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.

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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.

In order to control cable-driven parallel robots (CDPRs), it is necessary to keep all cable tensions within (positive) known limits during motion. For CDPRs having more cables than end-effector degrees of freedom, a feasible force distribution within cables should be computed beforehand. This paper aims at evaluating how a tension error in one cable affects the overall distribution of tensions in the other cables, by focusing on planar overconstrained CDPRs with four cables. The cable whose tension error more limitedly impact the force distribution is analytically determined by computing the right nullspace of the manipulator structure matrix. It is then shown how the cable least influencing the force distribution changes throughout the wrenchfeasible workspace. Lastly, the results of the proposed analysis are used to perform a motion-control experiment on a prototype, where, for any configuration of the end-effector, the cable least influencing the force distribution is tension-controlled, while the remaining ones are length-controlled.

Underactuated Cable-Driven Parallel Robots (CDPR) employ a number of cables smaller than the degrees of freedom (DoFs) of the end-effector (EE) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium configurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6-DoF prototypes actuated by 2, 3, and 4 cables. Additionally, in order to highlight the interest in a robotic context, this modelling strategy is applied to the trajectory planning of a 6-DoF 4-cable CDPR by means of a frequency-based method (multi-mode input shaping), and the latter is experimentally compared with traditional non-frequency-based motion planners.

Cable-driven parallel robots offer significant advantages in terms of workspace dimensions and payload capability. Their mechanical structure and transmission system consist of light and extendable cables that can withstand high tensile loads. Cables are wound and unwound by a set of motorized winches, so that the robot workspace dimensions mainly depend on the amount of cable that each drum can store. For this reason, these manipulators are attractive for many industrial tasks to be performed on a large scale, such as handling, pick-and-place, and manufacturing, without a substantial increase in costs and mechanical complexity with respect to a small-scale application. This paper presents the design of a planar overconstrained cable-driven parallel robot for quasi-static non-contact operations on planar vertical surfaces, such as laser engraving, inspection and thermal treatment. The overall mechanical structure of the robot is shown, by focusing on the actuation and guidance systems. A novel concept of the cable guidance system is outlined, which allows for a simple kinematic model to control the manipulator. As an application example, a laser diode is mounted onto the end-effector of a prototype to perform laser engraving on a paper sheet. Observations on the experiments are reported and discussed.

In this paper, we provide an analytical formulation for the geometricostatic problem of continuum planar parallel robots. This formulation provides to an analytical computation of a set of equations governing the equilibrium configurations. We also introduce a stability criterion of the computed configurations. This formulation is based on the use of Kirchhoff's rod deformation theory and finite-difference approximations. Their combination leads to a quadratic expression of the rod's deformation energy. Equilibrium configurations of a planar parallel robot composed of two hinged flexible rods are computed according to this new formulation and compared with the ones obtained with state-of-the-art approaches. By assessing equilibrium stability with the proposed technique, new unstable configurations are determined.

This paper presents a novel Cable-Driven Parallel Robot dedicated to laser-scanning operations. The proposed device can inspect low-accessibility environments thanks to a self-deployable end-effector, which can be inserted in a closed container through very small access areas, such as hatches, pipes, etc. The reconfigurable end-effector is suspended and actuated by extendable cables, and is equipped with an optical mirror, which is used to deflect a laser beam produced by a frame-fixed laser distance sensor. Thanks to its large orientation capabilities, the machine can record the position of points belonging to a large portion of the surface to be scanned, primarily by tilting and panning the end-effector. The robot is equipped with a frame-orientation calibration device, which can align the machine frame to earth gravity before operation. The robot capabilities are validated by a prototype, which experimentally reconstruct benchmark surfaces.