Download Advances in Robot Control by Sadao Kawamura; Mikhail Svinin PDF

By Sadao Kawamura; Mikhail Svinin

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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.

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