Giovanni Legnani

A homogeneous matrix approach to 3D kinematics and dynamics — I. Theory

Abstract In this paper we present a new approach to the kinematic and dynamic analysis of rigid body systems in the form of a consistent method employing 4 × 4 matrices. This method can be considered a powerful extension of the well known method of homogeneous transformations proposed by Denavit and Hartenberg. New matrices are introduced to describe the velocity and the acceleration, the momentum, the inertia of bodies and the actions (forces and torques) applied to them. Each matrix contains both the angular and the linear terms and so the “usual” kinematic and dynamic relations can be rewritten, halving the number of equations. The resulting notation and expressions are simple, and very suitable for computer applications. A useful tensor interpretation of this method is also explained, and some connections of this notation with the screw theory and dual-quantities are quoted.

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.

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.

On the Number and Placement of Accelerometers for Angular Velocity and Acceleration Determination

This paper identifies the minimum number of accelerometers nec-essary to measure rigid body acceleration. Notwithstanding thatonly 9 scalar unknowns must be identified, 12 devices compose aminimum set of transducers. This redundancy is necessary toavoid singularities in the equations. Conditions for the sensorplacement are given. It is also shown that when the determinationof the angular velocity is not required, a reduced set of 9 sensorscan be adopted. @DOI: 10.1115/1.1386649#

A Practical Approach to the Selection of the Motor-Reducer Unit in Electric Drive Systems

The selection of a motor-reducer unit in electrical servo-systems has a profound impact on the dynamic performance of a machine. This choice must be made considering all the limits imposed by each component of the system and all the operational constraints. This article proposes a useful and practical methodology for the correct sizing of a motor-reducer unit. The relationships between motor and transmission are investigated by introducing some easily calculated factors useful for comparing all the available motor-reducer couplings and selecting the best solution. The article suggests an innovative approach for the selection of a motor-reducer unit that involves solving the problem with the use of graphs that would allow showing all the possible alternatives.

A homogeneous matrix approach to 3D kinematics and dynamics—II. Applications to chains of rigid bodies and serial manipulators

In this paper we present applications of the new approach to the kinematic and dynamic analysis of systems of rigid bodies presented in Part I. An extension of the method to the Lagrangian formulation of the dynamics of chains of rigid bodies is also presented. The kinematic and dynamic analysis is preformed for a generic serial manipulator either in open and closed loop. Two numerical examples concerning an open loop and a closed loop are presented too. Two software packages based on our approach are also briefly introduced.

Iterative-Learning Hybrid Force/Velocity Control for Contour Tracking

In this paper, we propose a new method, which is based on an iterative-learning-control (ILC) algorithm, for the contour tracking of an object of unknown shape performed by an industrial robot manipulator. In particular, we consider (both implicit and explicit) hybrid force/velocity control whose performance is improved by repeating the task. Here, a time-based reference signal is not present, and therefore, a new approach has been developed, which is different from the typical applications of ILC. Experimental results show the effectiveness of the technique.

Harmonic drive transmissions: the effects of their elasticity, clearance and irregularity on the dynamic behaviour of an actual SCARA robot

This paper deals with the study of the effects of Harmonic Drives characteristics on the dynamic behaviour of industrial robots. These components are firstly analyzed on the basis of the technical literature and, as a result, a mechanical model with concentrated parameters is obtained. Finally, the influence of these parameters on the dynamic behaviour of an actual SCARA robot in our department is investigated by means of experimental tests and by a computer simulation program purposely written.

Gain scheduling for hybrid force/velocity control in contour tracking task

In this paper a gain scheduling approach is proposed for the hybrid force/velocity control of an industrial manipulator employed for the contour tracking of objects of unknown shape. The methodology allows to cope with the configuration dependent dynamics of the manipulator during a constrained motion and therefore a significant improvement of the performance results. Experimental results obtained with an industrial SCARA manipulator demonstrate the effectiveness of the technique.

Adaptive friction compensation for industrial robot control

We deal with the friction compensation in the model-based trajectory tracking control of an industrial robot manipulator. First it is shown that the variations of the friction term might significantly affect the control performances during the robot operations. Then, a simple adaptive scheme is proposed to solve the problem, allowing us to keep the trajectory tracking errors at a constant low level. Experimental results, obtained in a typical industrial environment, show the effectiveness of the method and how it is comparable with known neural-network-based techniques.