraction forces between nanotubes,overwhelmed by the strong friction and attraction forces between nanotubes and the substrate, normally are not enough to attract two nanotubes together. However,keeping a safe distance between nanotubes is necessary because nanotubes could have higher chance of collision during the manipulation process. This is because nanotubes occupy much bigger space than nano particles. In addition,deformations of nanotubes along the manipulation trajectories also increase the chance of collision. The safe distance between nanotubes is denoted as D2, which is empirically determined by one sixth of the length of the moving nanotube. The formal safety distance D is the bigger one between the D1and D2.

Boundary circles with radius D can be generated around obstacles. For a nano particle, a single boundary circle is created to surround it. For a nanotube obstacle, a series of boundary circles are created uniformly along the tube. The moving nanotube should not cross these boundary circles.Fig. 7(b) shows the boundary circles around the obstacles are generated.

In the next step, the edges that have equally maximum distances to pairs of neighboring boundary circles are created. Some of these edges can be linked together to form an optimal manipulation path. These edges are generated by creating an Apollonius Voronoi diagram for all boundary circles. The Apollonius Voronoi diagram is also known as the additively weighted Voronoi diagram, which can be thought of as the generalized Voronoi diagram of a set of disks under the Euclidean metric. Fig. 7(c) shows the obtained Apollonius Voronoi graph.

Not all edges, however, are eligible to become a part of manipulation path. The edges between neighboring boundary circles of individual nanotubes are considered as redundant and are eliminated. The remained edges are the potential manipulation paths with maximized distance between the obstacles. Fig. 7(d) shows the Voronoi graph after the redundant edges are removed. Then, by using A*search algorithm, the shortest path from the starting position to the destination is found by searching the remained edges of the simplified Apollonius Voronoi diagram[23]. A*search algorithm requires a starting point and a destination, which are both specified manually by operators. The bold dashed poly-line in Fig. 7(e) shows the optimal path generated with the A*searching algorithm.

Once a path is obtained, the path is examined for any sharp corner, which could result in the loss of contact between the AFM tip and the nanotube during manipulation.The sharp corners on the path are chamfered to avoid such potential errors. The distances between the path and obstacles are further checked. Path segments with distance less than 1.2D are identified as bottleneck segments and signaled to human operators. Then, the operator can decide whether the current path is acceptable or not. If the path is thought not safe enough, the edge of the bottleneck segment on the Voronoi diagram should be broken by the operator. Another detour path, safer but not the shortest, can be found with the same method to replace the previous one.

4.2 Preparation operation

If an AFM tip loses the nanotube during a long range manipulation, the substrate has to be rescanned to locate the lost nanotube. Because the scanning takes much longer time than the manipulation itself, losing nanotubes during manipulation should be avoided. A typical solution is to make the nanotube into U shape before the long range manipulation begins. During the course of long range movement, the AFM tip pushes the nanotube and remains inside the corner of the U shape at the same time. By this means, the nanotube is less likely to get lost of the contact of the AFM tip. The task of preparation operation is to make a nanotube form a U shape with the AFM tip inside its corner, i.e., the nanotube is prepared for the next step of long range maneuver.

Preparation operation has the following two steps:

(1) If the nanotube is curved, it must be straightened with the AFM tip.

(2) The AFM tip approaches the middle of a nanotube and pushes the nanotube into a symmetric U shape.

Fig. 8 shows the preparation operation. In Fig. 8(a), the AFM tip moves laterally to straighten the nanotube; in Fig.8(b), the AFM tip approaches to the middle of the nanotube;Fig. 8(c) shows that the nanotube deforms into a U shape with the AFM tip inside its corner, meaning the nanotube is ready for the next step long range maneuver.

Fig. 8. Preparation operation

4.3 Long range maneuver

As the preparation operation is conducted manually by the operator, the final position of the AFM tip is normally not exactly on the path. Therefore, the tip first has to be brought to the path in order to begin the long range maneuver.

The major concern of the design of the movement of AFM path is preventing the loss of nanotube during the maneuver. Two measures are taken in order to avoid the error.

(1) Full stop before turning. Therefore, the tip stops at the end of each segment of the path.

(2) The pushing force has to be below a threshold.During the pushing manipulation, the AFM tip often climbs up a little bit around the surface of nanotube. Strong pushing force could result in too much climb-up of the tip and eventually the loss of nanotube. Furthermore, too strong pushing force could even break the AFM tip. Fig. 9 shows the force control.

Fig. 9. Control scheme of AFM pushing force

Fig. 10 illustrates how a nanotube is pushed to its destination region.

Fig. 10. Long range maneuver

4.4 Haptic guidance fixture for finalization

The last step of nanotube manipulation is finalization, in which a nanotube must be moved and adjusted to be right in the position and shape that are defined by the NEMS CAD model. Normally, nanotube components of a NEMS have simplistic shapes, such a straight line or a polyline.Curves are rarely found as major part of a NEMS component. Although the component shapes appear simple,manipulating a nanotube accurately into its target shape is far from a trivial task. Firstly, this is because the real-time visual display of nanotube is unavailable. The complexity together with the limitations of autonomous robots (e.g.,limitations in artificial intelligence, sensor-data interpretation, and environment modeling) make it difficult to automate the finalization task of nanotube assembly. In fact, finalization task requires better-than-human levels of manipulation accuracy, but also need a human directly in the control loop to provide the intelligence. Therefore, we suggest that this task should be interactively performed by the human operator. Meanwhile, we propose a haptic guidance fixture to help the human operator with the finalization task.

Haptic guidance fixtures are software-generated force signals applied to human operators in order to improve the safety, accuracy, and speed of manipulation tasks[24]. They help humans perform manipulation tasks by guiding movement along desired paths. Our haptic guidance fixture assists the operator in moving the AFM tip along the shape of targets.

The benefits of the haptic guidance fixture can be illustrated with the example of a ruler, which is a common physical guidance fixture. With the help of a ruler, a human can draw a straight line faster and straighter than draw a line freehand. Similarly, haptic guidance fixture can apply forces to a human operator through a haptic device to help him or her draw a straight line.

The haptic guidance fixture for the finalization task can be considered as virtual rulers, whose shapes are defined by the shape of targets. Similar to drawing a line with a real life ruler, path-following becomes a trivial task by gliding along the virtual guidance fixture. A gliding operation means the tip moves along the virtual guidance while the direction of the repulsive reaction force from the virtual guidance fixture is roughly perpendicular to the tip’s movement direction. The forces from the guidance fixture are determined by the haptic rendering algorithm, which is similar to the haptic rendering algorithm for nanotubes. The repulsive forces constrain the movement of the virtual AFM tip so that the tip could glide along the virtual guidance fixture but could not penetrate it. As nanotubes could be very close to each other at finalization stages, haptic guidance fixtures are more than just virtual rulers. They also serve as virtual walls, preventing AFM tip crash into neighboring nanotubes.

Fig. 11 shows how the haptic guidance fixture helps human operator conduct a finalization task with better accuracy and efficiency. Firstly, a nanotube is moved close to the target to get ready for final adjustment, as shown in Fig. 11(a). The green line segments in Fig. 11(a) denote the target. In Fig. 11(b), the transparent wall, which bears the shape of the target, denotes the haptic guidance fixture. In Fig. 11(c), the nanotube is pushed to the target so that it is ready for the final gliding operations. Finally, the tip is repetitively moved to glide along the virtual guidance fixture. Arrows in Fig. 11(c) show the trend of movements of AFM tip. After a few rounds of gliding operations, the nanotube normally is made close enough to the target.Fig. 11(d) shows the form of the nanotube is finalized with the help of virtual guidance fixtures.

Fig. 11. Virtual guide for accurate finalization

4.5 Forbidden-region virtual fixture

During interactive manipulation tasks, such as preparation and finalization operations, the AFM tip could accidentally collide into other nanotubes, resulting in unintended movement and deformation of the nanotubes.These accidental collisions can greatly disturb the manipulation operations.

The solution is to use repulsive potential fields as forbidden-region virtual fixture. Repulsive forces are generated around nanotubes and other obstacles when the AFM tip enters into a specific threshold, so that the movements into restricted regions are limited. Therefore,the forbidden-region virtual fixture can prevent the AFM tip from accidentally colliding into already assembled NEMS structures and other prohibited regions of the workspace.

For dust obstacles, the geometrical representation of the threshold of the potential field is a spherical bulb with a dust as its center. While for a nanotube, the threshold of the potential field can be represented as a series of bulbs uniformly distributed along the nanotube. The size of these bulbs can be interactively adjusted by the human operator.

The formula of the potential field can be expressed as

Where d is the penetration distance, d0is a positive constant which represents the action distance of the potential field, λ is a position scaling factor.

The repulsive force is defined as the negative gradient of potential function:where?represents the gradient operator.

Fig. 12 shows the geometric representation of the virtual fixture for safety.

Fig. 12. Geometric representation of the virtual fixture for safety

5 Experiments and Results

The developed tools and methods have been implemented to manipulate nanotubes to assemble NEMS in our virtual simulator. An experiment is performed to virtually assemble a NEMS, as shown in Fig. 13(a), with nanotubes. In this example, the lengths of nanotubes are between 50 nm and 210 nm. The AFM image of a substrate with thirteen nanotubes randomly distributed on the substrate is shown in Fig. 13(b). The CAD model of a designed NEMS is also shown in Fig. 13(b). Fig. 13(c)shows the virtual scene of the nano environment and nanotubes, which are modeled based on the AFM image.The nanotubes are compared with the NEMS CAD model in order to identify the four most matched nanotubes, which are chosen to be assembled and form the NEMS nanostructure. In Fig. 13(c), four nanotubes are located and designated to their targets. The numbers in Fig. 13(c)represent the sequence of assembly. The Voronoi diagram is generated based on the CAD model and the nanotubes as shown in Fig. 13(d). Once the Voronoi diagram is generated,the nanotubes can be assembled, one after another, as shown in Figs. 13 (e) ?13(h).

Fig. 13. Example of NEMS assembly

For each nanotube, an optimized path is created firstly based on its position and the Voronoi diagram. Then, a preparation operation is performed to make the nanotube into a U shape. In the long range maneuver step, the virtual AFM tip is controlled to follow the desired path so that the nanotube is moved towards its destination. The nanotube is accurately adjusted to its targeted shape and position. Then,the substrate is scanned to verify the shape and position of the manipulated nanotube is within the tolerance of the NEMS design. With the updated nanotubes information, the Voronoi diagram can also be updated. The process continues until all nanotubes are manipulated to their destinations. In the end, as we can see in Fig. 13(h), the nanostructure conforms to the CAD design of NEMS after the assembly process is finished.

In this example, the total time of assembly takes around 5 min. On the other hand, the same virtual assembly task is performed totally manually, without the aid of path-planning and virtual guidance fixtures. We found that the assembly either failed because of accidental collisions between nanotubes, or it took much longer time and had bad accuracy.

6 Conclusions

The objective of this research is to put forward novel virtual tools and strategies to improve the efficiency,accuracy, ease and intuitiveness of the assembly process of nanotube-based NEMS. To test the proposed NEMS assembly techniques and virtual tools, a virtual nano-assembly simulator is built as a benchmark. We propose a general framework of NEMS assembly. In our framework, some tasks, such as path planning and long range maneuver, are automated; whist the preparation and finalization of nanotube manipulation, which particularly need the guidance of human intelligence, are performed interactively. Our semi-automatic NEMS assembly strategies provide an excellent balance between autonomy and direct human control. Besides the general framework,various tools and methods are invented to facilitate NEMS assembly and nanotube manipulation. These tools and methods are the major contributions of this paper.

The contributions of this study mainly include the followings:

(1) A Voronoi-diagram-based automatic path planning method;

(2) A four-step nanotube manipulation strategy;

(3) A haptic guidance fixture for the finalization of NEMS assembly;

(4) A forbidden-region virtual fixture for safe manipulation.

(5) A virtual nano-assembly simulator with visual and haptic feedback.

An experiment has been conducted to showcase and justify the proposed NEMS assembly strategies, tools and methods in our virtual simulator. The experimental results demonstrate that our methods enhanced the efficiency and accuracy. The above-mentioned virtual tools and methods are not solely the tools for the simulation in virtual environment. Instead, these tools are ready to be used in real-life nano assembly situation. In the future, these NEMS assembly tools will be implemented in our physical AFM manipulation platform.

[1] VENTRA D I, EVOY M S, HEFLIN J R. Introduction to nanoscale science and technology[M]. Boston: Kluwer Academic Publishers.2004.

[2] CUI Z, GU C Z. Nanofabrication challenges for NEMS[C]//2006 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems, Zhuhai, China, 2006: 607–610.

[3] SCHWAB K C, ROUKES M L. Putting mechanics into quantum mechanics[J]. Physics Today, 2005, 58(7): 36–42.

[4] FUKUDA T, ARAI F, DONG L X. Assembly of nanodevices with carbon nanotubes through nanorobotic manipulations[J].Proceedings of the IEEE, 2003, 91(11): 1 803–1 818.

[5] CHEN H P, XI N, LI G Y. CAD-guided automated nanoassembly using atomic force microscopy-based nonrobotics[J]. IEEE Transactions on Automation Science and Engineering, 2006, 3(3):208–217.

[6] BINNIG G, QUATE C, GERBER C. Atomic force microscope[J].Physical Review Letters, 1986, 56(3): 930–933.

[7] SCHAEFER D M. Fabrication of two-dimensional arrays of nanometric-size clusters with the atomic force microscopy[J].Applied Physics Letters, 1995, 66(8): 1 012–1 014.

[8] FALVO M R, TAYLOR R M. Nanometre-scale rolling and sliding of carbon nanotubes[J]. Nature, 1999, 397(1): 236–238.

[9] FERREIRA A, MAVROIDIS C. Virtual reality and haptics for nanorobotics[J]. IEEE Robotics and Automation Magazine, 2006,13(3): 78–92.

[10] TAYLOR R M. The nanomanipulator: A virtual-reality interface to a scanning tunneling microscope[R]. Univ. North Carolina: Chapel Hill, North Carolina, 1994.

[11] SITTI M, HASHIMOTO H. Teleoperated touch feedback from the surfaces at the nanoscale: modeling and experiments[J].IEEE/ASME Transactions on Mechatronics, 2003, 8(2): 287–298.

[12] AMMI M, FERREIRA A. Haptically generated paths of an AFM-based nanomanipulator using potential fields[C]//4th IEEE Conference on Nanotechnology, Munich, Germany, 2004: 355–357.

[13] AMMI M, FERREIRA A. Robotic assisted micromanipulation system using virtual fixtures and metaphors[C]//Robotics and Automation, 2007 IEEE International Conference, Rome, Italy,2007: 454–460.

[14] GAO Z, LECUYER A. A VR simulator for training and prototyping of telemanipulation of nanotubes[C]//Proceedings of the 2008 ACM Symposium of Virtual Reality Software and Technology, Bordeaux,France, 2008: 101–104.

[15] ISRAELACHVILI J. Intermolecular and surface forces[M].London: Academic Press, 1991.

[16] LI G, XI N, YU M, et al. Modeling of 3-D interactive forces in nanomanipulation[C]//Intl. Conference on Intelligent Robots and Systems, Las Vegas, Nevada, US, 2003: 2 127–2 132.

[17] TSERPES K I, PAPANIKOS P. Finite element modeling of single-walled carbon nanotubes[J]. Composites Part B: Engineering,2005, 36(5): 468–477.

[18] ZILLES C, SALISBURY J. A constraint based god-object method for haptic display[C]//Intl. Conference on Intelligent Robots and Systems, Human Robot Interaction, and Cooperative Robots,Washington, DC, US, 1995: 146–151.

[19] ARSENAULT R, WARE C. The importance of stereo and eye-coupled perspective for eye-hand coordination in fish tank VR[J]. Presence-Teleoperators and Virtual Environments, 2004,13(5): 549–559.

[20] GUTHOLD M, FALVO M R., MATTHEWS W G., et al. Controlled manipulation of molecular samples with the nanoManipulator[J].IEEE/ASME Transactions on Mechatronics, 2000, 5(2): 189–198.

[21] HANSEN L T, KUHLE A, SORENSEN A H, et al. A technique for positioning nanoparticles using an atomic force microscope[J].Nanotechnology, 1998, 9(4): 337–342.

[22] GAO Z, LECUYER A. Path-planning and manipulation of nanotubes using visual and haptic guidance[C]//Virtual Environments, Human-Computer Interfaces and Measurements Systems, 2009. VECIMS '09. IEEE International Conference, Hong Kong, China, 2009: 1–5.

[23] PATEL A J. Amit's A*pages[EB/OL]. (2009-02-01)[2010-02-16].http: //theory.stanford.edu/～amitp/GameProgramming/.

[24] ABBOTT J J, MARAYONG P, OKAMURA A M. Haptic virtual fixtures for robot-assisted manipulation[J]. Robotics Research, 2007,28: 49–64.