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Frog-leg robots are widely used for wafer-handling in semiconductor manufacturing. A typical frog-leg robot uses a magnetic coupler to achieve contactless transmission of motion between its driving motors, which operate at atmospheric pressure, and its end effector (blade) which operates within a vacuum chamber. However, the magnetic coupler is a lowstiffness transmission element that induces residual vibration during fast motions of the robot. Excessive residual vibration can cause collisions between the fragile wafer carried by the robot and cassette, hence damaging the wafer. While this problem could be solved by slowing down the robot, it comes at the cost of reduced productivity, which is undesirable. Therefore, this paper reports a preliminary investigation into input shaping (a popular vibration compensation technique) as a tool to reduce residual vibration of a frog-leg robot during high-speed motions. Two types of motions of the robot are considered: rotation and extension. A standard input shaper is shown to be very effective for mitigating residual vibration caused by rotational motion but is much less effective for extensional motion. The rationale is that the resonance frequencies of the robot are constant during rotation but they vary significantly during extension, hence reducing the effectiveness of standard input shaping. This necessitates the use of more advanced input shapers that can handle varying resonance frequencies to mitigate residual vibration during extensional motion in future work. 

Frog-legged robots are commonly used for silicon wafer handling in semiconductor manufacturing. However, their precision, speed and versatility are limited by vibration which varies with their position in the workspace. This paper proposes a methodology for modelling the pose-dependent vibration of a frog-legged robot as a function of its changing inertia, and its experimentally-identified joint stiffness and damping. The model is used to design a feedforward tracking controller for compensating the pose-dependent vibration of the robot. In experiments, the proposed method yields 65–73% reduction in RMS tracking error compared to a baseline controller designed for specific poses of the robot. 

Abstract This paper presents an investigation of zeros in the SISO dynamics of an undamped three degrees-of-freedom (3DOF) linear time invariant (LTI) flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros—marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP), and complex non-minimum phase (CNMP)—that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. Consequently, the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a 3DOF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped 3DOF system considered in this paper comprised one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros, (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero, and (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system. 

This paper presents an investigation of zeros in the SISO dynamics of an undamped three-DoF LTI flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros – marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP) and complex non-minimum phase (CNMP) – that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. And, that the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a three-DoF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped three-DoF system considered in this paper comprises of one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros. (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero. (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system.