The paper presents a nonlinear observer design using Automatic Differentiation (AD). In order to design a nonlinear observer, symbolic approaches are utilized for calculating the Lie derivatives and Lie brackets that are difficult to obtain for large-scale systems. Fortunately, the AD-based algorithm is applicable to high order systems. To verify the method, a simulation of 2-dimensional nonlinear system, i.e., the sagittal plane of a mono-wheel robot, is shown.
Objective: The aim of the present study was to determine the test–retest reliability of the angle of subjective verticality in healthy young persons. Methods: The participants were ten young healthy adults, five men and five women. The subjective postural vertical (SPV) was measured in the frontal plane (with eyes open and eyes closed) and in the sagittal plane (with eyes closed). Participants were retested 1 week after the first test. The test–retest reliability for each parameter was estimated using the intra-class correlation coefficient [ICC(1,1)], and the minimal detectable change (MDC) scores were established with a confidence level of 95%. Results: The test–retest reliability for the SPV was substantial (ICC ≥0.61). The MDC95 values of the SPVs ranged from 1.1° to 2.1°. Conclusions: The test–retest reliability of the postural vertical in the frontal and sagittal planes was sufficiently high in healthy young participants.
We examined whether a swing on gymnastic rings can be performed by control for achieving an inter-joint coordination. The swing in the sagittal plane was modeled by a three-segment model with two degrees of underactuation. The coordination was modeled by a linear relation among joint angles as a virtual holonomic constraint. The controller was constructed by the partial feedback linearization. The simulation results showed that the model had solutions similar to steady swings in gymnastics, and the swing amplitude can be increased by switching two inter-joint coordination.
[Purpose] The purpose of this study was to clarify the correlation between the range of spinal mobility on the sagittal plane and the dynamic balance ability of elderly people living in communities. [Subjects and Methods] The persons studied were 31 healthy elderly people living in the community (16 females and 15 males). The range of mobility of the participants’ spines in the sagittal plane was measured by using a spinal mouse®. Balance ability was evaluated by using Functional reach (FR), Timed up and go (TUG), and Maximum walking speed (MWS). [Results] A significant positive correlation between the flexion range of the lumbar vertebrae and the FR distance was identified, and a significant negative correlation between the extension range of the thoracic vertebrae and the time required for TUG was also identified. In addition, a significant positive correlation between the extension range of the entire spine and MWS, was identified. [Conclusion] The result of this study have clarified that mobility of the spine in the sagittal plane is associated with dynamic balance ability, which is related to falling.