Cooperative motion control of teams of agile unmanned vehicles presents modeling challenges at several levels.
The "microscopic equations" describing individual vehicle dynamics and their interaction with the environment
may be known fairly precisely, but are generally too complicated to yield qualitative insights at the level of
multi-vehicle trajectory coordination. Interacting particle models are suitable for coordinating trajectories, but
require care to ensure that individual vehicles are not driven in a "costly" manner. From the point of view of
the cooperative motion controller, the individual vehicle autopilots serve to "shape" the microscopic equations,
and we have been exploring the interplay between autopilots and cooperative motion controllers using a multivehicle
hardware-in-the-loop simulator. Specifically, we seek refinements to interacting particle models in order
to better describe observed behavior, without sacrificing qualitative understanding. A recent analogous example
from biology involves introducing a fixed delay into a curvature-control-based feedback law for prey capture by an
echolocating bat. This delay captures both neural processing time and the flight-dynamic response of the bat as it uses sensor-driven feedback. We propose a comparable approach for unmanned vehicle modeling; however, in contrast to the bat, with unmanned vehicles we have an additional freedom to modify the autopilot. Simulation results demonstrate the effectiveness of this biologically guided modeling approach.
"Understanding" the behavior of a biological system typically means formulating a sensible model, postulating a
feedback law (incorporating biologically plausible sensory measurements), and experimentally verifying that the
model and feedback law are consistent with nature. This approach is illustrated well in the work of K. Ghose,
T. K. Horiuchi, P. S. Krishnaprasad, and C. F. Moss (and colleagues) on insect pursuit by echolocating bats.
In work of F. Zhang, E. W. Justh, and P. S. Krishnaprasad, similar modeling principles and feedback laws have
also been shown to play an important role in biologically-inspired formation-control and obstacle-avoidance laws.
Building on this earlier work, we seek to identify a bio-inspired framework for cooperative swarming, in which
the apparently complicated trajectories of individuals are explained by feedback laws which take a relatively
simple form. The objectives of such swarming (e.g., for teams of unmanned vehicles) could include rendezvous,
target capture (or destruction), and cooperative sensing.
A conventional Zernike filter measures wavefront phase by superimposing the aberrated input beam with a phase-shifted version of its zero-order spectral component. The Fourier- domain phase-shifting is performed by a fixed phase-shifting dot on a glass slide in the focal plane of a Fourier- transforming lens. Using an optically-controlled phase spatial light modulator (SLM) instead of the fixed phase-shifting dot, we have simulated and experimentally demonstrated a nonlinear Zernike filter robust to wavefront tilt misalignments. In the experiments, a liquid-crystal light valve (LCLV) was used as the phase SLM. The terminology 'nonlinear' Zernike filter refers to the nonlinear filtering that takes place in the Fourier domain due to the phase change for field spectral components being proportional to the spectral component intensities. Because the Zernike filer output intensity is directly related to input wavefront phase, a parallel, distributed feedback system can replace the wavefront reconstruction calculations normally required in adaptive- optic phase correction systems. Applications include high- resolution phase distortion suppression for atmospheric turbulence, optical phase microscopy, and compensation of aberrations in optical system components. A factor of eight improvement in Strehl ratio was obtained experimentally, and simulation results suggest that even better performance could be obtained by replacing the LCLV with a more sophisticated optically-controlled phase SLM.
High-resolution phase-contrast wavefront sensors based on optically addressed phase spatial light modulators and micro- mirror/LC arrays are introduced. Wavefront sensor efficiency is analyzed for atmospheric turbulence-induced phase distortions described by the Kolmogorov and Andrews models. A nonlinear Zernike filter wavefront sensor based on an optically addressed liquid crystal phase spatial light modulator is experimentally demonstrated. The results demonstrate high-resolution visualization of dynamically changing phase distortions within the sensor time response of about 10 msec.
An opto-electronic technique for high-resolution wave-front phase imaging is presented and demonstrated experimentally. The technique is analogous to the conventional Zernike phase- contrast approach, but uses modern spatial light modulator technology to increase robustness and improve performance. Because they provide direct measurements of wave-front phase (rather than wave-front slope measurements, as in Shack- Hartmann sensors), robust phase-contrast sensors have potential applications in high-speed, high-resolution adaptive optic systems. Advantages of the opto-electronic approach over alternative advanced phase-contrast techniques (such as a related phase-contrast sensor which uses a liquid-crystal light valve exhibiting a Kerr-type optical response to perform Fourier filtering) are discussed. The SLM used for the experimental results is a 128 X 128-element pixilated phase-only liquid crystal spatial light modulator from Boulder Nonlinear Systems, Inc.