Trajectory generation to suppress oscillations in under-constrained cable-driven parallel robots

Cable-driven parallel robots (CDPRs) have many advantages over conventional link-based robot manipulators in terms of acceleration due to their low inertia. This paper concerns about under-constrained CDPRs, which have a less number of cables than six, often used favorably due to their simpler structures. Since a smaller number of cables than 6 are employed, however, their payloads have extra degrees of motion freedom and exhibit swaying motions or oscillation. In this paper, a scheme to suppress unwanted oscillatory motions of the payload of a 4-cable-driven CDPR based on a Zero-vibration (ZV) input-shaping scheme is proposed. In this method, a motion in the 3-dimensional space is projected onto the independent motions on two vertical planes perpendicular to each other. On each of the vertical plane, the natural frequency of the CDPR is computed based on a 2-cable-driven planar CDPR model. The precise dynamic model of a planar CDPR is obtained in order to find the natural frequency, which depends on the payload position. The advantage of the proposed scheme is that it is possible to generate an oscillation-free trajectory based on a ZV input-shaping scheme despite the complexity in the dynamics of the CDPR and the difficulty in computing the natural frequencies of the CDPR, which is required in any ZV input-shaping scheme. To verify the effectiveness of the proposed method, a series of computer simulations and experiments were conducted for 3- dimensional motions with a 4-cable-driven CDPR. Their results showed that the motions of the CDPR with the proposed method exhibited a significant reduction in oscillations of the payload. However, when the payload moves near the edges of its workspace, the improvement in oscillation reduction diminished as expected due to the errors in model projection.