期刊
INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
卷 39, 期 2-3, 页码 303-320出版社
SAGE PUBLICATIONS LTD
DOI: 10.1177/0278364919891775
关键词
Differential geometry; optimization; planning; quadrotors
类别
资金
- DARPA [HR001151626/HR0011516850]
- ARO [W911NF-08-2-0004]
- NSF [IIS1426840]
- ONR [N00014-07-1-0829]
- NASA Space Technology Research Fellowship
Manifolds are used in almost all robotics applications even if they are not modeled explicitly. We propose a differential geometric approach for optimizing trajectories on a Riemannian manifold with obstacles. The optimization problem depends on a metric and collision function specific to a manifold. We then propose our safe corridor on manifolds (SCM) method of computationally optimizing trajectories for robotics applications via a constrained optimization problem. Our method does not need equality constraints, which eliminates the need to project back to a feasible manifold during optimization. We then demonstrate how this algorithm works on an example problem on SO(3) and a perception-aware planning example for visual-inertially guided robots navigating in three dimensions. Formulating field of view constraints naturally results in modeling with the manifold R3xS2 , which cannot be modeled as a Lie group. We also demonstrate the example of planning trajectories on SE(3) for a formation of quadrotors within an obstacle filled environment.
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