Cable-suspended Parallel Robot Research Articles

Numerical and experimental investigation on the synthesis of extended Kalman filters for cable-driven parallel robots modeled through DAEs

Cable-driven parallel robots are parallel robots where light-weight cables replace rigid bodies to move an end-effector. Their peculiar design allows obtaining large workspaces, high-dynamic handlings, ease of reconfigurability and, in general, low-cost architecture. Knowing the full state variables of a cable robot may be essential to implement advanced control and monitoring strategies and imposes the development of state observers. In this work a general approach to develop nonlinear state observers based on an extended Kalman filter (EKF) is proposed and validated both numerically and experimentally by referring to a cable-suspended parallel robot. The state observer is based on a system model obtained by converting a set of differential algebraic equations into ordinary differential equations through different formulations: the penalty formulation, the Udwadia–Kalaba formulation, and the Udwadia–Kalaba–Phohomsiri formulation, which have been chosen since they can handle the presence of redundant constraints as often happens in cable-driven parallel robots. In the numerical investigation, the EKF is validated simulating encoders heavily affected by quantization errors to demonstrate the filtering capabilities of EKF. In the experimental investigation, a very challenging validation is proposed: only two sensors measuring the rotations of two motors are used to estimate the actual position and velocity of the end-effector. This result cannot be achieved by sole forward kinematics and clearly proves the effectiveness of the proposed observer.

Design and Inverse Kinematics Analysis of Cable-Suspended Parallel Robot ‘FarmPet’ for Agricultural Applications

Abstract: Farming is a very important part of our country in different manners. Traditional methods are not effective for matching today’s world requirements in farming. The world requires efficient & effective technological advancements in farming that are smart, cheap, effective as well as durable & can increase significantly yield. This need gave birth to the idea of a cable suspended farming robot, called "FarmPet". FarmPet is based on a simple mechanism which helps to hover a robot over the field with the help of multiple rope supports. Idea utilizes calculus equations, software programming & inverse kinematics to move the central robot. Through arrangement of four poles (minimum) with a stepper motor mounted on each, cables are driven from each motor and a central robot is fixed at the common end of the cables & is moved around the field supported by these cables. Software algorithms make the central robot move with constant velocity in a circular or straight line path over the field by continuously changing cable lengths in coordination. Robot is designed to perform agricultural tasks like pesticide sprinkling, insecticide sprinkling, spreading seeds, field surveillance, surveying crops & land mapping for efficient cropping without touching crops on ground or even disturbing sensitive crops. Practical testing on the model proved successful, calculations were found efficient and the algorithm worked.

Model predictive control for path tracking in cable driven parallel robots with flexible cables: collocated vs. noncollocated control

This paper proposes a novel control scheme for precise path tracking control in cable driven parallel robots (CDPRs) with axially-flexible cables, with particular focus to the challenging case of cable suspended parallel robots (CSPRs). To handle model nonlinearities while ensuring small computational effort, a controller made by two sequential control actions is developed. The first term is a position-dependent, model predictive control (MPC) with embedded integrator to compute the optimal cable tensions ensuring accurate path tracking and fulfilling the feasibility constraints; bounds on the feasible tensions are also included. The second control term transforms the optimal tensions into the commanded motor torques, and hence currents, that are evaluated through the kinetostatic model of the electric motors used for winding and unwinding the cables. Control design is performed through the robot dynamics model, formulated with the assumption of rigid cables. Moreover, the proposed control strategy is presented in two different architectures, collocated control and noncollocated control. Flexibility is handled by penalizing large tension variations in the cost function adopted in the controller design, plus some hard constraints on the maximum tension derivatives. These features, together with the embedding of the integrator within the MPC formulation, ensure smooth control tensions that allow handling the axial flexibility of the cables, although it is not explicitly considered in the controller design.To assess the performances of the proposed control algorithm, a kinematically-determined robot with a suspended, lumped end-effector is simulated by also adopting very flexible cables. Additionally, a simplified dynamic model of the electrical dynamics and the sensor quantization are included to provide a realistic representation of the real environments. The results, together with the fair comparison with a benchmark, corroborate the effectiveness of the proposed approach, its robustness, and its feasibility in real-time controllers due to the wise reduction of the computational effort.

Reconfiguration strategy for fully actuated translational cable-suspended parallel robots.

In Cable-Suspended Parallel Robots (CSPRs), reconfigurability, i.e., the possibility of modifying the position of the cable connection points on the base frame, is particularly interesting to investigate, since it paves the way for future industrial and service applications of CSPRs, where the base frame can also be replaced by mobile agents. This report focuses on fully actuated Translational Reconfigurable CSPRs (TR-CSPRs), i.e., reconfigurable CSPRs with a point mass end-effector driven by three cables. The objective of the work is twofold. First, it is shown that the Wrench Exertion Capability (WEC) performance index can be exploited to identify the configurations of the cable connection points optimizing a task-related performance in a single point or throughout the workspace, and hence to implement a workspace analysis. Then, by referring to the case of a TR-CSPR with a single reconfigurable connection point and in quasi-static working condition, an analytical approach is provided to reconfigure the robot while executing a task to avoid one of the paramount problems of cable robots: cable slackness. Brought together, the two contributions allow defining a reconfiguration strategy for TR-CSPRs. The strategy is presented by applying it to a numerical example of a TR-CSPR used for lifting and moving a load along a prescribed path: the use of the WEC allows analyzing the workspace and predicting if robot reconfigurability makes it possible to pass quasi-statically along all the points of a given path; then reconfigurability is exploited to avoid cable slackness along the path.

Dynamic Launch Trajectory Planning of a Cable-Suspended Translational Parallel Robot Using Point-to-Point Motions

In the last decade, cable-suspended parallel robots have attracted significant interest due to their large workspaces and high dynamic performances. However, a significant drawback is that cables must always be in tension to control the motion. Using launch motions to reach a target can enlarge the workspace of such robots. For a spatial translational cable robot suspended by six pairwise-parallel cables, an analytical method for planning point-to-point dynamic trajectories is proposed. Using a second-order Bézier curve trajectory, the mechanism starts from a static condition, passes through intermediate points, and finally launches an object towards a target. According to the kinematic constraint conditions on the position, the velocity and acceleration of the end-effector at a prescribed point, the parametric expressions for a dynamically-feasible trajectory can be determined. The feasibility of the trajectory is analyzed under the constraint that cable tensions must be positive at all times. By changing the position of the end point of the trajectory and the total motion time, the kinematic conditions on the position and velocity as well as the feasibility constraint can be satisfied. Finally, our point-to-point dynamic launch trajectories are verified by simulations and experiments.

Mass design method considering force control errors for two-redundant cable-suspended parallel robots

• Three design indexes were proposed to analyze the wrench-feasibility for cable-suspended parallel robots from a new perspective. • Comprehensive methodology is devised to design the mass (gravity) of the end-effector. • The methodology enables the selection of the force-controlled cable set from the possible combinations. For redundant cable-suspended parallel robots, gravity imposes a predictable minimum or maximum limit on the tension in all cables. The hybrid joint-space control strategy is adopted in this study. In this case, the chosen redundant cables are force-controlled, whereas the remaining ones are length-controlled in the joint space. This strategy aims at maintaining all cable tensions within the pre-defined force boundaries under the influence of force control errors. This is by designing the end-effector mass while simultaneously ensuring that the cable force control errors can be realized by the controllers in the physical world. Three design indexes are proposed for the basic mathematical framework and a comprehensive methodology is devised to design the end-effector mass (gravity) of cable-suspended parallel robots with two degrees of redundancy. A trajectory planning, based on the French CoGiRo layout, is adapted to validate the analysis and design process by using multibody dynamics simulations. Further, we found that the choice of the optimal cable combination is essential for performing force control, and control failures may occur when inappropriate combinations are selected.

Interval-analysis-based determination of the trajectory-reachable workspace of planar cable-suspended parallel robots

This paper proposes an interval-analysis-based algorithm to determine the trajectory-reachable workspace (TRW) of planar two-degree-of-freedom (DOF) cable-suspended parallel robots and planar three-DOF cable-suspended parallel robots. The TRW is a set of target points that the end-effector can reach along a given trajectory under the cable tension constraint. The method includes two sufficient conditions for a continuous set of target points to lie fully inside or outside the TRW. The two conditions can be verified by the implementation of interval-analysis-based methods. On the basis of these two verifiable sufficient conditions, a TRW determination method using branch-and-prune algorithms is presented. This method avoids the discretization of a continuous trajectory set, which guarantees the accuracy of TRW determination. Moreover, this method can determine the TRW when there are small uncertainties regarding the robot geometric parameters . • A new Trajectory-Reachable Workspace (TRW) determination method based on interval analysis. • High accuracy in determination TRW of planar cable-suspended parallel robots. • Computational time advantage in verification that a prescribed workspace belongs to TRW. • Small uncertainties on the geometric parameters can be handled in the determination of TRW.

Using Pose-Dependent Model Predictive Control for Path Tracking with Bounded Tensions in a 3-DOF Spatial Cable Suspended Parallel Robot

This paper proposes the preliminary results on a novel control architecture based on model predictive control (MPC) for cable-driven parallel robots (CDPRs) and applies them to a three degrees of freedom (3-DOF) robot with a suspended configuration, leading to a cable-suspended parallel robot (CSPR). The goal of the control scheme is ensuring accurate path tracking of the reference end-effector path, while imposing a priori positive cable tensions. To handle the nonlinearities characterizing the dynamic model that governs this kind of multibody system and to keep the computational effort low, a position-dependent MPC algorithm with an embedded integrator is designed to compute the optimal cable tensions required to track the end-effector commanded path. Such tensions must belong to the feasible domain defined through a lower bound, which is slightly greater than zero, to ensure that cables pull the end-effector, and an upper bound, to represent the maximum stress that cables can withstand without breaking. The resulting controller is nonlinear, although it performs a local linearization in the prediction at each time step to reduce the computational effort. The optimal tensions are then transformed into the commanded motor torques through the inverse dynamic model of the servomotors driving the winches, since no force measurement is adopted in the controller implementation. The control architecture is designed and numerically validated through a spatial CSPR with lumped end-effector, and driven by three cables (i.e., with a non-redundant configuration). Four different paths are assumed to highlight various features of the proposed controller.

Fractional order adaptive sliding-mode finite time control for cable-suspended parallel robots with unknown dynamics

Fractional order adaptive sliding-mode finite time control for cable-suspended parallel robots with unknown dynamics

Dynamic Modeling of a Cable Suspended Parallel Robot

Dynamic Modeling of a Cable Suspended Parallel Robot

Trajectory Planning of a CableBased Parallel Robot using Reinforcement Learning and Soft Actor-Critic

Industry 4.0 introduces the use of modular stations and better communication between agents to improve manufacturing efficiency and to lower the downtime between the customer and its final product. Among novel mechanisms that have a high potential in this new industrial paradigm are cable­suspended parallel robot (CSPR): their payload­to­mass ratio is high compared to their serial robot counterpart and their setup is quick compared to other types of parallel robots such as Gantry system, popular in the automotive industry but difficult to set up and to adapt while the production line changes. A CSPR can cover the workspace of a manufacturing hall and providing assistance to operators before they arrive at their workstation. One challenge is to generate the desired trajectories, so that the CSPR could move to the desired area. Reinforcement Learning (RL) is a branch of Artificial Intelligence where the agent interacts with an environment to maximize a reward function. This paper proposes the use of a RL algorithm called Soft Actor­Critic (SAC) to train a two degrees­of­freedom (DOFs) CSPR to perform pick­and­place trajectory. Even though the pick­and­place trajectory based on artificial intelligence has been an active research with serial robots, this technique has yet to be applied to parallel robots.

Algebraic Method-Based Point-to-Point Trajectory Planning of an Under-Constrained Cable-Suspended Parallel Robot with Variable Angle and Height Cable Mast

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots (CSPRs), point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot (UCPR) with variable angle and height cable mast as described in this paper. The end-effector of the UCPR with three cables can achieve three translational degrees of freedom (DOFs). The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed. The motion trajectory of the end-effector comprising six segments is given. The connection points of the trajectory segments (except for point P3 in the X direction) are devised to have zero instantaneous velocities, which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition. The trajectory is respectively planned using three algebraic methods, including fifth degree polynomial, cycloid trajectory, and double-S velocity curve. The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector. Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning. At the points where the velocity suddenly changes, the length and tension variation curves of the planned and unplanned three cables are compared and analyzed. The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment. The effectiveness and feasibility of fifth degree polynomial planning are validated.

Mathematical model of the artificial muscle with two actuators

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

Dynamic Point-To-Point Trajectory Planning for Three Degrees-of-Freedom Cable-Suspended Parallel Robots Using Rapidly Exploring Random Tree Search

Abstract This paper proposes a dynamic point-to-point trajectory planning technique for three degrees-of-freedom (DOFs) cable-suspended parallel robots. The proposed technique is capable of generating feasible multiple-swing trajectories that reach points beyond the footprint of the robot. Tree search algorithms are used to automatically determine a sequence of intermediate points to enhance the versatility of the planning technique. To increase the efficiency of the tree search, a one-swing motion primitive and a steering motion primitive are designed based on the dynamic model of the robot. Closed-form expressions for the motion primitives are given, and a corresponding rapid feasibility check process is proposed. An energy-based metric is used to estimate the distance in the Cartesian space between two points of a dynamic point-to-point task, and this system’s specific distance metric speeds up the coverage. The proposed technique is evaluated using a series of Monte Carlo runs, and comparative statistics results are given. Several example trajectories are presented to illustrate the approach. The results are compared with those obtained with the existing state-of-the-art methods, and the proposed technique is shown to be more general compared to previous analytical planning techniques while generating smoother trajectories than traditional rapidly exploring randomized tree (RRT) methods.

Dynamic transition trajectory planning of three-DOF cable-suspended parallel robots via linear time-varying MPC

This paper presents a dynamic transition trajectory planning technique for fully-actuated three-degree-of-freedom cable-suspended parallel robots. The proposed two-step technique can be used to plan transition trajectories to general periodic motions that extend beyond the static workspace of the mechanism. In the first step, the robot dynamics are linearized and partly decoupled by handling the less restricted gravity axis trajectory planning problem. The corresponding dynamic model and constraints of the other axes then become linear time-varying. Secondly, the generation of general periodic trajectories and the general transition trajectories is accomplished by convex optimization. The formulation of a constrained linear-quadratic optimal control problem for the dynamic transition task shows essential differences from previous works and extends to general cases. The proposed technique has the ability to generate general periodic trajectories and provides a universal transition planner. Indeed, there is no need to rely on a specific amplitude increment function, which makes the planning technique more flexible and applicable to general cases. Moreover, the quadratic programming problems can be solved reliably and rapidly. Example transition trajectories to harmonic and to non-harmonic periodic trajectories are given in order to illustrate the approach.

Design and Experimental Validation of a 3-DOF Underactuated Pendulum-Like Robot

This article presents the design and the experimental validation of a novel 3-degree-of-freedom (DOF) pendulum-like cable-driven robot capable of executing point-to-point motions by leveraging partial feedback linearization control and on-line trajectory planning based on adaptive frequency oscillators (AFOs). Unlike most cable-suspended parallel robots, which rely on at least n actuated cables to control n DOF, the proposed robot is capable of performing 3-DOF point-to-point motions, from a starting pose to a goal one within its dynamic workspace, by means of two actuators only. Feedback linearization allows the dynamics of the variable-length pendulum to be decoupled from the orientation of the end effector, enabling the device to use parametric excitation to control the oscillations of the variable-length pendulum, akin to a playground swing. A pool of AFOs is introduced to enable smooth, lag free on-line estimations of the current phase of the pendulum oscillation to inform the on-line planner and the parametric excitation controller. Experimental results demonstrate feasibility of the proposed design and control approach.

Experimental Validation of a Three-Degree-of-Freedom Cable-Suspended Parallel Robot for Spatial Translation With Constant Orientation

This paper shows an experimental validation for the design of a three-degree-of-freedom (DOF) cable-suspended parallel robot, which has six cables attached to the end-effector, arranged in three pairs, with each pair being driven by a single motor. For each pair, the moving platform attachment points and the winch cable guides on the fixed frame form a parallelogram, an arrangement that allows the end-effector to be positioned throughout its static workspace (SW) while maintaining a constant orientation. In this paper, the kinematic modeling of the robot is first described, along with its SW. Then, the robot's kinematic sensitivity is assessed in position and orientation such that an upper bound is found for the amplification of the cable positioning errors in Cartesian space. Finally, experimental results obtained using a proof-of-concept mechanism are described, which confirm the claim that the proposed design maintains a constant platform orientation in the SW.

Wrench Analysis of Cable-Suspended Parallel Robots Actuated by Quadrotor Unmanned Aerial Vehicles

Aerial cable towed systems (ACTSs) can be created by joining unmanned aerial vehicles (UAVs) to a payload to extend the capabilities of the system beyond those of an individual UAV. This paper describes a systematic method for evaluating the available wrench set and the robustness of equilibrium of ACTSs by adapting wrench analysis techniques used in traditional cable-driven parallel robots to account for the constraints of quadrotor actuation and dynamics. Case studies and experimental results are provided to demonstrate the analysis of different classes of ACTSs, as a means of evaluating the design and operating configurations.

A NOVEL METHODOLOGY FOR CHOOSING ACTUATORS OF CABLE-SUSPENDED PARALLEL ROBOTS

A novel methodology for choosing actuators of a CPR system was defined. This methodology was based on a novel procedure for analysis and synthesis of the workspace of Cable-suspended parallel robot, CPR system. Besides the kinematic and dynamic models of the CPR system, this procedure includes the complete mathematical model of the actuator as well. On this basis, this procedure presents a novel solution for the analysis and synthesis of CPR system’s workspace. When using the proposed methodology for choosing actuators of a CPR system, user and designer together define the corresponding technical requirements, one of them being the relative size of the feasible work space of the CPR system. Based on these requirements, the developed methodology tests available actuators from its data base and extracts the useful ones for the predefined specific purpose. The purpose of this research is to interconnect theoretical contributions from CPR system’s modelling and needs of the user and designer during their practical implementation. For this purpose, a user friendly program package called PPACM was generated. The program package PPACM and obtained results were validated through the presentation of several case studies.

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.