Distribution of singularity and optimal control of redundant parallel manipulators

Abstract

Singularity is a fundamental problem in the analysis of parallel mechanisms. The distribution of singularity in workspace will determine to a great extent the properties of parallel mechanisms. In this paper, we will study the distribution of actuator singularity, which can also be applied to analyze end-effector singularity. A very important observation has been made that these two kinds of singularities are caused by the parameterization of a configuration manifold by actuator coordinates or end-effector coordinates. Despite the various styles of singularities of parallel mechanisms, there are some rules which govern the behavior of stable singularities. These rules provide some useful ideas in the design of redundant parallel mechanisms so as to achieve better performance in high speed motion and improve their stiffness. Optimal kinematic and dynamic control algorithms are designed and implemented which make use of the redundancy of the parallel mechanism. Experimental results agree with our expectation.

Inverse-kinematics-based control of a redundantly actuated platform for rehabilitation

“…Obviously, this affects the dexterity of the mechanism meaning that for certain postures within the workspace, the mechanism is not able to produce forces and torques to complete its task. Actuation redundancy has been presented by several researchers as a way to eliminate mechanism singular postures and improve mechanism dexterity [17][18][19][20][21][22]. A study of different mechanism geometries, in the presence and absence of actuation redundancy, for the parallel mechanism studied in this paper was presented in reference [23], where the concept of over-actuation was applied to completely remove mechanism singularity and improve the dexterity of the parallel mechanism.…”

“…Obviously, this affects the dexterity of the mechanism meaning that for certain postures within the workspace, the mechanism is not able to produce forces and torques to complete its task. Actuation redundancy has been presented by several researchers as a way to eliminate mechanism singular postures and improve mechanism dexterity [17][18][19][20][21][22].…”

A Redundantly Actuated Chewing Robot Based on Human Musculoskeletal Biomechanics: Differential Kinematics, Stiffness Analysis, Driving Force Optimization and Experiment

“…Redundant actuation has been proved to be an effective method for eliminating singularities, improving manipulability, stiffness and torque distribution in parallel robots (PRs) [20][21][22]. Liu et al [23] investigated a two degrees of freedom (DOFs) planar mechanism and analyzed the distribution of singularity of this mechanism. Zhu and Dou studied the kinematic model and Jacobian matrix of a 2-DOF 3-RRR planar PRs [24].…”

Kinematic Parameters Auto-Calibration of Redundant Planar 2-DOF Parallel Manipulator

“…Yiu and Zhang studied the kinematics of the parallel manipulator (Yiu & Li, 2003b;Zhang, 2006). Liu studied the singularities of the parallel manipulator with a geometric method (Liu et al, 2001a;. Furthermore, the dynamics and controller design problem of the parallel manipulator were studied by Liu (Liu et al, 2001a;Liu et al, 2001b;Liu & Li, 2002), Kock (Kock & Schumacher, 2000a;Kock & Schumacher, 2000b), Yiu Yiu & Li, 2003a), Cheng (Cheng et al, 2003), Shen (Shen et al, 2003) and Zhang (Zhang & Cong, 2005).…”