Whole body dynamic behavior and control of human-like robots. Khatib, O. A. S. and L. AND Park, J. A. W. International Journal of Humanoid Robotics, 1(1):29-43, 2004.
Whole body dynamic behavior and control of human-like robots [link]Paper  doi  abstract   bibtex   
With the increasing complexity of humanoid mechanisms and their desired capabilities, there is a pressing need for a generalized framework where a desired whole-body motion behavior can be easily specified and controlled. Our hypothesis is that human motion results from simultaneously performing multiple objectives in a hierarchical manner, and we have analogously developed a prioritized, multiple-task control framework. The operational space formulation provides dynamic models at the task level and structures for decoupled task and posture control. This formulation allows for posture objectives to be controlled without dynamically interfering with the operational task. Achieving higher performance of posture objectives requires precise models of their dynamic behaviors. In this paper we complete the picture of task descriptions and whole-body dynamic control by establishing models of the dynamic behavior of secondary task objectives within the posture space. Using these models, we present a whole-body control framework that decouples the interaction between the task and postural objectives and compensates for the dynamics in their respective spaces.
@Article{Khatib2004,
  Title                    = {Whole body dynamic behavior and control of human-like robots},
  Author                   = {Khatib, O. AND Sentis, L. AND Park, J. AND Warren, J.},
  Journal                  = {International Journal of Humanoid Robotics},
  Year                     = {2004},
  Number                   = {1},
  Pages                    = {29-43},
  Volume                   = {1},
  Abstract                 = {With the increasing complexity of humanoid mechanisms and their desired capabilities, there is a pressing need for a generalized framework where a desired whole-body motion behavior can be easily specified and controlled. Our hypothesis is that human motion results from simultaneously performing multiple objectives in a hierarchical manner, and we have analogously developed a prioritized, multiple-task control framework. The operational space formulation provides dynamic models at the task level and structures for decoupled task and posture control.

This formulation allows for posture objectives to be controlled without dynamically interfering with the operational task. Achieving higher performance of posture objectives requires precise models of their dynamic behaviors. In this paper we complete the picture of task descriptions and whole-body dynamic control by establishing models of the dynamic behavior of secondary task objectives within the posture space. Using these models, we present a whole-body control framework that decouples the interaction between the task and postural objectives and compensates for the dynamics in their respective spaces.},
  Doi                      = {10.1142/S0219843604000058},
  Keywords                 = {ECE780, Control},
  Review                   = {Humanoids are high dimensionality robots, and contains redundant joints. We can divide up the control problem into two components: task dynamic behaviour (primary task), and posture behaviour (secondary task). Using the general Lagrange dynamic equation, they obtain a Jacobian that maps between force and torque (or between task and joint space, respectively). The torque equations are than separated into two independent sections, with one being responsible for task dynamics and the other being responsible for posture. 

They successfully implemented two control cases. The first case allows for both the primary task and the secondary task to be met. The second case provides conflicting joint space instructions between the primary and secondary tasks, but was still able to produce minimal mean square error.},
  Timestamp                = {2011.02.09},
  Url                      = {http://www.worldscientific.com/doi/abs/10.1142/S0219843604000058}
}
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