In the context of robotic control, synergies can form elementary units of behavior. By specifying taskdependent coordination behaviors at a low control level, one can achieve task-specific disturbance rejection. In this work we present an approach to learn the parameters of such lowlevel controllers by demonstration. We identify a synergy by extracting covariance information from demonstration data. The extracted synergy is used to derive a time-invariant state feedback controller through optimal control. To cope with the non-Euclidean nature of robot poses, we utilize Riemannian geometry, where both estimation of the covariance and the associated controller take into account the geometry of the pose manifold. We demonstrate the efficacy of the approach experimentally in a bimanual manipulation task.

 

In imitation learning, multivariate Gaussians are widely used to encode robot behaviors. Such approaches do not provide the ability to properly represent end-effector orientation, as the distance metric in the space of orientations is not Euclidean.

In this work we present an extension of common imitation learning techniques to Riemannian manifolds. This generalization enables the encoding of joint distributions that include the robot pose. We show that Gaussian conditioning, Gaussian product and nonlinear regression can be achieved with this representation. The proposed approach is illustrated with examples on a 2-dimensional sphere, with an example of regression between two robot end-effector poses, as well as an extension of Task-Parameterized Gaussian Mixture Model (TP-GMM) and Gaussian Mixture Regression (GMR) to Riemannian manifolds. 

The work is accompanied with source code that can be downloaded here.

 

  1. M J A Zeestraten, I Havoutis, S Calinon and D G Caldwell. Learning Task-Space Synergy using Riemannian Geometry. In Proc. IEEE/RSJ Intl Conf. on Intelligent Robots and Systems (IROS). September 2017, . PDF BibTeX

    @inproceedings{Zeestraten17IROS,
    	author = "Zeestraten, M. J. A. and Havoutis, I. and Calinon, S. and Caldwell, D. G.",
    	title = "Learning Task-Space Synergy using Riemannian Geometry",
    	booktitle = "Proc. {IEEE/RSJ} Intl Conf. on Intelligent Robots and Systems ({IROS})",
    	year = 2017,
    	month = "September",
    	address = "Vancouver, Canada",
    	pages = "",
    	pdf = "images/publications/Zeestraten-IROS2017.pdf"
    }
    
  2. M J A Zeestraten, I Havoutis, J Silvério, S Calinon and D G Caldwell. An Approach for Imitation Learning on Riemannian Manifolds. IEEE Robotics and Automation Letters (RA-L) 2(3):1240–1247, June 2017. PDF BibTeX

    @article{Zeestraten17RAL,
    	title = "An Approach for Imitation Learning on {R}iemannian Manifolds",
    	author = "Zeestraten, M.J.A. and Havoutis, I. and Silv\'erio, J. and Calinon, S. and Caldwell, D. G.",
    	journal = "{IEEE} Robotics and Automation Letters ({RA-L})",
    	year = 2017,
    	volume = 2,
    	number = 3,
    	pages = "1240--1247",
    	month = "June",
    	pdf = "images/publications/Zeestraten-RAL2017.pdf"
    }
    
  3. M J A Zeestraten, A Pereira, M Althoff and S Calinon. Online motion synthesis with minimal intervention control and formal safety guarantees. In Proc. IEEE Intl Conf. on Systems, Man, and Cybernetics. October 2016, . PDF BibTeX

    @inproceedings{Zeestraten16SMC,
    	author = "Zeestraten, M. J. A. and Pereira, A. and Althoff, M. and Calinon, S.",
    	title = "Online motion synthesis with minimal intervention control and formal safety guarantees",
    	booktitle = "Proc. {IEEE} Intl Conf. on Systems, Man, and Cybernetics",
    	year = 2016,
    	month = "October",
    	address = "Budapest, Hungary",
    	pdf = "images/publications/Zeestraten-SMC2016.pdf",
    	pages = ""
    }
    
  4. M Zeestraten, S Calinon and D G Caldwell. Variable Duration Movement Encoding with Minimal Intervention Control. May 2016, 497–503. PDF BibTeX

    @inproceedings{Zeestraten16ICRA,
    	author = "Zeestraten, M. and Calinon, S. and Caldwell, D. G.",
    	title = "Variable Duration Movement Encoding with Minimal Intervention Control",
    	year = 2016,
    	month = "May",
    	pdf = "images/publications/Zeestraten-ICRA2016.pdf",
    	address = "Stockholm, Sweden",
    	pages = "497--503"
    }