Analysis and Control of Robot Manipulators with Kinematic Redundancy

A closed-form solution formula for the kinematic control of manipulators with redundancy is derived, using the Lagrangian multiplier method. Differential relationship equivalent to the Resolved Motion Method has been also derived. The proposed method is proved to provide with the exact equilibrium state for the Resolved Motion Method. This exactness in the proposed method fixes the repeatability problem in the Resolved Motion Method, and establishes a fixed transformation from workspace to the joint space. Also the method, owing to the exactness, is demonstrated to give more accurate trajectories than the Resolved Motion Method. In addition, a new performance measure for redundancy control has been developed. This measure, if used with kinematic control methods, helps achieve dexterous movements including singularity avoidance. Compared to other measures such as the manipulability measure and the condition number, this measure tends to give superior performances in terms of preserving the repeatability property and providing with smoother joint velocity trajectories. Using the fixed transformation property, Taylor's Bounded Deviation Paths Algorithm has been extended to the redundant manipulators.

The Control of Human Arm Movement Models and Mechanical Constraints

A serial-link manipulator may form a mobile closed kinematic chain when interacting with the environment, if it is redundant with respect to the task degrees of freedom (DOFs) at the endpoint. If the mobile closed chain assumes a number of configurations, then loop consistency equations permit the manipulator and task kinematics to be calibrated simultaneously using only the joint angle readings; endpoint sensing is not required. Example tasks include a fixed endpoint (0 DOF task), the opening of a door (1 DOF task), and point contact (3 DOF task). Identifiability conditions are derived for these various tasks.

Contact Sensing: A Sequential Decision Approach to Sensing Manipulation Contact

This paper describes a new statistical, model-based approach to building a contact state observer. The observer uses measurements of the contact force and position, and prior information about the task encoded in a graph, to determine the current location of the robot in the task configuration space. Each node represents what the measurements will look like in a small region of configuration space by storing a predictive, statistical, measurement model. This approach assumes that the measurements are statistically block independent conditioned on knowledge of the model, which is a fairly good model of the actual process. Arcs in the graph represent possible transitions between models. Beam Viterbi search is used to match measurement history against possible paths through the model graph in order to estimate the most likely path for the robot. The resulting approach provides a new decision process that can be use as an observer for event driven manipulation programming. The decision procedure is significantly more robust than simple threshold decisions because the measurement history is used to make decisions. The approach can be used to enhance the capabilities of autonomous assembly machines and in quality control applications.

Pose Determination of a Grasped Object Using Limited Sensing

This report explores methods for determining the pose of a grasped object using only limited sensor information. The problem of pose determination is to find the position of an object relative to the hand. The information is useful when grasped objects are being manipulated. The problem is hard because of the large space of grasp configurations and the large amount of uncertainty inherent in dexterous hand control. By studying limited sensing approaches, the problem's inherent constraints can be better understood. This understanding helps to show how additional sensor data can be used to make recognition methods more effective and robust.

Design and Development of 3-DOF Modular Micro Parallel Kinematic Manipulator

This paper presents the research and development of a 3-legged micro Parallel Kinematic Manipulator (PKM) for positioning in micro-machining and assembly operations. The structural characteristics associated with parallel manipulators are evaluated and the PKMs with translational and rotational movements are identified. Based on these identifications, a hybrid 3-UPU (Universal Joint-Prismatic Joint-Universal Joint) parallel manipulator is designed and fabricated. The principles of the operation and modeling of this micro PKM is largely similar to a normal size Stewart Platform (SP). A modular design methodology is introduced for the construction of this micro PKM. Calibration results of this hybrid 3-UPU PKM are discussed in this paper.