Title
Design of a GUI: Definition of an arbitrary path for a cobot and corresponding collision detection

Abstract
The task of a cobot - "collaborative robot" [4] - is to support a human operator/worker. It was developed since usual robots are active elements and can work independently next to workers. In contrast, a cobot is a passive device. It needs a human operator to provide motive forces. The user defines the moving direction. Nonholonomic joints such as wheels, instead of servos, are steered in order to allow this movement with the least effort for the operator [5]. Constraints are software defined and lead to two different modes in which the cobot can move: The virtual caster and the virtual wall mode. In the former one, the wheel moves like a caster and its motion is unconstrained. Forces perpendicular to the actual moving direction of the cobot are minimized by steering the wheel in the new direction. Thus, the human collaborator can move the cobot in any direction wanted.

In the latter, the wheel is no longer steering to minimize perpendicular forces. The cobot is now in virtual wall mode. The wheel is steered tangent to the virtual wall and forces that tend to penetrate the constraint are ignored. Thus, the user has two possibilities: Moving the cobot along the wall or pushing it back to the unconstrained area.

Further there could be a path defined on which the cobot is allowed to move. Thus, the cobot is in virtual wall mode all the time and all forces perpendicular to the path are ignored. A detailed analysis of the two modes and their application has already been reported [6].

The aim of this project is to build a graphical user interface with which an arbitrary path in the xy-plane can be defined. Since a path is a conmovement, we further need to detect collision with the path.

Supported by the mouse the user defines points on the screen. These points are considered to be the corner points of the path and are connected by straight lines. Two adjacent lines are blended together with a curve in order to avoid the tangent and curvature discontinuities at the corner point joining them. To be able to choose an adequate smoothness for each blend, the user can also define its minimum curvature. To insure that the path is closed (polygon), the first point needs to be defined as the last one.

The second part of the project covers the collision detection. This is needed for the control system that is applied to keep the cobot on the defined path. The controller requires the following inputs:

1) the actual cobot position, 2) derived from 1) the minimum distance to the path, and 3) the path curvature and tangent at the point of minimum distance

With this, the controller can compare the actual position and moving direction to the desired

values, that the cobot should have, and react accordingly.

Source: Masters Thesis, Northwesten University, 1998

Paper Appndx

Title
Cobots: Robots for Collaboration with Human Operators

Abstract
A "cobot" is a robotic device which manipulates objects in collaboration with a human operator. A cobot provides assistance to the human operatorby setting up virtual surfaces which can be used to constrain and guide motion. While conventional servo-actuated haptic displays may be used inthis way also, an important distinction is that, while haptic displays are active devices which can supply energy to the human operator, cobots areintrinsically passive. This is because cobots do not use servos to implement constraint, but instead employ "steerable" nonholonomic joints. As aconsequence of their passivity, cobots are potentially well-suited to safety-critical tasks (e.g. surgery) or those which involve large interaction forces(e.g. automobile assembly). This paper focuses on the simplest possible cobot, which has only a single joint (a steerable wheel). Two control modesof this "unicycle cobot", termed "virtual caster" and "virtual wall" control, are developed in detail. Experimental results ar also presented.

Source: Proceedings of the International Mechanical Engineering Congress and Exhibition, Atlanta, GA, DSC-Vol. 58, pp. 433-39, 1996

Title
Nonholonomic Haptic Display

Abstract
Conventional approaches to haptic interface rely on high gain servos to implement virtual constraints. The role of the servo is to reduce the apparent degrees of freedom in such a way as to effectively constrain a human operator's motion. A significant drawback of this approach, however, is that the operator must interact directly with a high power system that is not inherently passive, and which may become unstable. In this paper, we present a novel approach to haptic display which allows virtual constraints to be implemented in a manner that is completely passive and therefore intrinsically safe. The key idea is to begin with a device having zero or one degree of freedom, and to use feedback control to increase the apparent degrees of freedom as necessary. This becomes possible with the use of nonholonomic joints, which have fewer degrees of freedom than generalized coordinates. The design and feedback control of several "programmable constraint machines" (PCMs) of this type are discussed.

Source: Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, Vol. 1, pp. 539-544, 1996