Abstract
Balance is an essential feature of humanoids but, despite a strong understanding of its laws and dynamics, it remains an open problem for control applications. Optimization-based control approaches explicitly include balance dynamics and constraints in the control problem in order to capture at best the behavior of the system and fully exploit it to reach complex control objectives. Although theoretically appealing, these approaches intrinsically induce a significant computational burden. In practice, this implies to resort to simplifications on the model and problem complexities, which limits the capacity to actually generate complex behaviors. In this chapter, an overview of the balance problem is first proposed. A general, abstract formulation of the balance control problem as an optimal control one is then derived. Three major approaches can be found in the literature, coping with the computational complexity of the general balance optimization problem. They range from offline motion planning to reactive whole-body control and are presented in the remainder of the chapter.
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References
Y. Abe, M. da Silva, J. Popović, Multiobjective control with frictional contacts, in Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Eurographics Association, 2007), pp. 249–258
S. Barthélemy, P. Bidaud, Stability measure of postural dynamic equilibrium based on residual radius, in Advances in Robot Kinematics: Analysis and Design (Springer, 2008), pp. 399–407
H.G. Bock, K.-J. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, in Proceedings of the 9th IFAC World Congress, 1984, pp. 242–247
K. Bouyarmane, A. Kheddar, Using a multi-objective controller to synthesize simulated humanoid robot motion with changing contact configurations, in 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2011), pp. 4414–4419
K. Bouyarmane, A. Kheddar, Humanoid robot locomotion and manipulation step planning. Adv. Robot. 26(10), 1099–1126 (2012)
C. Collette, A. Micaelli, C. Andriot, P. Lemerle, Dynamic balance control of humanoids for multiple grasps and non coplanar frictional contacts, in 2007 7th IEEE-RAS International Conference on Humanoid Robots (IEEE, 2007), pp. 81–88
S. Dalibard, A. El Khoury, F. Lamiraux, A. Nakhaei, M. Taïx, J.-P. Laumond, Dynamic walking and whole-body motion planning for humanoid robots: an integrated approach. Int. J. Robot. Res. 32(9–10), 1089–1103 (2013)
A. Del Prete, F. Nori, G. Metta, L. Natale, Prioritized motion–force control of constrained fully-actuated robots: task space inverse dynamics. Robot. Auton. Syst. 63, 150–157 (2015)
H. Diedam, D. Dimitrov, P.-B. Wieber, K. Mombaur, M. Diehl, Online walking gait generation with adaptive foot positioning through linear model predictive control, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2008), pp. 1121–1126
A. El Khoury, F. Lamiraux, M. Taix, Optimal motion planning for humanoid robots, in 2013 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2013), pp. 3136–3141
A. Escande, N. Mansard, P.-B. Wieber, Hierarchical quadratic programming: fast online humanoid-robot motion generation. Int. J. Robot. Res. 33(7), 1006–1028 (2014)
B. Faverjon, P. Tournassoud, A local based approach for path planning of manipulators with a high number of degrees of freedom, in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, 1987, pp. 1152–1159
A. Goswami, Postural stability of biped robots and the foot-rotation indicator (FRI) point. Int. J. Robot. Res. 18(6), 523–533 (1999)
K. Hauser, T. Bretl, J.-C. Latombe, K. Harada, B. Wilcox, Motion planning for legged robots on varied terrain. Int. J. Robot. Res. 27(11–12), 1325–1349 (2008)
B. Henze, C. Ott, M. Roa et al, Posture and balance control for humanoid robots in multi-contact scenarios based on model predictive control, in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2014), pp. 3253–3258
A. Herdt, N. Perrin, P.-B. Wieber, Walking without thinking about it, in 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2010), pp. 190–195
A. Herzog, L. Righetti, F. Grimminger, P. Pastor, S. Schaal, Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics, in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2014), pp. 981–988
A. Ibanez, P. Bidaud, V. Padois, Unified preview control for humanoid postural stability and upper-limb interaction adaptation, in 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2012), pp. 1801–1808
A. Ibanez, P. Bidaud, V. Padois, A distributed model predictive control approach for robust postural stability of a humanoid robot, in 2014 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2014), pp. 202–209
A. Ibanez, P. Bidaud, V. Padois, Emergence of humanoid walking behaviors from mixed-integer model predictive control, in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2014), pp. 4014–4021
S. Kajita, B. Espiau, Legged robots, in Springer Handbook of Robotics (Springer, Berlin, 2008), pp.361–389
S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa, Biped walking pattern generation by using preview control of zero-moment point, in Proceedings of the IEEE International Conference on Robotics and Automation, ICRA’03, vol. 2 (IEEE, 2003), pp. 1620–1626
O. Kanoun, F. Lamiraux, P.-B. Wieber, F. Kanehiro, E. Yoshida, J.-P. Laumond, Prioritizing linear equality and inequality systems: application to local motion planning for redundant robots, in IEEE International Conference on Robotics and Automation, ICRA’09 (IEEE, 2009), pp. 2939–2944
S. Kanzaki, K. Okada, M. Inaba, Bracing behavior in humanoid through preview control of impact disturbance, in 2005 5th IEEE-RAS International Conference on Humanoid Robots (IEEE, 2005), pp. 301–305
F. Keith, N. Wieber, P.-B.and Mansard, A. Kheddar, Analysis of the discontinuities in prioritized tasks-space control under discreet task scheduling operations, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011, pp. 3887–3892
O. Khatib, L. Sentis, J.-H. Park, A unified framework for whole-body humanoid robot control with multiple constraints and contacts, in European Robotics Symposium 2008 (Springer, 2008), pp. 303–312
J. Koenemann, A. Del Prete, Y. Tassa, E. Todorov, O. Stasse, M. Bennewitz, N. Mansard, Whole-body model-predictive control applied to the HRP-2 humanoid, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, 2015, p. 8
M. Krause, J. Englsberger, P.-B. Wieber, C. Ott, Stabilization of the capture point dynamics for bipedal walking based on model predictive control, in Robot Control, vol. 10, 2012, pp. 165–171
J.J. Kuffner Jr., S. Kagami, K. Nishiwaki, M. Inaba, H. Inoue, Dynamically-stable motion planning for humanoid robots. Auton. Robot. 12(1), 105–118 (2002)
S. Kuindersma, R. Deits, M. Fallon, A. Valenzuela, H. Dai, F. Permenter, T. Koolen, P. Marion, R. Tedrake, Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot. Auton. Robot. 40(3), 429–455 (2015)
S. LaValle, Planning Algorithms (Cambridge university press, New York, 2006)
S.-H. Lee, A. Goswami, A momentum-based balance controller for humanoid robots on non-level and non-stationary ground. Auton. Robot. 33(4), 399–414 (2012)
J. Lee, N. Mansard, J. Park, Intermediate desired value approach for task transition of robots in kinematic control. IEEE Trans. Robot. 28(6), 1260–1277 (2012)
S. Lengagne, J. Vaillant, E. Yoshida, A. Kheddar, Generation of whole-body optimal dynamic multi-contact motions. Int. J. Robot. Res. 32(9–10), 1104–1119 (2013)
M. Liu, A. Micaelli, P. Evrard, A. Escande, C. Andriot, Interactive virtual humans: a two-level prioritized control framework with wrench bounds. IEEE Trans. Robot. 28(6), 1309–1322 (2012)
M. Liu, R. Lober, V. Padois, Whole-body hierarchical motion and force control for humanoid robots. Auton. Robot. 40(3), 493–504 (2016)
M.Liu, Y. Tan, V. Padois, Generalized hierarchical control. Auton. Robot. 40(1), 17–31 (2016)
R. Lober, V. Padois, O. Sigaud, Multiple task optimization using dynamical movement primitives for whole-body reactive control, in Proceedings of the IEEE-RAS International Conference on Humanoid Robots (Humanoids), Madrid, 2014, pp. 193–198
R. Lober, V. Padois, O. Sigaud, Variance modulated task prioritization in whole-body control, in 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2015), pp. 3944–3949
N. Mansard, A. Remazeilles, F. Chaumette, Continuity of varying-feature-set control laws. IEEE Trans. Autom. Control 54(11), 2493–2505 (2009)
K. Mombaur, Using optimization to create self-stable human-like running. Robotica 27(03), 321–330 (2009)
I. Mordatch, E. Todorov, Z. Popović, Discovery of complex behaviors through contact-invariant optimization. ACM Trans. Graph. (TOG) 31(4), 43 (2012)
R.M. Murray, Z. Li, S.S. Sastry, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC PressI Llc, Boca Raton, 1994)
C. Ott, M. Roa, G. Hirzinger et al, Posture and balance control for biped robots based on contact force optimization, in 2011 11th IEEE-RAS International Conference on Humanoid Robots (Humanoids) (IEEE, 2011), pp. 26–33
N. Perrin, D. Lau, V. Padois, Effective generation of dynamically balanced locomotion with multiple non-coplanar contacts, in International Symposium on Robotics Research (ISRR’15), 2015
T. Petrič, L. žlajpah, Smooth continuous transition between tasks on a kinematic control level: obstacle avoidance as a control problem. Robot. Auton. Syst. 61(9), 948–959 (2013)
J.E. Pratt, R. Tedrake, Velocity-based stability margins for fast bipedal walking, in Fast Motions in Biomechanics and Robotics (Springer, 2006), pp. 299–324
L. Righetti, J. Buchli, M. Mistry, S. Schaal, Inverse dynamics control of floating-base robots with external constraints: a unified view, in 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), pp. 1085–1090
L. Saab, O.E. Ramos, F. Keith, N. Mansard, P. Soueres, J. Fourquet, Dynamic whole-body motion generation under rigid contacts and other unilateral constraints. IEEE Trans. Robot. 29(2), 346–362 (2013)
J. Salini, V. Padois, P. Bidaud, Synthesis of complex humanoid whole-body behavior: a focus on sequencing and tasks transitions, in 2011 IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2011), pp. 1283–1290
B.J. Stephens, C.G. Atkeson, Push recovery by stepping for humanoid robots with force controlled joints, in 2010 10th IEEE-RAS International Conference on Humanoid Robots (Humanoids) (IEEE, 2010), pp. 52–59
Y. Tassa, T. Erez, E. Todorov, Synthesis and stabilization of complex behaviors through online trajectory optimization, in 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, 2012), pp. 4906–4913
M. Vukobratović, J. Stepanenko, On the stability of anthropomorphic systems. Math. biosci. 15(1), 1–37 (1972)
P.-B. Wieber, On the stability of walking systems, in Proceedings of the International Workshop on Humanoid and Human Friendly Robotics, 2002
P.-B. Wieber, Trajectory free linear model predictive control for stable walking in the presence of strong perturbations, in 2006 6th IEEE-RAS International Conference on Humanoid Robots (IEEE, 2006), pp. 137–142
P.-B. Wieber, R. Tedrake, S. Kuindersma, Modeling and control of legged robots, in Springer Handbook of Robotics, ed. by B. Siciliano, O. Khatib, 2nd edn. (Springer, Berlin/Heidelberg, 2015)
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Ibanez, A., Bidaud, P., Padois, V. (2017). Optimization-Based Control Approaches to Humanoid Balancing. In: Goswami, A., Vadakkepat, P. (eds) Humanoid Robotics: A Reference. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7194-9_71-1
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DOI: https://doi.org/10.1007/978-94-007-7194-9_71-1
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