The Hidden Robot: An Efficient Concept Contributing to the Analysis of the Controllability of Parallel Robots in Advanced Visual Servoing Techniques

Briot, Sébastien; Martinet, Philippe; Rosenzveig, Victor

doi:10.1109/tro.2015.2489499

Cited by 19 publications

(25 citation statements)

References 42 publications

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“…This result can be easily extended to the cases of the hidden robots of the UraneSX and the I4L. More developments on the controllability analysis of parallel robots controlled using leg-direction-based visual servos can be found in [51].…”

Section: Discussionmentioning

confidence: 82%

Minimal representation for the control of parallel robots via leg observation considering a hidden robot model

Briot¹,

Rosenzveig²,

Martinet

et al. 2016

Mechanism and Machine Theory

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Previous works on the visual servoing of parallel robots using the observation of their leg directions validated the feasibility of the approach but they have enlighten two main surprising results for which no answer was given: (i) the observed robot which is composed of n legs could be controlled in most cases using the observation of only m leg directions (m < n), and that (ii) in some cases, the robot did not converge to the desired end-effector pose, even if the observed leg directions did (i.e. there was not a global diffeomorphism between the observation space and the robot space). Recently, it was shown that the visual servoing of the leg directions of the Gough-Stewart platform and the Adept Quattro with 3 translational degrees of freedom was equivalent to controlling other virtual robots that have assembly modes and singular configurations different from those of the real ones. These hidden robot models are tangible visualizations of the mapping between the observation space and the real robots Cartesian space. Thanks to this concept, all the aforementioned points were answered for the mentioned robots. In this paper, the concept of hidden robot model is generalized for any type of parallel robots controlled using visual servos based on the observation of the leg directions. It is shown that the concept of hidden robot model is a powerful tool that gives useful insights about the visual servoing of robots using leg direction observation. With the concept of hidden robot model, the singularity problem of the controller can be addressed and the convergence issues of the controller can be explained, understood and solved. All these results are validated in simulations and through experiments on a Quattro robot.

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Section: Discussionmentioning

confidence: 82%

Minimal representation for the control of parallel robots via leg observation considering a hidden robot model

Briot¹,

Rosenzveig²,

Martinet

et al. 2016

Mechanism and Machine Theory

Self Cite

View full text Add to dashboard Cite

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“…In this context, controllability of the robot is essential. Briot et al [76] proposed an interesting approach to the analysis of the controllability of parallel mechanisms. Figure 14.…”

Section: Discussionmentioning

confidence: 99%

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Schulz

2019

Robotics

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In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.

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“…In the present section, thanks to the concept of hidden robot [25], we provide a physical interpretation of the elementary edges ( Fig. 1) for the cases SE(2), R 3 × S 1 and SE(3) exploiting the definition of virtual kinematic chains that can be associated to the bearing measurements.…”

Section: Physical Interpretation Of the Bearing Rigidity Graphmentioning

confidence: 99%

“…In order to give a physical interpretation of bearing rigidity, we will extend a concept developed by the first author in the recent years which is named "hidden robot". This concept was first introduced in [24,25] in order to determine the singularity cases of a vision-based controller dedicated to parallel robots [26]. It was then extended to more general cases, such as the observation of image points [27] or image lines [28].…”

Section: Introductionmentioning

confidence: 99%

“…The basic idea shown in [25,27] is that the mappings involved in the visual observation of geometric primitives (for estimating the pose of an object or for visual servoing) are equivalent to mappings representing the geometric and kinematic properties of given closed-loop mechanisms. By geometric property, we mean that the solutions of the Forward Geometric Model of the closed-loop mechanism under consideration are also the solutions of the 3-D localization problem associated with the considered observations.…”

Section: Introductionmentioning

confidence: 99%

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Physical Interpretation of Rigidity for Bearing Formations: Application to Mobility and Singularity Analyses

Briot

Giordano

2019

Journal of Mechanisms and Robotics

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Research on formation control and cooperative localization for multi-robot systems has been an active field over the last years. A powerful theoretical framework for addressing formation control and localization, especially when exploiting onboard sensing, is that of formation rigidity (mainly studied for the cases of distance and bearing measurements). Rigidity of a formation depends on the topology of the sensing/communication graph but also on the spatial arrangement of the robots, since special configurations ('singularities' of the rigidity matrix), which are hard to detect in general, can cause a rigidity loss and prevent convergence of formation control/localization algorithms based on formation rigidity. The aim of this paper is to gain additional insights into the internal structure of bearing rigid formations by considering an alternative characterization of formation rigidity using tools borrowed from the mechanical engineering community. In particular, we show that bearing rigid graphs can be given a physical interpretation related to virtual mechanisms, whose mobility and singularities can be analyzed and detected in an analytical way by using tools from the mechanical engineering community (Screw theory, Grassmann geometry, Grassmann-Cayley algebra). These tools offer a powerful alternative to the evaluation of the mobility and singularities typically obtained by numerically determining the spectral properties of the bearing rigidity matrix (which typically prevents drawing general conclusions). We apply the proposed machinery to several case formations with different degrees of actuation, and discuss known (and unknown) * Address all correspondence to this author. singularity cases for representative formations. The impact on the localization problem is also discussed. IntroductionFormation control and cooperative localization for multi-robot teams has been a topic of extensive research over the last years [1-7]. Among the many challenges, considerable efforts are still devoted to devising decentralized formation controllers and/or localization schemes based on only local (onboard) sensing and communication. When considering these sensing/communication requirements, one has to face several challenges related to the decentralized design of the control/estimation algorithms, as well as the constraints arising from the use of onboard sensors. For instance, typical sensors only measure part of the relative pose among robot pairs (e.g., a distance or a bearing vector), while knowledge of the full relative pose is often needed for implementing formation control schemes. Also, a sensor provides measurements naturally expressed in the body-frame of the robot carrying it, and therefore one also faces the need of letting the robots agree over some common shared frame where to express all the individually collected measurements for then communicating them to the other robots in the group.In this context, a powerful theoretical framework for addressing decentralized formation control/localization from onboard ...

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The Hidden Robot: An Efficient Concept Contributing to the Analysis of the Controllability of Parallel Robots in Advanced Visual Servoing Techniques

Cited by 19 publications

References 42 publications

Minimal representation for the control of parallel robots via leg observation considering a hidden robot model

Minimal representation for the control of parallel robots via leg observation considering a hidden robot model

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Physical Interpretation of Rigidity for Bearing Formations: Application to Mobility and Singularity Analyses

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