Rest-to-Rest Trajectory Planning for Underactuated Cable-Driven Parallel Robots

Abstract

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.

Design of a Planar Cable-Driven Parallel Robot for Non-Contact Tasks

“…These assumptions neglect not only all effects caused by the elastic nature of cables, which may be negligible in some small-to-medium-scale applications, but also the kinematics of the guidance system. Geometrical-model errors can be limited by accounting for the pulley geometry [4,32], but the model and control complexity is usually increased. As an alternative, if the standard kinematic model is to be used without inherent geometrical errors, special design techniques of the actuation units and guidance systems can be used, as discussed in the following.…”

“…In general, the presence of pulleys in the guidance system makes the system reliable, but complicates the geometrical model of the robot. This issue can be faced in two ways: by adopting a more complex model, which includes pulley kinematics for CDPR control [4,32,43], or by ignoring the actual geometry of the system, and accepting several modeling errors. Otherwise, particular layout and orientations of the pulley system must be adopted.…”

“…The proposed cable-loop arrangement realized with one cable avoids possible cable slackness during EE motion, which may happen if the parallelogram is made of two separate cables driven by the same winch. Two of the swivel pulleys (2,5) are fixed to the base and form the proximal guidance unit, while the other two (3,4) are attached to the platform and form the distal guidance unit. The distance a between the two pulleys composing each group is equal.…”

“…This allows cables to pull one against the other and to keep the overall system controllable over a wide range of externally applied loads. In other cases, to increase accessibility and reduce hardware complexity, suspended architectures with less cables than EE DoFs can be used, though they are more difficult to control [4,5].…”

Motion control of a cable-suspended robot using image recognition with coordinate transformation

“…25 For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. Hereafter, the article studies the trajectory planning for underactuated CDPRs in the case of rest-to-rest motions, when both motion time and path geometry are prescribed in the study by Ida`et al 26 Unfortunately, the control algorithm demonstrated in those studies are complex and their implementation is laborious, so employing them in real-time control is tough. Furthermore, the aforementioned findings focus on controlling the suspended platform and none proposes the control schemes to grasp objects with different shapes and colors.…”