By V Hlavaty
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Corollary 3 In the vicinity of stationary points, natural motion decays exponentially. Proof: Follows from the solution type of the autonomous dynamical system. 4 Vector-Parameterization of Configuration Space ¯ q ) onto n-dimensional We are interested in the projection of vector field n(¯ C space. The projection, n(¯ q ) = [adjJ (q)] t∗ (q∗ ), can be interpreted as a parameterized vector field, t∗ (q∗ ) playing the role of an n-parameter. Consequently, Eq. (11) can be regarded as a parameterized autonomous dynamical system [32].
This paper presents the recent advances in control theory of robots with uncertain kinematics and dynamics. Several approximate Jacobian controllers, that do not require exact knowledge of either kinematics or dynamics of robots, are presented. The control problems are formulated based on Lyapunov analysis. By using sensory feedback of the robot end effector position, it is shown that the end effector is able to follow a desired motion with uncertainties in kinematics and dynamics. This gives the robot a high degree of flexibility in dealing with unforseen changes and uncertainties in its kinematics and dynamics, which is similar to human reaching movements and tool manipulation.
14. 7 s (stage 1 in the lower right figure). ). 9 Conclusions Until recently, not much attention has been paid to the useful role of kinematically singular configurations in motion tasks. The ill-conditioning of the inverse problem around such configurations has been tackled mostly within linear model frameworks. It has been shown here that a non-linear, differentialgeometric approach to kinematic inversion can lead to improved models. 5 time [s] Fig. 12. Motion through a stationary point, with constant twist magnitude, gravity disturbance and dynamic closed-loop control with filter.
GEOMETRY OF EINSTEIN'S UNIFIED FIELD THEORY by V Hlavaty
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