I. Definition of the Subject and Its Importance Mechanical devices for computation appear to be l... more I. Definition of the Subject and Its Importance Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating to thousands of years and with surprising applications even in relatively recent times. (b) Technical & Practical: The use of mechanical devices for computation persists and has not yet been completely displaced by widespread use of microprocessor-based computers. Mechanical computers have found applications in various emerging technologies at the micro-scale that combine mechanical functions with computational and control functions not feasible by purely electronic processing. Mechanical computers also have been demonstrated at the molecular scale, and may also provide unique capabilities at that scale. The physical designs for these modern micro and molecularscale mechanical computers may be based on the prior designs of the large-scale mechanical computers constructed in the past. (c) Impact of Physical Assumptions on Complexity of Motion Planning, Design, and Simulation The study of computation done by mechanical devices is also of central importance in providing lower bounds on the computational resources such as time and/or space required to simulate a mechanical system observing given physical laws. In particular, the problem of simulating the mechanical system can be shown to be computationally hard if a hard computational problem can be simulated by the mechanical system. A similar approach can be used to provide lower bounds on the computational resources required to solve various motion planning tasks that arise in the field of robotics. Typically, a robotic motion planning task is specified by a geometric description of the robot (or collection of robots) to be moved, its initial and final positions, the obstacles it is to avoid, as well as a model for the type of feasible motion and physical laws for the movement. The problem of planning such as robotic motion planning task can be shown to be computationally hard if a hard computational problem can be simulated by the robotic motion-planning task. II. Introduction to Computational Complexity Abstract Computing Machine Models. To gauge the computational power of a family of mechanical computers, we will use a widely known abstract computational model known as the Turing Machine, defined in this section. The Turing Machine. The Turing machine model formulated by Alan Turing [1] was the first complete mathematical model of an abstract computing machine that possessed universal computing power. The machine model has (i) a finite state transition control for
A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousand... more A Very Large Scale Robotic (VLSR) system may consist of from hundreds to perhaps tens of thousands or more autonomous robots. The costs of robots are going down, and the robots are getting more compact, more capable, and more flexible. Hence, in the near future, we expect to see many industrial and military applications ofVLSR systems in tasks such as assembling, transporting, hazardous inspection, patrolling, uarding and attacking. In this paper, we propose anew approach for distributed autonomous control of VLSR systems. We define simple artificial force laws between pairs of robots or robot groups. The force laws are inverse-power force laws, incorporating both attraction and repulsion. The force laws can be distinct and to some degree they reflect he 'social relations ' among robots. Therefore we call our method social potential fields. An individual robot's motion is controlled by the resultant artificial force imposed by other obots and other components of the s...
llowing neighboring tiles in an assembly to associate by sticky ends on each side, one could incr... more llowing neighboring tiles in an assembly to associate by sticky ends on each side, one could increase the computational complexity of languages generated by linear self-assemblies. Surprisingly sophisticated calculations can be performed with singlelayer linear assemblies when contiguous strings of DNA trace through individual tiles and the entire assembly multiple times. In essence, a "string tile" is the collapse of a multilayer assembly into a simpler superstructure by allowing individual tiles to carry multiple segments of the reporter strands, thereby allowing an entire row of a truth table to be encoded within each individual tile. "String tile" arithmetic implementations have a number of advantageous properties. (i) Input and output strings assemble simultaneously. (ii) Each row in the truth table for the function being calculated is represented as a single tile type, where all input and output bits are encoded on that tile. Each pairwise operation is dire...
Given a univariate complex polynomial f(x) of degree n with rational coe cients expressed as a ra... more Given a univariate complex polynomial f(x) of degree n with rational coe cients expressed as a ratio of two integers < 2, the root problem is to nd all the roots of f(x) up to speci ed precision 2 . In this paper we assume the arithmetic model for computation. We give an improved algorithm for nding a well-isolated splitting interval and for fast root proximity veri cation. Using these results, we give an algorithm for the real root problem: where all the roots of the polynomial are real. Our real root algorithm has time cost of O(n log n(logn+ log b)); where b = m + . Our arithmetic time cost is thus O(n log n) even in the case of high precision b n. This is within a small polylog factor of optimality, thus (perhaps surprisingly) upper bounding the arithmetic complexity of the real root problem to nearly the same as basic arithmetic operations on polynomials. The symmetric tridiagonal problem is: given an n n symmetric tridiagonal matrix, with 3n nonzero rational entries each ex...
We were engaged in research in various areas of robotic movement planning. The movement planning ... more We were engaged in research in various areas of robotic movement planning. The movement planning problems investigated were static movement problems (where the obstacles do not move), minimum distance path planning, compliant motion control (which involves planning without complete knowledge of the position of the robot) and related frictional movement problems, motion planning with independently moving obstacles, and kinodynamic movement planning (where the dynamics are taken into account including driving forces and torque), motion planning within potential elds such as gravitational force potential elds and magnetic elds and pursuit movement games (which involve movement control planning with an adversary). Most of our e orts were involved in the latter problems which have been investigated less. This paper will present some of our lates results on these various problems. Also this paper will include some improved algorithms we developed for the fundamental algebraic and combinat...
This chapter overviews the current state of the emerging discipline of DNA nanorobotics that make... more This chapter overviews the current state of the emerging discipline of DNA nanorobotics that make use of synthetic DNA to self-assemble operational molecular-scale devices. Recently there have been a series of quite astonishing experimental results—which have taken the technology from a state of intriguing possibilities into demonstrated capabilities of quickly increasing scale and complexity. We first state the challenges in molecular robotics and discuss why DNA as a nanoconstruction material is ideally suited to overcome these. We then review the design and demonstration of a wide range of molecular-scale devices; from DNA nanomachines that change conformation in response to their environment to DNA walkers that can be programmed to walk along predefined paths on nanostructures while carrying cargo or performing computations, to tweezers that can repeatedly switch states. We conclude by listing major challenges in the field along with some possible future directions.
DNA computing 1 potentially provides a degree of parallelism far beyond that of conventional sili... more DNA computing 1 potentially provides a degree of parallelism far beyond that of conventional silicon-based computers. A number of researchers 2 have experimentally demonstrated DNA computing in solving instances of the satisfiability problems. Self-assembly of DNA nanostructures is theoretically an efficient method of executing parallel computation where information is encoded in DNA tiles and a large number of tiles can be self-assembled via sticky-end associations. Winfree et al. 3 have shown that representations of formal languages can be generated by self-assembly of branched DNA nanostructures and that 2-dimensional DNA selfassembly is Turing-universal (i.e. capable of universal computation). Mao et al. 4 experimentally implemented the first algorithmic DNA self-assembly which performed a logical computation (cumulative XOR), however that study only executed two computations on fixed inputs. To further explore the power of computing using DNA self-assembly, experimental demonst...
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