Manipulation – “Robotic manipulation refers to the ways robots interact with the objects around them: grasping an object, opening a door, packing an order into a box, folding laundry… All these actions require robots to plan and control the motion of their hands and arms in an intelligent way.” – University of Leads
Closed Form Solution – Generally, problems are said to have a closed-form solution if they can be expressed by simple functions and mathematical operations. For example, the motion of a simple pendulum can be modeled with physics equations (closed form) but the interaction of a robot manipulator with objects is too complex to capture with physics equations (no closed form solution). – Brilliant and Wolfram Mathworld
Degrees of Freedom (DOF or DoF) – “Degrees of freedom are specific, defined modes in which a mechanical device or system can move. The number of degrees of freedom is equal to the total number of independent displacements or aspects of motion.” Note that Degrees of Freedom has other uses, such as in statistics. Here we refer to usage in physics and mechanics. – Techtarget
End Effectors – End effectors of robot arms interact with the world or a task. They can be tools (such as welding torches), sensors (such as cameras), or grippers (like those seen in this video). Researchers of robot manipulation study the many forms of grippers and how to use them effectively.