A manipulator is fundamentally a reprogrammable, multifunctional mechanical arm intended to move parts, tools, and specialized device through preprogrammed motions for the performance of various tasks. With the advances in technology over last decades Parallel manipulator became more popular for industrial purpose. Parallel manipulators are used for variety of tasks such as flight simulator [1], medical tools [2-4], pick and place operations. The kinematics of parallel manipulator differs from serial manipulator.Parallel manipulator consists of two platforms one of which is fixed and another is moving platform. These two platforms are connected to each other with the help of limbs. These limbs may consist of revolute or translational joints. Each limb is driven individually. Such type of structure results in closed kinematic mechanism. The kinematic analysis of parallel manipulator is difficult and it has been focus of many researchers [5][6][7][8]. The trajectory control of parallel mechanism like this present unique challenges because the dynamics of parallel manipulator are highly coupled and nonlinear. The precision depends on the accuracy of each actuator as well as on the synchronization of the actuators. In last few decades researchers have focused on optimal control theory and formulated the well-known optimal state feedback controller known as linear quadratic regulator, this approach reduces the deviation in state trajectories of a system maintaining minimum control effort. A very detailed study of optimal control is presented in [18]. To get the optimal control signal algebraic Riccati equation
Research Article
AbstractA parallel three degrees of freedom (3-DOF) manipulator known as Maryland manipulator is considered in this paper. The manipulator model considered in this paper is more practical because the offset lengths are not taken zero. The trajectory tracking control of the Maryland manipulator is done using linear-quadratic regulator (LQR) based proportional-integral-derivative (PID) controller. Three sequential trajectories are used to provide complete dynamic analysis of the manipulator. The manipulator considered here is more practical because the offset lengths are not taken zero unlike previous research articles. The motivation behind using PID controller is its simplicity and effectiveness. The manipulator is a highly coupled and nonlinear system so the correct determination of control signal is very important to achieve good tracking performance. The process for selecting the PID parameters is discussed in detail and the simulations results are used to show the efficacy of the controller.