Dynamic transition trajectory planning of three-DOF cable-suspended parallel robots via linear time-varying MPC

This paper presents a dynamic transition trajectory planning technique for fully-actuated three-degree-of-freedom cable-suspended parallel robots. The proposed two-step technique can be used to plan transition trajectories to general periodic motions that extend beyond the static workspace of the mechanism. In the first step, the robot dynamics are linearized and partly decoupled by handling the less restricted gravity axis trajectory planning problem. The corresponding dynamic model and constraints of the other axes then become linear time-varying. Secondly, the generation of general periodic trajectories and the general transition trajectories is accomplished by convex optimization. The formulation of a constrained linear-quadratic optimal control problem for the dynamic transition task shows essential differences from previous works and extends to general cases. The proposed technique has the ability to generate general periodic trajectories and provides a universal transition planner. Indeed, there is no need to rely on a specific amplitude increment function, which makes the planning technique more flexible and applicable to general cases. Moreover, the quadratic programming problems can be solved reliably and rapidly. Example transition trajectories to harmonic and to non-harmonic periodic trajectories are given in order to illustrate the approach.