2020
DOI: 10.1109/mra.2020.2980548
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Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

Abstract: This paper presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. We first discuss the roles of Riemannian manifolds, geodesics and parallel transport in robotics. We then present several forms of manifolds that are already employed in robotics, by also listing manifolds that have been underexploited so far but that have potentials in future robot learning applications. A varied range of techniques emp… Show more

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Cited by 54 publications
(41 citation statements)
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“…9 exhibits the demonstrated, retrieved and recorded orientation trajectories in the approaching phase. All of these trajectories converge to the orientation [1, 0, 0, 0] T because the demonstrated orientation data are displayed with respect to the pre-assembly frame and then the corresponded η in the tangent space are computed by (4) to learn the GMM based policy. In this experiment, since only z position with respect to the pre-assembly frame is used as query variable of GMR, the retrieved orientation trajectories (blue curves) overlap each other.…”
Section: Experiments Results and Discussionmentioning
confidence: 99%
“…9 exhibits the demonstrated, retrieved and recorded orientation trajectories in the approaching phase. All of these trajectories converge to the orientation [1, 0, 0, 0] T because the demonstrated orientation data are displayed with respect to the pre-assembly frame and then the corresponded η in the tangent space are computed by (4) to learn the GMM based policy. In this experiment, since only z position with respect to the pre-assembly frame is used as query variable of GMR, the retrieved orientation trajectories (blue curves) overlap each other.…”
Section: Experiments Results and Discussionmentioning
confidence: 99%
“…In robotics, it is well established that estimating uncertain spatial relationships is fundamentally important for stateestimation [11,12], robot control [13], or active SLAM [14].…”
Section: B Links and Differences With Existing Literaturementioning
confidence: 99%
“…For simplicity, only positions of the two parts of the cursor mouse are considered since the orientation of them is constant during the assembly process. However, it is not difficult to exploiting the 6D pose data with the unit quaternion representation of the orientation [29]. Figure 16 exhibits the demonstration data of the bimanual assembly process in Cartesian space.…”
Section: A Case Study: Robotic Pcb Assemblymentioning
confidence: 99%