Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein's equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon's model in the gravitational field of a Schwarzschild black hole is discussed. Certain "reciprocity relations" between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon's model for extended bodies in general relativity.Comment: 14 pages, Latex svjour2.cls article class, 7 eps figure files. To appear on General Relativity and Gravitation, 200

Towards sensor-based manipulation of flexible objects

International audience— This paper presents the FLEXBOT project, a joint LIRMM-QUT effort to develop (in the near future) novel methodologies for robotic manipulation of flexible and deformable objects. To tackle this problem, and based on our past experiences, we propose to merge vision and force for manipulation control, and to rely on Model Predictive Control (MPC) and constrained optimization to program the object future shape. Index Terms— Control for object manipulation, learning from human demonstration, sensor fusion based on tactile, force and vision feedback. I. CONTEXT This abstract does not present experimental results, but aims at giving some preliminary hints on how flexible robot manipulation should be realized in the near future, particularly in the context of the FLEXBOT project, jointly submitted to the PHC FASIC Program 1 by LIRMM and QUT researchers. The objective of FLEXBOT is to solve one of the most challenging open problems in robotics. In fact, we aim at developing novel methodologies enabling robotic manipulation of flexible and deformable objects. The motivation comes from numerous applications, including the domestic, industrial, and medical examples 2 shown in Fig. 1. Many difficulties emerge when dealing with flexible manipulation. In the first place, the object deformation model (involving elasticity or plasticity) must be known, to derive the robot control inputs required for reconfiguring its shape. Ideally, this model should be derived online, while manipulating , with a simultaneous estimation and control approach, as commonly done in active perception and visual servoing. Hence perception, particularly from vision and force, will be indispensable. This leads to a second major difficulty: deformable object visual tracking. In fact, most current visual object tracking algorithms rely on rigidity, an assumption that is not valid here. A third challenge will consist in generating control inputs that comply with the shape the object is expected to have in the near future. In the next section, we provide a brief survey of the state of art on flexible object manipulation. We then conclude by proposing some novel methodologies for addressing the problem