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A Computational Framework for Environment-Aware Robotic Manipulation Planning

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Robotics Research

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 3))

Abstract

In this paper, we present a computational framework for direct trajectory optimization of general manipulation systems with unspecified contact sequences, exploiting environmental constraints as a key tool to accomplish a task. Two approaches are presented to describe the dynamics of systems with contacts, which are based on a penalty formulation and on a velocity-based time-stepping scheme, respectively. In both cases, object and environment contact forces are included among the free optimization variables, and they are rendered consistent via suitably devised sets of complementarity conditions. To maximize computational efficiency, we exploit sparsity patterns in the linear algebra expressions generated during the solution of the optimization problem and leverage Algorithmic Differentiation to calculate derivatives. The benefits of the proposed methods are evaluated in three simulated planar manipulation tasks, where essential interactions with environmental constraints are automatically synthesized and opportunistically exploited.

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Notes

  1. 1.

    For simplicity of description, we assume that the number of friction directions d is the same at each contact, although this is not necessary.

  2. 2.

    The positive/negative sign must be chosen if, considering equilibrium of body \(\ell \), the unit normal vector \(n_i\) is facing into/away from body \(\ell \).

  3. 3.

    In situations where the relative contact velocity and the friction vector are both zero, \(\gamma \ge 0\) can be arbitrary and has no physical meaning.

  4. 4.

    Replacing the bracketed term in (9c) with \([\mu \lambda _N - E^\top \lambda _T]\), as commonly performed in literature [48], would call for unrealistically strict and physically unmotivated conditions to ensure adhesive friction.

  5. 5.

    Embedding contact dynamics into the numerical optimization problem as nonlinear constraints, where many other implicit constraints are already present, does not justify explicit or semi-implicit discretization schemes, which are, instead, legitimate when building fast simulators [21, Sect. 5].

  6. 6.

    With a slight abuse of notation, we still use n and m to denote the dimension of \(x\) and \(c(x)\), respectively, and \(f(x)\) to denote \(f(\varvec{v})\).

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Acknowledgements

This work is supported by the grant no. 600918 “PACMAN” - Probabilistic and Compositional Representations of Object for Robotic Manipulation - within the FP7-ICT-2011-9 program “Cognitive Systems”. European Research Council and under the ERC Advanced Grant no. 291166 SoftHands (A Theory of Soft Synergies for a New Generation of Artificial Hands).

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Authors and Affiliations

  1. Department of Civil and Industrial Engineering, University of Pisa, Pisa, Italy

    Marco Gabiccini, Alessio Artoni & Gabriele Pannocchia

  2. Department of Electrical Engineering, KU Leuven, Leuven, Belgium

    Joris Gillis

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  1. Marco Gabiccini
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  2. Alessio Artoni
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  3. Gabriele Pannocchia
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  4. Joris Gillis
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Correspondence to Marco Gabiccini .

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Editors and Affiliations

  1. Istituto Italiano di Tecnologia, Genova, Italy, University of Pisa, Pisa, Italy , Pisa, Italy

    Antonio Bicchi

  2. Inst. für Informatik, Albert-Ludwigs-Universität Freiburg Inst. für Informatik, Freiburg, Germany

    Wolfram Burgard

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Gabiccini, M., Artoni, A., Pannocchia, G., Gillis, J. (2018). A Computational Framework for Environment-Aware Robotic Manipulation Planning. In: Bicchi, A., Burgard, W. (eds) Robotics Research. Springer Proceedings in Advanced Robotics, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-60916-4_21

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