Chapter 5 Lagrangian Dynamics of Manipulators

Service robots can be thought of as having two types of motion: (a) locomotion of the entire robot, which can be either legged or wheeled, and (b) motion of the manipulator limbs, e.g., object manipulation by the “hands” etc. While the first type is very specialised, in particular in the case of legged motion, the second is fairly generic and can be discussed in detail without making a very heavy demand on the mathematical background of the reader. With that in mind, in the following, the author considers the dynamics of two types of systems, which are known as serial or open-loop, and parallel or closed-loop manipulators. The examples of these would be the hands of a humanoid robot, when considered in isolation, and when clasped together or holding an object with both hands, respectively. The examples considered here would be planar in order to keep them simple; however, the formulation presented would be general, so that the reader can, very easily, use it to model and simulate spatial manipulators.