Geometric Analysis Theory And Control Methods For Parallel Robots

Parallel mechanical architectures have been receiving increasing attention since it was originally proposed in the context of tire-testing machines and flight simulators. The main motivation behind the use of such architectures is that they can provide better stiffness and accuracy theoretically than serial kinematic chains. However, due to the closed-loop existing in parallel robots, the motions of these mechanisms are rather complex. Some theoretical problems, such as singularities, kinematics, dynamics, control and optimal machine synthesis, are still in open problem. Moreover, there is not an unified theory used to study these problems up to now.In this dissertation, some modern mathematic tools, including differential geometry, Riemannian geometry and Lie group, are used to discuss some theoretical topics on singularity, kinematics, dynamics, actuator-redundant control of general parallel robots, and an unified geometric framework of mechanism analysis and controller design for parallel manipulators are studied. Subsequent research contents and innovations are presented in this dissertation.1. Based on one exterior differential form on ambient space, the singularity problem is systemically studied and an unified geometric framework for analyzing singularities of parallel robots is developed. Based on the topological and geometric properties of configuration spaces, this dissertation proposes a fine classification of singularities of parallel robots, which is coordinate-independent. After the singular distributions introduced, the high order properties of singularities, including second singularity and degenerate singularity, are adequately explored. Simultaneously, the identification approach and underlying physical significations of various singularities are researched. The proposed theory is successfully applied to analysis of some typical parallel mechanisms.2. Based on the relations between parameters of mechanisms and topology of configuration space, the singularity-free parameters design problem of a general parallel robot is studied. According to the stability of singularities under these parameters perturbation, the singularities can be classified into the stable and unstable ones. Subsequently, the bifurcations of trajectory at parameterized singularities of parallel robots are studied in the framework of static bifurcation theory. The conclusion is drawn that the bifurcations and unstable singularities of parallel robots can be removed by optimal parameters design.3. Based on noninvariant holonomic constraints on Lie group SE(3), the motion of a kind of special mechanisms that have not full degree-of-freedom are studied and the results give us better geometric interpretations of the motion of these manipulators. By identifying the configuration space of end-effector with the homogeneous space of SE(3), and transforming the kinematics problems into the optimization process with constraints, kinematics of these robots can be solved through iterative approach.4. Using the Riemannian geometry language, the modeling and control of general parallel robots are studied. Based on the properties of Riemannian submanifold embedded in ambient space, the tangent and cotangent bundles of configuration space are projected onto free-motion subspace and constraint subspace. By the Riemannian connection of configuration manifold, the dynamic equations of parallel robots in joint space and workspace have a very concise form. Since all joints/links have only one degree of freedom, the parallel robot can be modeled in joint space as a mechanical control system on a Riemannian manifold and the motion of the end-effector can be viewed as a rigid body transformation in Lie group SE(3). Corresponding controller can be design through the control theoryon manifold. Lastly, a robust control algorithm for the simply five-links mechanism is presented and experiments results shows the controller is asymptotically stable.5. Based on the projection constructed by geometric method, the dynamics of a parallel manipulator is decoupled in...