Reconfigurable Cable-Driven Parallel Robots Research Articles

Using differential-algebraic equations and natural coordinates for modelling and simulating cable-driven parallel robots

This paper proposes a comprehensive approach to the dynamic modelling of Cable-Driven Parallel Robots (CDPRs) by means of Differential-Algebraic Equations (DAEs). CDPRs are usually modelled through a minimal set of Ordinary Differential Equations (ODEs), often by making some simplification or just focusing on the unconstrained platform/end-effector dynamics. The alternative use of redundant DAEs provides several benefits since several non-ideal properties and peculiar operations of CDPRs can be easily and accurately modelled. To provide a comprehensive modelling frame, the typical components of a CDPR with rigid cables are here discussed and modelled by exploiting the concept of DAEs, which use redundant coordinates and embed kinematic constraints in the algebraic part of the equations. Through such advantageous features, it is possible to model swivelling guiding pulleys with non-negligible dimensions and mass. The use of rheonomous constraints is proposed as well, to represent in a simple way the effect of the movable exit-points, that are widely adopted in reconfigurable CDPRs. Finally, the use of Natural Coordinates is proposed for representing spatial end-effectors and modelling some challenging operations such as its overturning or the picking of heavy objects. Numerical simulations and the comparison with the results provided by a benchmark software are shown to demonstrate the accuracy and the computational efficiency of the proposed approach.

Optimal Reconfiguration Planning of a 3-DOF Point-Mass Cable-Driven Parallel Robot

Cable-driven parallel robots (CDPRs) have attracted much attention due to their advantages, such as large workspace and excellent load capacity. However, their adaptability to different tasks has been limited because of fixed configurations. To improve this, a novel 3-DOF point-mass reconfigurable CDPR (RCDPR) has been designed, and its configuration can be changed by adjusting the positions of multiple cable anchors. Since wrench feasible workspace (WFW) is an essential criterion that describes the configuration characteristics, an optimal reconfiguration planning method is proposed to schedule the sequence and number of all movable cable anchors for adjusting the WFW range. Based on a two-level optimization process, the method can realize static reconfiguration (SR) or dynamic reconfiguration (DR) of the RCDPR. If SR cannot provide the required WFW by finding a static optimal configuration, the WFW range will be dynamically adjusted by DR. Besides, the number of movable cable anchors is minimized in DR by applying <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -norm optimization to the anchor velocity sequences. Simulations and experiments are implemented, and the results show that the proposed method can automatically determine when, which, and how the cable anchors move under physical constraints, and reducing the number of movable cable anchors can indeed save actuator energy effectively.

Cable Attachment Optimization for Reconfigurable Cable-Driven Parallel Robots Based on Various Workspace Conditions

Cable Attachment Optimization for Reconfigurable Cable-Driven Parallel Robots Based on Various Workspace Conditions

Cable failure tolerant control and planning in a planar reconfigurable cable driven parallel robot.

The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations.

Real-Time Reconfiguration Planning for the Dynamic Control of Reconfigurable Cable-Driven Parallel Robots

Abstract The movable anchor points make reconfigurable cable-driven parallel robots (RCDPRs) advantageous over conventional cable-driven parallel robots with fixed anchor points, but the movable anchor points also introduce an inherent problem—reconfiguration planning. Scholars have proposed reconfiguration planning approaches for RCDPRs, taking into account the statics and kinematics of RCDPRs. However, a real-time reconfiguration planning approach that considers the dynamics of an RCDPR and is computationally efficient enough to be integrated into the RCDPR's dynamic controller is still not available in the literature yet. This paper develops a real-time reconfiguration planning approach for RCDPRs. A novel reconfiguration value function is defined to reflect the “value” of an RCDPR configuration and provide a reference index for the reconfiguration planning of an RCDPR. And then, the developed approach conducts reconfiguration planning based on the value of RCDPR configurations. The developed approach is computationally efficient, reducing the reconfiguration planning time by more than 93%, compared to single iteration of a box-constrained optimization-based reconfiguration planning approach. Such a high efficiency allows the developed approach to be integrated into an RCDPR's dynamic controller that usually runs with a high frequency. Integrating reconfiguration planning and dynamic control enhances the control performance of the RCDPR. To verify the effectiveness of the developed approach and the integration of reconfiguration planning and dynamic control for RCDPRs, a case study of an RCDPR with seven cables and four movable anchor points is conducted.

Optimal wrench-closure configuration of spatial reconfigurable cable-driven parallel robots

In this paper, a method for computing the optimal actuation of reconfigurable cable-driven parallel robots is presented. By using this method, the imperfect ability in exerting torque and limited orientation workspace of these robots may be improved. In a cable-driven parallel robot with reconfigurability, the attachment points of cables on the base are adjusted with regard to the movement of the end-effector on a trajectory. In such a design the redundant degree-of-freedom of the robot is increased accordingly. For an arbitrary pose of the end-effector, a spherical zone is defined in which the called wrench-closure condition is satisfied for a prescribed range of orientation. Taking the volume of such zone into consideration the optimal configuration of the robot may be determined. This configuration is found by appropriately changing the position of the moving attachment points on the base of the robot. By repeating this computation for a number of points on a specified trajectory, appropriate actuation plans are achieved. The computed optimal actuation guarantees balance of any external wrench by tension force of cables when the end-effector moves close to its trajectory. For a case of spatial reconfigurable cable-driven parallel robot, the optimal actuation is found based on Particle Swarm Optimization and performance of the robot is compared to the one with fixed cable attachment points on base. The result shows significant improvement of the performance of reconfigurable spatial cable-driven parallel robot.

Wrench-Feasible Workspace of Mobile Cable-Driven Parallel Robots

Abstract Cable-driven parallel robots (CDPRs) hold numerous advantages over conventional parallel robots in terms of high speed and large workspace. Cable-driven parallel robots whose workspace can be further increased by the modification of their geometric architecture are known as reconfigurable cable-driven parallel robots. A novel concept of reconfigurable cable-driven parallel robots that consists of a classical cable-driven parallel robot mounted on multiple mobile bases is known as mobile CDPR. This paper proposes a methodology to trace the wrench-feasible workspace of mobile cable-driven parallel robots by determining its available wrench set. Contrary to classical cable-driven parallel robots, we show that the available wrench set of a mobile cable-driven parallel robot depends, not only on the cable tension limits but also on the static equilibrium conditions of the mobile bases. The available wrench set is constructed by two different approaches known as convex hull approach and hyperplane shifting method. Three case studies are carried out for the validation of the proposed methodology. The proposed approach is experimentally validated on a mobile cable-driven parallel robot with a point-mass end-effector and two mobile bases.

Typical configuration analysis of a modular reconfigurable cable-driven parallel robot

To obtain better flexibility and multifunction in varying practical applications, several typical configurations of a modular reconfigurable cable-driven parallel robot are analyzed in this article. The spatial topology of the modular reconfigurable cable-driven parallel robot can be reconfigured by manually detaching or attaching the different number of modular branches as well as changing the connection points on the end-effector to satisfy diverse task requirements. The structure design of the modular reconfigurable cable-driven parallel robot is depicted in detail, including the design methodology, mechanical description, and control architecture. The inverse kinematics and dynamics of the modular reconfigurable cable-driven parallel robot considering diverse configurations are derived according to the vector closed rule and Lagrange method, respectively. The numerical simulation and related experiments of a typical configuration are achieved and analyzed. The results verify the effectiveness and feasibility of the inverse kinematics and dynamics models for the modular reconfigurable cable-driven parallel robot.

Discrete reconfiguration planning for Cable-Driven Parallel Robots

Cable-Driven Parallel Robots (CDPRs) are a class of parallel robots whose legs consist of cables. In most previous studies, the positions of the cable connection points on the moving platform and on the base frame are fixed, these positions being determined during the CDPR design. However, such fixed-configuration CDPRs are not always suitable and some situations require reconfiguration capabilities, e.g. a cluttered environment where cable collisions with objects in the CDPR workspace cannot be completely avoided without reconfigurations. This paper deals with Reconfigurable Cable-Driven Parallel Robots (RCDPRs) whose cable connection points on the base frame can be positioned at a possibly large but discrete set of possible locations. Means to select and optimize the sequence of discrete reconfigurations allowing the RCDPR moving platform to follow a prescribed path are introduced. A so-called feasibility map is first generated. For each possible configuration of the RCDPR, this map stores the feasible or unfeasible character of each point of the discretized prescribed path, according to user-defined constraints which ensure a proper functioning of the RCDPR. The feasibility map is next analyzed in order to determine minimum sets of configurations which allow the RCDPR to follow the whole prescribed path. Finally, the corresponding discrete reconfiguration planning problem is represented as a graph whose nodes correspond to feasible RCDPR reconfigurations. The arcs of the graph are weighted by a user-defined cost function so that the graph can be searched for an optimal reconfiguration strategy using Dijkstra’s algorithm.