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Learning Control

  • Sylvain Calinon
  • Dongheui Lee
Reference work entry

Abstract

This chapter presents an overview of learning approaches for the acquisition of controllers and movement skills in humanoid robots. The term learning control refers to the process of acquiring a control strategy to achieve a task. While the definition is in some cases restrained to trial-and-error learning, we present here learning control in a broader perspective, with a focus on the representation of skills to be acquired, and on the different learning strategies that can contribute to the acquisition of robust and adaptive controllers for humanoids.

References

  1. 1.
    B. Akgun, A. Thomaz, Simultaneously learning actions and goals from demonstration. Auton. Robot. 40(2), 211–227 (2016)CrossRefGoogle Scholar
  2. 2.
    S. An, D. Lee, Prioritized inverse kinematics with multiple task definitions, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2015, pp. 1423–1430Google Scholar
  3. 3.
    A. Anandkumar, R. Ge, D. Hsu, S.M. Kakade, M. Telgarsky, Tensor decompositions for learning latent variable models. J. Mach. Learn. Res. 15(1), 2773–2832 (2014)Google Scholar
  4. 4.
    C.G. Atkeson, Using local models to control movement, in Advances in Neural Information Processing Systems (NIPS), vol. 2, 1989, pp. 316–323Google Scholar
  5. 5.
    C.G. Atkeson, A.W. Moore, S. Schaal, Locally weighted learning for control. Artif. Intell. Rev. 11(1–5), 75–113 (1997)Google Scholar
  6. 6.
    D.A. Bristow, M. Tharayil, A.G. Alleyne, A survey of iterative learning control. IEEE Control. Syst. 26(3), 96–114 (2006)Google Scholar
  7. 7.
    A.E. Bryson, Dynamic Optimization (Addison Wesley Longman, Menlo Park, 1999)Google Scholar
  8. 8.
    J. Buchli, F. Stulp, E. Theodorou, S. Schaal, Learning variable impedance control. Int. J. Robot. Res. 30(7), 820–833 (2011)CrossRefGoogle Scholar
  9. 9.
    S. Calinon, A tutorial on task-parameterized movement learning and retrieval. Intell. Serv. Robot. 9(1), 1–29 (2016)CrossRefGoogle Scholar
  10. 10.
    S. Calinon, A.G. Billard, Active teaching in robot programming by demonstration, in Proceedings of IEEE International Symposium on Robot and Human Interactive Communication (Ro-Man), Jeju, 2007, pp. 702–707Google Scholar
  11. 11.
    S. Calinon, F. D’halluin, E.L. Sauser, D.G. Caldwell, A.G. Billard, Learning and reproduction of gestures by imitation: an approach based on hidden Markov model and Gaussian mixture regression. IEEE Robot. Autom. Mag. 17(2), 44–54 (2010)CrossRefGoogle Scholar
  12. 12.
    S. Calinon, Z. Li, T. Alizadeh, N.G. Tsagarakis, D.G. Caldwell, Statistical dynamical systems for skills acquisition in humanoids, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Osaka, 2012, pp. 323–329Google Scholar
  13. 13.
    S. Calinon, T. Alizadeh, D.G. Caldwell, On improving the extrapolation capability of task-parameterized movement models, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, 2013a, pp. 610–616Google Scholar
  14. 14.
    S. Calinon, P. Kormushev, D.G. Caldwell, Compliant skills acquisition and multi-optima policy search with EM-based reinforcement learning. Robot. Auton. Syst. 61(4), 369–379 (2013b)CrossRefGoogle Scholar
  15. 15.
    S. Calinon, D. Bruno, D.G. Caldwell, A task-parameterized probabilistic model with minimal intervention control, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, 2014, pp. 3339–3344Google Scholar
  16. 16.
    W.S. Cleveland, Robust locally weighted regression and smoothing scatterplots. Am. Stat. Assoc. 74(368), 829–836 (1979)MathSciNetCrossRefGoogle Scholar
  17. 17.
    B. Dariush, M. Gienger, B. Jian, C. Goerick, K. Fujimura, Whole body humanoid control from human motion descriptors, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2008, pp. 2677–2684Google Scholar
  18. 18.
    M. de Lasa, A. Hertzmann, Prioritized optimization for task-space control, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St Louis, 2009, pp. 5755–5762Google Scholar
  19. 19.
    N. Dehio, R.F. Reinhart, J.J. Steil, Multiple task optimization with a mixture of controllers for motion generation, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, 2015, pp. 6416–6421Google Scholar
  20. 20.
    E. Demircan, L. Sentis, V.D. Sapio, O. Khatib, Human motion reconstruction by direct control of marker trajectories, in Advances in Robot Kinematics, 2008, pp. 263–272Google Scholar
  21. 21.
    A. Dietrich, A. Albu-Schäffer, G. Hirzinger, On continuous null space projections for torque-based, hierarchical, multi-objective manipulation, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2012, pp. 2978–2985Google Scholar
  22. 22.
    P. Evrard, E. Gribovskaya, S. Calinon, A.G. Billard, A. Kheddar, Teaching physical collaborative tasks: object-lifting case study with a humanoid, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Paris, 2009, pp. 399–404Google Scholar
  23. 23.
    D. Forte, A. Gams, J. Morimoto, A. Ude, On-line motion synthesis and adaptation using a trajectory database. Robot. Auton. Syst. 60(10), 1327–1339 (2012)CrossRefGoogle Scholar
  24. 24.
    S. Furui, Speaker-independent isolated word recognition using dynamic features of speech spectrum. IEEE Trans. Acoust. Speech Signal Process. 34(1), 52–59 (1986)CrossRefGoogle Scholar
  25. 25.
    A. Gams, B. Nemec, A. Ijspeert, A. Ude, Coupling movement primitives: interaction with the environment and bimanual tasks. IEEE Trans. Robot. 30(4), 816–830 (2014a)CrossRefGoogle Scholar
  26. 26.
    A. Gams, J. Van den Kieboom, M. Vespignani, L. Guyot, A. Ude, A. Ijspeert, Rich periodic motor skills on humanoid robots: riding the pedal racer, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2014b, pp. 2326–2332Google Scholar
  27. 27.
    M.A. Giese, A. Mukovskiy, A.-N. Park, L. Omlor, J.-J.E. Slotine, Real-time synthesis of body movements based on learned primitives, in Statistical and Geometrical Approaches to Visual Motion Analysis: International Dagstuhl Seminar (Springer, Berlin/Heidelberg, 2009), pp. 107–127Google Scholar
  28. 28.
    V. Gómez, H.J. Kappen, J. Peters, G. Neumann, Policy search for path integral control, in Proceedings of European Conference on Machine Learning and Knowledge Discovery in Databases, vol. 8724 (Springer, New York, 2014), pp. 482–497Google Scholar
  29. 29.
    M. Gonzalez-Fierro, C. Balaguer, N. Swann, T. Nanayakkara, Full-body postural control of a humanoid robot with both imitation learning and skill innovation. Int. J. Humanoid Rob. 11(2), 1–34 (2014)CrossRefGoogle Scholar
  30. 30.
    S. Hak, N. Mansard, O. Stasse, J.P. Laumond, Reverse control for humanoid robot task recognition. IEEE Trans. Syst. Man Cybern. B Cybern. 42(6), 1524–1537 (2012)CrossRefGoogle Scholar
  31. 31.
    M. Hersch, F. Guenter, S. Calinon, A.G. Billard, Dynamical system modulation for robot learning via kinesthetic demonstrations. IEEE Trans. Robot. 24(6), 1463–1467 (2008)CrossRefGoogle Scholar
  32. 32.
    M. Howard, S. Klanke, M. Gienger, C. Goerick, S. Vijayakumar, Behaviour generation in humanoids by learning potential-based policies from constrained motion. Appl. Bionics Biomech. 5(4), 195–211 (2008)CrossRefGoogle Scholar
  33. 33.
    K. Hu, D. Lee, Prediction-based synchronized human walking motion imitation by a humanoid robot. Automatisierungstechnik 60(11), 705–714 (2012)Google Scholar
  34. 34.
    K. Hu, C. Ott, D. Lee, Online human walking imitation in task and joint space based on quadratic programming, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2014), pp. 3458–3464Google Scholar
  35. 35.
    K. Hu, C. Ott, D. Lee, Online iterative learning control of zero-moment point for biped walking stabilization, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2015, pp. 5127–5133Google Scholar
  36. 36.
    J. Hwangbo, C. Gehring, H. Sommer, R. Siegwart, J. Buchli, ROCK*: efficient black-box optimization for policy learning, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), 2014, pp. 535–540Google Scholar
  37. 37.
    A. Ijspeert, J. Nakanishi, P. Pastor, H. Hoffmann, S. Schaal, Dynamical movement primitives: learning attractor models for motor behaviors. Neural Comput. 25(2), 328–373 (2013)MathSciNetCrossRefGoogle Scholar
  38. 38.
    A.J. Ijspeert, J. Nakanishi, S. Schaal, Trajectory formation for imitation with nonlinear dynamical systems, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2001, pp. 752–757Google Scholar
  39. 39.
    T. Inamura, N. Kojo, M. Inaba, Situation recognition and behavior induction based on geometric symbol representation of multimodal sensorimotor patterns, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2006, pp. 5147–5152Google Scholar
  40. 40.
    S. Kern, S.D. Mueller, N. Hansen, D. Bueche, J. Ocenasek, P. Koumoutsakos, Learning probability distributions in continuous evolutionary algorithms – a comparative review. Nat. Comput. 3(1), 77–112 (2004)MathSciNetCrossRefGoogle Scholar
  41. 41.
    S. M. Khansari-Zadeh, A. Billard, Learning stable non-linear dynamical systems with Gaussian mixture models. IEEE Trans. Robot. 27(5), 943–957 (2011)CrossRefGoogle Scholar
  42. 42.
    S. M. Khansari-Zadeh, A. Billard, Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions. Robot. Auton. Syst. 62(6), 752–765 (2014)Google Scholar
  43. 43.
    S. Kim, C. Kim, J.H. Park, Human-like arm motion generation for humanoid robots using motion capture database, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2006, pp. 3486–3491Google Scholar
  44. 44.
    S. Kim, S. Hong, D. Kim, A walking motion imitation framework of a humanoid robot by human walking recognition from IMU motion data, in 9th IEEE-RAS International Conference on Humanoid Robots, 2010, pp. 343–348Google Scholar
  45. 45.
    S. Kim, A. Shukla, A. Billard, Catching objects in flight. IEEE Trans. Robot. 30(5), 1049–1065 (2014)CrossRefGoogle Scholar
  46. 46.
    J. Kober, J. Peters, Imitation and reinforcement learning: practical algorithms for motor primitives in robotics. IEEE Robot. Autom. Mag. 17(2), 55–62 (2010)CrossRefGoogle Scholar
  47. 47.
    J. Koenemann, F. Burget, M. Bennewitz, Real-time imitation of human whole-body motions by humanoids, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2014, pp. 2806–2812Google Scholar
  48. 48.
    P. Kormushev, S. Calinon, R. Saegusa, G. Metta, Learning the skill of archery by a humanoid robot iCub, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Nashville, 2010, pp. 417–423Google Scholar
  49. 49.
    P. Kormushev, D.N. Nenchev, S. Calinon, D.G. Caldwell, Upper-body kinesthetic teaching of a free-standing humanoid robot, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Shanghai, 2011a, pp. 3970–3975Google Scholar
  50. 50.
    P. Kormushev, B. Ugurlu, S. Calinon, N. Tsagarakis, D.G. Caldwell, Bipedal walking energy minimization by reinforcement learning with evolving policy parameterization, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, 2011b, pp. 318–324Google Scholar
  51. 51.
    D.P. Kroese, S. Porotsky, R.Y. Rubinstein, The cross-entropy method for continuous multi-extremal optimization. Methodol. Comput. Appl. Probab. 8, 383–407 (2006)MathSciNetCrossRefGoogle Scholar
  52. 52.
    D. Kulic, C. Ott, D. Lee, J. Ishikawa, Y. Nakamura, Incremental learning of full body motion primitives and their sequencing through human motion observation. Int. J. Robot. Res. 31(3), 330–345 (2012)CrossRefGoogle Scholar
  53. 53.
    J. Kwon, F.C. Park, Natural movement generation using hidden Markov models and principal components. IEEE Trans. Syst. Man Cybern. B 38(5), 1184–1194 (2008)Google Scholar
  54. 54.
    D. Lee, C. Ott, Incremental motion primitive learning by physical coaching using impedance control, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2010, pp. 4133–4140Google Scholar
  55. 55.
    D. Lee, C. Ott, Incremental kinesthetic teaching of motion primitives using the motion refinement tube. Auton. Robot. 31(2), 115–131 (2011)CrossRefGoogle Scholar
  56. 56.
    D. Lee, C. Ott, Y. Nakamura, Mimetic communication model with compliant physical contact in human-humanoid interaction. Int. J. Robot. Res. 29(13), 1684–1704 (2010)Google Scholar
  57. 57.
    S.H. Lee, I.H. Suh, S. Calinon, R. Johansson, Learning basis skills by autonomous segmentation of humanoid motion trajectories, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Osaka, 2012, pp. 112–119Google Scholar
  58. 58.
    S. Levine, C. Finn, T. Darrell, P. Abbeel, End-to-end training of deep visuomotor policies. J. Mach. Learn. Res. 17(39), 1–40 (2016)Google Scholar
  59. 59.
    H.-C. Lin, M. Howard, S. Vijayakumar, Learning null space projections, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2015, pp. 2613–2619Google Scholar
  60. 60.
    M. Liu, Y. Tan, V. Padois, Generalized hierarchical control. Auton. Robot. 40(1), 17–31 (2016)CrossRefGoogle Scholar
  61. 61.
    R. Lober, V. Padois, O. Sigaud, Multiple task optimization using dynamical movement primitives for whole-body reactive control, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Madrid, 2014, pp. 193–198Google Scholar
  62. 62.
    R. Lober, V. Padois, O. Sigaud, Variance modulated task prioritization in whole-body control, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, 2015, pp. 3944–3949Google Scholar
  63. 63.
    R.W. Longman, K.D. Mombaur, Investigating the use of iterative learning control and repetitive control to implement periodic gaits, in Fast Motions in Biomechanics and Robotics (Springer, 2006), pp. 189–218Google Scholar
  64. 64.
    G.J. Maeda, G. Neumann, M. Ewerton, R. Lioutikov, O. Kroemer, J. Peters, Probabilistic movement primitives for coordination of multiple human-robot collaborative tasks. Auton. Robot. 41(3), 593–612 (2017)CrossRefGoogle Scholar
  65. 65.
    J.R. Medina, D. Lee, S. Hirche, Risk-sensitive optimal feedback control for haptic assistance, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2012, pp. 1025–1031Google Scholar
  66. 66.
    V. Modugno, G. Neumann, E. Rueckert, G. Oriolo, J. Peters, S. Ivaldi, Learning soft task priorities for control of redundant robots, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Stockholm, 2016Google Scholar
  67. 67.
    F.L. Moro, M. Gienger, A. Goswami, N.G. Tsagarakis, An attractor-based whole-body motion control (WBMC) system for humanoid robots, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Atlanta, 2013, pp. 42–49Google Scholar
  68. 68.
    M. Mühlig, M. Gienger, J. Steil, Interactive imitation learning of object movement skills. Auton. Robot. 32(2), 97–114 (2012)CrossRefGoogle Scholar
  69. 69.
    J. Nakanishi, J. Morimoto, G. Endo, G. Cheng, S. Schaal, M. Kawato, Learning from demonstration and adaptation of biped locomotion. Robot. Auton. Syst. 47(2–3), 79–91 (2004)CrossRefGoogle Scholar
  70. 70.
    K. Neumann, J.J. Steil, Learning robot motions with stable dynamical systems under diffeomorphic transformations. Robot. Auton. Syst. 70, 1–15 (2015)CrossRefGoogle Scholar
  71. 71.
    C. Ott, D. Lee, Y. Nakamura, Motion capture based human motion recognition and imitation by direct marker control, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), 2008, pp. 399–405Google Scholar
  72. 72.
    C. Ott, B. Henze, D. Lee, Kinesthetic teaching of humanoid motion based on whole-body compliance control with interaction-aware balancing, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2013, pp. 4615–4621Google Scholar
  73. 73.
    A. Paraschos, C. Daniel, J. Peters, G. Neumann, Probabilistic movement primitives, in Advances in Neural Information Processing Systems (NIPS) (Curran Associates, Inc. 2013), pp. 2616–2624Google Scholar
  74. 74.
    N. Perrin, P. Schlehuber-Caissier, Fast diffeomorphic matching to learn globally asymptotically stable nonlinear dynamical systems. Syst. Control Lett. 96, 51–59 (2016)MathSciNetCrossRefGoogle Scholar
  75. 75.
    R.A. Peters, C. Campbell, W. Bluethmann, E. Huber, Robonaut task learning through teleoperation, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2003, pp. 2806–2811Google Scholar
  76. 76.
    N. Pollard, J. Hodgins, M. Riley, C. Atkeson, Adapting human motion for the control of a humanoid robot, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2002, pp. 1390–1397Google Scholar
  77. 77.
    L.R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77(2), 257–285 (1989)CrossRefGoogle Scholar
  78. 78.
    S. Roberts, M. Osborne, M. Ebden, S. Reece, N. Gibson, S. Aigrain, Gaussian processes for time-series modelling. Phil. Trans. R. Soc. A 371(1984), 1–25 (2012)MathSciNetCrossRefGoogle Scholar
  79. 79.
    L. Rozo, J. Silvério, S. Calinon, D.G. Caldwell, Learning controllers for reactive and proactive behaviors in human-robot collaboration. Front. Robot. AI 3(30), 1–11 (2016)Google Scholar
  80. 80.
    E. Rueckert, J. Mundo, A. Paraschos, J. Peters, G. Neumann, Extracting low-dimensional control variables for movement primitives, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Seattle, 2015, pp. 1511–1518Google Scholar
  81. 81.
    J. Salini, V. Padois, P. Bidaud, Synthesis of complex humanoid whole-body behavior: a focus on sequencing and tasks transitions, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2011, pp. 1283–1290Google Scholar
  82. 82.
    E.L. Sauser, B.D. Argall, G. Metta, A.G. Billard, Iterative learning of grasp adaptation through human corrections. Robot. Auton. Syst. 60(1), 55–71 (2012)CrossRefGoogle Scholar
  83. 83.
    M. Saveriano, S. An, D. Lee, Incremental kinesthetic teaching of end-effector and null-space motion primitives, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2015, pp. 3570–3575Google Scholar
  84. 84.
    S. Schaal, C.G. Atkeson, Constructive incremental learning from only local information. Neural Comput. 10(8), 2047–2084 (1998)CrossRefGoogle Scholar
  85. 85.
    J. Schreiter, P. Englert, D. Nguyen-Tuong, M. Toussaint, Sparse Gaussian process regression for compliant, real-time robot control, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2015, pp. 2586–2591Google Scholar
  86. 86.
    J. Silvério, L. Rozo, S. Calinon, D.G. Caldwell, Learning bimanual end-effector poses from demonstrations using task-parameterized dynamical systems, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, 2015, pp. 464–470Google Scholar
  87. 87.
    F. Stulp, O. Sigaud, Path integral policy improvement with covariance matrix adaptation, in Proceedings of International Conference on Machine Learning (ICML), 2012, pp. 1–8Google Scholar
  88. 88.
    F. Stulp, O. Sigaud, Robot skill learning: from reinforcement learning to evolution strategies. Paladyn J. Behav. Robot. 4(1), 49–61 (2013)Google Scholar
  89. 89.
    F. Stulp, O. Sigaud, Many regression algorithms, one unified model – a review. Neural Netw. 69, 60–79 (2015)CrossRefGoogle Scholar
  90. 90.
    F. Stulp, J. Buchli, E. Theodorou, S. Schaal, Reinforcement learning of full-body humanoid motor skills, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), Nashville, 2010, pp. 405–410Google Scholar
  91. 91.
    N. Sugimoto, J. Morimoto, Trajectory-model-based reinforcement learning: application to bimanual humanoid motor learning with a closed-chain constraint, in Proceedings of IEEE International Conference on Humanoid Robots (Humanoids), 2013, pp. 429–434Google Scholar
  92. 92.
    K. Sugiura, N. Iwahashi, H. Kashioka, S. Nakamura, Learning, generation, and recognition of motions by reference-point-dependent probabilistic models. Adv. Robot. 25(6–7), 825–848 (2011)CrossRefGoogle Scholar
  93. 93.
    W. Takano, Y. Nakamura, Real-time unsupervised segmentation of human whole-body motion and its application to humanoid robot acquisition of motion symbols. Robot. Auton. Syst. 75(Part B), 260–272 (2016)CrossRefGoogle Scholar
  94. 94.
    A.K. Tanwani, S. Calinon, Learning robot manipulation tasks with task-parameterized semi-tied hidden semi-Markov model. IEEE Robot. Autom. Lett. (RA-L) 1(1), 235–242 (2016)CrossRefGoogle Scholar
  95. 95.
    J. Ting, M. Kalakrishnan, S. Vijayakumar, S. Schaal, Bayesian kernel shaping for learning control, in Advances in Neural Information Processing Systems (NIPS), 2008, pp. 1673–1680Google Scholar
  96. 96.
    E. Todorov, M.I. Jordan, Optimal feedback control as a theory of motor coordination. Nat. Neurosci. 5, 1226–1235 (2002)CrossRefGoogle Scholar
  97. 97.
    A. Ude, A. Gams, T. Asfour, J. Morimoto, Task-specific generalization of discrete and periodic dynamic movement primitives. IEEE Trans. Robot. 26(5), 800–815 (2010)CrossRefGoogle Scholar
  98. 98.
    S. Vijayakumar, A. D’souza, S. Schaal, Incremental online learning in high dimensions. Neural Comput. 17(12), 2602–2634 (2005)MathSciNetCrossRefGoogle Scholar
  99. 99.
    A. Werner, D. Trautmann, D. Lee, R. Lampariello, Generalization of optimal motion trajectories for bipedal walking, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015, pp. 1571–1577Google Scholar
  100. 100.
    A. Whiten, N. McGuigan, S. Marshall-Pescini, L.M. Hopper, Emulation, imitation, over-imitation and the scope of culture for child and chimpanzee. Phil. Trans. R. Soc. B 364(1528), 2417–2428 (2009)CrossRefGoogle Scholar
  101. 101.
    C.K.I. Williams, C.E. Rasmussen, Gaussian processes for regression, in Advances in Neural Information Processing Systems (NIPS), 1996, pp. 514–520Google Scholar
  102. 102.
    A.G. Wilson, Z. Ghahramani, Generalised Wishart processes, in Annual Conference on Uncertainty in Artificial Intelligence (Barcelona, 2011)Google Scholar
  103. 103.
    S. Wrede, C. Emmerich, R. Ricarda, A. Nordmann, A. Swadzba, J.J. Steil, A user study on kinesthetic teaching of redundant robots in task and configuration space. J. Hum.-Robot Interact. 2(1), 56–81 (2013)CrossRefGoogle Scholar
  104. 104.
    M.J.A. Zeestraten, S. Calinon, D.G. Caldwell, Variable duration movement encoding with minimal intervention control, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Stockholm, 2016, pp. 497–503Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Idiap Research InstituteMartignySwitzerland
  2. 2.Department of Electrical and Computer EngineeringTechnical University of MunichMünchenGermany
  3. 3.Institute of Robotics and MechatronicsGerman Aerospace CenterWeβlingGermany

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