In the present paper, we show that the pairing inversion problem of Ateipairing can be solved under the assumption that we have a generic algorithm for solving “exponentiation inversion” problem. With such an algorithm, the inversion problem of Ateipairing can be solved without solving the Miller inversion. Thus, the pairing inversion problem of Ateipairing is reduced to the exponentiation inversion problem.

This paper proposes a new active sensor system (active antenna) that can detect not only the contact location between an insensitive flexible beam and an environment but also the information of the environment's surface where the beam makes contact. The active antenna is simply composed of a flexible beam, actuators to move the beam, position sensors to measure the rotational angle of the beam, and a moment sensor. We first show that the contact distance under no lateral slip is proportional to the rotational compliance that the beam can sense at the rotational center. The lateral slip, which possibly occurs according to the pushing direction and the environment's geometry, overestimates the rotational compliance, and as a result, brings a large sensing error for the localizing contact point. The goal of this paper is to find the contact location under such conditions. We explore how to detect a lateral slip and how to determine the new pushing direction to avoid it. We show an algorithm that can search for the pushing direction which can avoid any lateral slip. The convergence of this algorithm is shown and a practical utilization of this algorithm is also discussed with a trade-off between the number of trials and the sensing accuracy.

This paper discusses the 3D vision based active antenna (3D-VBAA) that can detect the contact force and the contact point between an insensitive elastic antenna and a 3D environment. The 3D-VBAA is composed of an insensitive flexible antenna, two actuators, two position sensors, a camera, and a one-axis moment sensor. By utilizing the antenna's shape mapped into the calibration, plane C, the vision sensor can provide both the contact distance and a force component on C. The moment sensor output allows us to evaluate the force component normal to C. The 3D-VBAA can work even under a compliant object, while the 3D active antenna cannot. We show that the coupling effect between vision and moment sensor depends on the implementation angle of the CCD camera. We verify our idea experimentally.

This paper proposes the vision based active antenna (VBAA) that can detect the contact force, the stiffness of the environment, and the contact location between an insensitive elastic antenna and an environment, through the observation of the antenna's shape by a camera. We show that both the contact location and the contact force can be estimated by measuring two arbitrary points on the antenna after a pushing motion; even though the exact contact point is hidden by occlusion. By considering the geometrical relationship between. The virtual (without environment) and the real (with environment) displacements of the contact point, the stiffness of the environment can also be estimated, which our conventional active antenna can not do. We present the basic working principle of the VBAA and give experimental verification.

This paper is an extended version of the vision based active antenna (VBAA) that can detect the contact force, the stiffness of the environment, and the contact location between an insensitive elastic antenna and an environment, through the observation of the antenna's shape by a camera. If measured points are on the antenna, two arbitrary points are sufficient for computing the contact location and the contact force uniquely. In a practical application of VBAA, however, the measured points are not always on the antenna. In this paper, we show the condition for uniquely obtaining both contact location and contact force under the situation that the measured points are not always on the antenna. We also show a new compensation method to improve the sensing accuracy. We further verify our idea experimentally.

This paper discusses a 3-D Active Antenna that can detect the contact location between an insensitive flexible beam and a 3-D environment through the measurement of the rotational compliance of the beam in contact with the environment. The lateral slip, which possibly occurs for the 3-D Active Antenna, overestimates the rotational compliance, and as a result, brings a large sensing error for the localizing contact point. The goal of this paper is to find the contact point under such conditions. In the first step, we push the antenna to the environment. If no lateral slip is detected during this motion, the contact point can be obtained through a similar method used for the 2-D model. If a lateral slip is confirmed, the pushing direction is changed continuously until development of any lateral slip is finally avoided. The authors explore how to detect a lateral slip and how to determine the new pushing direction to avoid it. The authors show an algorithm which can search not only the contact distance but also the normal direction of the environment's surface, even under the appearance of a lateral slip during the first step. The basic idea is also verified by experiments.

This paper discusses the sensing accuracy of the active antenna that can detect the contact location between an insensitive flexible beam and an environment through the measurement of the rotational compliance of the beam in contact with the environment. During pushing motion of antenna, the contact point generally shifts on the environment's surface, which either underestimates or overestimates the rotational compliance and eventually brings a sensing error for localizing the contact point. The goal of this paper is to consider the effect of the environment's curvature on the rotational compliance. We show that the rotational compliance of the antenna being in contact with a curved environment depends on not only the contact distance but also on a new nondimensional parameter including the pushing angle and the environment's curvature where the antenna makes contact. We further show experimental results to support the theoretical analysis for various environments with different curvature.