Self-Feedback Motion Control for Cable-Driven Parallel Manipulators

This article proposes a closed-loop control scheme based on joint-angle feedback for cable-driven parallel manipulators (CDPMs), which is able to overcome various difficulties resulting from the flexible nature of the driven cables to achieve higher control accuracy. By introducing a unique structure design that accommodates built-in encoders in passive joints, the seven degrees of freedom (7-DOF) CDPM can obtain joint angle values without external sensing devices, and it is used for feedback control together with a proper closed-loop control algorithm. The control algorithm has been derived from the time differential of the kinematic formulation, which relates the joint angular velocities to the time derivative of cable lengths. In addition, the Lyapunov stability theory and Monte Carlo method have been used to mathematically verify the self-feedback control law that has tolerance for parameter errors. With the aid of co-simulation technique, the self-feedback closed-loop control is applied on a 7-DOF CDPM and it shows higher motion accuracy than the one with an open-loop control. The trajectory tracking experiment on the motion control of the 7-DOF CDPM demonstrated a good performance of the self-feedback control method.

Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods

In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases.

Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot configuration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the final configuration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex field, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efficient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to find a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.

Three-degree-of-freedom Parallel Manipulator to Track the Sun for Concentrated Solar Power Systems

In concentrated solar power(CSP) generating stations, incident solar energy is reflected from a large number of mirrors or heliostats to a faraway receiver. In typical CSP installations, the mirror needs to be moved about two axes independently using two actuators in series with the mirror effectively mounted at a single point. A three degree-of-freedom parallel manipulator, namely the 3-RPS parallel manipulator, is proposed to track the sun. The proposed 3-RPS parallel manipulator supports the load of the mirror, structure and wind loading at three points resulting in less deflection, and thus a much larger mirror can be moved with the required tracking accuracy and without increasing the weight of the support structure. The kinematics equations to determine motion of the actuated prismatic joints in the 3-RPS parallel manipulator such that the sun's rays are reflected on to a stationary receiver are developed. Using finite element analysis, it is shown that for same sized mirror, wind loading and maximum deflection requirement, the weight of the support structure is between 15% and 60% less with the 3-RPS parallel manipulator when compared to azimuth-elevation or the target-aligned configurations.

Kinematic Design of a 6-DOF Parallel Manipulator with Decoupled Translation and Rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.