Flatness-Based Control in Successive Loops for Delta Parallel Robots in the Task Space

Delta parallel robots are widely used in industry for executing various manufacturing tasks at high speed. Such robots exhibit a highly complex and nonlinear kinematic and dynamic model. In this article, the control problem of 3-DOF delta parallel robots is considered. The joint kinematic and dynamic model of these robots for operation in the task space is formulated in state-space form and is shown to be differentially flat. The control problem for these robotic systems is solved with the use of a flatness-based control approach, which is implemented in successive loops. To apply the multi-loop flatness-based control method, the state-space model of the delta parallel robot is separated into subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system, and control of it can be performed with inversion of its dynamics as in the case of input-output linearized systems. The state variables of the subsequent (i+1)-th subsystem become virtual control inputs for the preceding i-th subsystem. Exogenous control inputs are applied to the last subsystem. The stabilizing feedback control signal is computed at the last subsystem, by tracing backwards at each sampling instance the virtual control inputs of all N-1 preceding subsystems. The whole control method is implemented in successive loops, and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves stabilization of the delta parallel robot without the need for diffeomorphisms and complicated state-space model transformations.