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The locomotion and orientation of free-swimming microorganisms have been widely studied for more than a century. With few exceptions, only the two-dimensional translational velocity of the organism in question is ever reported, yet a complete description of motion requires a three-dimensional description of both the translational and rotational velocities. Recent theoretical work, considering both the translational and rotational velocities, has demonstrated that a previously unrecognized orientation mechanism exists - helical klinotaxis. Efforts to test the predictions of this theory are described, concluding that helical klinotaxis is probably utilized by a diverse assemblage of free-swimming microorganisms.

A broad diversity of microorganisms and larval aquatic animals swim along a helical trajectory. Helical movement toward or away from stimuli involves the detection of gradients, alteration of the helical trajectory, and gradient tracking. Using sensory and neural circuitry models from swimming simulations of tadpole-like ascidian larvae (Phylum Chordata, Subphylum Urochordata), we built and tested a single-sensor, surface-swimming, tail-flapping robot that swims up a light gradient and holds station at an orbital around an area of high intensity. We implemented the same neural circuitry in a terrestrial, wheeled robot with a single photoresistor; it exhibited similar navigational behavior. We also mathematically modeled single-sensor robots navigating in plane. The simulated robots showed the importance of sensor placement and excitation field on navigational behavior. When the sensor placement and excitation field of the simulated robot matched that of the embodied robots, navigational behavior was similar. These results 1) tested and supported a proposed neural circuitry model, 2) showed the simplicity and effectiveness of using a single light sensor for navigation, and 3) demonstrated the use of helical motion in two dimensions. [ABSTRACT FROM AUTHOR]

Presents a study which described the finite helix fit technique whereby a three-dimensional trajectory is completely described by its velocity, curvature and torsion. Materials and methods; Results of the study; Discussion.