Model inversion for trajectory control of reconfigurable underactuated cable-driven parallel robots

Reconfiguration of the exit points can be effectively adopted in cable-driven parallel robots (CDPR) to expand the robot workspace and to achieve better performances than traditional CDPRs. This feature can be further exploited in underactuated CDPRs, where the number of independent active cables (and hence of control forces) is smaller than the number of degrees of freedom of the end-effector to be controlled, and therefore motion planning and control is more difficult due to some unactuated coordinates that constraint the feasible trajectory through a second-order nonholonomic constraint. Reconfigurable underactuated CDPRs (RU-CDPRs) are investigated in this paper, by proposing a new method for the inversion of their dynamic model for trajectory tracking, by solving two challenging problems. The first one is the inverse dynamic problem, to compute the motor torques controlling the cable lengths and hence the cable tensions. Then, by exploiting the use of rheonomous constraints, the reconfiguration strategy is developed, by calculating the commanded trajectory of the movable exit-points. The method leads to a very accurate tracking of the reference trajectory with negligible transient and residual oscillations, by compensating for the unconstrained load attitude of oscillating. By defining the reference to a suitable subset of coordinates of the end-effector, the proposed method exploits the input–output normal form of the dynamic model of the unconstrained end-effector and relies, as usual in non-flat underactuated systems, in the solution of both algebraic and differential equations. The correctness of the proposed method is then provided through numerical simulation with a meaningful example of RU-CDPR, by also showing its reduced computational effort and its feasibility.