Application of Multivariate Statistical Approaches to Complex Robotic System Analyses
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Ever-increasing development of robotic systems to different areas of application often leads to a complex architecture of the system. Complexity, on one hand, increases the difficulty in modeling and escalates the computational burden due to the curse of dimensionality, and hence, exacerbates the modeling uncertainty. However, on the other hand, more complex structures often provide more flexibility in design of such systems. These flexibilities can be exploited in order to improve a variety of the performance indices. In this dissertation, we are seeking two main objectives: (i) systematic approaches to better encounter the stochastic behavior of the complex robotic systems when only partial/limited information is available (which is a result of complexity), and (ii) probabilistic frameworks to systematically exploit the flexibilities offered by the complexity in order to optimize both the deterministic and probabilistic performance indices. Along our first objective, we adopt and develop ideas based on random matrix theory (RMT) in order to model the behavior of the robotic manipulators when only limited information is available to construct the stochastic model. We perform our analyses in both kinematic and static arrangements that provide frameworks for motion and wrench uncertainty characterizations, respectively. Our second objective is followed by the analyses of random vectors relying on the theories from directional statistics. We develop probabilistic formulations that utilize the redundancy (and in some sense the complexity) in the multi-agent systems to (i) reduce (or manipulate) the uncertainty in the system response, and (ii) quantify and improve the capacity of the system output in both kinematic (system workspace) and static (wrench capacity) frameworks. We back up our developments with different numerical simulations to investigate the critical aspects of different scenarios and validate our approaches using real-system experimental analyses.