Studying the Effect of Different Optimization Criteria on Humanoid Walking Motions

The generation of stable, efficient and versatile walking motions for humanoid robots is still an open field of research. Several approaches have been implemented on humanoids in the past years, but so far none has led to a walking performance that is anywhere close to humans. This may be caused by limitations of the robotic hardware, but we claim that it is also due to the methods chosen for motion generation which do not fully exploit the capabilities of the hardware. Often, several characteristics of the gait, such as foot placement or step time, are fixed in advance in a suboptimal way for the robot. In this paper we discuss the potential of our optimal control techniques based on dynamical models of the humanoid robot for the generation of improved walking motions. We apply the method to a 3D dynamic model of the humanoid robot HRP-2 with 36 DOF and 30 actuators. Robot specific stability constraints (such as ZMP constraints) can be taken into account in the optimization. We present results for five different objective functions, and evaluate the influence of free foot placement and a relaxation of ZMP constraints.

[1]  Nicolas Mansard,et al.  Dynamic motion capture and edition using a stack of tasks , 2011, 2011 11th IEEE-RAS International Conference on Humanoid Robots.

[2]  Kai Henning Koch,et al.  Optimization-Based Walking Generation for Humanoid Robot , 2012, SyRoCo.

[3]  Richard W. Longman,et al.  Human-like actuated walking that is asymptotically stable without feedback , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[4]  K. Kreutz-Delgado,et al.  Optimal biped walking with a complete dynamical model , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[5]  Martin Buss,et al.  Towards an autonomous, humanoid, and dynamically walking robot: modeling, optimal trajectory planning, hardware architecture, and experiments , 2003 .

[6]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects , 2003, Comput. Chem. Eng..

[7]  Richard W. Longman,et al.  Self-stabilizing somersaults , 2005, IEEE Transactions on Robotics.

[8]  Kazuhito Yokoi,et al.  The 3D linear inverted pendulum mode: a simple modeling for a biped walking pattern generation , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[9]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[10]  S. Kajita,et al.  Study of dynamic biped locomotion on rugged terrain-theory and basic experiment , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[11]  M. Vukobratovic,et al.  On the stability of anthropomorphic systems , 1972 .

[12]  Shuuji Kajita,et al.  Pattern Generation of Biped Walking Constrained on Parametric Surface , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[13]  Nicolas Mansard,et al.  Generic dynamic motion generation with multiple unilateral constraints , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Takashi Matsumoto,et al.  Real time motion generation and control for biped robot -2nd report: Running gait pattern generation- , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  Katja D. Mombaur,et al.  Using optimization to create self-stable human-like running , 2009, Robotica.

[16]  Carlos Canudas-de-Wit,et al.  Generation of energy optimal complete gait cycles for biped robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[17]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[18]  Florence Billet,et al.  The HuMAnS toolbox, a homogenous framework for motion capture, analysis and simulation , 2006 .

[19]  Shuuji Kajita,et al.  ZMP-Based Biped Running Control , 2007, IEEE Robotics & Automation Magazine.

[20]  Robert K. Josephson.  Principles of Animal Locomotion.ByR McNeill Alexander.Princeton (New Jersey): Princeton University Press. $49.50. xi + 371 p; ill.; index. ISBN: 0‐691‐08678‐8. 2003. , 2003 .

[21]  A. Ruina,et al.  EÆciency , Speed , and Scaling of 2 D Passive Dynamic Walking , 1999 .

[22]  Atsuo Takanishi,et al.  Development of a bipedal humanoid robot-control method of whole body cooperative dynamic biped walking , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[23]  Takashi Matsumoto,et al.  Real time motion generation and control for biped robot -1st report: Walking gait pattern generation- , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[24]  Guy Bessonnet,et al.  Optimal Gait Synthesis of a Seven-Link Planar Biped , 2004, Int. J. Robotics Res..

[25]  K. Mombaur,et al.  Modeling and Optimal Control of Human-Like Running , 2010, IEEE/ASME Transactions on Mechatronics.

[26]  Fumio Kanehiro,et al.  Humanoid robot HRP-2 , 2008, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[27]  T. Takenaka.  The control system for the Honda humanoid robot. , 2006, Age and ageing.

[28]  A. Ruina,et al.  Efficiency, speed, and scaling of two-dimensional passive-dynamic walking , 2000 .