Operational Space Dynamics

Abstract

Robotic platforms are typically designed to interact with the environment at specific task space nodes on the system. For a manipulator, the set of task space nodes may consist of a single end-effector node. For a humanoid system, the arm end-effectors are task space nodes, while the feet are such nodes for legged systems. The set of task space nodes define the operational space of the system. The control problem requires managing the motion state as well as the force interactions with the envi- ronment for the task space nodes. Operational space control (OSC) is an approach to robot system control that focuses on the dynamical behavior of a system from the task (or operational) space perspective [100–103]. It is especially useful for ap- plications involving contact between the end-effector and the environment, such as occurs in hybrid force/position control, or for artificial potential field approaches to collision avoidance and path planning. The advantage of the OSC approach over joint space control is that the control problem is posed directly in terms of task space variables. One issue is the added analytical and computational complexity of operational space dynamics. As will be seen in later chapters, the importance of operational space dynamics quantities extends to the dynamics of systems subject to closure constraints, as well as to the dynamics of under-actuated and free-flying systems. In this chapter, we study and analyze operational space dynamics and as- sociated efficient computational algorithms for a robotic system.