Optimal Trajectories for Vibration Reduction Based on Exponential Filters

In this paper, a new type of trajectory, based on an exponential jerk, is presented along with filters for their online generation. The goal is to generalize constant jerk trajectories, widely used in industrial applications, in order to reduce vibrations of motion systems. As a matter of fact, constant jerk trajectories do not assure a complete vibration suppression when the damping of the resonant modes is not negligible. The values of the parameters (decay rate and duration) of the jerk impulses that allow residual vibration cancellation are derived in an analytical way as a function of the dynamic characteristics of the plant. Comparisons with the well-known input shaping techniques and with system-inversion-based filters show the advantages of the proposed method in terms of robustness with respect to modeling errors, smoothness of the resulting trajectory, and time duration of the motion under velocity and acceleration constraints

Multidimensional Trajectories Generation with Vibration Suppression Capabilities: the Role of Exponential B-splines

In this paper, exponential B-spline trajectories are presented and discussed. They are generated by means of a chain of filters characterized by a truncated exponential impulse response. If properly tuned, the filters applied to a vibrating plant are able to cancel the oscillations and in this sense the resulting splines are optimized with respect to the problem of vibrations suppression. Different types of exponential B-spline are illustrated, with one or more exponential filters in the chain, and the procedure for the interpolation of a given set of desired via-points, with a proper choice of the control points, is shown. As a matter of fact, exponential B-splines, generated by means of dynamic filters, combine the vibration suppression capability of input shapers and smoothing filters with the possibility of exactly interpolating some via-points. The advantages of these curves are experimental proved by considering the motion of a spherical pendulum connected to the flange of an industrial robot

Damped Harmonic Smoother for Trajectory Planning and Vibration Suppression

In this brief, a novel filter for online trajectory generation is presented. The filter can be categorized as an input smoother since it acts on the input signal by increasing its continuity level. When fed with simple signals, as, e.g., a step input, it behaves like a trajectory generator that produces harmonic motions. Moreover, it can be combined with other filters, and in particular, with smoothers having a rectangular impulse response, in order to generate (online) more complex trajectories compliant with several kinematic constraints. On the other hand, being a filter, it possesses the capability of shaping the frequency spectrum of the output signal. This possibility can be profitably exploited to suppress residual vibration by imposing that the zeros of the filter cancel the oscillatory dynamics of the plant. For this purpose, the standard harmonic filter has been generalized in order to consider not only the natural frequency but also the damping coefficient of the plant. In this manner, the so-called ``damped harmonic filter" and the related ``damped harmonic trajectory" have been defined. By means of theoretical considerations, supported by experimental tests, the novel approach has been compared with the existing methods, and the advantages of its use have been proved

Manipulating liquids with robots: A sloshing-free solution

This paper addresses the problem of suppressing sloshing dynamics in liquid handling robotic systems by an appropriate design of position/orientation trajectories. Specifically, a dynamic system, i.e. the exponential filter, is used to filter the desired trajectory for the liquid-filled vessel moved by the robot and counteract the sloshing effect. To this aim, the vessel has been modelled as a spherical pendulum of proper mass/length subject to the accelerations imposed by the robot and the problem has been approached in terms of vibration suppression to cancel the residual oscillations of the pendulum, i.e. the pendulum swing at the end of the reference rest-to-rest motion. In addition, in order to reduce the relative motion between liquid and vessel, an orientation compensation mechanism has been devised aiming to maintain the vessel aligned with the pendulum during the motion. The effectiveness of the proposed approach, both in simple point-to-point motions and complex multi-point trajectories, has been proved by means of an exhaustive set of experimental tests on an industrial manipulator that moves a cylindrical vessel filled with water. This innovative solution effectively uses all the degrees of freedom of the robotic manipulator to successfully suppress sloshing, thus significantly improving the performances of the robotic system. Furthermore, the proposed solution, showing a high degree of robustness as well as intrinsic design simplicity, is very promising for designing novel industrial robotics applications with a short time-to-market across key manufacturing sectors (e.g., food and beverage, among others)

Identification of natural frequency components of articulated flexible structures

M.S.Wayne J. Boo

Feedforward control of Variable Stiffness Joints robots for vibrations suppression

This paper presents a new feedforward controller based on a continuous-time finite impulse response filter, designed to minimize the vibrations that usually affect robot manipulators with elastic joints. In particular, Variable Stiffness Joints (VSJ) robots are considered, since they are usually characterized by a very low level of damping which makes the problem of the oscillations quite important. The proposed approach allows to simplify the overall control structure of VSJ robots, which is based on a decentralized control of each servomotor, imposing the desired position and the desired stiffness at each joint, and on a novel feedforward control, filtering the reference signals. After analyzing some of the filter properties and the method for the parameters choice, experimental results on a VSJ robot demonstrate the importance of the proposed filtering action for minimizing vibrations and oscillations

Zero-phase velocity tracking of vibratory systems with actuation constraints

In this paper, a novel filter for precise tracking of constant velocity signals is presented, which allows the reduction of residual vibrations along with the compliance with kinematic constraints that affect the actuation system. A technique achieving both these two objectives at the same time is the main contribution of the work. The filter is based on a cascade of smoothers, i.e. dynamic filters that act on the input signal by increasing its continuity level. Unfortunately, when applied to a generic input composed by ramp (and step) functions, the filter introduces a phase delay not acceptable in many applications where moving parts have to be mated, such as high-speed automatic machines. In order to guarantee a perfect synchronization between the original and the filtered reference signal, once the transient is terminated, a proper compensation scheme has been designed. Moreover, the expressions of the smoothers parameters which assure vibration cancellation at specific frequencies and compliance with given bounds on velocity and acceleration have been analytically deduced. By means of an extensive experimental activity, the effectiveness of the proposed approach has been demonstrated, by comparing its performances with the results of well established approaches for vibrations suppression or signal derivatives limitation

FIR filters for online trajectory planning with time- and frequency-domain specifications

In this paper, the use of FIR (Finite Impulse Response) filters for planning minimum-time trajectories for robots or automatic machines under constraints of velocity, acceleration, etc. is presented and discussed. In particular, the relationship between multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments, each one possibly characterized by constraints on one or more specific derivatives (i.e. velocity, acceleration, jerk, etc.), and FIR filters disposed in a cascade configuration is demonstrated and exploited in order to design a digital filter for online trajectory planning. The connection between analytic functions and dynamic filters allows a generalization of these trajectories, usually obtained by second- or third-order polynomial functions (e.g. trapezoidal velocity and double S velocity trajectories), to a generic order with only a modest increase of the complexity. As a matter of fact, the computation of trajectories with higher degree of continuity simply requires additional FIR filters in the chain. Moreover, the modular structure of the planner provides a direct frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrate the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectories generation and residual vibrations suppression