The Momentum Equilibrium Principle: Foot Contact Stabilization with Relative Angular Momentum/Velocity

The spatial momentum relation of an underac-tuated articulated multibody system on a floating base is a dynamic equilibrium relation between its coupling and relative momenta. The relative momentum is the difference between the system momentum and the momentum of the composite-rigid-body (CRB) that is obtained when the joints are locked. This relation is referred to as the momentum equilibrium principle. The focus in this work is on the angular momentum component of the momentum equilibrium principle. It is clarified that the relative angular momentum component can be represented in terms of the so-called relative angular velocity that is used as a control input in a balance controller. The balance controller proposed here is a whole-body controller that has independent inputs for center of mass (CoM) velocity and base-link angular velocity control. In addition, the relative angular velocity control input endows the controller with the unique property of generating an appropriate upper-limb motion that can stabilize the system momentum. More specifically, it is shown that when the relative angular velocity is derived from the reaction null-space (RNS) of the system, it becomes possible to stabilize the unstable states with a rolling foot/feet. The formulation is simple and yet quite efficient — there is no need to modify the contact model to account for the transitions between the stable and unstable contact states. There is also no need to command the upper-limb motion directly. A few simulation examples are presented to demonstrate and discuss the properties of the controller.

[1]  Joonhong Lim,et al.  FOR KINEMATIC CONTROL OF REDUNDANT MANIPULATORS , 1988 .

[2]  David E. Orin,et al.  Centroidal Momentum Matrix of a humanoid robot: Structure and properties , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[3]  KanounO.,et al.  Kinematic Control of Redundant Manipulators , 2011 .

[4]  Marko B. Popovic,et al.  Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications , 2005, Int. J. Robotics Res..

[5]  Kazuhito Yokoi,et al.  Resolved momentum control: humanoid motion planning based on the linear and angular momentum , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[6]  Jerry E. Pratt,et al.  Exploiting inherent robustness and natural dynamics in the control of bipedal walking robots , 2000 .

[7]  Alin Albu-Schäffer,et al.  Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion , 2015, IEEE Transactions on Robotics.

[8]  Bernd Henze,et al.  Passivity-based whole-body balancing for torque-controlled humanoid robots in multi-contact scenarios , 2016, Int. J. Robotics Res..

[9]  D. Nenchev.  Differential Kinematics , 2017 .

[10]  Dragomir N. Nenchev,et al.  Balance Stabilization with Angular Momentum Damping Derived from the Reaction Null-Space , 2018, 2018 IEEE-RAS 18th International Conference on Humanoid Robots (Humanoids).

[11]  Jerrold E. Marsden,et al.  Quasivelocities and symmetries in non-holonomic systems , 2009 .

[12]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[13]  Sergey V. Drakunov,et al.  Capture Point: A Step toward Humanoid Push Recovery , 2006, 2006 6th IEEE-RAS International Conference on Humanoid Robots.

[14]  David E. Orin,et al.  Centroidal dynamics of a humanoid robot , 2013, Auton. Robots.

[15]  Richard M. Murray,et al.  Nonlinear Control of Mechanical Systems: A Lagrangian Perspective , 1995 .

[16]  Vinutha Kallem,et al.  Rate of change of angular momentum and balance maintenance of biped robots , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[17]  Gordon Cheng,et al.  Full-Body Compliant Human–Humanoid Interaction: Balancing in the Presence of Unknown External Forces , 2007, IEEE Transactions on Robotics.

[18]  Hirochika Inoue,et al.  Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[19]  Taku Komura,et al.  Stepping motion for a human-like character to maintain balance against large perturbations , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[20]  Shuuji Kajita,et al.  A universal stability criterion of the foot contact of legged robots - adios ZMP , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[21]  Takashi Matsumoto,et al.  Real time motion generation and control for biped robot -3rd report: Dynamics error compensation- , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[22]  A. Liegeois,et al.  Automatic supervisory control of the configuration and behavior of multi-body mechanisms , 1977 .

[23]  Atsuo Kawamura,et al.  Bipedal Trajectory Generation Based on Combining Inertial Forces and Intrinsic Angular Momentum Rate Changes: Eulerian ZMP Resolution , 2012, IEEE Transactions on Robotics.

[24]  Tsuneo Yoshikawa,et al.  Analysis and Control of Articulated Robot Arms with Redundancy , 1981 .

[25]  Kazuhisa Mitobe,et al.  Control of walking robots based on manipulation of the zero moment point , 2000, Robotica.

[26]  Johannes Englsberger,et al.  Integration of vertical COM motion and angular momentum in an extended Capture Point tracking controller for bipedal walking , 2012, 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012).

[27]  James P. Ostrowski.  Computing reduced equations for robotic systems with constraints and symmetries , 1999, IEEE Trans. Robotics Autom..

[28]  Taku Komura,et al.  A Feedback Controller for Biped Humanoids that Can Counteract Large Perturbations During Gait , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[29]  Ambarish Goswami,et al.  A Biomechanically Motivated Two-Phase Strategy for Biped Upright Balance Control , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[30]  Sylvain Bertrand,et al.  Walking on partial footholds including line contacts with the humanoid robot atlas , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).

[31]  D. N. Nenchev,et al.  Reaction Null Space of a multibody system with applications in robotics , 2013 .

[32]  Victor B. Zordan,et al.  Momentum control for balance , 2009, ACM Trans. Graph..

[33]  S. Nakaoka,et al.  Choreonoid: Extensible virtual robot environment built on an integrated GUI framework , 2012, 2012 IEEE/SICE International Symposium on System Integration (SII).

[34]  Sung-Hee Lee,et al.  A momentum-based balance controller for humanoid robots on non-level and non-stationary ground , 2012, Auton. Robots.