Autonomous Multi-Robot Sensor-Based Cooperation for Nanomedicine
Adriano Cavalcanti Department of Computer Science, Darmstadt University of Technology, Germany, Email:
[email protected]
Robert A. Freitas Jr. Zyvex Corporation, USA, Email:
[email protected] Abstract This work presents a new approach within advanced graphics simulations for the problem of nano-assembly automation and its application to medicine using collective robotics. The problem under study concentrates its main focus on autonomous control for nanorobot teams coordination as a suitable way to perform a large range of tasks and assembly manipulation in a complex environment. Keywords: nanomedicine, multi-robot coordination, motion planning, assembly automation, genetic algorithms.
1. Introduction The present paper describes the design and simulation of autonomous multi-robot teams at atomic scales with distinct tasks to assemble biomolecules into larger biomolecules for nanomedicine [05]. Recent developments in the field of biomolecular computing have demonstrated positively the feasibility of processing logic tasks by bio-computers [01], which is a promising first step to enable future nanoprocessors with increasing complexity, power of information storage and data processing capacity. Other advances in the sense of building biosensors [12] and nano-kinetic devices have advanced [11] recently too. Many classical objections to the feasibility of nanotechnology, such as quantum mechanics, thermal motions and friction, have already been considered and resolved [04]. Building patterns and manipulating atoms with the use of Scanning Probe Microscopes (SPM) as in Atomic Force Microscopy and Scanning Tunneling Microscopy is a promising approach for the construction of nanoelectromechanical systems (NEMS) with 3-
D precision at up to 0.01nm resolution. However these manual manipulations require much time and such repetitive tasks give imprecise results when performed on a large number of molecules. Approaches for nano-planning systems have been presented [09] as a first step towards automating 2D assembly tasks in nanorobotics.
2. Proposed design For our experiments we chose a nanomanipulation in a liquid environment, which is most relevant within the presented application in nanomedicine. It was demonstrated that momentby-moment computer control of arm trajectories is the appropriate paradigm for macroscale robots, but not for nanoscale robots [05]. For nanoscale robots, the appropriate manipulator control is often trajectory trial and error, also known as sensor based motion control [07]. 2.1 Virtual Environment A suitable starting point for our hypotheses, formulations and experiments was to consider
International Journal of Nonlinear Science and Numerical Simulation.August 2002. Nanotechnology Special Edition.
Figure 1. Nanorobot avoiding obstacle.
Figure 2. Molecular sorting rotor.
the robot design derived from macro and micro robotic using biological models and comprised of some basic nanoscale components such as molecular sorting rotors and a telescoping manipulator [04]. The robot design adopted concepts provided from underwater robotics [13] – keeping in mind, however, the kinetics assumptions that the nanorobot lives in a world of viscosity, where friction, adhesion, and viscous forces are paramount and gravitational forces are of little or no importance [05]. The design should be robust enough to operate in a complex environment with movement in sixdegrees-of-freedom. The study of non-penetrating rigid bodies for dynamic constrained simulation has an enormous impact for physically based simulation in computer graphics [02]. The authors decided to use physically based simulation to consider kinetics and frictional aspects required specially for rigid body motion with hydrodynamics at low Reynolds number [05] and molecular assembly manipulation. The nanorobot navigation uses sensors which report collisions and identify when an encountered object is an obstacle to be avoided or a molecule to be caught (figure 1). While some molecules are being captured (figure 2), other molecules will be assembled internally by the robot arm (telescoping manipulators), which will be carried inside the robot. The robot will push out the assembled molecule to the delivery point.
The delivery positions will change their colours, indicating the opening or closing of the team A and B’s delivery orifice, which will indicate for the agents if they could perform their delivery in the correct order (figure 3). 2.2 Evolutionary Multi-robot Teams The approach for the nanomedicine problem here could be described as the applicability of two multi-robot teams in timely sequenced work for the capture, assembly, transport and delivery of biomolecular pieces to a predefined set of organ inlets. Developments in multi-robot cooperative work have demonstrated that we should consider emulating the methods of the social insects [08], because nature is showing us how to build decentralized and distributed systems using agents with similar structures, preprogrammed actions and goals. Kube [08] has pointed out that a careful decomposition of the main problem task into subtasks with action based on local sensor-based perception could generate multi-robot coherent behaviours without explicit communication. We have decomposed the total set of organ inlets, assigning for each pair of nanorobots a specified number of organ inlets to be attended by the nanorobots at each time-step of the simulation. Each pair is comprised of nanorobots from team A and B. The organ inlets selected to be fed at time t have to be fed first by the agent A and so forth. The multirobot team behaviour interactivity rule is described as follows:
Step 1:
rΩ walk randomly to capture g and h;
Step 2:
if ∑ g = ∑ h ⇒ assemble f(rΩ )=g+h;
Step 3:
if ∑ f(rΩ ) < min, repeat step 1;
Step 4:
rΩ achieve next delivery goal;
Step 5:
if delivery_permition = true delivery: f(rΩ ) = f(rΩ ) -1;
Step 6:
if f(rΩ )>0 repeat step 4;
Step 7:
repeat step 1;
⇒
Where g, h, and Ω∈{A,B}; Here g and h represents the kind of molecule to be assembled by each multi-robot team; Ω denotes if the robot r belongs to team A or B; min is the minimum defined to be captured by each robot at time step t. The importance of cooperative team work has led us to choose a decision control model with adaptive evolutionary characteristics such as mutation, crossover, chromosome selection, adaptability [03]. Each solution here is represented as a chromosome describing the agent decision on how, when and what organ inlets to attend. Next is described the multiobjective model for the dynamic decision problem. Max
s.t.
fr =
n m
∑∑ wit − y t
(1)
t =1 i =1
yt = Qt − d
Qt =
∑ xit ≤ L
(2) (3)
xit = µ it ximax
(4)
µit ≤ ∆max i t + 1 wi = wit − γz t + x it i
(5) (6)
wimin ≤ wit ≤ wimax
(7)
µ it ∈ {{0,1} ∨ { 0.00,...,1.00}}
(8)
where r, t, i: respectively robot, time, organ inlet. max, min: maximum and minimum capacity. n: size of time in the simulated scenery.
Figure 3. Delivery to the organ inlet represented by the white cylinder. m: L: yt : xit : Qt : wit : zit : d: γ: µit : ∆:
total of organ inlets to be feed. robot load capacity. distance to the desired assembled mean. amount injected in the organ inlet i. total assembled molecule by r. chemical state of the organ inlet i. consumption by organ inlet i. desired assembled substances rate. look ahead nutritional levels. boolean variable. max to be injected in organ inlet i;
Equation 1 represents our fitness or objective function, where the robots maximize the protein levels for the selected organ inlets. Here the variable y induces the robot to catch a number of molecules as closely as possible to the desired delivery mean. The robot motion control and trajectory planning used a feedforward or acyclic neural networks [06]. The proposed nanorobot model includes no kind of nanorobot self-replicating behaviour, thus it uses the evolutionary approach strictly for the combinatorial analyses, allowing the nanorobots to react cooperatively in a complex environment with a well defined pre-programmed set of actions for the biomolecular assembly task. Furthermore the present architecture used real time and parallel processing techniques to provide a realistic multi-robot collective behaviour.
[03] Cavalcanti, A., A Virtual Environment for Evolutionary Autonomous Optimization of Real Time Stochastic Control Design, Proc. of IEEE Int'l Conf. on Information, Decision and Control, Adelaide, Australia, 2002, pp. 83-88.
Simulation: 24 time-steps
250
target:63
frequency
200 150
[04] Drexler, K. E., Nanosystems: molecular machinery, manufacturing, and computation, Wiley & Sons, 1992.
100 50 0 1
32
63
94
Percentage nutritional state all organs
Figure 4. Multi-robot cooperative reaction.
3. Simulation and Conclusions The present work considers the importance of nanosystems design in nanomedicine using multirobot teams exhibiting cooperative behaviour as a suitable design approach for massively parallel assembly automation in nanotechnology. A coherent team behaviour with a fast adaptive reaction was suitably achieved with the organs’ nutritional level parameter starting at 65%. It could be demonstrated (figure 4) that the implemented model generates satisfactory performances for maintaining the organs’ nutritional levels. The most ideal state was considered to be a level ranging between 50 and 70%. We considered in the simulation a level of 90% as near to an overdose and 10% as near to deficiency state. The coherent behaviour displayed for the transport task can also be attributed to the common goal shared by the individual medical nanorobots along with an identical set of interaction rules.
4. References [01] Adleman, L. M., On Constructing A Molecular Computer, DNA Based Computers, 1995, http://olymp.wuwien.ac.at/usr/ai/frisch/local.html . [02] Baraff, D., Fast contact force computation for nonpenetrating rigid bodies, Proc. of ACM SIGGRAPH 94 Conf, 1994, pp. 23-34.
[05] Freitas Jr., R. A., Nanomedicine, Landes Bioscience, 1999, www.landesbioscience.com/nanomedicine . [06] Grzeszczuk, R., Terzopoulos, D., Hinton, G., NeuroAnimator: Fast neural network emulation and control o physics-based models. In M. Cohen, ed., Proc. of ACM SIGGRAPH 98 Conf., 1998, pp. 142-148. [07] Khatib, M., Bouilly, B., Simeon, T., Chatila, R., Indoor Navigation with Uncertainty using Sensor Based Motions, Proc. IEEE Int'l Conf. on Robotics and Automation, 1997, pp. 33793384. [08] Kube, C. R., Collective Robotics: from Local Perception to Global Action, PhD thesis, Dept. of Computer Science, University of Alberta, Edmonton, 1997. [09] Makaliwe, J. H., Requicha, A. A. G., Automatic planning of nanoparticle assembly tasks, Proc. IEEE Int'l Symp. on Assembly and Task Planning, Fukuoka, Japan, 2001, pp. 288293. [11] Stracke, R., Böhm, K. J., Burgold, J., Schacht, H., Unger, E., Physical and Technical parameters determining the functioning of a knesin-based cell-free motor system, Nanotechnology 11, UK, 2000, pp. 52-56. [12] Sun, J., Gao, M., Feldmann, J., Electric Field Directed Layer-by-Layer Assembly of Highly Fluorescent CdTe Nanoparticles, Journal of Nanoscience and Nanotechnology, Vol.1, No.2, American Scientific Publishers, 2001, pp. 2127. [13] Whitcomb, L. L., Underwater Robotics: out of the research laboratory and into the Field, IEEE Int'l Conf. on Robotics and Automation, 2000, pp. 85-90.
