649 results about "Euler angles" patented technology

An apparatus and method employing principles of stereo vision for determining one or more orientation parameters and especially the second and third Euler angles θ, ψ of an elongate object whose tip is contacting a surface at a contact point. The apparatus has a projector mounted on the elongate object for illuminating the surface with a probe radiation in a known pattern from a first point of view and a detector mounted on the elongate object for detecting a scattered portion of the probe radiation returning from the surface to the elongate object from a second point of view. The orientation parameters are determined from a difference between the projected and detected probe radiation such as the difference between the shape of the feature produced by the projected probe radiation and the shape of the feature detected by the detector. The pattern of probe radiation is chosen to provide information for determination of the one or more orientation parameters and can include asymmetric patterns such as lines, ellipses, rectangles, polygons or the symmetric cases including circles, squares and regular polygons. To produce the patterns the projector can use a scanning arrangement or a structured light optic such as a holographic, diffractive, refractive or reflective element and any combinations thereof. The apparatus is suitable for determining the orientation of a jotting implement such as a pen, pencil or stylus.

An elastic wave device includes a support layer with a through-hole or a recess opened at an upper surface thereof, a piezoelectric thin film arranged on the support layer to extend above the recess or the through-hole of the support layer, and an IDT electrode defined on at least one of upper and lower surfaces of the piezoelectric thin film in a region of the piezoelectric thin film, the region extending above the recess, or the through-hole. A secondary mode of a plate wave, which contains a U1 component as a main component, is utilized. The piezoelectric thin film is made of LiTaO3, and Euler angles (φ, θ, ψ) of the LiTaO3 fall within specific ranges.

This invention relates to a system for estimating the position, velocity and orientation of a vehicle, by determining the components of two noncollinear constant unit vectors b,b according to vehicle body axes; and determining the components of the noncollinear constant unit vectors {right arrow over (g)}t,{right arrow over (e)}t according to Earth's axes. The system further determines the three components of angular velocity b of the vehicle in body axes; corrects the angular velocity b with a correction uω and obtains a corrected angular velocity {circumflex over (ω)}b=b+uω; a control module implementing a control law to calculate the correction uω, where the control law is:uω=σ(b×ĝb+b×êb)  [1]where σ is a positive scalar,such that upon using the corrected angular velocity {circumflex over (ω)}b=b+uω as input to a module for integrating the kinematic equations, the latter are stable in the ISS sense and the error in the estimation of the direction cosine matrix {circumflex over (B)} and of the Euler angles {circumflex over (φ)} is bounded.