A repetitive control scheme for industrial robots based on b-spline trajectories

In this paper, a novel repetitive control scheme is presented and discussed. The general framework is the control of repetitive tasks of robotic systems or, more in general, of automatic machines. The key idea of the proposed scheme consists in modifying the reference trajectory provided to the plant in order to compensate for external loads or unmodelled dynamics that cyclically affect it. By exploiting the dynamic filters for the B-spline trajectory planning, it has been possible to integrate the trajectory generation within a repetitive control scheme able to modify in real-time the reference signal with the aims of nullify interpolation errors. Experimental results obtained controlling two joints of a standard industrial manipulator are reported, showing the effectiveness of the proposed method

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

A Repetitive Control Scheme Based on B-Spline Trajectories Modification

In many applications of interest in industrial robotics, tasks are cyclic and must be repeated over and over. In this context, it seems natural to exploit the intrinsic properties of repetitive control schemes, where the cyclic nature of "disturbances" and/or unmodeled dynamic effects can be exploited to reduce the tracking errors. In this paper, we propose a new repetitive control scheme, where the main idea consists in the modification of the reference trajectory in order to compensate for the periodic undesired effects. By exploiting the dynamic filters for the B-spline generation, it is possible to integrate the trajectory planning within a repetitive control scheme able to modify in real-time the reference signal with the aims of nullify interpolation errors. By means of an extensive experimental activity on a servo mechanism pros and cons of the proposed approach are analyzed

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

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

Improving the Accuracy of Industrial Robots via Iterative Reference Trajectory Modification

In this paper, a novel repetitive control (RC) scheme is presented and discussed. The general framework is the control of repetitive tasks of robotic systems or, more in general, of automatic machines. The key idea of the proposed scheme consists in modifying the reference trajectory provided to the plant in order to compensate for external loads or unmodeled dynamics that cyclically affect it. By exploiting the fact that uniform B-spline trajectories can be generated by means of dynamic filters, the trajectory planning phase has been integrated within an RC scheme that is able to modify in real time the reference signal in order to nullify the tracking errors occurring at the desired via-points. Because of this mechanism, the control scheme is very suitable for the application to industrial plants with off-the-shelf, unmodifiable controllers. Experimental results obtained with a standard industrial manipulator both in joint space and in workspace show the effectiveness of the proposed method

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

Online Trajectory Planning for Vibration Suppression and Perfect Tracking

In this thesis the problem of trajectory planning for automatic machines is addressed, considering in particular the problem of vibration suppression and perfect tracking. Two different trajectory generators based on dynamic filters are developed and implemented. These novel trajectory planners are designed respectively for residual vibrations suppression and perfect tracking of periodic trajectories. Both solutions are very effective and easy to implement, exploiting the realization of dynamic filters by means of FIR filters. In the first part of the thesis the problem of residual vibrations in motion control of robots is addressed. In a review fashion the most widespread feed-forward techniques for residual vibration suppression are analyzed in detail and implemented in simulation. Moreover all the analysis are performed with a control system perspective in order to give a unified point of view allowing to compare all the solutions despite their differences. In Chapter 5 a novel trajectory generator based on Exponential Filters is presented, analyzed and compared with the most commonly used feed-forward techniques for vibration suppression, proving comparable performances with the state of the art. The analysis and comparison procedure is performed both in simulation and in experimental activities. This new method is developed first for simple SISO LTI systems and then extended to MIMO systems. In Chapter 6 a new repetitive control scheme based on B-Spline Trajectory Generator that exploits dynamic filters is presented. The novel scheme integrates the trajectory generator and the repetitive controller in a single discrete time feedback loop achieving perfect tracking for periodic motions. In appendix, the development of a 6-axis Force/Torque sensor for underwater activities based on optoelectronic components is reported. The description covers the entire process from the concept to the development of a simulation model and finally to the prototype realization, along with an extensive experimental activity

A Plug-In Feed-Forward Control for Sloshing Suppression in Robotic Teleoperation Tasks

In this paper, the problem of suppressing sloshing dynamics in liquid handling robotic systems has been faced by designing a dynamic filter that starting from the desired motion of the liquid container calculates the complete position/orientation trajectory for the robot end-effector. Specifically, a design philosophy mixing a filtering technique that suppresses the frequency contributions of the reference motion that may cause liquid oscillations and an active compensation of lateral accelerations by a proper container re-orientation has been adopted. In principle, the latter contribution requires the knowledge of acceleration of the reference trajectory, but because of the use of an harmonic smoother that performs a shaping of the original motion, it is possible to obtain the value of the acceleration in runtime. In this way, the proposed methods can be applied also to reference motions that are not known in advance, e.g. commands directly provided by a human operator. This possibility has been demonstrated by means of a number of experimental tests in which the user teleoperates the robot carrying the container with the liquid by simply moving in the free space its hand, whose 3D position is detected by a motion capture system

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)