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Non-flat surfaces pose difficulties for robots operating in unstructured environments. Reconstructions of uneven surfaces may only be partially possible due to non-compliant end-effectors and limitations on vision systems such as transparency, reflections, and occlusions. This study achieves blind surface reconstruction by harnessing the robotic manipulator's kinematic data and a compliant tactile sensing module, which incorporates inertial, magnetic, and pressure sensors. The module's flexibility enables us to estimate contact positions and surface normals by analyzing its deformation during interactions with unknown objects. While previous works collect only positional information, we include the local normals in a geometrical approach to estimate curvatures between adjacent contact points. These parameters then guide a spline-based patch generation, which allows us to recreate larger surfaces without an increase in complexity while reducing the time-consuming step of probing the surface. Experimental validation demonstrates that this approach outperforms an off-the-shelf vision system in estimation accuracy. Moreover, this compliant haptic method works effectively even when the manipulator's approach angle is not aligned with the surface normals, which is ideal for unknown non-flat surfaces., Comment: 7 pages, 9 figures, 2024 IEEE International Conference on Robotics and Automation (ICRA 2024)

We study how regularity along a submanifold of a differential or microdifferential system can propagate from a family of submanifolds to another. The first result is that a microdifferential system regular along a lagrangian foliation is regular. However, when restricted to a fixed submanifold the corresponding result is true only under a condition on the characteristic variety.

A holonomic D-module on a complex analytic manifoldadmits always a b-function along any submanifold. If the module is regular, itadmits also a regular b-function, that is a b-function with a condition on the order of the lower terms of the equation.There is a weaker condition of regularity: regularity alonga submanifold. We prove that a module which is regular alonga submanifold admits a regular b-function along this submanifold.

In the theory of Lie groups, the irreducibility of a unitary representation is not preserved in general by restriction to a subgroup. Kirillov's conjecture says that it is preserved for the groups Gl(n,R) or Gl(n,C) when the subgroup is the subgroup of matrices leaving invariant a non zero vector. This conjecture was proved by Barush using a detailed study of nilpotent orbits. In fact, it is not difficult to see that the conjecture is equivalent to the fact that some system of partial differential equations has no singular distributions as solutions. This system of equations is a regular holonomic D-module and we give a proof of the result by an explicit calculation of the roots of the b-functions associated to this D-module.

A famous theorem of Harish-Chandra shows that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We give here an algebraic version of this theorem in terms of polynomials associated with a holonomic D-module.

A celebrated theorem of Harich-Chandra asserts that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We show that this result is a consequence of an algebraic property of a holonomic D-module defined by Kashiwara and Hotta.

The invariant eigendistributions on a reductive Lie algebra are solutions of a holonomic D-module which has been proved to be regular by Kashiwara-Hotta. We solve here a conjecture of Sekiguchi saying that in the more general case of symmetric pairs, the corresponding module are still regular.