Singularity of cable-driven parallel robot with sagging cables: preliminary investigation

International audienceThis paper addresses for the first time the singu-larity analysis of cable-driven parallel robot (CDPR) with sagging cables using the Irvine model. We present the mathematical framework of singularity analysis of CDPR using this cable model. We then show that, besides a cable model representation singularity, both the inverse and forward kinematics (IK and FK) have a singularity type, called parallel robot singularity, which correspond to the singularity of an equivalent parallel robot with rigid legs. We then show that both the IK and FK have also full singularities, that are not parallel robot singularity and are obtained when two of the IK or FK solution branches intersect. IK singularity will usually lie on the border of the CDPR workspace. We then exhibit an algorithm that allow one to prove that a singularity exist in the neighborhood of a given pose and to estimate its location with an arbitrary accuracy. Examples are provided for parallel robot, IK and FK singularities. However we have not been able to determine examples of combined singularity where both the IK and FK are singular (besides parallel robot singularity)

Integrated Trajectory-Tracking and Vibration Control of Kinematically-Constrained Warehousing Cable Robots

With the explosion of e-commerce in recent years, there is a strong desire for automated material handling solutions including warehousing robots. Cable driven parallel robots (CDPRs) are a relatively new concept which has yet to be explored for high-speed pick-&-place applications in the industry. Compared to rigid-link parallel robots, a CDPR possesses significant advantages including: large workspace, low moving inertia, high-speed motion, low power consumption, and incurring minimal maintenance cost. On the other hand, the main disadvantages of the CDPRs are the cable’s unilateral force exerting capability and low rigidity which is resulting in undesired vibrations of their moving platform. Kinematically-constrained CDPRs (KC-CDPRs) include a special class of CDPRs which provide a considerably higher level of stiffness in undesired degrees of freedom (DOFs) via connecting a set of constrained cables to the same actuator. Nevertheless, undesired vibrations of the moving platform are still their main problem which request more attention and investigation. Dynamic modeling, stiffness optimization, vibration and trajectory-tracking control, and stiffness-based trajectory-planning of redundant KC-CDPRs are studied in this thesis. As a new technique, we separate the moving platform’s vibration equations from its desired (nominal) equations of motion. The obtained vibration model forms a linear parametric variable (LPV) dynamic system which is based for the following contributions: 1) Proposing a new tension optimization approach to minimize undesired perturbations under external disturbances in a desired direction; and demonstrating the effectiveness of kinematically-constrained actuation method in vibration attenuation of CDPRs in undesired DOFs. 2) Providing the opportunity of using a wide class of well-established robust and optimal LPV-based control methods, such as H∞ control techniques, for trajectory-tracking control of CDPRs to minimize the effect of disturbances on the robot operation; and showing the effectiveness of kinematically-constrained actuation method in control design simplification of such robots. 3) Proposing the concept of stiffness-based trajectory-planning to find the stiffness-optimum geometry of trajectories for KC-CDPRs; and designing a time-optimal zero-to-zero continuous-jerk motion to track such trajectories. All the proposed concepts are developed for a generic KC-CDPR and verified via numerical analysis and experimental tests of a real planar warehousing KC-CDPR

Low Mobility Cable Robot with Application to Robotic Warehousing

Cable-based robots consist of a rigid mobile platform connected via flexible links (cables, wires, tendons) to a surrounding static platform. The use of cables simplifies the mechanical structure and reduces the inertia, allowing the mobile platform to reach high motion acceleration in large workspaces. These attributes give, in principle, an advantage over conventional robots used for industrial applications, such as the pick and place of objects inside factories or similar exterior large workspaces. However, unique cable properties involve new theoretical and technical challenges: all cables must be in tension to avoid collapse of the mobile platform. In addition, positive tensions applied to cables may affect the overall stiffness, that is, cable stretch might result in unacceptable oscillations of the mobile platform. Fully constrained cable-based robots can be distinguished from other types of cable-based robots because the motion and force generation of the mobile platform is accomplished by controlling both the cable lengths and the positive cable tensions. Fully constrained cable-based robots depend on actuator redundancy, that is, the addition of one or more actuated cables than end-effector degrees of freedom. Redundancy has proved to be beneficial to expand the workspace, remove some types of singularities, increase the overall stiffness, and support high payloads in several proposed cable-based robot designs. Nevertheless, this strategy demands the development of efficient controller designs for real-time applications. This research deals with the design and control of a fully constrained cable-based parallel manipulator for large-scale high-speed warehousing applications. To accomplish the design of the robot, a well-ordered procedure to analyze the cable tensions, stiffness and workspace will be presented to obtain an optimum structure. Then, the control problem will be investigated to deal with the redundancy solution and all-positive cable tension condition. The proposed control method will be evaluated through simulation and experimentation in a prototype manufactured for testing

Redundant Hybrid Cable-Driven Robots: Modeling, Control, and Analysis

Serial and Cable-Driven Parallel Robots (CDPRs) are two types of robots that are widely used in industrial applications. Usually, the former offers high position accuracy at the cost of high motion inertia and small workspace envelope. The latter has a large workspace, low motion inertia, and high motion accelerations, but low accuracy. In this thesis, redundant Hybrid Cable-Driven Robots (HCDRs) are proposed to harness the strengths and benefits of serial and CDPRs. Although the study has been directed at warehousing applications, the developed techniques are general and can be applied to other applications. The main goal of this research is to develop integrated control systems to reduce vibrations and improve the position accuracy of HCDRs. For the proposed HCDRs, the research includes system modeling, redundancy resolution, optimization problem formulation, integrated control system development, and simulation and experimental validation. In this thesis, first, a generalized HCDR is proposed for the step-by-step derivation of a generic model, and it can be easily extended to any HCDRs. Then, based on an in-plane configuration, three types of control architecture are proposed to reduce vibrations and improve the position accuracy of HCDR. Their performance is evaluated using several well-designed case studies. Furthermore, a stiffness optimization algorithm is developed to overcome the limitations of existing approaches. Decoupled system modeling is studied to reduce the complexity of HCDRs. Control design, simulations, and experiments are developed to validate the models and control strategies. Additionally, state estimation algorithms are proposed to overcome the inaccurate limitation of Inertial Measurement Unit (IMU). Based on these state observers, experiments are conducted in different cases to evaluate the control performance. An Underactuated Mobile Manipulator (UMM) is proposed to address the tracking and vibration- and balance-control problems. Out-of-plane system modeling, disturbance analysis, and model validation are also investigated. Besides, a simple but effective strategy is developed to solve the equilibrium point and balancing problem. Based on the dynamic model, two control architectures are proposed. Compared to other Model Predictive Control (MPC)-based control strategies, the proposed controllers require less effort to implement in practice. Simulations and experiments are also conducted to evaluate the model and control performance. Finally, redundancy resolution and disturbance rejection via torque optimization in HCDRs are proposed: joint-space Torque Optimization for Actuated Joints (TOAJ) and joint-space Torque Optimization for Actuated and Unactuated Joints (TOAUJ). Compared to TOAJ, TOAUJ can solve the redundancy resolution problem as well as disturbance rejection. The algorithms are evaluated using a Three-Dimensional (3D) coupled HCDR and can also be extended to other HCDRs