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The structural flexibility of industrial robot arms makes them vibrate when they are commanded to move at fast operation speeds. Among the control strategies, feedforward control stands out as an interesting approach to suppress vibration since it does not create stability issues and works for repeating and non-repeating tasks. Currently, the state-of-the-art feedforward controller dedicated to suppressing residual vibration in robot arms is time-varying input shaping (TVIP). However, TVIP falls short in trajectory tracking tasks since the method adds delays in the commands creating errors in tracking and thereby contouring trajectories. Therefore, this paper proposes the use of an alternate feedforward method, known as the filtered B-splines (FBS) approach, to suppress vibration in six DOF robots while maintaining tracking accuracy. Since time-varying FBS (TVFBS) requires full frequency response functions (FRFs), compared to only natural frequencies and damping ratios for TVIP, we propose a framework for estimating the FRFs of serial kinematic chain 6-degree-of-freedom robots. Residual vibration reduction experiments and trajectory tracking experiments, in which the dynamics of a UR5e collaborative robot change considerably, were carried out to validate the model prediction framework. TVFBS reduced the end-effector vibration by 87% while improving tracking performance in both the y (22%) and z (29%) directions. On the other hand, TVIP worsened the tracking performance (-683.43% for the y and -662.37% for the z direction) despite the excellent vibration reduction (98%). Hence, TVFBS demonstrated significantly better tracking performance than TVIP while retaining comparable vibration reduction. 

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. 

The future of intelligent manufacturing machines involves autonomous selection of process parameters to maximize productivity while maintaining quality within specified constraints. To effectively optimize process parameters, these machines need to adapt to existing uncertainties in the physical system. This paper proposes a novel framework and methodology for feedrate optimization that is based on a physics-informed data-driven digital twin with quantified uncertainty. The servo dynamics are modeled using a digital twin, which incorporates the known uncertainty in the physics-based models and predicts the distribution of contour error using a data-driven model that learns the unknown uncertainty on-the-fly by sensor measurements. Using the quantified uncertainty, the proposed feedrate optimization maximizes productivity while maintaining quality under desired servo error constraints and stringency (i.e., the tolerance for constraint violation under uncertainty) using a model predictive control framework. Experimental results obtained using a 3-axis desktop CNC machine tool and a desktop 3D printer demonstrate significant cycle time reductions of up to 38% and 17% respectively, while staying close to the error tolerances compared to the existing methods. 

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. 

Delta 3D printers can significantly increase throughput in additive manufacturing by enabling faster and more precise motion compared to conventional serial-axis 3D printers. Further improvements in motion speed and part quality can be realized through model-based feedforward vibration control, as demonstrated on serial-axis 3D printers. However, delta machines have not benefited from model-based controllers because of the difficulty in accurately modeling their position-dependent, coupled nonlinear dynamics. In this paper, we propose an efficient framework to obtain accurate linear parameter-varying models of delta 3D printers at any position within their workspace from a few frequency response measurements. We decompose the dynamics into two sub-models–(1) an experimentally-identified sub-model containing decoupled vibration dynamics; and (2) an analytically-derived sub-model containing coupled dynamics–which are combined into one using receptance coupling. We generalize the framework by extending the analytical model of (2) to account for differing mass profiles and dynamic models of the printer’s end-effector. Experiments demonstrate reasonably accurate predictions of the position-dependent dynamics of a commercial delta printer, augmented with a direct drive extruder, at various positions in its workspace. Note to Practitioners—This work aims to equip high-speed 3D printers, like delta machines, with model-based controllers to complement their speed with high-accuracy. Due to the coupled kinematic chains of the delta, complex control methodologies, some of which require real-time state measurements, are often used to achieve satisfactory control performance. Our modeling approach provides an efficient methodology for obtaining accurate linear models without the need for real-time measurements, thus enabling practitioners to design linear model-based feedforward controllers to achieve the high throughput and accuracy desired in additive manufacturing (AM). The models we develop in this paper are intended for use with feedforward vibration compensation methods, which can be beneficial for both industrial-scale AM machines that have high-powered servo motors and feedback controllers, as well as consumer-grade AM machines which use stepper motors in feedforward control. 

A hybrid filtered basis function (FBF) approach is proposed in this paper for feedforward tracking control of linear systems with unmodeled nonlinear dynamics. Unlike most available tracking control techniques, the FBF approach is very versatile; it is applicable to any type of linear system, regardless of its underlying dynamics. The FBF approach expresses the control input to a system as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through a linear model of the system's dynamics and the unknown coefficients are selected such that tracking error is minimized. The linear models used in existing implementations of the FBF approach are typically physics-based representations of the linear dynamics of a system. The proposed hybrid FBF approach expands the application of the FBF approach to systems with unmodeled nonlinearities by learning from data. A hybrid model is formulated by combining a physics-based model of the system's linear dynamics with a data-driven linear model that approximates the unmodeled nonlinear dynamics. The hybrid model is used online in receding horizon to compute optimal control commands that minimize tracking errors. The proposed hybrid FBF approach is shown in simulations on a model of a vibration-prone 3D printer to improve tracking accuracy by up to 65.4%, compared to an existing FBF approach that does not incorporate data.