Hidden chaotic path planning and control of a two-link flexible robot manipulator

Robotics is an emerging and interesting area in many fields of technical science. In general, a robot manipulator (rigid/flexible) is a more focused research direction in comparison with other areas of robotics. Specifically, flexible manipulators are more applicable in many fields when compared with its rigid counterparts because of many advantages like lightweight, more workspace, lower energy consumption, smaller in size, mobility, etc. These advantages give rise to many control challenges like underactuation, nonminimum phase, noncollocation, control spillover, uncertainties, nonlinearities, complex dynamical behaviours, etc. Path planning or trajectory tracking problem is considered as an interesting and challenging control problem for a flexible manipulator in comparison with the regulation problem. In recent decades, the theory of chaos is used in various technical fields. Aperiodic long time, highly sensitive to initial conditions, unpredictable behaviours, etc. are the fundamental properties of a chaotic signal arising out of a deterministic nonlinear system. Many continuous/discrete/fractional order autonomous and non-autonomous chaotic dynamical systems are available in the literature. In the recent past, more attention has been given to the design and applications of hidden chaotic dynamical systems. The path planning problem of a flexible manipulator requires a reference signal. Various reference signals are used in the literature. Recently, a chaotic signal is used as a reference signal for path planning. However, we have not found any paper wherein a reference signal using a hidden chaotic system is used for path planning. The use of a signal from a hidden chaotic attractor for path planning of a flexible manipulator can provide a new domain of research. Hidden chaotic path planning/trajectory tracking of a two-link flexible manipulator is the aim of this chapter. Use of hidden chaotic attractors as a path/trajectory reference creates extra challenges and complexity in controlling the flexible manipulator. Thus, controlling a flexible manipulator in such a scenario is a challenging task. The dynamics of a two-link flexible manipulator is first modelled using assumed modes method and divided into two parts using two-time scale separation principle (singular perturbation). One subsystem is called as the slow subsystem involving with the rigid parts and another subsystem is called as the fast subsystem which incorporates the flexible dynamics. Separate control techniques are applied to each subsystem. An adaptive sliding mode control technique is designed for the slow subsystem which tackles the uncertainties and helps in fast tracking of the desired hidden chaotic trajectory. A backstepping controller is designed for the fast subsystem system for quick suppression of tip deflections and vibration suppressions. The proposed control techniques are validated using a reference chaotic signal generated from a 3-D hidden attractors chaotic system in MATLAB simulation environment and results are demonstrated. The results reveal that the objective of the chapter is achieved successfully by the proposed control techniques.