© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

9.3.3 Sensors and Manipulator Control

In addition to end-effectors, it will often be convenient to position various classes of sensors along the length of a manipulator, or at the tip. Monitoring control cable lengths, pneumatic chamber pressures, drive shaft rotations or strut lengths can allow a controller to know the position of a manipulator tip to the accuracy of one control increment, assuming no external forces and assuming regular recalibrations by periodically returning the arm to a precisely known "home" position. If low-stress stretch-inelastic metrological cables are embedded in the manipulator structure, then physical displacements of those cables in response to an applied load may be compared to no-load force/distance profiles, revealing the external force vector. Thus actual tip displacements are recorded directly by the metrological cables, and force feedback is continuously available. End effectors may include a wide variety of additional useful sensors, including gripper force and adhesion sensors, chemotactic sensors, vibration and acoustic sensors, electric or magnetic sensors, thermal or optical sensors, and so forth (Chapter 4).

Techniques for precise nanomanipulator control had received insufficient formal attention as of 1998. Pure open loop control (e.g., dead reckoning with no sensory feedback) could be sufficient in some molecular manufacturing operations. In this regard the inkjet printer might be a more suitable conceptual model than the robot arm, since a printer can build up considerable three-dimensional complexity during repeated passes over the workpiece following a simple linear chain of instructions in a raster pattern. Adding the ability to sense a fiducial structure near the workpiece can provide periodic checks on registration and reduce placement error, and Drexler¹⁰ has described the use of sterically complementary probes or alignment pegs to help guide end-effectors precisely to their targets.

However, force reflection and other sensory feedback are likely to play important roles in nanomedical manipulator control. J.S. Hall, cited in Drexler,¹⁰ points out that the ratios of the times and energies consumed by a typical nanomechanical computation to the times and energies consumed by a typical nanomanipulator motion are enormously greater than the corresponding ratios for microprocessor computation and macromechanical robotic arm motion. In other words, computation is relatively cheap for macroscale robotic manipulators while arm motion is relatively cheap for nanoscale robotic manipulators. Thus the moment-by-moment computer control of arm trajectories is the appropriate paradigm for macroscale robots, but not for nanoscale robots. For nanoscale robots, the appropriate manipulator control paradigm is often trajectory trial-and-error, also known as sensor-based motion control^1623,1638 or "groping."

Using trajectory trial-and-error, the nanomanipulator is moved generally in the direction of a desired endpoint, then is stopped and sensory feedback from the tip is obtained and examined for a match with the target destination profile. Given only a partial match, the arm is next moved in some direction and new sensory feedback is sampled. If the profile match has improved, another increment of motion is applied in the same direction; if the match has deteriorated, another direction is tried. Much like a blind man groping for his knife and fork by feeling around on the surface of a dinner table until he finds the utensils, the nanomanipulator is directed by trial-and-error progressively toward its goal, until the target is unambiguously located.

Efficient search algorithms for detecting and avoiding local maxima, identifying saddle points, rejecting outliers, and minimizing search times are well-known to mathematicians. In some cases, chemonavigational sensory readings may be taken using sensor pads (Section 4.2.5) at the manipulator tip to determine proximity to specific cellular processes or organelles. Unknown objects may be examined by haptic (tactile) exploration¹⁶²² or by other means. Outside the cell, extracellular matrix (ECM) elements may be repeatedly chemotactically sampled to allow a nanomanipulator to feel its way toward a particular structure or node. Deployment of multiple nanomanipulators from a single device permits the simultaneous coordinated manipulation of several objects in the environment. In many cases, Brownian transport may suffice to bring a molecular target to the nanorobot arm.

If a nanomanipulator can be moved in minimum increments of DL at mean velocity v_arm throughout a typical work volume V_work, then an efficient search algorithm can locate any target volume of size DL³ that lies within V_work in at most N_trial ~ log₂(V_work/DL³) trials, requiring a search time t_search ~ N_trial Dt where the mean time per nanomanipulator motion is Dt <~ V_work^1/3 / v_arm assuming a reasonably smooth gradient in roughly cubical work volume. Taking DL = 1 nm, v_arm = 1 cm/sec, and V_work = 0.1 micron³ for a cell-repair type manipulator, then N_trial ~ 27 trials and Dt <~ 46 microsec, giving t_search <~ 1 millisec for the nanomanipulator arm to search for (and find) its intracellular target using the trial-and-error paradigm. This is consistent with the estimated time to search cell surfaces for specific markers (Eqn. 8.5). For the telescoping nanomanipulator to be used in molecular manufacturing as described by Drexler,¹⁰ and taking DL ~ 0.25 nm, v_arm = 1 cm/sec, and V_work = 3 nm³, then N_trial ~ 8 trials and Dt <~ 0.1 microsec, giving t_search <~ 1 microsec.

Other control paradigms might also be useful in molecular manufacturing applications requiring high placement accuracy, possibly including full closed-loop operation in special cases.

Last updated on 21 February 2003