It's been a few years since studying in this area, but one approach we used to use for modelling and control of manipulators (mostly industrial robotic arms) wa

It's been a few years since studying in this area, but one approach we used to use for modelling and control of manipulators (mostly industrial robotic arms) was Screw Theory. Here's a recent paper using one of these approaches: http://www.intechopen.com/books/international_journal_of_advanced_robotic_systems/improved-inverse-kinematics-algorithm-using-screw-theory-for-a-six-dof-robot-manipulator http://www.intechopen.com/books/international_journal_of_adv... One approach that could be used for a system like Big Dog would be a feed-forward control loop with kinematic/dynamic modelling of the robot. These approaches use knowledge of the system dynamics to predict the output based on changing inputs or disturbances.