IEEE Robotics & Automation Magazine - June 2020 - 44

orientations are encoded uniquely in a representation that
does not contain singularities. Such an approach is
employed in this application on S 3 to learn and retrieve
the evolution of robot end-effector orientations by adapting
them to the orientation of objects and tools in the robot
workspace. This approach was successfully tested during
field trials in the Mediterranean Sea, offshore of Marseille,
France, where seven extended dives at four sites (8-, 30-,
48-, and 100-m water depths) were performed with the
underwater robot while connected via satellite to the teleoperation center in Brussels, Belgium; see [41] for a general
description of the experiment.
Further Perspectives and Conclusions
This article showed that a wide range of challenges in robot
learning and adaptive control can be recast as statistical
modeling and information fusion on Riemannian manifolds.
Such an interpretation can avoid potential misuses of algorithms in robotics that might originate from Riemannian
geometry and that are treated with a limited view. One such
example is to perform all computations in a single tangent
space (typically, at the origin of the manifold) instead of considering the closest tangent spaces to avoid distortions.
Another example concerns domain adaptation and transfer
learning, which require the realignment of data to cope with
nonstationarities. For example, sensory data collected by different subjects or throughout several days should use the
Riemannian notion of parallel transport instead of only
recentering the data [42].
This article also showed that the combination of statistics
and differential geometry offers many research opportunities
and can contribute to recent challenges in robotics. Further
work can be organized in two categories. First, the field of
robotics is abundant with new techniques proposed by
researchers because of its interdisciplinary aspect and the
richness of the problems it involves. The common factor in
many of these developments is that they rely on some form of
statistics and/or propagation of uncertainty. These models
and algorithms are typically developed for standard Euclidean
spaces, where an extension to Riemannian manifolds has several benefits to offer.
Second, some Riemannian manifolds remain largely
underexploited in robotics despite the fact that they are
mathematically well understood and characterized by simple closed-form expressions. Grassmann manifolds seem
particularly promising to handle problems in robotics with
high-dimensional data points and only few training data,
where subspaces are required in the computation to keep
the most essential characteristics of the data. They are also
promising in problems in which hierarchies are considered
(such as inverse kinematics with kinematically redundant
robots) because they provide a geometric interpretation of
null-space structures. Other Riemannian manifolds, such
as hyperbolic manifolds, also seem propitious for bringing a probabilistic treatment to dynamical systems, treebased structures, graphs, Toeplitz/Hankel matrices, and
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autoregressive models. Finally, a wide range of metric
learning problems in robotics could benefit from a Riemannian geometry treatment.
Acknowledgments
I would like to thank Noémie Jaquier, who provided relevant
suggestions for the writing and organization of the article
and carefully proofread the manuscript. This work was supported by the Swiss National Science Foundation/German
Research Foundation project TACT-HAND and by the
European Commission's Horizon 2020 program (Memory of
Motion project, http://www.memmo-project.eu/, grant
780684; and DexROV project, http://www.dexrov.eu/, grant
635491).
References
[1] F. C. Park, J. E. Bobrow, and S. R. Ploen, "A lie group formulation of
robot dynamics," Int. J. Robotics Res., vol. 14, no. 6, pp. 609-618, 1995.
doi: 10.1177/027836499501400606.
[2] J. M. Selig, Geometric Fundamentals of Robotics. Berlin: SpringerVerlag, 2005.
[3] T. D. Barfoot and P. T. Furgale, "Associating uncertainty with threedimensional poses for use in estimation problems," IEEE Trans. Robotics, vol. 30, no. 3, pp. 679-693, June 2014. doi: 10.1109/TRO.2014.
2298059.
[4] M. J. A. Zeestraten, I. Havoutis, J. Silvério, S. Calinon, and D. G.
Caldwell, "An approach for imitation learning on Riemannian manifolds," IEEE Robot. Autom. Lett., vol. 2, no. 3, pp. 1240-1247, June 2017.
doi: 10.1109/LRA.2017.2657001.
[5] N. Jaquier and S. Calinon, "Gaussian mixture regression on symmetric positive definite matrices manifolds: Application to wrist
motion estimation with sEMG," in Proc. IEEE/RSJ Intl Conf. Intelligent
Robots and Systems (IROS), Vancouver, Canada, Sept. 2017, pp. 59-64.
doi: 10.1109/IROS.2017.8202138.
[6] T. Lee and F. C. Park, "A geometric algorithm for robust multibody
inertial parameter identification," IEEE Robot. Autom. Lett., vol. 3, no.
3, pp. 2455-2462, 2018. doi: 10.1109/LRA.2018.2799426.
[7] S. Traversaro, S. Brossette, A. Escande, and F. Nori, "Identification of
fully physical consistent inertial parameters using optimization on
manifolds," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems
(IROS), Oct. 2016, pp. 5446-5451. doi: 10.1109/IROS.2016.7759801.
[8] T. Yoshikawa, "Manipulability of robotic mechanisms," Int. J.
Robotics Res., vol. 4, no. 2, pp. 3-9, 1985. doi: 10.1177/027836498500400201.
[9] "PbDlib robot programming by demonstration software library,"
Idiap Research Institute, Martigny, Switzerland, 2020. Accessed on:
Mar. 10, 2020. [Online]. Available: http://www.idiap.ch/software/pbdlib/
[10] X. Pennec, "Intrinsic statistics on Riemannian manifolds: Basic
tools for geometric measurements," J. Math. Imag. Vision, vol. 25, no. 1,
pp. 127-154, 2006. doi: 10.1007/s10851-006-6228-4.
[11] P. A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on Matrix Manifolds. Princeton, NJ: Princeton Univ. Press,
2007.
[12] S. Arimoto, M. Yoshida, M. Sekimoto, and K. Tahara, "A Riemannian-geometry approach for modeling and control of dynamics of
object manipulation under constraints," J. Robotics, vol. 2009, pp. 1-16,
Mar. 2009, Art. no. 892801. doi: 10.1155/2009/892801.


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