Trajectory tracking control of parallel robots in the presence of joint drive flexibility

Trajectory tracking control of parallel manipulators is aimed in the presence of flexibility at the joint drives. Joint structural damping is also considered in the dynamic model. The system is first converted into an open-tree structure by disconnecting a sufficient number of unactuated joints. The closed loops are then expressed by constraint equations. It is shown that, in a parallel robot with flexible joint drives, the acceleration level inverse dynamics equations are singular because the control torques do not have an instantaneous effect on the end-effector accelerations due to the elastic media. Eliminating the Lagrange multipliers and the intermediate variables, a fourth-order input–output relation is obtained between the actuator torques and the end-effector position variables. The proposed control law decouples and linearizes the system and achieves asymptotic stability by feedback of positions and velocities of the actuated joints and rotors. As a case study, a three degree of freedom, two legged planar parallel manipulator is simulated to illustrate the performance of the method. The end-effector desired trajectory is chosen such that the kinematic and drive singular positions are avoided.