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.
Similar content being viewed by others
References
Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: BigDog, the rough-terrain quadruped robot. IFAC Proc. Vol. 41(2), 10822–10825 (2008)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Orin, D.E., Goswami, A, Lee, S. -H.: Centroidal dynamics of a humanoid robot. Auton. Robots 35(2-3), 161–176 (2013)
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)
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)
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)
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)
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)
Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, New York (2008)
Dai, H.: Robust multi-contact dynamical motion planning using contact wrench set. Diss Massachusetts Institute of Technology (2016)
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)
Raibert, M.H.: Legged Robots that Balance. MIT Press, Cambridge (1986)
Caron, S., Pham, Q-C, Nakamura, Y.: ZMP support areas for multicontact mobility under frictional constraints. IEEE Trans. Robot. 33(1), 67–80 (2016)
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)
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)
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)
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)
Ferreau, H., Potschka, A., Kirches, C.: qpOASES: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6(4), 327–363 (2014)
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)
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).
Author information
Authors and Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
(MP4 69.6 MB)
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-021-01406-1