Equilibrium Configuration Analysis and Equilibrium-Based Trajectory Generation Method for Under-Constrained Cable-Driven Parallel Robot

Abstract

Under-constrained cable-driven parallel robots (UCCDPRs) manipulate the end-effector (EE) by employing fewer number of cables than the degree of freedom of the EE, which causes unwanted swaying motions and oscillations. These unwanted vibrations can be suppressed by using the regenerated EE trajectory through the input-shaper. However, in the case of the UCCDPR systems, generating the feasible EE trajectory and deriving the natural frequency for designing the input-shaper is not straightforward since finding the stable equilibrium configuration is challenging. This paper proposes a novel methodology to find the stable equilibrium configuration of the general UCCDPRs in the assigned EE position. With the proposed method, the EE trajectory can be reproduced as a vibration suppression trajectory through an input shaper designed based on the analysis of the natural frequencies, as well as generating feasible EE trajectories based on the equilibrium configuration. Also, even if the orientation trajectory is not given and only the position trajectory is given, the cable length to follow the given position trajectory of the EE can be obtained based on the equilibrium configuration corresponding to the given position trajectory. Computer simulations and hardware experiments were conducted to verify the effectiveness and performance of the proposed method.INDEX TERMS Cable-driven parallel robots, underconstrained robots, underactuated robots, equilibrium configuration, natural frequency, input shaping, trajectory generation. I. INTRODUCTIONCable-driven parallel robots (CDPRs) are a group of parallel robots that control their end-effector (EE) or payload by employing several cables, instead of rigid links, actuated by servo-controlled winches. CDPRs have many advantages compared with conventional link-based parallel and serial manipulators. Since cables have low inertia, the mass of the total moving parts of a CDPR system is small, making high-speed operations possible and reducing its energy consumption. In addition, CDPRs can have a broad workspace and their structural simplicity makes it easy to adjust the The associate editor coordinating the review of this manuscript and approving it for publication was Hassen Ouakad .