In this paper, a null space damping method is proposed which solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is quite stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudoinverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by computer simulation.
A switched-capacitor N -path circuit can be employed for filtering an RF signal, as well as a passive downconverter. A known limitation of an N-path filter is that in addition to downconverting signals around the desired center frequency, the circuit also downconverts signals located around harmonics of the center frequency. An N-path filter that uses a PWM representation of a sinusoidal LO to mitigate harmonic downconversion is proposed in this work. Single-edge naturalsampling pulse-width modulated (PWM) clocks are used to drive the switches in the N-path filter. The potential for employing PWM for providing gain control is also described.
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