Trajectory Optimization On Manifolds with Applications to SO(3) and R3XS2 Article Swipe
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· 2018
· Open Access
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· DOI: https://doi.org/10.15607/rss.2018.xiv.023
· OA: W2807330992
Manifolds are used in almost all robotics applications even if they are not explicitly modeled.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 visualinertially guided robots navigating in 3 dimensions.Formulating field of view constraints naturally results in modeling with the manifold R 3 × S 2 which cannot be modeled as a Lie group.
