Manipulators (Mechanism)

A well designed robot manipulator should have adequate workspace and good static-dynamic performance. It is well known that serial manipulators, while compared to similar size parallel ones, have larger workspace. However, due to their cantilever-like structure, the serial manipulators suffer from the disadvantage of having relatively poor static-dynamic performance. Contrarily, for fully parallel manipulators the good static-dynamic performance comes from the sacrifice of the workspace. Therefore, manipulators with more general geometries, in particular those with both the serial and the parallel modules, namely the hybrid manipulators, have attracted much of the research attention in robotics recently. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when they are considered in the above general context. The research described in this dissertation is an undertaking toward the establishment of a general theory of coordination for robotic mechanisms with general parallel or hybrid structures. The scope of this research is concentrated in the kinematics aspect of the aforementioned class of robot manipulators with the main emphasis on the velocity (instantaneous) kinematics. A kinestatic approach, which is based on screw system theory, is adopted in this dissertation. This kinestatic approach leads to the establishment of a fundamental theorem, dubbed as the Parallel Manipulator Coordination Theorem, which integrates the idea of parallel and serial manipulators. Furthermore, the theorem enables us to develop an analysis strategy for systematic formulation and characterization of robotic mechanisms with general parallel (non-redundant) and hybrid geometries. The analysis strategy entails constraints, statics, velocity, and singularity considerations. One distinct advantage of using the screw system theory as the analysis tool is that it facilitates the analysis in a fashion that physical meanings are preserved through out the derivation. The very aspect of preserving the physical meaning distinguishes this method from other algebraically-based and numerically-based methods. An intelligent fault-tolerant system has been studied at the end. The technique and conclusions from the study of parallel manipulator modules have been used to analyze the proposed design.

Parallel manipulators have their special characteristics in contrast to the traditional serial type of robots. Stewart platform is a typical six degree of freedom fully parallel robot manipulator. The goal of this research is to enhance the accuracy and the restricted workspace of the Stewart platform. The first part of the dissertation discusses the effect of three kinematic constraints: link length limitation, joint angle limitation and link interference, and kinematic parameters on the workspace of the platform. An algorithm considering the above constraints for the determination of the volume and the envelop of Stewart platform workspace is developed. The workspace volume is used as a criterion to evaluate the effects of the platform dimensions and kinematic constraints on the workspace and the dexterity of the Stewart platform. The analysis and algorithm can be used as a design tool to select dimensions, actuators and joints in order to maximize the workspace. The remaining parts of the dissertation focus on the accuracy enhancement. Manufacturing tolerances, installation errors and link offsets cause deviations with respect to the nominal parameters of the platform. As a result, if nominal parameters are being used, the resulting platform pose will be inaccurate. An accurate kinematic model of Stewart platform which accommodates all manufacturing and installation errors is developed. In order to evaluate the effects of the above factors on the accuracy, algorithms for the forward and inverse kinematics solutions of the accurate model are developed. The effects of different manufacturing tolerances and installation errors on the platform accuracy are investigated based on this model. Simulation results provide insight into the expected accuracy and indicate the major factors contributing to the inaccuracies. In order to enhance the accuracy, there is a need to calibrate the platform, or to determine the actual values of the kinematic parameters (Parameter Identification) and to incorporate these into the inverse kinematic solution (Accuracy Compensation). An error-model based algorithm for the parameter identification is developed. Procedures for the formulation of the identification Jacobian and for accuracy compensation are presented. The algorithms are tested using simulated measurements in which the realistic measurement noise is included. As a result, pose error of the platform are significantly reduced.

The dissertation focuses on robot manipulator dynamic modeling, and inertial
and kinematic parameters identification problem. An automatic dynamic parameters
derivation symbolic algorithm is presented. This algorithm provides the linearly
independent dynamic parameters set. It is shown that all the dynamic parameters are
identifiable when the trajectory is persistently exciting. The parameters set satisfies
the necessary condition of finding a persistently exciting trajectory. Since in practice the system data matrix is corrupted with noise, conventional
estimation methods do not converge to the true values. An error bound is given for
Kalman filters. Total least squares method is introduced to obtain unbiased
estimates.
Simulations studies are presented for five particular identification methods.
The simulations are performed under different noise levels.
Observability problems for the inertial and kinematic parameters are
investigated. U%wer certain conditions all L%wearly Independent Parameters
derived from are observable.
The inertial and kinematic parameters can be categorized into three parts
according to their influences on the system dynamics. The dissertation gives an
algorithm to classify these parameters.

A "hybrid" telerobotic simulation system that is suitable for telemanipulation rehearsal, operator training, human factors study and operator performance evaluation has been developed. The simulator also has the capabilities for eventual upgrade for supervisory control. It is capable of operation in the conventional rate-control, master/slave control and a data driven preprogrammed mode of operation. It has teach/playback capability which allows an operator to generate joint commands for real time teleoperation. For high-level task execution, the operator selects a specific task from a set of menu options and the simulator automatically generates the required joint commands. The simulator was developed using a three dimensional graphic model of an increasingly popular manipulator, TITAN 7F. A closed-form solution for inverse kinematics of the manipulator was found. Degeneracies from inverse kinematics solutions were observed to exist for certain arm configurations, although the manipulator can physically attain such configurations. An approach based on known facts about the manipulator geometry and physical constraints coupled with heuristics was used to generate physically attainable joint solutions from the inverse kinematics. The conditions that cause solution degeneracy were demonstrated to be related to singularity conditions. A novel object interaction detection strategy was implemented for more realistic telemanipulation. The object detection technique was developed based on the use of superellipsoid, which has a convenient inside-outside function for interference testing. The manipulator, with its end-effector and payloads, if any, were modeled as superquadric ellipsoids. A systematic way of determining transformation matrices between the superquadric manipulator links was developed. The interaction detection technique treats both moving and stationary objects in a consistent manner and has proved to be easy to implement and optimize for real-time applications. The feature has been applied for the simulation of pick-and-place operations and collision detection. It is also used to provide visual feedback as a low-cost force reflection and can be interfaced with a bilateral controller for force reflection simulation.

Theoretical and practical issues of kinematic modeling, measurement, identification and compensation are addressed in this dissertation. A comprehensive robot calibration methodology using a new Complete and Parametrically Continuous (CPC) kinematic model is presented. The dissertation focuses on model-based robot calibration techniques. Parametric continuity of a kinematic model is defined and discussed to characterize model singularity. Irreducibility is defined to facilitate error model reduction. Issues of kinematic parameter identification are addressed by utilizing generic forms of linearized kinematic error models. The CPC model is a complete and parametrically continuous kinematic model capable of describing geometry and motion of a robot manipulator. Owing to the completeness of the CPC model, the transformation from the base frame to the world frame and from the tool frame to the last link frame can be modeled with the same modeling convention as the one used for internal link transformations. Due to the parametric continuity of the CPC model, numerical difficulties in kinematic parameter identification using error models are reduced. The CPC model construction, computation of the link parameters from a given link transformation, inverse kinematics, transformations between the CPC model and the Denavit-Hartenberg model, and linearized CPC error model construction are investigated. New methods for self-calibration of a laser tracking coordinate-measuring-machine are reported. Two calibration methods, one based on a four-tracker system and the other based on three trackers with a precision plane, are proposed. Iterative estimation algorithms along with simulation results are presented. Linear quadratic regulator (LQR) theory is applied to design robot accuracy compensators. In the LQR algorithm, additive corrections of joint commands are found without explicitly solving the inverse kinematic problem for an actual robot; a weighting matrix and coefficients in the cost function can be chosen systematically to achieve specific objective such as emphasizing the positioning accuracy of the end-effector over its orientation accuracy and vice versa and taking into account joint travelling limits as well as singularity zones of the robot. The results of the kinematic identification and compensation experiments using the PUMA robot have shown that the CPC modeling technique presented in this dissertation is a convenient and effective means for accuracy improvements of industrial robots.