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Force feedback exploiting tactile and proximal force/torque sensing

Theory and implementation on the humanoid robot iCub

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Abstract

The paper addresses the problem of measuring whole-body dynamics for a multiple-branch kinematic chain in presence of unknown external wrenches. The main result of the paper is to give a methodology for computing whole body dynamics by aligning a model of the system dynamics with the measurements coming from the available sensors. Three primary sources of information are exploited: (1) embedded force/torque sensors, (2) embedded inertial sensors, (3) distributed tactile sensors (i.e. artificial skin). In order to cope with external wrenches applied at continuously changing locations, we model the kinematic chain with a graph which dynamically adapts to the contact locations. Classical pre-order and post-order traversals of this dynamically evolving graph allow computing whole-body dynamics and estimate external wrenches. Theoretical results have been implemented in an open-source software library (iDyn) released under the iCub project. Experimental results on the iCub humanoid robot show the effectiveness of the proposed approach.

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Notes

  1. Internal wrenches are of particular interest because their projection on the joints can be used to estimate joint torques (Sciavicco and Siciliano 2005).

  2. Given a force f∈ℝ3 and a moment μ∈ℝ3, a wrench w∈ℝ6 is the vector . Force/torque sensors, which actually measure a wrench, are named according to the physics terminology, where μ is called torque. In this paper, to discriminate from the joint torque τ, we call μ moment according to the mechanical terminology.

  3. The method we will present in next sections is not strictly dependent on the notation and algorithms employed for the computations. Custom choices can also be adopted.

  4. The method can be easily generalized for revolutionary and linear joints.

  5. Within this context, a crucial role is played by the distributed tactile sensor, primarily used to compute the presence and the location of externally applied wrenches. Even if the tactile sensor would be capable of measuring also the component of the force normal to the skin surface, this information is not used in this paper where we focus on computing both the applied force and torque (i.e. the whole externally applied wrench) exploiting the embedded sensors.

  6. According to our kinematic convention an edge e i,j is fixed on the i-th link. Therefore a sensor fixed in the i-th link, will be represented by e i,s , i.e. an edge from the link to the sensor.

  7. In the classical recursive kinematic computation (Sciavicco and Siciliano 2005) there is a one-to-one correspondence between links and joints (see Fig. 1) thus resulting in a set of kinematic equations slightly different from the ones of Eq. (1). Classically, the i-th link has two joints and associated reference frames 〈i〉 and 〈i−1〉, respectively. Only 〈i〉 is attached to the i-th link while 〈i−1〉 is attached to the link i−1. The rotation between these two links is around the z-axis of 〈i−1〉 by an angle which is denoted by θ i and therefore the analogous of Eq. (1) in Sciavicco and Siciliano (2005) refer to \(\dot{\theta}_{i}\) in place of \(\dot{\theta}_{j}\) and z i−1 in place of z i . In our notation, we get rid of this common labeling for joints and links by explicitly distinguishing the link represented with the node v and the attached joints represented with the edges i, j, … and associated frames 〈i〉, 〈j〉, … whose axes are therefore z i , z j , … with associated angles θ i , θ j .

  8. With slight abuse of notation we indicated with \(r_{\star, C_{v}}\) the vector connecting the generic frame 〈⋆〉 to the one placed on the center of mass C v of the v-th link.

  9. Kinematic chains are often grounded and therefore there exists a base link with null angular kinematics, ω=[0,0,0]⊤, \(\dot{\omega}=[0, 0, 0]^{\top}\) and gravitational linear acceleration \(\ddot{p}=g\), being g the vector representing the gravity force. This situation is mathematically equivalent to an inertial sensor attached to the base link and measuring constantly ω=0, \(\dot{\omega}=0\) and \(\ddot{p}= g\).

  10. See also Remark 2.

  11. pre- and post-order refer to different classical graph visiting algorithms (Cormen et al. 2002).

  12. Practically, these equations can be obtained by defining an arbitrary ◊ connected to an arbitrary node. A post-order traversal of the graph with ◊ as root determines the equations by simply assuming that the wrench associated to the edge connected to ◊ is null.

  13. Moreover, this is not the only information that it is possible to extract from the method. Joint torques are here found as one component of the wrenches flowing through the edges. These wrenches allow having a better representation of the possible contact situation, which can be used as a virtual measurement, to perform every kind of tasks involving force detection and control.

  14. The description of the iCub kinematics can be found online (iCub Project 2011).

  15. Each vertex is named as X−k, where X={H, LA, RA, RL,LL, T} is a code for the limb (head, torso, right/left arm/leg) and k means that the corresponding link is the k-th for that specific limb.

  16. This application also highlights the importance of the inertial sensor, which allows performing the Newton-Euler computations without a fixed base frame (as it is usually assumed in its classical applications).

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Acknowledgements

The authors wish to thank Dr. Ugo Pattacini for the iKin software library, upon which iDyn was built. The authors acknowledge the support for the CHRIS, ITALK, Viactors and Roboskin Projects provided by the European Commission grant agreement number FP7-ICT-215805, FP7-ICT-214668, FP7-ICT-231554, FP7/2007-2013 No. 231500.

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Authors and Affiliations

  1. Department of Robotics Brain and Cognitive Sciences, Istituto Italiano di Tecnologia, Via Morego 30, 16163, Genova, Italy

    Matteo Fumagalli, Serena Ivaldi, Marco Randazzo, Lorenzo Natale, Giorgio Metta, Giulio Sandini & Francesco Nori

  2. Department of Control Engineering, University of Twente, Enschede, The Netherlands

    Matteo Fumagalli

  3. Institut des Systemes Intelligents et de Robotique, University Pierre et Marie Curie, Paris, France

    Serena Ivaldi

  4. Department of Informatics, Systems and Communications (DIST), University of Genova, Genova, Italy

    Giorgio Metta & Giulio Sandini

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  1. Matteo Fumagalli
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  2. Serena Ivaldi
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  4. Lorenzo Natale
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  5. Giorgio Metta
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  6. Giulio Sandini
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  7. Francesco Nori
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Correspondence to Serena Ivaldi.

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M. Fumagalli and S. Ivaldi equally contributed to this work.

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Fumagalli, M., Ivaldi, S., Randazzo, M. et al. Force feedback exploiting tactile and proximal force/torque sensing. Auton Robot 33, 381–398 (2012). https://doi.org/10.1007/s10514-012-9291-2

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