This paper studies the phenomenon of sloshing in the field of automatic machines for packaging liquid products, with specific reference to containers with planar motions. After introducing two equivalent discrete models based on a mass-spring-damper system borrowed from the literature (one linear and one non-linear), a novel method is proposed to evaluate the sloshing height of the liquid, namely the deviation of its free surface at the wall of the container from the equilibrium condition. The merits of this method are that it is easy to use, requiring no experimental evaluation of the system parameters or computationally expensive fluid dynamic simulations, and it gives good results also for highly dynamical motions. Moreover, though this paper focuses on cylindrical containers performing rectilinear movements, the presented technique can be extended to containers of arbitrary shape and generic planar motions. The method is validated by experimental tests using cylindrical containers of different dimensions and many rectilinear motion laws with maximum accelerations up to $12~m/s^{2}$ . The results are compared with those obtained by using other methods of equal complexity available in the literature, showing the effectiveness of the proposed technique.

This paper studies the design of anti-sloshing trajectories for application in automatic machines for packaging liquid products, with specific reference to cylindrical containers and emphasis on prescribed motion durations. Different strategies, based on a discrete linear model of the sloshing phenomenon and applicable in real-time, are analyzed to perform anti-sloshing feedforward control of the container motion: FIR filters (input shapers and others), dynamic-model inversion, and IIR filters. Unlike the previous literature, these strategies are applied to highly dynamical motion laws, with maximum accelerations from 4m=s² to 13m=s². The effectiveness of the proposed anti-sloshing trajectories is assessed by experiments.

This paper proposes a hybrid position–force control strategy for overconstrained cable-driven parallel robots (CDPRs). Overconstrained CDPRs have more cables (m) than degrees of freedom (n), and the idea of the proposed controller is to control n cables in length and the other $m-n$ ones in force. Two controller implementations are developed, one using the motor torque and one using the motor following-error in the feedback loop for cable force control. A friction model of the robot kinematic chain is introduced to improve the accuracy of the cable force estimation. Compared to similar approaches available in the literature, the novelty of the proposed control strategy is that it does not rely on force sensors, which reduces the hardware complexity and cost. The developed control scheme is compared to classical methods that exploit force sensors and to a pure inverse kinematic controller. The experimental results show that the new controller provides good tracking of the desired cable forces, maintaining them within the given bounds. The positioning accuracy and repeatability are similar those obtained with the other controllers. The new approach also allows an online switch between position and force control of cables.