Positive Solutions For a Schr\"odinger-Bopp-Podolsky system in R3\mathbb R^{3}

We consider the following Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$ $$\left\{ \begin{array}{c} -\varepsilon^{2} \Delta u + V(x)u + \phi u = f(u)\\ -\varepsilon^{2} \Delta \phi + \varepsilon^{4} \Delta^{2}\phi = 4\pi u^{2}\\ \end{array} \right.$$ where $\varepsilon > 0$ with $V:\mathbb{R}^{3} \rightarrow \mathbb{R}, f:\mathbb{R} \rightarrow \mathbb{R}$ satisfy suitable assumptions. By using variational methods, we prove that the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of $M$, the set of minima of the potential $V$

The Role of Impedance Modulation and Redundancy Resolution in Human-Robot Interaction

In this work, redundancy resolution and impedance modulation strategies have been employed to enhance intuitiveness and stability in physical human-robot interaction during co-manipulation tasks. An impedance strategy to control a redundant manipulator is defined in the Cartesian space. Different modulation laws for the impedance parameters are tested in combination with different strategies to solve redundancy. The stability of the coupled human-robot system is guaranteed ensuring that the impedance parameters vary in a range evaluated experimentally. Through an extensive experimental study on a 7-DOF KUKA LWR4 arm, we show that using redundancy to decouple the equivalent inertia at the end-effector enables a more flexible choice of the impedance parameters and improves the performance during manual guidance. Moreover, variable impedance is more performant with respect to constant impedance due to a favourable compromise between accuracy and execution time and the enhanced comfort perceived by humans during manual guidance

Variable Impedance Control of Redundant Manipulators for Intuitive Human–Robot Physical Interaction

This paper presents an experimental study on human-robot comanipulation in the presence of kinematic redundancy. The objective of the work is to enhance the performance during human-robot physical interaction by combining Cartesian impedance modulation and redundancy resolution. Cartesian impedance control is employed to achieve a compliant behavior of the robot's end effector in response to forces exerted by the human operator. Different impedance modulation strategies, which take into account the human's behavior during the interaction, are selected with the support of a simulation study and then experimentally tested on a 7-degree-of-freedom KUKA LWR4. A comparative study to establish the most effective redundancy resolution strategy has been made by evaluating different solutions compatible with the considered task. The experiments have shown that the redundancy, when used to ensure a decoupled apparent inertia at the end effector, allows enlarging the stability region in the impedance parameters space and improving the performance. On the other hand, the variable impedance with a suitable modulation strategy for parameters' tuning outperforms the constant impedance, in the sense that it enhances the comfort perceived by humans during manual guidance and allows reaching a favorable compromise between accuracy and execution time

Tracking Fractures of Deformable Objects in Real-Time with an RGB-D Sensor

This paper introduces a method able to track in real-time a 3D elastic deformable objects which undergo fractures, using the point cloud data provided by an RGB-D sensor. Our framework relies on a prior visual segmentation of the object in the image. The segmented point cloud is registered by non-rigidly fitting the mesh, based on the Finite Element Method to physically model elasticity, and on geometrical point-to-point correspondences to compute external forces exerted on the mesh. Fractures are handled by processing the stress tensors computed on the mesh of the FEM model, in order to detect fracturable nodes. Local remeshing around fracturable nodes is then performed to propagate the fracture. The real-time performance of the system is demonstrated on real data involving various deformations and fractures

Redundancy resolution in human-robot co-manipulation with cartesian impedance control

In this paper the role of redundancy in Cartesian impedance control of a robotic arm for the execution of tasks in co-manipulation with humans is considered. In particular, the problem of stability is experimentally investigated. When a human operator guides the robot through direct physical interaction, it is desirable to have a compliant behaviour at the end effector according to a decoupled impedance dynamics. In order to achieve a desired impedance behaviour, the robot’s dynamics has to be suitably reshaped by the controller. Moreover, the stability of the coupled human-robot system should be guaranteed for any value of the impedance parameters within a prescribed region. If the robot is kinematically or functionally redundant, also the redundant degrees of freedom can be used to modify the robot dynamics. Through an extensive experimental study on a 7-DOF KUKA LWR4 arm, we compare two different strategies to solve redundancy and we show that, when redundancy is exploited to ensure a decoupled apparent inertia at the end effector, the stability region in the parameter space becomes larger. Thus, better performance can be achieved by using, e.g., variable impedance control laws tuned to human intentions

Real-time tracking of 3D elastic objects with an RGB-D sensor

This paper presents a method to track in real-time a 3D textureless object which undergoes large deformations such as elastic ones, and rigid motions, using the point cloud data provided by an RGB-D sensor. This solution is expected to be useful for enhanced manipulation of humanoid robotic systems. Our framework relies on a prior visual segmentation of the object in the image. The segmented point cloud is registered first in a rigid manner and then by non-rigidly fitting the mesh, based on the Finite Element Method to model elasticity, and on geometrical point-to-point correspondences to compute external forces exerted on the mesh. The real-time performance of the system is demonstrated on synthetic and real data involving challenging deformations and motions

Learning Grasps in a Synergy-based Framework

In this work, a supervised learning strategy has been applied in conjunction with a control strategy to provide anthropomorphic hand-arm systems with autonomous grasping capabilities. Both learning and control algorithms have been developed in a synergy-basedframework in order to address issues related to high dimension of the configuration space, that typically characterizes robotic hands and arms with humanlike kinematics. An experimental setup has been built to learn hand-arm motion from humans during reaching and grasping tasks. Then, a Neural Network (NN) has been realized to generalize the grasps learned by imitation. Since the NN approximates the relationship between the object characteristics and the grasp configuration of the hand-arm system, a synergy-based control strategy has been applied to overcome planning errors. The reach-to-grasp strategy has been tested on a setup constituted by the KUKA LWR 4+Arm and the SCHUNK 5-Finger Hand

Impedance control of redundant manipulators for safe human-robot collaboration

In this paper, the impedance control paradigm is used to design control algorithms for safe human-robot collaboration. In particular, the problem of controlling a redundant robot manipulator in task space, while guaranteeing a compliant behavior for the redundant degrees of freedom, is considered first. The proposed approach allows safe and dependable reaction of the robot during deliberate or accidental physical interaction with a human or the environment, thanks to null-space impedance control. Moreover, the case of control for co-manipulation is considered. In particular, the role of the kinematic redundancy and that of the impedance parameters modulation are investigated. The algorithms are verified through experiments on a 7R KUKA lightweight robot arm