Intelligent Autonomous Systems

T. Kanade, L.O. Hertzberger, F.C.A. Groen
1991 Robotics and Autonomous Systems  
At CWI (Centrum voor Wiskunde en Informatica) a desk-top Virtual Reality apparatus, the Personal Space Station, was built which enables its users to interact with a computer generated 3D scene by manipulating real-world objects. A mirror reflects the generated scene in such a way that virtual objects seem to coincide with their realworld counterparts, in personal space, the natural space in which humans for instance connect two Lego bricks together or place their cups of coffee. The Personal
more » ... ce Station (PSS) measures where the real objects are and what their pose is in order to be able to generate a matching virtual scene. Unfortunately the measurements are not free of noise: Small, fast oscillations in rotational motion estimates disturb the virtual reality experience. To counteract the noise, rotation data can be processed by computationally cheap linear filters suitable for on-line use, although rotations form a cyclic non-linear space. Quaternions are a compact and convenient representation of rotations. Their linear tangent spaces are easily entered and left through the quaternion logarithm and exponent, which is exploited by a method found in the literature ([Lee2002]). It linearizes the filtering task by application of a finite impulse response (FIR) filter in rotational tangent space. In this report an automated procedure is described to tune a FIR filter to the application using captured motion data from the PSS. The resulting filter is extended with prediction based on velocity extrapolation and quantitative methods are presented to evaluate filter performance during the actual use of the PSS. A comparison is made between performances of the FIR filter and a predictive Double Exponential Smoothing (DES) and Kalman filter, both acting linearly on quaternion components. The FIR filter, apart from being the computationally cheapest method, performs best when the rotational signal is heavily oversampled. DES and Kalman perform comparably and better than FIR at lower lags, which is useful in applications with less oversampling. The DES algorithm is extremely memory friendly and has only two free parameters, whereas the Kalman filter requires much more to be tuned. The standard Kalman filter used is relatively computation power-friendly while performing at the same level as DES, although in other work the (extended) Kalman filter is reported to be extremely expensive compared with DES of the same performance. The experiments also show that errors introduced by disregarding the non-linear nature of rotations turn out to be of no significance for the PSS and similar applications if quaternions are employed. 1
doi:10.1016/0921-8890(91)90033-h fatcat:zam4yck6r5amxlcevkta27o2ii