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SummaryA new mathematical formulation of robot and obstacles is presented such that for on-line collision recognition only robot joint positions in the workspace are required. This reduces calculation time essentially because joint positions in workspace can be computed every time from the joint variables through robot geometry. It is assumed that the obstacles in the workspace of the manipulator are represented by convex polygons. For every link of the redundant robot and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside this ellipsis.In addition to this, a collision avoidance method is presented which allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. The method is based on the generalized inverse with boundary ellipse functions as optimization criteria. The method permits the tip of the hand to approach any arbitrary point in the free space while the kinematic control algorithm maximizes the boundary ellipse function of the critical link. The effectiveness of the proposed methods is discussed by theoretical considerations and illustrated by simulations of the motion of three- and four-link planar manipulators between obstacles.

To establish a qualitative and quantitative model of blood glucose response to stress hormone exposure, healthy subjects (HS) on and off somatostatin (250 micrograms/h) as well as insulin dependent diabetic patients were infused with either epinephrine (E), glucagon (G), cortisol (F), growth hormone (GH) or with a cocktail of these hormones raising plasma stress hormones to values seen in severe diabetic ketoacidosis. The developed input/output model consists of two submodels interconnected in series plus two additional submodels for correction of gains describing both sensitivity of tissue response and utilisation as well as provision of glucose. It was shown and confirmed experimentally that blood glucose response to stress hormones was essentially nonlinear. Furthermore, the mathematical models for healthy subjects and for insulin dependent diabetic patients proved to be of the same structure and differed only in the values of some typical parameters. The model raises the possibility to describe and in part to predict blood glucose response to stress hormone exposure in healthy man and insulin dependent diabetic patients.

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The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.