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Improved Online Adjustment of Step Timing and Location for Legged Locomotion

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Abstract

Online step adaptation is critical for legged locomotion to resist disturbances, while current approaches mainly focus on step location regardless of step timing. This paper proposes an online adaptation algorithm that deals with both step timing and step location. A model predictive control framework is developed based on centroidal dynamics to predict robot state trajectories, which are utilized to simultaneously optimize step timing and location with full considerations on capturability, feasibility and reachability. Then, a swing foot trajectory generation method is presented to accommodate mutiple constraints on kinematics and actuators. Moreover, a heuristic compensation is enhanced to the step location for quadruped trotting locomotion, increasing the anti-disturbance ability of legged locomotion. Various push-recovery simulation and experiment on an 18 degree-of-freedom legged robot are implemented to verify the proposed algorithm.

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References

  1. Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: BigDog, the rough-terrain quadruped robot. IFAC Proc. Vol. 41(2), 10822–10825 (2008)

    Article  Google Scholar 

  2. Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.: Learning, planning, and control for quadruped locomotion over challenging terrain. Int. J. Robot. Res. 30(2), 236–258 (2011)

    Article  Google Scholar 

  3. Gehring, C, Coros, S., Hutter, M., Bloesch, M., Hoepflinger, M., Siegwart, R.: Control of dynamic gaits for a quadrupedal robot. In: IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, pp 3287–3292 (2013)

  4. Hutter, M., Gehring, C., Bloesch, M., Hoepflinger, M.H., Remy, C.D., Siegwart, R.: StarlETH: a compliant quadrupedal robot for fast, efficient, and versatile locomotion. In: Adaptive Mobile Robotics, pp 483–490 (2012)

  5. Barasuol, V., Buchli, J., Semini, C., Frigerio, M., De Pieri, E.R., Caldwell, D.G.: A reactive controller framework for quadrupedal locomotion on challenging terrain. In: IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, pp 2554–2561 (2013)

  6. Semini, C., Tsagarakis, N.G., Guglielmino, E., Focchi, M., Cannella, F., Caldwell, D.G.: Design of HyQ—a hydraulically and electrically actuated quadruped robot. Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng. 225(6), 831–849 (2011)

    Article  Google Scholar 

  7. Havoutis, I, Ortiz, J., Bazeille, S., Barasuol, V., Semini, C., Caldwell, D.G.: Onboard perception-based trotting and crawling with the Hydraulic Quadruped Robot (HyQ). In: IEEE/RSJ International Conference on Intelligent Robot and Systems (IROS), Tokyo, pp 6052–6057 (2013)

  8. Winkler, AW, Havoutis, I., Bazeille, S., Ortiz, J., Focchi, M., Dillmann, R., Caldwell, D., Semini, C.: Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots. In: IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, pp 6476–6482 (2014)

  9. Winkler, AW, Mastalli, C., Havoutis, I., Focchi, M., Caldwell, D.G., Semini, C.: Planning and execution of dynamic whole-body locomotion for a hydraulic quadruped on challenging terrain. In: IEEE International Conference on Robotics and Automation (ICRA), Seattle, pp 5148–5154 (2015)

  10. Mastalli, C, Havoutis, I., Winkler, A.W., Caldwell, D.G., Semini, C.: On-line and on-board planning and perception for quadrupedal locomotion. In: IEEE International Conference on Technologies for Practical Robot Applications (TePRA), Woburn, pp 1–7 (2015)

  11. Mastalli, C, Focchi, M., Havoutis, I., Radulescu, A., Calinon, S., Buchli, J., Caldwell, D.G., Semini, C.: Trajectory and foothold optimization using low-dimensional models for rough terrain locomotion. In: IEEE International Conference on Robotics and Automation (ICRA), Singapore, pp 1096–1103 (2017)

  12. Fankhauser, P., Bjelonic, M., Bellicoso, C.D., Miki, T., Hutter, M.: Robust rough-terrain locomotion with a quadrupedal robot. In: IEEE International Conference on Robotics and Automation (ICRA), Brisbane, pp 1–8 (2018)

  13. Hutter, M., Gehring, C., Jud, D., Lauber, A., Bellicoso, C.D., Tsounis, V., Hwangbo, J., Bodie, K., Fankhauser, P., Bloesch, M.: ANYmal—a highly mobile and dynamic quadrupedal robot. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, pp 38–44 (2016)

  14. Di Carlo, J., Wensing, P.M., Katz, B., Bledt, G., Kim, S.: Dynamic locomotion in the MIT Cheetah 3 through convex model-predictive control. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, pp 1–9 (2018)

  15. Bledt, G., Powell, M.J., Katz, B., Di Carlo, J., Wensing, P.M., Kim, S.: MIT Cheetah 3: design and control of a robust, dynamic quadruped robot. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, pp 2245–2252 (2018)

  16. Takenaka, T., Matsumoto, T., Yoshiike, T.: Real time motion generation and control for biped robot − 1st report: Walking gait pattern generation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, pp 1084–1091 (2009)

  17. Khadiv, M., Kleff, S., Herzog, A.: Stepping stabilization using a combination of DCM tracking and step adjustment. In: International Conference on Robotics and Mechatronics (ICROM), Tehran, pp 130–135 (2016)

  18. Kamioka, T., Kaneko, H., Takenaka, T., Yoshiike, T.: Simultaneous optimization of ZMP and footsteps based on the analytical solution of divergent component of motion. In: IEEE International Conference on Robotics and Automation (ICRA), Brisbane, pp 1763–1770 (2018)

  19. Englsberger, J., Ott, C., Albu-Schäffer, A.: Three-dimensional bipedal walking control based on Divergent Component of Motion. IEEE Trans. Robot. 31(2), 355–368 (2015)

    Article  Google Scholar 

  20. Feng, S., Xinjilefu, X., Atkeson, C.G., Kim, J.: Robust dynamic walking using online foot step optimization. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, pp 5373–5378 (2016)

  21. Diedam, H., Dimitrov, D., Wieber, P. -B., Mombaur, K., Diehl, M.: Online walking gait generation with adaptive foot positioning through Linear Model Predictive control. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, pp 1121–1126 (2008)

  22. Herdt, A., Diedam, H., Wieber, P.-B., Dimitrov, D.: Online walking motion generation with automatic footstep placement. Adv. Robot. 24(5–6), 719–737 (2010)

    Article  Google Scholar 

  23. Koolen, T., De Boer, T., Rebula, J., Goswami, A., Pratt, J.: Capturability-based analysis and control of legged locomotion, Part 1: theory and application to three simple gait models. Int. J. Robot. Res. 31(9), 1094–1113 (2012)

    Article  Google Scholar 

  24. Pratt, J., Koolen, T., De Boer, T., Rebula, J., Cotton, S., Carff, J., Johnson, M., Neuhaus, P.: Capturability-based analysis and control of legged locomotion, Part 2: application to M2V2, a lower-body humanoid. Int. J. Robot. Res. 31(10), 1117–1133 (2012)

    Article  Google Scholar 

  25. Castano, J.A., Li, Z., Zhou, C., Tsagarakis, N.: Dynamic and reactive walking for humanoid robots based on foot placement control. Int. J. Humanoid Robot. 13(2), 1550041 (2016)

    Article  Google Scholar 

  26. Griffin, R.J., Wiedebach, G., Bertrand, S., Leonessa, A., Pratt, J.: Walking stabilization using step timing and location adjustment on the humanoid robot, Atlas. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, pp 667–673 (2017)

  27. Kryczka, P., Kormushev, P., Tsagarakis, N.G., Caldwell, D.G.: Online regeneration of bipedal walking gait pattern optimizing footstep placement and timing. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, pp 3352–3357 (2015)

  28. Orin, D.E., Goswami, A, Lee, S. -H.: Centroidal dynamics of a humanoid robot. Auton. Robots 35(2-3), 161–176 (2013)

    Article  Google Scholar 

  29. Barthélemy, S., Bidaud, P.: Stability measure of postural dynamic equilibrium based on residual radius. In: Lenarčič, J., Wenger, P. (eds.) Advances in robot kinematics: analysis and design, pp 399–407. Springer, Dordrecht (2008)

  30. Koyanagi, K., Hirukawa, H., Hattori, S., Morisawa, M., Nakaoka, S., Harada, K., Kajita, S.: A pattern generator of humanoid robots walking on a rough terrain using a handrail. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, pp 2617–2622 (2008)

  31. Zheng, Y., Lin, M.C., Manocha, D., Adiwahono, A.H., Chew, C.M.: A walking pattern generator for biped robots on uneven terrains. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, pp 4483–4488 (2010)

  32. Bledt, G., Wensing, P.M., Kim, S.: Policy-regularized model predictive control to stabilize diverse quadrupedal gaits for the MIT cheetah. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, pp 4102–4109 (2017)

  33. Boussema, C., Powell, M.J., Bledt, G., Ijspeert, A.J., Wensing, P.M., Kim, S.: Online gait transitions and disturbance recovery for legged robots via the feasible impulse set. IEEE Robot. Autom. Lett. 4(2), 1611–1618 (2019)

    Article  Google Scholar 

  34. Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, New York (2008)

    Book  Google Scholar 

  35. Dai, H.: Robust multi-contact dynamical motion planning using contact wrench set. Diss Massachusetts Institute of Technology (2016)

  36. Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K., Hirukawa, H.: The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, pp 239–246 (2001)

  37. Raibert, M.H.: Legged Robots that Balance. MIT Press, Cambridge (1986)

    Book  Google Scholar 

  38. Caron, S., Pham, Q-C, Nakamura, Y.: ZMP support areas for multicontact mobility under frictional constraints. IEEE Trans. Robot. 33(1), 67–80 (2016)

    Article  Google Scholar 

  39. Fukuda, K., Prodon, A.: Double description method revisited. In: Franco-Japanese and Franco-Chinese Conference on Combinatorics and Computer Science, Brest, pp 91–111 (1995)

  40. Li, M, Jiang, Z, Wang, P.: Control of a quadruped robot with bionic springy legs in trotting gait. J. Bionic Eng. 11(2), 188–198 (2014)

    Article  Google Scholar 

  41. Focchi, M., Del Prete, A., Havoutis, I., Featherstone, R., Caldwell, D.G., Semini, C.: High-slope terrain locomotion for torque-controlled quadruped robots. Auton. Robots 41(1), 259–272 (2017)

    Article  Google Scholar 

  42. Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72(1–2), 3–21 (2008)

    Article  MathSciNet  Google Scholar 

  43. Ferreau, H., Potschka, A., Kirches, C.: qpOASES: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6(4), 327–363 (2014)

    Article  MathSciNet  Google Scholar 

  44. Bloesch, M., Hutter, M., Hoepflinger, M.A., Leutenegger, S., Gehring, C., Remy, C.D., Siegwart, R.: State estimation for legged robots: consistent fusion of leg kinematics and IMU. Robotics 17, 17–24 (2013)

    Google Scholar 

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Funding

This paper was funded in part by the National Natural Science Foundation of China (grant number: 61903101), in part by the National Postdoctoral Program for Innovative Talents (grant number: BX201700064),in part by the China Postdoctoral Science Foundation (grant number: 2018M631933), and in part by the Fundamental Research Funds for the Central Universities (grant number: HIT.NSRIF.2020021).

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List of all authors: Hao Sun, Junjie Yang, Hao An, Changhong Wang.

Hao An and Changhong Wang contributed to the idea of the proposed algorithm;

Hao Sun performed the experiment and wrote the manuscript;

Junjie Yang helped perform the analysis with constructive discussions.

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Correspondence to Hao An.

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Sun, H., Yang, J., An, H. et al. Improved Online Adjustment of Step Timing and Location for Legged Locomotion. J Intell Robot Syst 102, 37 (2021). https://doi.org/10.1007/s10846-021-01406-1

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  • DOI: https://doi.org/10.1007/s10846-021-01406-1

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