Higher-order kinematics of mechanisms has been applied in servo motor control, human-robot interaction and machinery life design fields, etc. The representations of acceleration and jerk by screws have been fully developed by researchers with the methods of the differential of the matrix representation of SE(3) group. Clifford algebra, which is tighter and with higher computational efficiency than the matrix method, is another representation of the motions of rigid bodies. It has been used in position kinematics, grub task motion planning, and robot vision for its convenience of geometric representations and calculations. As far as we know, the work of higher-order kinematics of mechanisms based on Clifford algebra is rare. First, after recalling the based theory of motion representation in conformal geometric algebra (CGA), the mathematical relationships between flag and motor are built. Second, a method for the higher-order kinematics modeling of serial chain mechanisms is proposed. Finally, the higher-order kinematics of the 3-RRS parallel mechanism is built to prove the correctness of the algorithm. This work further enriches the application of CGA for the higher-order kinematics modeling of parallel mechanisms.
The least square estimation is widely used in parameter estimation. When the measurement error submits to Gaussian distribution, as a maximum likelihood estimate, the precision of the least squares estimation is high, otherwise, especially when the gross error exist, the precision of the estimation is lower. The robust estimation is a parameter estimation that some suitable estimation method is been used to relieve the impact of gross error when it is inevitable and find out the optimal parameter or the parameter nearby. The robust estimation algorithm is injected into sub-pixel locating. As a result, the impact of impulse noise could be reduced greatly and the precision of sub-pixel location could be higher.
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