Experimental Control of Flexible Robot Manipulators

Flexible-link robotic manipulators are mechanical devices whose control can be rather challenging, among other reasons because of their intrinsic under-actuated nature. This chapter presents various experimental studies of diverse robust control schemes for this kind of robotic arms. The proposed designs are based on several control strategies with well defined theoretical foundations whose effectiveness are demonstrated in laboratory experiments. First it is experimented a simple control method for trajectory tracking which exploits the two-time scale nature of the flexible part and the rigid part of the dynamic equations of flexible-link robotic manipulators: a slow subsystem associated with the rigid motion dynamics and a fast subsystem associated with the flexible link dynamics. Two experimental approaches are considered. In a first test an LQR optimal design strategy is used, while a second design is based on a sliding-mode scheme. Experimental results on a laboratory two-dof flexible manipulator show that this composite approach achieves good closed-loop tracking properties for both design philosophies, which compare favorably with conventional rigid robot control schemes. Next the chapter explores the application of an energy-based control design methodology (the so-called IDA-PBC, interconnection and damping assignment passivity-based control) to a single-link flexible robotic arm. It is shown that the method is well suited to handle this kind of under-actuated devices not only from a theoretical viewpoint but also in practice. A Lyapunov analysis of the closed-loop system stability is given and the design performance is illustrated by means of a set of simulations and laboratory control experiments, comparing the results with those obtained using conventional control schemes for mechanical manipulators. The outline of the chapter is as follows. Section 2 covers a review on the modeling of flexible-link manipulators. In subsection 2.1 the dynamic modelling of a general flexible multilink manipulator is presented and in subsection 2.2 the methodology is applied to a laboratory flexible arm. Next, some control methodologies are outlined in section 3. Two control strategies are applied to a two-dof flexible robot manipulator. The first design, in subsection 3.1, is based on an optimal LQR approach and the second design, in subsection 3.2, is based on a sliding-mode controller for the slow subsystem. Finally, section 4 covers the IDA-PBC method. In subsection 4.1 an outline of the method is given and in subsection