Constraint Manifold Optimization for Robotic Inference and Planning With Constraints
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Zhang, Yetong
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Abstract
Addressing constraints in optimization problems within robotics has posed a longstanding challenge. However, state-of-the-art constrained optimization methods still face several issues in solving large-scale constrained optimization problems. A powerful alternative to constrained optimization methods is manifold optimization, with the advantages of lower complexity and better numerical properties. This dissertation proposes a novel approach by leveraging manifold optimization to tackle constrained optimization problems in robotics. Moreover, it extends this framework to handle a broader spectrum of inequality-constrained optimization problems by extending the manifold optimization algorithm to manifolds with boundaries and corners. Finally, we enhance the efficiency of the proposed frameworks by developing infeasible optimization methods and the cost-aware retraction method. The effectiveness of our proposed framework is demonstrated through extensive experimentation across diverse robotic inference and planning scenarios under a wide variety of constraints. Results consistently illustrate that our approach outperforms traditional constrained optimization methods, yielding solutions with higher optimality and faster convergence.
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2024-07-08
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Dissertation