Antonio Visioli

Global minimum-jerk trajectory planning of robot manipulators

A new approach based on interval analysis is developed to find the global minimum-jerk (MJ) trajectory of a robot manipulator within a joint space scheme using cubic splines. MJ trajectories are desirable for their similarity to human joint movements and for their amenability to path tracking and to limit robot vibrations. This makes them attractive choices for robotic applications, in spite of the fact that the manipulator dynamics are not taken into account. Cubic splines are used in a framework that assures overall continuity of velocities and accelerations in the robot movement. The resulting MJ trajectory planning is shown to be a global constrained minimax optimization problem. This is solved by a newly devised algorithm based on interval analysis and proof of convergence with certainty to an arbitrarily good global solution is provided. The proposed planning method is applied to an example regarding a six-joint manipulator and comparisons with an alternative MJ planner are exposed.

Fuzzy logic based set-point weight tuning of PID controllers

A methodology, based on fuzzy logic, for the tuning of proportional-integral-derivative (PID) controllers is presented. A fuzzy inference system is adopted to determine the value of the weight that multiplies the set-point for the proportional action, based on the current output error and its time derivative. In this way, both the overshoot and the rise time in set-point following can be reduced. The values of the proportional gain and the integral and derivative time constant are determined according to the well-known Ziegler-Nichols formula so that a good load disturbance attenuation is also assured. The methodology is shown to be effective for a large range of processes and is valuable for industrial settings since it is intuitive, it requires only a small extra computational effort, and it is robust with regard to parameter variations. The tuning of the parameters of the fuzzy module can be easily done by hand or by means of an autotuning procedure based on genetic algorithms.

Modified anti-windup scheme for PID controllers

Eigenstructure assignment in multivariable linear systems via output feedback is investigated. Three problems are proposed that are related to a type of generalised Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalised Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is presented for the proposed eigenstructure assignment problems. General parametric expressions for both the closed-loop eigenvector matrices and the output feedback gain are established in terms of certain parameter vectors. These parameter vectors provide the design degrees of freedom and can be utilised to achieve desired specifications. Based on the proposed results and the Matlab Optimisation Toolbox, a Matlab file is created, which finds a solution that gives minimum closed-loop eigenvalue sensitivities for the problem of eigenstructure assignment via output feedback.

Minimum-time system-inversion-based motion planning for residual vibration reduction

In this paper, we present a novel approach, based on system inversion, for the point-to-point motion planning of vibratory servosystems. The idea is to define a suitable parameterized motion law of the load which assures that no oscillations occurs during and at the end of the motion; then, by means of a noncausal system inversion, the command function of the system is determined with a continuous derivative of an arbitrary order. A procedure that minimizes the duration of the movement, taking into account actuator constraints, can then be performed. Comparisons with the well-known input shaping techniques have been performed via both a simulation example and an experimental setup. The proposed method, which is inherently robust to modeling errors, emerges as a very flexible and competitive technique.

On the trajectory tracking control of industrial SCARA robot manipulators

In this paper, the authors discuss, from an experimental point of view, the use of different control strategies for the trajectory tracking control of an industrial selective compliance assembly robot arm robot, which is one of the most employed manipulators in industrial environments, especially for assembly tasks. Specifically, they consider decentralized controllers such as proportional-integral-derivative-based and sliding-mode ones and model-based controllers such as the classical computed-torque one and a neural-network-based controller. A simple procedure for the estimation of the dynamic model of the manipulator is given. Experimental results provide a detailed framework about the cost/benefit ratio regarding the use of the different controllers, showing that the performance obtained with decentralized controllers may suffice in a large number of industrial applications, but in order to achieve low tracking errors also for high-speed trajectories, it might be convenient to adopt a neural-network-based control scheme, whose implementation is not particularly demanding.

Global minimum-time trajectory planning of mechanical manipulators using interval analysis

The paper addresses the global minimum-time trajectory planning of an m -joint mechanical manipulator. Using a joint space scheme with given intermediate points to be interpolated by piecewise cubic polynomials, a novel bisecting-plane algorithm is proposed to schedule the times between adjacent knots under velocity, acceleration, and jerk constraints. This algorithm, which is proved to be globally convergent with certainty within an arbitrary precision, uses an interval procedure (a subroutine adopting tools and ideas of interval analysis) in proving that a local minimum is actually a global one. A worked example for the six-joint case is exposed, and computational results of a C+ + implementation are included.

Friction compensation in hybrid force/velocity control of industrial manipulators

This paper deals with the implementation of a hybrid force/velocity controller for the automatic edge following of two-dimensional unknown planar contours performed by an industrial robot manipulator. In particular, the authors address the problem of compensating the joint friction effects that have to be taken into account in the controller design in order to achieve a reasonable performance with regards to normal force and tangential velocity errors. For that reason, two model-based friction-compensation methods are compared: a static method, based on a previously identified model, and an adaptive method, where joint friction parameters are recursively updated. By means of an extensive experimental activity, it is shown that, in spite of its simplicity and despite the friction effects changing in time during the robot operations, the devised adaptive procedure obtains a high performance in different operating conditions.

Using stable input-output inversion for minimum-time feedforward constrained regulation of scalar systems

The paper approaches the feedforward minimum-time smooth control of non-minimum-phase linear scalar systems for set-point regulation. The aim is to synthesize a bounded input subject to non-saturating constraints on the input and its derivatives till a prespecified arbitrary order. The provided solution relies on a stable input-output dynamic inversion technique and an ad hoc parameterized family of output transition functions. The synthesized minimum-time input that exhibits pre- and post-actuation is determined by means of easily-implementable closed-form expressions. Examples are given to illustrate the methodology.

An interval algorithm for minimum-jerk trajectory planning of robot manipulators

We present an approach to finding the minimum-jerk cubic spline joint trajectory of a robot manipulator, using interval analysis. Minimum-jerk trajectories are desirable for their amenability to path tracking and to limit robot vibrations whilst cubic splines are used in order to ensure continuity of velocities and accelerations in the robot movement. The optimization problem, that can be seen as a constrained minimax problem, is solved through the use of interval analysis that guarantees that the global minimum is found with an arbitrary precision. We describe the employed algorithm and computational results are also presented.

Planning and real-time modifications of a trajectory using spline techniques

In this paper, methods based on various spline techniques for planning and fast modifications of a trajectory for robot manipulators are investigated. Algebraic and trigonometric splines, their combined use, and the use of the B-spline technique are analyzed and compared in detail. In so doing, we focus on the performance of sudden changes in a predefined trajectory, e.g. obstacle avoidance in real-time applications. Some comparative examples illustrate our results.