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Model Predictive Motion Control based on Generalized Dynamical Movement Primitives

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Abstract

In this work, experimental data is used to estimate the free parameters of dynamical systems intended to model motion profiles for a robotic system. The corresponding regression problem is formed as a constrained non-linear least squares problem. In our method, motions are generated via embedded optimization by combining dynamical movement primitives in a locally optimal way at each time step. Based on this concept, we introduce a model predictive control scheme which allows generalization over multiple encoded behaviors depending on the current position in the state space, while leveraging the ability to explicitly account for state constraints to the fulfillment of additional tasks such as obstacle avoidance. We present a numerical evaluation of our approach and a preliminary verification by generating grasping motions for the anthropomorphic Shadow Robot hand/arm platform.

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References

  1. Hwang, J.H., Arkin, R., Kwon, D.S.: Mobile robots at your fingertip: Bezier curve on-line trajectory generation for supervisory control. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 2, 2003, pp. 1444–1449

  2. Aleotti, J., Caselli, S.: Robust trajectory learning and approximation for robot programming by demonstration. Robot. Auton. Syst. 54(5), 409–413 (2006)

    Article  Google Scholar 

  3. Schittkowski, K.: Numerical Data Fitting in Dynamical Systems. Kluwer Academic Publishers (2002)

  4. Billard, A., Calinon, S., Dillmann, R., Schaal, S.: Robot programming by demonstration. In: Siciliano, B., Khatib, O. (eds.) Handbook of Robotics, pp 1371–1394. Springer (2008)

  5. Flash, T., Hogans, N.: The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5, 1688–1703 (1985)

    Google Scholar 

  6. Weitschat, R., Haddadin, S., Huber, F., Albu-Schauffer, A.: Dynamic optimality in real-time: a learning framework for near-optimal robot motions. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5636–5643 (2013)

  7. Khansari-Zadeh, S.M., Billard, A.: A dynamical system approach to realtime obstacle avoidance. Auton. Robot. 32(4), 433–454 (2012)

    Article  Google Scholar 

  8. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. IJRR 5(1), 90–98 (1986)

    MathSciNet  Google Scholar 

  9. Feix, T., Pawlik, R., Schmiedmayer, H., Romero, J., Kragic, D.: A comprehensive grasp taxonomy. In: RSS: Workshop on Understanding the Human Hand for Advancing Robotic Manipulation (2009)

  10. Shadow Robot Company, The shadow dextrous hand. [Online]. Available: http://www.shadowrobot.com/hand/

  11. Bernardino, A., Henriques, M., Hendrich, N., Zhang, J.: Precision grasp synergies for dexterous robotic hands. In: Proceedings of the IEEE International Conference on Robotics and Biomimetics, pp. 62–67 (2013)

  12. Ijspeert, A.J., Nakanishi, J., Schaal, S.: Learning attractor landscapes for learning motor primitives. In: Advances in Neural Information Processing Systems. MIT Press (2003)

  13. Ude, A., Gams, A., Asfour, T., Morimoto, J.: Task-specific generalization of discrete and periodic dynamic movement primitives. IEEE Trans. Robot. 26(5), 800–815 (2010)

    Article  Google Scholar 

  14. Khansari-Zadeh, S., Billard, A.: Learning stable nonlinear dynamical systems with gaussian mixture models. IEEE Trans. Robot. 27(5), 943–957 (2011)

    Article  Google Scholar 

  15. Forte, D., Gams, A., Morimoto, J., Ude, A.: On-line motion synthesis and adaptation using a trajectory database. Robot. Auton. Syst. 60(10), 1327–1339 (2012)

    Article  Google Scholar 

  16. Krug, R., Dimitrov, D.: Representing movement primitives as implicit dynamical systems learned from multiple demonstrations. In: Proceedings of the International Conference on Advanced Robotics, pp. 1–8 (2013)

  17. Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S.: Dynamical movement primitives: learning attractor models for motor behaviors. Neural Comput. 25, 328–373 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kormushev, P., Calinon, S., Caldwell, D.: Robot motor skill coordination with em-based reinforcement learning. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3232–3237 (2010)

  19. Stulp, F., Schaal, S.: Hierarchical reinforcement learning with movement primitives. In: 11th IEEE-RAS International Conference on Humanoid Robots, 231–238 (2011)

  20. Stulp, F., Theodorou, E., Buchli, J., Schaal, S.: Learning to grasp under uncertainty. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 5703–5708 (2011)

  21. Kober, J, Peters, J.: Policy search for motor primitives in robotics. Mach. Learn. 84(1-2), 171–203 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  22. Nemec, B., Vuga, R., Ude, A.: Efficient sensorimotor learning from multiple demonstrations. Adv. Robot. 27(13), 1023–1031 (2013)

    Article  Google Scholar 

  23. Pastor, P., Hoffmann, H., Asfour, T., Schaal, S.: Learning and generalization of motor skills by learning from demonstration. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 763–768 (2009)

  24. Matsubara, T., Hyon, S., Morimoto, J.: Learning stylistic dynamic movement primitives from multiple demonstrations. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 1277–1283 (2010)

  25. Calinon, S., Li, Z., Alizadeh, T., Tsagarakis, N., Caldwell, D.: Statistical dynamical systems for skills acquisition in humanoids. In: IEEE-RAS International Conference on Humanoid Robots, 323–329 (2012)

  26. Muelling, K., Kober, J., Kroemer, O., Peters, J.: Learning to select and generalize striking movements in robot table tennis. IIJR 3, 263–279 (2013)

    Google Scholar 

  27. Gribovskaya, E., Khansari-Zadeh, S.M., Billard, A.: Learning non-linear multivariate dynamics of motion in robotic manipulators. IJRR 30(1), 80–117 (2011)

    Google Scholar 

  28. Hoffmann, H., Pastor, P., Park, D.-H., Schaal, S.: Biologically-inspired dynamical systems for movement generation: automatic real-time goal adaptation and obstacle avoidance. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2587–2592 (2009)

  29. Gams, A., Nemec, B., Zlajpah, L., Wachter, M., Ijspeert, A., Asfour, T., Ude, A.: Modulation of motor primitives using force feedback: interaction with the environment and bimanual tasks. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 5629–5635 (2013)

  30. Saveriano, M., Lee, D.: Point cloud based dynamical system modulation for reactive avoidance of convex and concave obstacles. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5380–5387 (2013)

  31. Raković, S.V., Mayne, D.Q.: Robust model predictive control for obstacle avoidance: discrete time case. In: Assessment and Future Directions of Nonlinear Model Predictive Control, pp 617–627. Springer (2007)

  32. Shiller, Z., Sharma, S., Stern, I., Stern, A.: Online obstacle avoidance at high speeds. IJRR 32(9–10), 1030–1047 (2013)

    Google Scholar 

  33. Pecora, F., Cirillo, M., Dimitrov, D.: On mission-dependent coordination of multiple vehicles under spatial and temporal constraints. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5262– 5269 (2012)

  34. Anderson, S., Karumanchi, S., Iagnemma, K.: Constraint-based planning and control for safe, semi-autonomous operation of vehicles. In: IEEE Intelligent Vehicles Symposium, pp. 383–388 (2012)

  35. Wangmanaopituk, H.V.S., Kongprawechnon, W.: Collaborative nonlinear model-predictive motion planning and control of mobile transport robots for a highly flexible production system. Science Asia (2010)

  36. Da Silva, M., Abe, Y., Popović, J.: Simulation of human motion data using short-horizon model-predictive control. Comput. Graph. Forum. 27(2), 371–380 (2008)

    Article  Google Scholar 

  37. Khalil, H.: Nonlinear Systems. Prentice Hall (2002)

  38. Rückert, E., d’Avella, A.: Learned parametrized dynamic movement primitives with shared synergies for controlling robotic and musculoskeletal systems. Front. comput. Neurosci. 7 (2013)

  39. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.: Constrained model predictive control: stability and optimality. Automatica 36(6), 789–814 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  40. Houska, B., Ferreau, H., Diehl, M.: ACADO Toolkit – an open source framework for automatic control and dynamic optimization. Opt. Control Appl. Methods 32(3), 298–312 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Krug, R., Dimitrov, D. Model Predictive Motion Control based on Generalized Dynamical Movement Primitives. J Intell Robot Syst 77, 17–35 (2015). https://doi.org/10.1007/s10846-014-0100-3

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  • DOI: https://doi.org/10.1007/s10846-014-0100-3

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