Advances in Robot Kinematics and Computational Geometry

Recently, research in robot kinematics has attracted researchers with different theoretical profiles and backgrounds, such as mechanical and electrica! engineering, computer science, and mathematics. It includes topics and problems that are typical for this area and cannot easily be met elsewhere. As a result, a specialised scientific community has developed concentrating its interest in a broad class of problems in this area and representing a conglomeration of disciplines including mechanics, theory of systems, algebra, and others. Usually, kinematics is referred to as the branch of mechanics which treats motion of a body without regard to the forces and moments that cause it. In robotics, kinematics studies the motion of robots for programming, control and design purposes. It deals with the spatial positions, orientations, velocities and accelerations of the robotic mechanisms and objects to be manipulated in a robot workspace. The objective is to find the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and to discover and visualise analytical tools for understanding and evaluation of motion properties ofvarious mechanisms used in a robotic system.

Computational Advances in Robot Kinematics.- 1. Workspace and Trajectory Analysis.- Characterizing the Workspace of the Spherical Image of Cooperating Robots.- On the Kinematics of Nonsingular and Singular Posture Changing Manipulators.- Determination of the Workspace Boundary of a General n-Revolute Manipulator.- Local Pictures for General Two-Parameter Planar Motions.- Limited Existence of Three-Dimensional Conformal Mapping in Robots.- 2. Computational Geometry in Kinematics.- Geometric Analysis of Spatial Rigid-Body Dynamics with Multiple Friction Contacts.- An Inverse Design Algorithm for a G2 Interpolating Spline Motion.- Geometry of Parallel-Jaw Gripper Grasps in the Plane.- Computational Geometry in the Synthesis of Skew Gear Teeth.- 3. Kinematic Errors and Calibration.- A CAD Tool for Remote Calibration of Space Station Robotic Test Bed.- Kinematic Calibration and the Product of Exponentials Formula.- A Systematic Approach to Model Arbitrary Non Geometric Kinematic Errors.- 4. Kinematics of Mobile Robots.- The Wheeled Actively Articulated Vehicle (WAAV): An Advanced Off-Road Mobility Concept.- Limitations of Kinematic Models for Wheeled Mobile Robots.- A Spatial Leg Mechanism With Anthropomorphic Properties for Ambulatory Robots.- An Investigation of the Kinematic Control of a Six-Legged Walking Robot.- 5. Kinematic Performance.- Kinematic Isotropy in 3R Positioning Manipulators.- An Object Shape Dependent Kinematic Manipulability Measure for Path Planning and Shape Optimization.- Application of Dexterity Indices to Spatial Articulated Hands.- Characterization of Kinematic and Static Performances of Robotic Geared Wrists.- 6. Kinematics in Control.- A Dynamically Consistent Strategy for Manipulator Control at Singularities.- Third-Order Control of a Planar System Tracking Constant Curvature Paths.- Control of Manipulators With Flexible Joints and Links by Non Linear Inversion, Modal Damping and Joints Stiffening.- Inverse Kinematic Solution and Mixed Control Law for Redundant Robot in the Cartesian Space.- 7. Force and Elasticity Analysis.- An Inverse Force Analysis of a Spatial Three-Spring System.- A Two-Arm Robot Can Be Stronger Than Two Arms - Experiments on Optimal Force Distribution in Two-Arm Robot.- Minimum Joint Torque Configurations of Planar Multiple-Link Manipulator.- 8. Inverse Kinematics.- Positional Inverse Kinematic Problems in Tn × Rm Solved in T2(n+m).- Explicit Modelling of General Task Spaces for Inverse Kinematics.- On the General Solution of the Inverse Kinematics of Six-Degrees-of-Freedom Manipulators.- Coping with Joint Velocity Limits in First-Order Inverse Kinematics Algorithms.- Hybrid Position-Orientation Decoupling in Robot Manipulators.- Dual Basis of Screw-Vectors for Inverse Kinestatic Problems in Robotics.- 9. Kinematic Design.- A Comparison of Two Minimally-Singular Articulated Arm-Subassemblies.- Design and Multi Objective Optimization of a Linkage for a Haptic Interface.- Design of a Three-dof Tendon-driven Manipulator with the Characteristics of Equal Maximum Tensions.- Spherical 3 d. o. f Geared Wrist with no Aligned Singularity.- 10. Kinematic Analysis.- Is There a Most General Kinematic Chain?.- Zero-Magnitude Screws in a 3-System of Finite Displacement Screws.- True Straight-line Linkages Having a Rectilinear Translating Bar.- On the Reduction of Parameters in Kinematic Equations.- 11. Parallel Manipulators.- Symbolic-Form Forward Kinematics of a 5-4 Fully-Parallel Manipulator.- Evaluation of the Errors When Solving the Direct Kinematics of Parallel Manipulators With Extra Sensors.-A Special Type of Singular Stewart-Gough Platform.- A Smart Kinestatic Interactive Platform.- 12. Task and Motion Planning.- Strategic Collision Avoidance of Two Robot Arms in the Same Work Cell.- A Collision-Detection Scheme Based on Convex-Hulls Concept for Generating Kinematically Feasible Robot Trajectories.- Collision-Avoidance Robot Path Planning Using Fully Cartesian Coordinates.- Planning Grasp Points and Base Locations of Single Robots and Cooperating Robot Systems.- Vision-Based Robot Path Planning.- Author Index.