Coordinated Control of a Mobile Manipulator

In this technical report, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation capability offered by fixed-base manipulators and the mobility offered by mobile platforms. While mobile manipulators offer a tremendous potential for flexible material handling and other tasks, at the same time they bring about a number of challenging issues rather than simply increasing the structural complexity. First, combining a manipulator and a platform creates redundancy. Second, a wheeled mobile platform is subject to nonholonomic constraints. Third, there exists dynamic interaction between the manipulator and the mobile platform. Fourth, manipulators and mobile platforms have different bandwidths. Mobile platforms typically have slower dynamic response than manipulators. The objective of the thesis is to develop control algorithms that effectively coordinate manipulation and mobility of mobile manipulators. We begin with deriving the motion equations of mobile manipulators. The derivation presented here makes use of the existing motion equations of manipulators and mobile platforms, and simply introduces the velocity and acceleration dependent terms that account for the dynamic interaction between manipulators and mobile platforms. Since nonholonomic constraints play a critical role in control of mobile manipulators, we then study the control properties of nonholonomic dynamic systems, including feedback linearization and internal dynamics. Based on the newly proposed concept of preferred operating region, we develop a set of coordination algorithms for mobile manipulators. While the manipulator performs manipulation tasks, the mobile platform is controlled to always bring the configuration of the manipulator into a preferred operating region. The control algorithms for two types of tasks - dragging motion and following motion - are discussed in detail. The effects of dynamic interaction are also investigated. To verify the efficacy of the coordination algorithms, we conduct numerical simulations with representative task trajectories. Additionally, the control algorithms for the dragging motion and following motion have been implemented on an experimental mobile manipulator. The results from the simulation and experiment are presented to support the proposed control algorithms

Exact Dynamics of the SU(K) Haldane-Shastry Model

The dynamical structure factor $S(q,\omega)$ of the SU(K) (K=2,3,4) Haldane-Shastry model is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of free quasi-particles which are generalization of spinons in the SU(2) case; the excited states relevant to $S(q,\omega)$ consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Near the boundaries of the region where $S(q,\omega)$ is nonzero, $S(q,\omega)$ shows the power-law singularity. It is found that the divergent singularity occurs only in the lowest edges starting from $(q,\omega) = (0,0)$ toward positive and negative q. The analytic result is checked numerically for finite systems via exact diagonalization and recursion methods.Comment: 35 pages, 3 figures, youngtab.sty (version 1.1

On Feedback Linearization of Mobile Robots

A wheeled mobile robot is subject to both holonomic and nonholonomic constraints. Representing the motion and constraint equations in the state space, this paper studies the feedback linearization of the dynamic system of a wheeled mobile robot. The main results of the paper are: (1) It is shown that the system is not input-state linearizable. (2) If the coordinates of a point on the wheel axis are taken as the output equation, the system is not input-output linearizable by using a static state feedback; (3) but is input-output linearizable by using a dynamic state feedback. (4) If the coordinates of a reference point in front of the mobile robot are chosen as the output equation, the system is input-output linearizable by using a static state feedback. (5) The internal motion of the mobile robot when the reference point moves forward is asymptotically stable whereas the internal motion when the reference point moves backward is unstable. A nonlinear feedback is derived for each case where the feedback linearization is possible

Coordinating Locomotion and Manipulation of a Mobile Manipulator

A mobile manipulator in this study is a manipulator mounted on a mobile platform. Assuming the end point of the manipulator is guided, e.g., by a human operator to follow an arbitrary trajectory, it is desirable that the mobile platform is able to move as to position the manipulator in certain preferred configurations. Since the motion of the manipulator is unknown a priori, the platform has to use the measured joint position information of the manipulator for motion planning. This paper presents a planning and control algorithm for the platform so that the manipulator is always positioned at the preferred configurations measured by its manipulability. Simulation results are presented to illustrate the efficacy of the algorithm. The use of the resulting algorithm in a number of applications is also discussed

Studies on the Mechanism of Bile Pigment Formation in Vivo. III. On the Transition of Biliverdin, and Bilirubin in the Bile of Rabbits.

1. In the bile of rabbits, the metabolisms of biliverdin and bilirubin are in a solucible state, and which have a ratio of 2: 1 in normal animals. 2. In the production of biliverdin, the liver, especially the parenchyma of the liver has a very important role, while that of the reticulo-endothelial system is rather minor. However, in the case of glucose administration, the reduction of bilirubin from biliverdin is performed in the reticulo-endothelial system, thus conferring an important part of this system. 3. The production of bilirubin is performed primarily extrahepatically, and the participation of the extrahepatical reticuloendothelial system is of a conservative nature, thus denying us any willingness to agree to the theory of bilirubin production in the reticulo-endothelial system. 4. On administration of hemolysed blood, bile pigments in bile demonstrate a remarkable increase, while as compared when injected into the auricle veins in cases of administration through the portal vein a decline in the functions of the liver reticulo-endothelial system is seen, causing a decrease in biliverdin amount. In the former modus of administration, an occasional stimulation of the liver reticulo- endothelial system is seen, causing reduction of biliverdin to bilirubin. 5. Concluding from these facts, biliverdin in rabbit bile occupies the role of an intermediate product in the production and metabolism of bilirubin.</p

キケロ主義論争と雄弁の衰退 -エラスムス的「適正」をめぐって-

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