Cable-driven parallel robots (CDPRs) are under-actuated if they use a number of cables smaller than the degrees of freedom (DoF) of the end-effector (EE). For these robots, the constraint deficiency on the EE may lead to undesirable EE oscillations along the path that it is supposed to track. This paper proposes a trajectory-planning method for underactuated CDPRs which is robust against dynamic-model uncertainties or parameter variation, aiming at minimizing EE oscillations along a prescribed path. Oscillation reduction and robustness are achieved by means of Zero-Vibration Multi-Mode Input Shaping and Dynamic Scaling of a reference trajectory. Simulation results show the effectiveness of the method on a 3-cable 6-DoF robot.
This paper studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when the motion time and the path geometry are prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary motion is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector motions leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motion of the end-effector may arise. In this paper, we propose a novel trajectory-planning technique that allows the end-effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a Boundary Value Problem, formulated as the problem of finding a solution to the differential equations of motion, with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a 6-Degree-of-Freedom spatial CDPR suspended by 3 cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed.
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