Superfast 3D Shape Measurement with Application to Flapping Wing Mechanics Analysis

Beiwen Li, Purdue University

Abstract

The goal of measurement is to allow a person to perceive the three-dimensional (3D) world around us, to know about a substance, and to obtain or produce new knowledge. However, performing accurate measurements of dynamically deformable objects has always been a challenging task, which in fact has huge potential to applications in areas of manufacturing, robotics, non-destructive evaluations, etc. Over a decade of efforts, scientists have made significant progresses along this direction. In particular, the binary defocusing method, which performs fringe analysis upon the camera captured distorted 1-bit binary patterns projected by an out-of-focus projector, has reached unprecedented superfast measurement speeds (e.g. kHz) with high spatial resolutions. Despite of the speed breakthrough, there are still a number of challenges associated with such technology: (1) requiring an out-of-focus projector brings about difficulty in achieving high measurement accuracy; (2) motion induced artifacts and errors are still present if measuring a scene with fast moving objects; (3) it is difficult to perform subsequent analysis (e.g. deformation, mechanics, etc.) solely by interpreting those uncorrelated frames of acquired dynamic 3D data. The first challenge is mainly caused by the difficulty of performing an accurate calibration for a camera-projector system with an out-of-focus projector. To deal with this problem, we have theoretically proved and experimentally validated that a camera pixel can be virtually mapped to a projector pixel in phase domain even if the projector is substantially out-of-focus. Based on this foundation, we developed novel calibration approaches that can successfully achieve high accuracy under different scales: in a macro-scale measurement range [e.g. 150 mm(H) X 250 mm(W) X 200 mm(D)], we achieved an accuracy up to 73 µm; in a medium-scale measurement range [e.g. 10 mm(H) X 8 mm(W) X 5 mm(D)] , we achieved an accuracy up to 10 µm. The second challenge is quite common in dynamic measurements if the sampling rate is not high enough to keep up with the object motion. Although employing hardware with higher measurement speeds is always a potential solution, it is more desirable to innovate software algorithms to reduce the hardware cost. We developed two different software approaches to deal with the problems associated with object motion: (1) a single-shot absolute 3D recovery method to increase the sampling rate; (2) a motion induced error reduction framework. The first approach successfully overcame the difficulty of absolute 3D recovery for existing single-shot fringe analysis methods by taking advantage of the geometric constraints of a camera-projector system. The second approach successfully alleviated motion induced errors and artifacts by hybridizing the merits of two commonly used fringe analysis techniques: Fourier transform and phase shifting. Addressing both aforementioned challenges has enabled us to perform simultaneous superfast and high-accuracy 3D shape measurements with reduced motion induced errors or artifacts. Under such platform, we are seeking to introduce the technologies to a different field and explore an application. Finally, a particular topic presented in this dissertation is our research on 3D strain analysis of robotic flapping wings. Measuring dense 3D strain map of flapping wings could potentially produce new knowledge for the design of bio-inspired flapping wing robots. Such topic, however, is not well documented so far owing to the lack of an appropriate technological platform to measure dense 3D strain maps of the wings. In this dissertation research, we first measured the dynamic 3D geometries of a robotic bird with rapid flapping wings (e.g. 25 cycles/second) using a superfast image acquisition rate of 5,000 Hz. Then, we developed a novel geometry-based dense 3D strain measurement framework based on geodesic computation and Kirchhoff-Love shell theory. Such an innovation could potentially benefit bio-inspired robotics designers by introducing a new method of geometric and mechanical analysis, which could be used for better design of robotic flapping wings in the future. In summary, this dissertation research substantially advances the research of 3D shape measurement by achieving simultaneous superfast and high-accuracy measurements. Meanwhile, it demonstrates the potential of such technology by developing geometry-based 3D data analytics tools and exploring an application. Contributions of this research could potentially benefit a variety of different fields in both academic and industrial practices, where both speed and accuracy are major concerns and where subsequent mechanics analysis are necessary.

Degree

Ph.D.

Advisors

Zhang, Purdue University.

Subject Area

Mechanical engineering

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