Virtual reality technologies have made remarkable progress in recent years. In particular, head-mounted displays are widely used in the entertainment field because they can be realized as a passive device without human interaction. However, virtual reality also needs a haptic display device to present force to the user, but it is difficult to realize this type of device because the user must interact with it. Position and force sensors are necessary to reproduce the force accurately. These sensors mean that the haptic display becomes large and expensive. If the number of sensors could be reduced, then the haptic display can become small and inexpensive. Haptic displays could be made cheaply if they could be realized without using expensive force sensors. Here, we proposed a control law for realization of sensorless haptic displays using a model-following control. An external force estimation observer was applied to control law and realize a sensorless haptic display. Our experimental results confirm the proposed method. Therefore, haptic displays can be realized without using a force sensor.

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The aim of the present article is to give a linear dependence criterion of analytic functions in one variable, taking values close to the integers at positive integers. This result is a generalization of theorems due to G. Pólya, Ch. Pisot, as well as those proven by e.g., J.-P. Bésivin. Our result gives numerical conditions at any general infinite sequence, so as the analytic functions to be linearly dependent, of an explicit order of growth.

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Organisms can act autonomously because biological neural networks process the environmental information in continuous time. Therefore, organisms have inspired many applications of autonomous control to small-size robots. The authors are studying a small-size robot controlling without software programs using hardware neural networks (HNN). Two types of a robot, the quadruped-robot and the hexapod-robot, have proposed such as research results of the project. The quadruped-robot system is 130 mm wide, 140 mm long, 100 mm high. The hexapod-robot system is 4.0 mm wide, 4.0 mm long, and 5.0 mm high. The current paper shows the mechanical features of the small-size robots. Also, the authors describe the basic characteristics of HNNs that generate the gait for small-size robots. The pulses emitted by the HNN create oscillating patterns of electrical activity. The basic components (pulse-type hardware neuron model) of the HNN has the features of a class II neuron model, which behaves like a resonator. Thus, gait generation by the HNNs mimics the synchronization phenomena in biological neural networks. Consequently, our constructed HNNs can generate small-size robot gaits without requiring software programs.

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