By Sadao Kawamura; Mikhail Svinin
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This e-book constitutes the refereed court cases of the sixth foreign and Interdisciplinary convention on Modeling and utilizing Context, CONTEXT 2007, held in Roskilde, Denmark in August 2007. The forty two revised complete papers awarded have been conscientiously reviewed and chosen from a complete of 121 submissions. The papers care for the interdisciplinary subject of modeling and utilizing context from numerous issues of view, starting from desktop technological know-how, particularly man made intelligence and ubiquitous computing, via cognitive technological know-how, linguistics, organizational sciences, philosophy, and psychology to program components resembling drugs and legislations.
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Or, alternatively, for any b, the same error dynamics is obtained with x˙ d = q˙∗ t∗ where q˙∗ is derived from Eq. (45). The block scheme of the controller is shown in Fig. 7. Note that the null q )Ke(t) of the space component bn(¯ q ) and the orthogonal component J † (¯ solution yield the feedforward and feedback controller actions, q˙ f f and q˙ f b , respectively. Note also that the feedforward action does not depend upon a generalized inverse, as in conventional schemes. Thus, instabilities related to ill-conditioning can be alleviated.
The next two simulations demonstrate the possibility to initialize motion at a singularity. A simple way to achieve this is to choose input b as a linear function of time: b = k1 t, where k1 is an arbitrary constant and t denotes time. Figure 5 shows the result of a simulation when motion was initialized at a regular point singularity. 8 rad/(ms)2 . From the graphs it is evident that motion can be initialized without any instability. Dragomir N. 5 2 x [m] Fig. 3. Approach to a stationary point with natural motion.
The x − y graph in the lower left part of the ﬁgure shows the workspace boundary (the full circle) and the path described by the end-tip (the circular arc). Note that the q∗ speed graph is actually the graph of determinant det J . After about 3 s, change of its sign is observed which indicates motion through the kinematic singularity at the intersection point between workspace boundary and end-tip arc. Thereby, the end-tip is reﬂected from the workspace boundary back along the arc. Prolonging the simulation time to 12 s generates a circular arc that intersects the workspace boundary at two points.