本論文では,マニピュレータの冗長自由度を利用したコンプライアンス制御の一手法を提案した.作業中にロボットの途中リンクと環境とが接触するような状況に対して,マニピュレータの姿勢に十分な柔軟特性を持たせることで回避できることが数値実験,実機実験により示された.またマニピュレータの途中の点の柔軟度が明確に定義されたことにより,環境に応じたより良い姿勢の評価指標として利用できる.今後,複数点の制御点設定時における階層的な剛性パラメータ設定アルゴリズムの考察,つまりマニピュレータの姿勢の任意点に任意の柔軟特性を指定するアルゴリズムの導出が課題である.

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This paper describes a control strategy of null space motion of a two wheels driven mobile manipulator. Recently, robot is utilized in various industrial fields and it is preferable for the robot manipulator to have multiple degrees of freedom motion. Several studies of kinematics for null space motion have been proposed. However stability analysis of null space motion is not enough. Furthermore, these approaches apply to stable systems, but they do not apply unstable systems. Then, in this research, base of manipulator equips with two wheels driven mobile robot. This robot is called two wheels driven mobile manipulator, which becomes unstable system. In the proposed approach, a control design of null space uses passivity based stabilizing. A proposed controller is decided so that closed-loop system of robot dynamics satisfies passivity. This is passivity based control. Then, control strategy is that stabilizing of the robot system applies to work space observer based approach and null space control while keeping end-effector position. The validity of the proposed approach is verified by simulations and experiments of two wheels driven mobile manipulator.

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本稿では，ニューラルネットの積分表現に関する最近の研究結果を紹介する．深層学習の理論研究において，積分表現を用いてニューラルネットを関数解析的に取り扱う方法が発展しつつある．ところが，積分表現作用素Sが定義される空間の構造は多くのことが未解明である．さらに，には無限次元の

ker Sが存在するということもあまり認知されていない．本稿では，積分表現に纏わる複数の問題を取り上げながら，それぞれの文脈においてやker Sの特徴づけについて考察を加えていく．

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A stable control system is easily designed with the simple adaptive control (SAC) method by using the almost strictly positive real (ASPR) condition of a plant. For the plant that does not satisfy ASPR, an SAC system can be designed by adding a parallel feed-forward compensator (PFC) to the plant. However, in this case, steady-state error between the plant output and the reference model output may remain because of the PFC output. To solve this problem, the null-space adjustor which cancels the PFC input on the steady-state of the system, has been proposed. In our study, an SAC system with the null-space adjustor was extended using a disturbance compensator. We showed the boundedness of the signal in the proposed SAC system and confirmed the effectiveness of the proposed method by the numerical simulation.

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This paper describes a control scheme for the stable operation of a two-wheel driven mobile manipulator. The manipulator has excellent mobility and manipulability, and is capable of many functions. Therefore, it is very effective for use in human environments. However, since the mobile manipulator is unstable, it is difficult to perform specific tasks such as tasks requiring the precise movement of the manipulator and those that need large power, even if its attitude is controlled. Hence, in this paper, landing motion control is proposed to enable the stable operation of the manipulator. In addition, in order to switch from the landing mode to the moving mode, rising motion control is proposed. The validity of the proposed method was confirmed by experimental results.

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This paper describes a control strategy to realize grasping and cooperative motion in multiple mobile manipulators. In the general approach, the stable grasping motion is well realized, but the emergent motion such as the obstacle avoidance motion and the collision avoidance motion among the robots are not taken into account in the cooperative motion of multiple mobile manipulators. In the practical application, however, the above issue is important to realize an adaptive and sophisticated motion. The proposed approach introduces the null space motion based on the grasping matrix and the absolute position of target object in the grasping motion of the manipulator. In this case, each motion of mobile manipulator is given independently of the grasping and the cooperative motion, and the emergent motion is determined arbitrary. This is one of the remarkable features of the proposed strategy. Several numerical and experimental results show the validity of the proposed approach.

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This paper discusses a connection between the Wronski matrix and observability of linear time-invariant systems as well as their unobservable subspaces. For a linear time-invariant single-output system, its observability is closely related to linear independence of a set of functions associated with the output. Hence, there is a connection between observability and the Wronski matrix, which is often used for deciding linear independence of a set of functions. In discussing observability and the unobservable subspace in this context, it matters whether the Wronski matrix can describe the necessary and sufficient condition for an arbitrary set of functions to be linearly independent. This paper first reviews the known facts about the relationship between linear independence of a set of functions and the Wronski matrix, as well as an additional condition under which linear independence can be decided in a necessary and sufficient fashion through the Wronski matrix. Then, well-known conditions on observability and characterization of the unobservable subspace of linear time-invariant systems are revisited from the viewpoint of the null space of the Wronski matrix.

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In this paper, we proposed to design a null-space compensation control system for linear time invariant systems with multi-input redundant channels. In the input redundant systems, control input vector may have null-space component of the plant parameter vector. The null-space component does not contribute to the generation of the control force which drives the plant. If a control input that does not include the null-space component can be generated, efficient control is achieved in the sense of minimizing the norm of the control input. In the proposed method, a model reference adaptive control (MRAC) method was used to design the control system that compensates for the null-space component even if the plant parameters are unknown. The effectiveness of the proposed null-space compensation control system was shown by numerical examples.

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The governing equations for multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. It is desirable for efficient and accurate analysis to eliminate the Lagrange multipliers and dependent variables. As a method to solve the DAEs by eliminating the Lagrange multipliers, there is a method called the null space method. In a previous report, the author presented a method which extends the null space method and reduced the order to the degree of freedom of the system. However, the presented method is for a system with constraints not depending on time explicitly. In this report, a method applicable to a system with constraints depending on time explicitly is presented. Finally, the presented method is applied to four-bar linkages.

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In this paper, we propose a null-space compensation control for linear first-order systems with redundant two input channels. In the input redundant systems, control input vector generally has null-space component of the plant parameter vector. The null-space component does not contribute to the generation of the control force which drives the plant state. If a control input that does not include the null-space component can be generated, efficient control is achieved from the viewpoint of minimizing the norm of the control input. In the proposed method, an adaptive control method is used to design a control system that compensates for the null-space component, even if the plant parameter vector is unknown. The effectiveness is shown by numerical examples.

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This paper proposes position and force hybrid control of a mobile manipulator to cooperate with its subsystems which are a wheeled mobile robot and a manipulator arm. These subsystems have different dynamical characteristics. Moreover, a wheeled mobile robot is subject to nonholonomic constraints. In general, these issues are taken into consideration in developing a planning and control algorithm. This paper describes a unified approach to control a mobile manipulator which can regarded as a redundant manipulator. In the proposed approach, realizing the high manipulability of the end-effector's motion, the redundancy of the whole system is utilized under consideration of the dynamical behavior. Then equivalent mass matrix is introduced as a performance index of the end-effector's dynamical motion. The effectiveness of the proposed control methods is confirmed by several experimental results.

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This paper describes a decoupling force control strategy of redundant manipulator by workspace observer. In general, the calculation process of the redundant manipulator becomes complicated as the number of degree-of-freedom motion increases since the controller includes the pseudo inverse Jacobian matrix. To improve this issue, we develop a simplification method of the inverse kinematics solution including null space calculation by using the transposed Jacobian matrix, and the workspace observer. Here the stable condition of the proposed controller is also shown. Its condition is an important index to construct the stable workspace observer.
The validity of the proposed method is confirmed by the numerical and experimental results in the 3link planar redundant manipulator.

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Redundant multi-degree-of-freedom (MDOF) bilateral system in workspace is expected to be a key technology for the development of next generation robots because of the variety of feasible tasks. Nowadays, four channel bilateral structures based on acceleration control have been introduced to realize both position and force tracking in a bilateral control system. Additionally, torque observers have been implemented to facilitate force feedback without the use of torque/force sensors. However, differences in controller composition between the joint space and workspace are still unclear. In particular, observer designs in both spaces are important for a realization of torque/force sensorless bilateral control. This paper presents a performance evaluation of an MDOF force sensorless bilateral system performed by considering the design space of observers by numerical and experimental analyses.

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The governing equations for multibody systems are often formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. As a method to solve the DAEs by eliminating the Lagrange multipliers, there is a method called the null space method. In a previous report, one of the authors presented procedure to formulate the governing equations of multibody systems by using the variational principle called the modified Hamilton's principle. The governing equation obtained by the presented procedure involves the Lagrange multipliers. In this report, use of the null space method in the modified Hamilton's principle is discussed. Then, a new method to obtain the null space matrix is presented. Finally, numerical examples are shown.

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Optical tomography is a new modality of non invasive measurement of physiological information, and some algorithms using the technique of the ill-posed inverse problem have been developed to obtain images. These algorithms, however, are still at the early stage and significant improvement is expected to obtain better images toward practical and clinical applications. This paper describes the rationale of a novel image reconstruction method that estimates the nullspace contribution using prior knowledge in a maximum-a posteriori-probability (MAP) framework. We illustrate and verify our concept for two cases of optical tomographic reconstruction ; one using simulated and the other using experimental data. The improvement by using our nullspace-MAP algorithm over the conventional Newton-Raphson scheme is found to be significant for the two examples.

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The control of the imbalance of wheel load in a railway vehicle is important in maintaining running safety against a flange climb derailment. This paper discusses a control method for quasi-static wheel load variation in transition curves by utilizing the leveling devices that are widely installed on recent railway vehicles with air suspentions. We propose a hardware construction to control wheel load variation by using pneumatically controllable leveling valve rod, of which the length is adjustable by using pneumatic cylinders. We also propose an in-vehicle control method, which means that the control method does not depend on the relative position between the vehicle and the earth (e.g. GPS) explicitly. We confirmed that 30% of wheel load inbalance is reduced at its maximum by appling the proposed control method in a transition curve through a running test by the use of a real railway vehicle.

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A symbolic calculation method for internal forces of redundantly actuated parallel manipulators is proposed. The internal forces of the redundantly actuated parallel manipulators are calculated from the null space of the transposed Jacobian matrix (TJM). Conventional researches have mainly treated n×(n+1) TJM, the redundancy of the parallel manipulator is one. For the parallel manipulators with greater redundancy, the system with n×m TJM has been divided into n×(n+1) sub mechanisms. However, for general parallel manipulators, investigating only the n×(n+1) sub mechanisms may not result in the entire workspace. In this paper, the internal forces of redundantly actuated parallel manipulators of n×m TJM are directory derived without using sub mechanisms. Null space of n×m matrix is directly derived using the Cramer's rule of linear algebra. Redundantly actuated DELTA parallel manipulators, three translational motions with m actuators, are introduced as examples of the proposed method. The kinematic model of the manipulator covers several types of rod actuation methods, e.g., rotational motor, linear motor, prismatic joint, and cable driven. The 3×m TJM of the kinematic model is consisted by multiplies of simple matrices; 3×m matrix, each column of it corresponds to the unit direction vector of the rod, and m×m diagonal matrix. Null space of the 3×m TJM of the DELTA is symbolically derived. By the simple characteristics of the TIM, the internal forces of the DELTA are derived as simple formulas.

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Redundant manipulator is useful for posture control with keeping the desired end-effector position by using its redundancy. This makes it possible to realize dexterous motion such as obstacle avoidance motion with achieving the target task. However, the more degree-of-freedom motion increase, the smaller the stiffness of redundant manipulator is. This induces unacceptable vibration in the manipulator motion. To address this issue, this paper describes a strategy of vibration suppression by using workspace observer and resonance ratio control based nullspace control. The validity of the proposed approach is confirmed by simulations and experiments.

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