Cable-suspended Parallel Robot Research Articles

Dynamically feasible motions of a class of purely-translational cable-suspended parallel robots

We consider dynamic motions of a spatial robot suspended by six cables, arranged so as to form three parallelograms. Each parallelogram is composed by two parallel cables sharing the same length. Due to this arrangement, the end-effector can only translate. The cables in each parallelogram can be actuated by one motor: only three motors are then required, which reduces the robot complexity and cost. This robot may perform pick-and-place operations over large workspaces. We find tight conditions for feasibility of dynamic trajectories for the general architecture, and also special conditions such that the robot is dynamically equivalent to a 3-cable robot with a point-mass end-effector: then, the feasibility conditions previously developed for the dynamic trajectories of 3-cable point-mass robots can be profitably reused for the present case. To practically realize such dynamic trajectories, we also analyze the reachable, singularity-free and interference-free workspace, finding analytical expressions of their loci. Finally, we perform experiments where the robot follows dynamic trajectories outside its static workspace, thus finding confirmation that the orientation remains approximately constant.

Periodic Trajectory Planning Beyond the Static Workspace for 6-DOF Cable-Suspended Parallel Robots

This paper proposes a dynamic trajectory planning technique for six-degree-of-freedom (6-DOF) cable-suspended parallel robots (CSPRs). First, a passive mechanical system that is equivalent to the CSPR is introduced to provide insight and facilitate the design of trajectories that can extend beyond the robot's static workspace. The tilt-and-torsion angle convention is used to develop the mathematical model and impose restrictions for the rotational component of the trajectories. The dynamic differential equations that govern the translational component of the trajectories are shown to become linear under some conditions. Natural frequencies of an equivalent passive linear system of constant-stiffness springs are, thus, obtained and the set of linear differential equations associated with this system is integrated to produce a general solution for natural, periodic trajectories. This approach is used to produce pure translation trajectories and more complex motion that includes changes in position and orientation. An experimental implementation is also presented using a 6-DOF prototype and a supplementary video file is included to demonstrate the results.

Dynamic Point-to-Point Trajectory Planning Beyond the Static Workspace for Six-DOF Cable-Suspended Parallel Robots

This paper proposes a point-to-point dynamic trajectory planning technique for reaching a series of poses with a six-degree-of-freedom (six-DOF) cable-suspended parallel robot. Each trajectory segment is designed to have zero translational and rotational velocity at its endpoints; transitions between segments have translational and rotational acceleration continuity. This formulation facilitates the synthesis of trajectories that extend beyond the static workspace of the robot. A basis motion is introduced, which is a mathematical function that can be adapted for each coordinate direction along each trajectory segment. Kinematic constraints are satisfied through the selection of the coefficients for this function. Dynamic constraints are imposed by defining feasible regions within the workspace for each segment endpoint, based on the previous endpoint. Spherical linear interpolation (SLERP) is used to produce singularity-free, optimally interpolated rotational trajectory segments. An experimental implementation is presented using a six-DOF prototype and a supplementary video file is included to demonstrate the results.

Dynamic trajectory planning for a spatial 3-DoF cable-suspended parallel robot

This paper deals with continuous path motion planning of a spatial 3-DoF cable-suspended parallel robot considering the robot’s dynamic constraints. First, based on the analysis of the algebraic and geometric properties of cable tension constraints, we present the sufficient and necessary conditions for the end-effector to pass through parallel singularities along straight line paths. Then, a piecewise linear interpolation method is introduced, showing that any target points above cable exit points can be connected in sequence via some intermediate points in the static workspace of the mechanism. The intermediate points are properly selected to avoid collisions between cables and obstacles, and the resulting trajectory is modified using quintic polynomials to enhance the performance. Afterwards, conditions for a general planar curve determined by three points to be feasible are given, and a general curve interpolation method is presented. Finally, three types of periodic trajectories are designed. Using the proposed trajectory planning method, not only can the positive cable tension constraints be satisfied, but the safety and the continuity of tensions can also be ensured. The effectiveness of the method is examined through simulations and experiments.

On the Design of a 4 Degrees-of-freedom Pick and Place Cable Suspended Parallel Manipulator

This paper proposes the design and control strategy for a four degrees-of-freedom spatial cable-suspended parallel robot for pick and place operations. Pick and place is a repetitive task requiring payload changes for the movement to pick-up the object, and the movement to the nal pose to release the manipulated object. In this paper, a new robust control strategy has been proposed, together with proper trajectories for the required operation. The control strategy consists on the system decoupling and linearization by means of a feedforward term and a cascade PD controller. The main advantage of the proposed solution is that its design can be scalable in size spanning from centimeters to meters with a relatively good positioning accuracy. Finally, simulations are reported to show the overall performances of the proposed con guration for pick and place operations with a medium size manipulator.

Tracking Control and Vibration Reduction of Flexible Cable-Suspended Parallel Robots using a Robust Input Shaper

The control of flexible cable-driven parallel robots usually requires not only the feedback from the joints, but the feedback from the end-effector pose or cable tension. This paper presents a new approach for reducing the vibration of flexible cable-suspended robots, using only the feedback from the joints. First, the dynamic equations of a 6DOF cable-suspended parallel robot with elastic cables were derived by Gibbs-Appel formulation. Subsequently, three different control approaches were investigated based on the computation load and required sensors. As a result, a feedback linearization method based on the rigid model of the system was selected. In order to reduce the vibration, a robust input shaping method was employed to prevent excitation of natural modes. Simulation results revealed that the proposed approach leads to a noticeable vibration and settling time reduction in cases of low and high cable stiffness, respectively. Moreover, another simulation compares the presented approach with a composite controller, which uses the feedbacks from the end-effector and actuators. Thereafter, the performance of the approach in vibration reduction is quantitatively shown. Finally, experimental validation of the approach was accomplished by frequency analysis of the vibration obtained from the IMU sensor, attached to the end-effector.

Dynamic Modeling and Feedback Linearization Control of Wheeled Mobile Cable-Driven Parallel Robot Considering Cable Sag

Cable robots are one of the subcategories of parallel robots used particularly for the applications where the large workspace is required. This type of robots can cover larger workspace compared with serial robots or parallel robots with rigid links. The main issues of cable robots are the cable flexibility due to the need to long cable length as well as inappropriate cable tension distribution in the proximity of the workspace boundaries. By combining a cable robot with a wheeled mobile robot, an unlimited area of workspace can be reached with shorter cable length. Moreover, as the end-effector does not need to come close to its boundary in the mobile platform frame to reach any desired point in the workspace, the tensions are distributed appropriately. The cable sagging in the cable robots is another issue that increases the system error and deviation of the end-effector from the desired trajectory. Therefore, this paper presents the dynamic modeling and control of a cable-suspended parallel robot with a wheeled mobile platform considering the weight of the cable. To this end, the dynamic equations of the wheeled mobile cable robot are obtained using Gibbs–Appel method. Then, the equations related to the weight and sagging of the cable are added to the equations of motion. Control of the system using feedback linearization method is presented. Furthermore, investigating the effect of cable sag on the tension and the end-effector pose of the closed-loop system is demonstrated. Finally, verification is carried out by comparing the simulation and experimental results.

The trajectory generation algorithm for the cable-suspended parallel robot—The CPR Trajectory Solver

The CPR Trajectory Solver is a procedure defined in this paper which is used to generate a smooth reference trajectory of CPR system’s camera which has a task to monitor and track the object in real time. We have generated a data base of four primitive trajectories (primitives) which are chosen by the CPR Trajectory Solver during the generation of camera’s complex reference trajectory. For trajectory generation, the CPR Trajectory Solver uses the knowledge about the current positions and velocity orientations of the camera and object and then it defines the goal position and velocity orientation of the camera. The CPR Trajectory Solver chooses one of the generated primitives for interconnecting the current and goal positions of the camera. After completing the chosen primitive, the CPR Trajectory Solver establishes the new positions and velocity orientations of the object. This process is repeated cyclically until the real time object monitoring and tracking task is completed. For the purpose of analysing and using the defined algorithm, we have synthesized a program package: CPRTS (CPRTrajectory Solver). By using this program package, the simulation experiments of the camera’s trajectory generation for the purpose of the object monitoring and tracking are presented. By using the CPR Trajectory Solver, motion autonomy of CPR system’s camera is increased. The camera has a task to follow and monitor the chaotically moving object.

Geometry-Based Trajectory Planning of a 3-3 Cable-Suspended Parallel Robot

This paper addresses the dynamic trajectory planning of a spatial cable-suspended parallel robot with three cables and three-degree-of-freedom. A new $s-\ddot{s}$ plane ( $s$ is the path parameter) method is presented to devise dynamically feasible point-to-point trajectories and periodic trajectories that are not fully located in the static workspace (SW) of the robot. First, the unilateral cable tension constraints are explicitly converted into geometry constraints in the $s-\ddot{s}$ plane. Then, a set of reachable workspaces is defined, which can be obtained analytically and the volumes of which are all much larger than the volume of the SW. By designing dynamic point-to-point trajectories directly in the $s-\ddot{s}$ plane, any points in the reachable workspaces can be reached in sequence via some intermediate points in the SW. The $s-\ddot{s}$ plane method also offers insights into planning periodic circular trajectory and transition trajectory for oscillations along a straight line, which is considered to be more efficient than the algebraic method provided in the literature. The proposed method always guarantees positive and continuous cable tensions and yields analytical results. The performance of the method is evaluated through numerical simulations and experiments.

Design and Optimal Control of an Underactuated Cable-Driven Micro–Macro Robot

In this paper, a planar underactuated cable-driven micro-macro robot is presented. The system consists of two-link passive serial manipulator attached to a cable-suspended parallel robot. The system is conceived for applications requiring point-to-point motions inside large workspaces in the presence of obstacles: The serial arm allows us to reach points close to the obstacles that would not be reachable by the cable robot alone due to cable-obstacle interference. The kinematic and dynamic models are presented and the differential flatness framework is applied to make the system controllable for point-to-point movements. In addition, a multiobjective optimization framework is presented, which allows us to choose the design parameters that minimize two conflicting objective functions (movement time and control effort) for a given movement task. This novel approach allows designers to infer useful information about the influence of the design parameters on the dynamic performance of the system.

Dynamics of the process of the rope winding (unwinding) on the winch

• “Jumpy” nonlinear in one row radially multilayered rope winding on the winch • Cable suspended system with three “jumpy” winding (unwinding) subsystems • Simulation experiments which show “jumpy” winding (unwinding) process • Two software packages: JUMPWIND OW and JUMPWIND RSCPR The aim of this paper is the analysis and definition of the phenomenon of non-linear and pulsed nature of dynamic process of the rope winding (unwinding) on the winch. This process is characterized with sudden and abrupt jumps of dynamic variables which describe the rope winding (unwinding) process. Because of that, we have named this process: process of the rope jumpy non-linear in one row radially multilayered winding (unwinding) on the winch. Because of the easier understanding of this jumpy concept of the winding (unwinding) process, we have first analysed this concept under idealized circumstances when the rotational speed of the winch is constant. To show that this process is even more complex in the real working conditions (when it is part of a complex system), we have analysed it during the implementation of the task of ropes suspended RSPCR (Rigid ropes S-type Cable-suspended Parallel Robot) system which carries a camera in 3 D space. Defined concept of jumpy process of rope winding (unwinding) on the winch is even more expressed at the RSCPR system, because in this case there is a strong coupling between three subsystems for ropes winding (unwinding). These effects have been demonstrated through simulation experiments for the real RSCPR system. This result has far wider significance, because the rope winding (unwinding) process can be an integral part of any complex system which is suspended by ropes. For verification of the results presented in this paper, we have developed two novel program packages named: J U M P W I N D − O W and J U M P W I N D − R S C P R . We have confirmed this theoretical concept through experimental results on one system consisting of motor and a winch.

Dynamic Point-to-Point Trajectory Planning of a Three-DOF Cable-Suspended Parallel Robot

This paper proposes a dynamic trajectory planning method for point-to-point motion of three-degree-of-freedom (three-DOF) cable-suspended parallel robots. Natural frequencies as well as associated ...

Cable-suspended CPR-D type parallel robot

This paper deals with the analysis and synthesis of a newly selected Cable-suspended Parallel Robot configuration, named CPR-D system. The camera carrier workspace has the shape of a parallelepiped. The CPR-D system has a unique Jacobian matrix that maps the relationship between internal and external coordinates. This geometric relationship is a key solution for the definition of the system kinematic and dynamic models. Because of the CPR-D system complexity, the Lagrange principle of virtual work has been adapted. Two significant Examples have been used for the CPR-D system analysis and validation.

Trajectory Generation for Three-Degree-of-Freedom Cable-Suspended Parallel Robots Based on Analytical Integration of the Dynamic Equations

This paper proposes a trajectory generation technique for three degree-of-freedom (3-dof) planar cable-suspended parallel robots. Based on the kinematic and dynamic modeling of the robot, positive constant ratios between cable tensions and cable lengths are assumed. This assumption allows the transformation of the dynamic equations into linear differential equations with constant coefficients for the positioning part, while the orientation equation becomes a pendulum-like differential equation for which accurate solutions can be found in the literature. The integration of the differential equations is shown to yield families of translational trajectories and associated special frequencies. This result generalizes the special cases previously identified in the literature. Combining the results obtained with translational trajectories and rotational trajectories, more general combined motions are analyzed. Examples are given in order to demonstrate the results. Because of the initial assumption on which the proposed method is based, the ratio between cable forces and cable lengths is constant and hence always positive, which ensures that all cables remain under tension. Therefore, the acceleration vector remains in the column space of the Jacobian matrix, which means that the mechanism can smoothly pass through kinematic singularities. The proposed trajectory planning approach can be used to plan dynamic trajectories that extend beyond the static workspace of the mechanism.

Dynamic trajectory planning study of planar two-dof redundantly actuated cable-suspended parallel robots

This paper analyzes a set of dynamic trajectories for planar two-dof redundantly actuated cable-suspended parallel mechanisms. In recent literature, the global dynamic trajectory planning problem of cable-suspended mechanisms was addressed and some of the characteristic properties of such robots were revealed. In this paper, actuation redundancy is introduced and the dynamic trajectory planning is addressed using a series of periodic trajectories (i.e. straight line and circular periodic trajectories) and the application of the antipodal theorem. The experimental results obtained show that introducing actuation redundancy increases the dynamic capabilities of the robots. Also, cable tensions acquired via tension sensors confirm that cables always remain taut during all experimental verifications at feasible frequencies and that they are consistent with the tension variations predicted by theory. Furthermore, special frequencies are specified that are similar to those encountered with non-redundant mechanisms. Additionally, an alternative architecture is proposed to deal with cable interferences and it is shown that the novel architecture leads to improved dynamic capabilities when compared to the original architecture.

Geometry Selection of a Redundantly Actuated Cable-Suspended Parallel Robot

This paper is dedicated to the geometry selection of a redundantly actuated cable-suspended parallel robot intended to manipulate heavy payloads over a wide workspace. Cable-suspended refers here to cable-driven parallel robots in a crane-like setting, where all the cable drawing points are located on top of the base frame, gravity being used to keep the cables taut. Geometry selection consists of determining the relative positions of the cable drawing points on the base frame and of the cable attachment points on the mobile platform together with the cable arrangement between these two sets of points. An original performance index is introduced. It is defined as the maximum acceptable distance between the mobile platform geometric center and the center of mass of the set consisting of the platform and a payload. This performance index is of particular interest in heavy payload handling applications. Used within a two-phase geometry selection strategy, it yields a new cable-suspended robot geometry having a very large workspace to footprint ratio and able to handle heavy payloads. A large-dimension redundantly actuated cable-suspended robot was built in order to demonstrate these capabilities.

The rigid S-type cable-suspended parallel robot design, modelling and analysis

SUMMARYThis paper presents design, modelling and analysis of the selected Rigid ropes S-type Cable-suspended Parallel Robot (RSCPR). The characteristic of this system is its geometric construction which defines the kinematic model through the Jacobian matrix. The relationship between external and internal forces is defined by the Lagrange principle of virtual work. The Jacobian matrix is directly involved in the application of the Lagrange principle of virtual work and generation of the dynamic model of the RSCPR system. Selected examples of the CPR system types are analysed and the comparison of their results is presented. The software package named ORIGI has been developed for the RSCPR model verification.

Dynamic Point-to-Point Trajectory Planning of a Two-DOF Cable-Suspended Parallel Robot

This paper presents two trajectory-planning approaches for the point-to-point motion of planar two-degree-of-freedom (dof) cable-suspended parallel mechanisms. The proposed techniques can be used to plan trajectories that extend beyond the static workspace of the mechanism. Trajectories are specified as a list of target points that must be reached in sequence, with a zero velocity at each of the target points. In the first technnique, polynomial trajectories are designed to connect the target points, while the second approach uses trigonometric functions. Both techniques ensure continuity of the accelerations. Based on the dynamic model of the robot, algebraic inequalities are obtained that represent the constraints on cable tensions. These inequalities are used to determine the feasibility of the planned trajectories. Polynomial trajectories must be discretized in order to verify feasibility, while trajectories that are based on trigonometric functions can be verified globally, based on a set of simple algebraic equations. Example trajectories are given in order to illustrate the approach. An experimental validation is also presented using a two-dof prototype, and two video extensions are provided to demonstrate the results.

Workspace Analysis and Performance Evaluation of a 6/6 Cable-Suspended Parallel Robot

This paper mainly addressed the workspace analysis and performance evaluation of a special class of the 6/6 cable-suspended parallel robot. Based on the screw theory and the static equilibrium, the Jacobian matrix of the cable -suspended parallel robot is constructed. The workspace volume is characterized as the set of points where the centroid of the moving platform can reach with tensions in all suspension cables for a constant orientation. This paper attempts to tackle some aspects of optimal design of this special class of the 6/6 cable-suspended parallel robot by addressing the variations of the workspace volume and the accuracy of the robot using different geometric configurations, different ratios and orientations of the moving platform. The global condition index is used as a performance index of a robot with respect to the force and velocity transmission over the whole workspace.

Inverse Kinematics and Singularity Analysis for a 3-DOF Hybrid-Driven Cable-Suspended Parallel Robot

This paper addresses the kinematics and graphical representation of the singularity configuration of a hybrid-driven cable-suspended parallel robot (HDCPR) with three translational degrees of freedom (DOFs). Applying the closed-loop vector method and geometric methodology, inverse kinematics of the HDCPR needed for singularity analysis is performed. For the sake of singularity condition calculation within the reachable workspace, the procedure utilizing analytical methodology and gradual search algorithm is presented. Simulation results demonstrate the validity of the kinematics and singularity analysis developed.