The kinematic analysis of redundant serial manipulators with$2n+1$revolute joints (integer$n \geq 3$), which we call circular manipulators, is presented in this article. The structure of the kinematic chain of circular manipulators has special properties that can be seen in the Denavit–Hartenberg parameters: all orthogonal distances are zero, all even-numbered offsets are zeros, but odd-numbered offsets are not. Typical manipulators that fulfill these properties are redundant 7R serial chains ($n=3$) that mimic the human arm, e.g., the lightweight robot arm KUKA LBR iiwa. This 7R circular manipulator has self-motion as rotation around an axis that goes through two fixed points for a fixed pose. First, radical reparametrization is presented based on the swivel angle of the closed-form inverse kinematics solution for the 7R circular manipulator. Second, for a six-dimensional task, the inverse kinematics solution for redundant serial manipulators with$2n+1$revolute joints ($n\geq 3$) is reparametrized by the swivel angle and other$2n-6$rotation parameters. From a geometric point of view, for a circular manipulator with$2n+1$revolute joints, one can have${n(n-1)}/{2}$choices of such circular rotations. Third, we conjecture numerical kinematic singularities for circular manipulators in a recursive formula, confirming$n=5,6,7$.

Using the effects of quantum mechanics for computing challenges has been an often discussed topic for decades. The frequent successes and early products in this area, which we have seen in recent years, indicate that we are currently entering a new era of computing. This paradigm shift will also impact the work of robotic scientists and the applications of robotics. New possibilities as well as new approaches to known problems will enable the creation of even more powerful and intelligent robots that make use of quantum computing cloud services or co-processors. In this position paper, we discuss potential application areas and also point out open research topics in quantum computing for robotics. We go into detail on the impact of quantum computing in artificial intelligence and machine learning, sensing and perception, kinematics as well as system diagnosis. For each topic we point out where quantum computing could be applied based on results from current research.

The control system for a mobile robot typically assumes fixed kinematics according to the drive's geometry and functionality. Faults in the system, for example a blocked steering actuator, will then lead to an undesired behaviour, unless one takes care of specific single and/or multiple faults explicitly. We present a novel model-programmed procedure for on-line kinematics reasoning that allows a robot to deduce the (inverse)-kinematics of the drive and also its kinematic abilities for the specific modes of operation and some falt modes during operation. As a consequence, we can reconfigure a robot drive to compensate for some faults and also inform a higher level control system about changed mobility capabilities of a robot. Being fault tolerant is, however, only one advantage of our approach that derives the kinematics control strategy from a geometric and functional model of the drive. We can easily adapt the controller for various robot drives, handle drives that change their geometry and functionality during run-time and also provide the basis for a flexible control scheme for self-configuring multi-robot systems.

Modern drives of mobile robots are complex machines. Because of this complexity, as well as of wear and aging of components, faults occurs in such systems quite frequently at runtime. In order to use such drives in truly autonomous robots it is desirable that the robot is able to automatically react to such faults. Therefore, the robot needs reasoning and reconfiguration capabilities in order to be able to detect, localize and repair such faults on-line. In this paper we propose a model-based diagnosis and reconfiguration framework which allows an autonomous robot to detect and compensate faults in its drive. Moreover, we present an implementation for a real robot platform. Finally, we report experimental results which shows that the proposed framework is able to correctly cope with injected faults in the drive hardware, like broken motors.