Inge Troch

Collision-avoidance control for redundant articulated robots

A 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.

Collision-Avoidance for Redundant Robots through Control of the Self-Motion of the Manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.

Base invariance of the manipulability index

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 mechanisms 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 mechanisms geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.

Blood glucose response to stress hormone exposure in healthy man and insulin dependent diabetic patients: prediction by computer modeling

To establish a qualitative and quantitative model of blood glucose response to stress hormone exposure, healthy subjects (HS) on and off somatostatin (250 mu gf/h) and insulin-dependent diabetic patients were infused with either epinephrine, glucagon, cortisol, growth hormone, or 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 utilization 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, differing only in the values of some typical parameters.<<ETX>>

A new on-line method to avoid collisions with links of redundant articulated robots

A new mathematical formulation of robot and obstacles is presented such that for on-line collision recognition only robot joint positions in workspace are required. This reduces calculation time essentially because joint positions in workspace can be computed every time from the joint variable through robot geometry. It is supposed 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 in 2D is defined in workspace such that there is no collision if the robot joints are outside these ellipses. First, some methods are presented for the automatic determination of these ellipse functions from the obstacle and robot data. Then, the boundary ellipse functions are used as optimization criterion in a collision-avoidance method. The method permits the tip of the hand to follow a given path 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 manipulators between obstacles.

Data reduction for manipulator path planning

Today, in robot applications continuous paths often result from CAD or other planning tools. We present here an approach to the question that has been discussed for a long time, i.e. how to approximate a given path by a second one in such a way that the latter lies in a tube of given radius e around the first. The approximation should be a (normally cubic) spline with a small number of breakpoints. The strategy is based on algorithms used in “computer aided geometric design” and is applied to examples from industrial and surgical robotics.

Implementation der Optimierungsumgebung GOMA in ACSL

Der vorliegende Beitrag beschaftigt sich mit der Integration von Optimierungsmoglichkeiten in Simulationssprachen. Nach einer kurzen Ubersicht wird eine Implementierungsmoglichkeit von Optimierungs-algorithmen in Simulationssprachen vom CSSL-Typ angegeben. Dabei wird im wesentlichen das von der Simulationssprache erzeugte „Simulations-Hauptprogramm“ erweitert. In der Folge wird der Optimierungs-Preprozessor „GOMA“ vorgestellt, der automatisch fur ein ACSL-Modell diese Programmerweiterungen generiert; im besonderen wird auf die komplexe und unter Umstanden mehrdeutige Wertubergabe zwischen Simulations- und Optimierungsprogramm eingegangen.

Global optimal control of redundant robot

A global optimal control algorithm was developed with the aim of finding a control which satisfies some special requirements in the sense of obtaining singular position free movement of the redundant robot mechanism. The solution of the developed global optimal control algorithm is a boundary value problem. The additional constraints in the boundary value problem were constructed with the use of an optimization process. The usefulness of the developed global optimal control algorithm is demonstrated by the example of the 3 DOFs planar redundant robot mechanism of SCARA type.

A New view of the Decoupling Problem for Industrial Robots

Nonlinear couplings between the various joints of a robotic arm cause trouble in robot control. One possibility to overcome these difficulties is offered by the concept of nonlinear decoupling. The latter leads to independent linear SISO systems, each of them describing the movement of one joint. Thus, an application of control concepts for linear SISO systems is possible. However, at present such decoupling controls are computed from the mathematical model of the arm, the so-called drive equations, whereas actuator dynamics are considered only in a secondary way. In this paper the decoupling problem for robots is investigated by accounting also for the actuator dynamics from the very beginning. This results in decoupling laws requiring a complete state feedback, i.e. not only joint positions and velocities but also the states of the various actuators have to be used. Further, formulas are given which make the computation of those states unsuitable for direct measurements.

Erstellung von Modellen für die Dynamik von Industrierobotern mit Hilfe hybrider Simulation

Es wird uber Simulationsstudien berichtet, bei denen versucht wurde fur das System „Roboter-Getriebe-Antrieb“ lineare Ersatzmodeile zu entwickeln, die zumindest fur einige Robotertypen fur den Zweck des Reglerentwurfs hinreichend genau sind. Hiebei erweist sich ein modularer Programmaufbau — wie er in besonders einfacherWeise auf einem Hybridrechner realisiert werden kann — als besonders zweckmasig, da hiedurch z.B. ein Vergleich verschiedener Ansatze fur die Reibung oder unterschiedlicher Antriebsarten in einfacher und problemangepaster Weise moglich wird.