The International Journal of Robotics Research Study, Ahead of Publish.
We offer unique, convex leisures for turning and position evaluation issues that can a posteriori warranty worldwide optimality for useful dimension sound degrees. Some such leisures exist in the literary works for certain trouble configurations that think the matrix von Mises-Fisher circulation (a.k.a., matrix Langevin circulation or chordal range) for isotropic rotational unpredictability. Nonetheless, one more usual method to stand for unpredictability for turnings and positions is to specify anisotropic sound in the linked Lie algebra. Beginning with a sound design based upon the Cayley map, we specify our evaluation issues, transform them to Quadratically Constrained Quadratic Programs (QCQPs), after that unwind them to Semidefinite Programs (SDPs), which can be addressed utilizing conventional interior-point optimization techniques; worldwide optimality adheres to from Lagrangian solid duality. We initially demonstrate how to accomplish fundamental turning and position averaging. We after that transform to the extra complicated trouble of trajectory evaluation, which includes lots of position variables with both private and inter-pose dimensions (or movement priors). Our payment is to create SDP leisures for all these issues based upon the Cayley map (consisting of the recognition of repetitive restraints) and to reveal them operating in useful setups. We wish our outcomes can include in the brochure of valuable evaluation issues whose options can be a posteriori ensured to be worldwide optimum.
发布者：Timothy D. Barfoot，转转请注明出处：https://robotalks.cn/certifiably-optimal-rotation-and-pose-estimation-based-on-the-cayley-map/
