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 Controllers from Demonstration. In Proc. IEEE/RSJ Intl Conf. on Intelligent Robots and Systems (IROS). September 2017, . BibTeX

    @inproceedings{Zeestraten17IROS,
    	author = "Zeestraten, M. J. A. and Havoutis, I. and Calinon, S. and Caldwell, D. G.",
    	title = "Learning Task-Space Synergy Controllers from Demonstration",
    	booktitle = "Proc. {IEEE/RSJ} Intl Conf. on Intelligent Robots and Systems ({IROS})",
    	year = 2017,
    	month = "September",
    	address = "Vancouver, Canada",
    	pages = ""
    }
    
  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 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"
    }
    
  4. 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. 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",:w address="Budapest, Hungary},
    	pdf = "images/publications/Zeestraten-SMC2016.pdf",
    	pages = ""
    }