Alessandro Gasparetto

Trajectory Planning in Robotics

Trajectory planning is a fundamental issue for robotic applications and automation in general. The ability to generate trajectories with given features is a key point to ensure significant results in terms of quality and ease of performing the required motion, especially at the high operating speeds necessary in many applications. The general problem of trajectory planning in Robotics is addressed in the paper, with an overview of the most significant methods, that have been proposed in the robotic literature to generate collision-free paths. The problem of finding an optimal trajectory for a given path is then discussed and some significant solutions are described.

Model Predictive Control of a Flexible Links Mechanism

Vibration suppression in flexible link manipulator is a recurring problem in most robotic applications. Solving this problem would allow to increase many times both the operative speed and the accuracy of manipulators. In this paper an innovative controller for flexible-links mechanism based on MPC (Model Predictive Control) with constraints is proposed. So far this kind of controller has been employed almost exclusively for controlling slow processes, like chemical plants, but the authors’ aim is to show that this approach can be successfully adapted to plants whose dynamical behavior is both nonlinear and fast changing. The effectiveness of this control system will be compared to the performance obtained with a classical industrial control. The reference mechanism chosen to evaluate the effectiveness of this control strategy is a four-link closed loop planar mechanism laying on the horizontal plane driven by a torque-controlled electric actuator.

Experimental Validation of Minimum Time-jerk Algorithms for Industrial Robots

In this paper, we present a minimum-time/jerk algorithm for trajectory planning and its experimental validation. The algorithm search for a trade-off between the need for a short execution time and the requirement of a sufficiently smooth trajectory, which is the well known necessary condition to limit the vibration during fast movements. The trade-off is achieved by adjusting the weight of two suitable functions, able to consider both the execution time and the squared-jerk integral along the whole trajectory. The main feature of this algorithm is its ability to smooth the trajectory’s profile by adjusting the intervals between two consecutive via-points so that the overall time is minimally delayed. The practical importance of this technique lies in the fact that it can be implemented in any industrial manipulator without a hardware upgrade. The algorithm does not need for a dynamic model of the robot: only the mechanical constraints on the position, velocity and acceleration ranges have to be set a priori. The experimental proof is provided in this paper by comparing the results of the proposed algorithm with those obtained by adopting some classical algorithms.

A Technique to Analytically Formulate and to Solve the 2-Dimensional Constrained Trajectory Planning Problem for a Mobile Robot

A new technique for trajectory planning of a mobile robot in a two-dimensional space is presented in this paper. The main concept is to use a special representation of the robot trajectory, namely a parametric curve consisting in a sum of harmonics (sine and cosine functions), and to apply an optimization method to solve the trajectory planning problem for the parameters (i.e., the coefficients) appearing in the sum of harmonics. This type of curve has very nice features with respect to smoothness and continuity of derivatives, of whatever order. Moreover, its analytical expression is available in closed form and is very suitable for both symbolic and numerical computation. This enables one to easily take into account kinematic and dynamic constraints set on the robot motion. Namely, non-holonomic constraints on the robot kinematics as well as requirements on the trajectory curvature can be expressed in closed form, and act as input data for the trajectory planning algorithm. Moreover, obstacle avoidance can be performed by expressing the obstacle boundaries by means of parametric curves as well. Once the expressions of the trajectory and of the constraints have been set, the trajectory planning problem can be formulated as a standard mathematical problem of constrained optimization, which can be solved by any adequate numerical method. The results of several simulations are also reported in the paper to show the effectiveness of the proposed technique to generate trajectories which meet all requirements relative to kinematic and dynamic constraints, as well as to obstacle avoidance.

A System Theory Approach to Mode Coupling Chatter in Machining

Chatter is an undesired phenomenon of self-excited vibrations that occurs during many machining operations. This paper ana-lyzes mode coupling chatter from the point-of- view of the system theory. A simplified mathematical model of the cutting process is established, from which the equations of the system are obtained. Then, the eigenvalues and the eigenvectors of the system are evaluated, and a simple stability condition is formulated. The tool trajectories both in the stable and unstable case are studied. Finally, an example of mode coupling chatter in a machine for wood cutting and its stabilization is presented.

On the Modeling of Flexible-Link Planar Mechanisms: Experimental Validation of an Accurate Dynamic Model

The experimental validation of an accurate dynamic model of flexible multi-body planar mechanisms is presented in this paper. The proposed mathematical model, which is valid for whatever planar mechanism with any number of flexible links, accounts for the geometric and inertial nonlinearities of the mechanism, and considers coupling effects among rigid-body and elastic motion as well. In order to experimentally validate the dynamic model, a flexible five-bar planar linkage actuated by two electric motors is employed as a test case. The experimentally measured deformations and accelerations of the flexible links are compared with the numerical results obtained by simulating the system dynamic behavior through the mathematical model. It turns out that the experimental results are in good agreement with the numerical ones, thus proving that the dynamical model proposed is very effective in the difficult task of accurately representing the dynamic behavior of flexible mechanisms.

Efficient force distribution and leg posture for a bio-inspired spider robot

Legged walking and climbing robots have recently achieved important results and developments, but they still need further improvement and study. As demonstrated by recent works, bio-mimesis can lead to important technical solutions in order to achieve efficient systems able to climb, walk, fly or swim (Saunders et al., 2006 [36], Ayers, 2001 [25], Safak and Adams, 2002 [26]). In this paper, taking into account the anatomy and the adhesive and locomotion capabilities of the spider (i.e., an eight-legged system), we present on the one hand a study of the foot force and torque distribution in different operative and slope conditions and, on the other hand, a posture evaluation by comparing different leg configurations in order to minimize the torque effort requirements.

Eigenvalue Analysis of Mode-Coupling Chatter for Machine-Tool Stabilization

The mode-coupling chatter phenomenon, due to self-excited vibrations occurring during many machining operations, is studied in this paper. Although mode-coupling chatter has been widely treated in the specialized literature, the authors propose here an approach that is rather different from the classical one, namely, an eigenvalue analysis of chatter based on system theory. A mathematical model of the workpiece- tool system is established first, so as to define the system equations. A closed-form equation, expressing the stability condition of the system as a function of the system parameters, and particularly of the angle between the feed direction and the piece surface, is then obtained from the eigenvalues of the system. Moreover, a study of the eigenvectors of the system enables one to analytically express the tool trajectories, both in the stable and in the unstable case. The model thus formulated and the related considerations about the system stability are then employed in a real case. Namely, a wood-cutting machine subject to mode-coupling chatter is considered, and a technique for stabilization, based on the considerations made on the model, is presented. The authors believe that the eigenvalue analysis of mode-coupling chatter presented in this paper provides a more detailed and complete analysis of the phenomenon than what is currently present in the literature.

Mirror synthesis in a mechatronic system for superficial defect detection

This paper deals with the problem of defect detection on highly reflective surfaces making use of vision systems. A new mechatronic system has been developed, based on a nonflat mirror. According to the method described in this paper, the light rays emitted from a source hit a suitably designed nonflat mirror, and are reflected so as to illuminate the curved surface under investigation. The path of the light rays from the source of light to the mirror and then to the object surface is mathematically traced making use of the optical geometry laws. After the reflection on the object surface, the light rays are collected by a charge-coupled device (CCD) camera and elaborated by a vision system, which manages to detect the surface defects as shadows of various shape and size within the picture. Simulations have been carried out in order to provide the optimal mirror shape. Moreover, a prototype of the mechatronic system, including the synthesized mirror, has been built to perform some experimental tests to validate the method. The results, reported in the paper, definitively show the effectiveness of the proposed method.

A Mechanical Model for the Adhesion of Spiders to Nominally Flat Surfaces

In dry attachment systems of spiders and geckos, van der Waals forces mediate attraction between substrate and animal tarsus. In particular, the scopula of Evarcha arcuata spiders allows for reversible attachment and easy detachment to a broad range of surfaces. Hence, reproducing the scopula’s roughness compatibility while maintaining anti-bunching features and dirt particle repellence behavior is a central task for a biomimetic transfer to an engineered model. In the present work we model the scopula of E. arcuata from a mechano-elastic point of view analyzing the influence of its hierarchical structure on the attachment behavior. By considering biological data of the gecko and spider, and the simulation results, the adhesive capabilities of the two animals are compared and important confirmations and new directives in order to reproduce the overall structure are found. Moreover, a possible suggestion of how the spider detaches in an easy and fast manner is proposed and supported by the results.