Efficient and Guaranteed Geometric Methods for Motion Generation and Perception

Fan, Taosha

doi:https://doi.org/10.21985/n2-dzrg-4654

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Efficient and Guaranteed Geometric Methods for Motion Generation and Perception

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Even though a number of techniques have been developed for motion generation and perception, few of them focus on the computational efficiency and theoretical guarantees at the same time. Typically, improved guarantees come with increased complexity, making theoretically guaranteed methods challenging use in real-time applications. Thus, existing methods usually have to ignore either efficiency or guarantees in practical implementation. Nevertheless, numerous problems in motion generation and perception require computational efficiency as well as theoretical guarantees, making the implementation of existing techniques strictly limited. To address this issue, we present efficient and guaranteed methods for motion generation and perception by utilizing geometry and optimization. In this thesis, we develop fast algorithms for higher-order variational integrators with linear- and quadratic-time complexity for integration and linearization, respectively; we make use of the complex number representation to solve the planar graph-based SLAM that is not only certifiably correct but also more efficient and robust; we propose majorization minimization methods for distributed pose graph optimization that have provable convergence to first-order critical points and can be accelerated with no loss of theoretical guarantees; we present a sparse constrained formulation for 3D human pose and shape estimation with which a linear-time algorithm is derived to compute the Gauss-Newton direction and the optimization time is reduced from tens of seconds to several milliseconds. In spite of the theoretical guarantees, all of these aforementioned methods achieve the state-of-the-art performances in terms of both accuracy and efficiency for their specific applications in motion generation and perception.

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