A spatial operator algebra for manipulator modeling and control
International Journal of Robotics Research
Modelling and Control of Robot Manipulators
Modelling and Control of Robot Manipulators
Efficient synthesis of physically valid human motion
ACM SIGGRAPH 2003 Papers
Rigid Body Dynamics Algorithms
Rigid Body Dynamics Algorithms
ACM SIGGRAPH 2009 papers
Exploiting angular momentum to enhance bipedal center-of-mass control
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Angular momentum control in coordinated behaviors
MIG'10 Proceedings of the Third international conference on Motion in games
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The center of mass (CoM) of a humanoid robot occupies a special place in its dynamics. As the location of its effective total mass, and consequently, the point of resultant action of gravity, the CoM is also the point where the robot's aggregate linear momentum and angular momentum are naturally defined. The overarching purpose of this paper is to refocus our attention to centroidal dynamics: the dynamics of a humanoid robot projected at its CoM. In this paper we specifically study the properties, structure and computation schemes for the centroidal momentum matrix (CMM), which projects the generalized velocities of a humanoid robot to its spatial centroidal momentum. Through a transformation diagram we graphically show the relationship between this matrix and the well-known joint-space inertia matrix. We also introduce the new concept of "average spatial velocity" of the humanoid that encompasses both linear and angular components and results in a novel decomposition of the kinetic energy. Further, we develop a very efficient $$O(N)$$ O ( N ) algorithm, expressed in a compact form using spatial notation, for computing the CMM, centroidal momentum, centroidal inertia, and average spatial velocity. Finally, as a practical use of centroidal dynamics we show that a momentum-based balance controller that directly employs the CMM can significantly reduce unnecessary trunk bending during balance maintenance against external disturbance.