Discussions on Inverse Kinematics based on Levenberg-Marquardt Method and Model-Free Adaptive (Predictive) Control

In this brief, the current robust numerical solution to the inverse kinematics based on Levenberg-Marquardt (LM) method is reanalyzed through control theory instead of numerical method. Compared to current works, the robustness of computation and convergence performance of computational error are analyzed much more clearly by analyzing the control performance of the corrected model free adaptive control (MFAC). Then mainly motivated by minimizing the predictive tracking error, this study suggests a new method of model free adaptive predictive control (MFAPC) to solve the inverse kinematics problem. At last, we apply the MFAPC as a controller for the robotic kinematic control problem in simulation. It not only shows an excellent control performance but also efficiently acquires the solution to inverse kinematic

Configuration control of seven-degree-of-freedom arms

A seven degree of freedom robot arm with a six degree of freedom end effector is controlled by a processor employing a 6 by 7 Jacobian matrix for defining location and orientation of the end effector in terms of the rotation angles of the joints, a 1 (or more) by 7 Jacobian matrix for defining 1 (or more) user specified kinematic functions constraining location or movement of selected portions of the arm in terms of the joint angles, the processor combining the two Jacobian matrices to produce an augmented 7 (or more) by 7 Jacobian matrix, the processor effecting control by computing in accordance with forward kinematics from the augmented 7 by 7 Jacobian matrix and from the seven joint angles of the arm a set of seven desired joint angles for transmittal to the joint servo loops of the arm. One of the kinematic functions constraints the orientation of the elbow plane of the arm. Another one of the kinematic functions minimizes a sum of gravitational torques on the joints. Still another kinematic function constrains the location of the arm to perform collision avoidance. Generically, one kinematic function minimizes a sum of selected mechanical parameters of at least some of the joints associated with weighting coefficients which may be changed during arm movement. The mechanical parameters may be velocity errors or gravity torques associated with individual joints

Tressage automatisé de pièces complexes avec solution inverse itérative asservie en angle

RÉSUMÉ Le tressage est un procédé de préformage textile utilisé dans l’industrie aéronautique. Les bobines disposées sur la piste circulaire de la tresseuse tournent en directions opposées tandis qu’au centre de la tresseuse, le mandrin représentant la contre-forme de la pièce à fabriquer, avance. Le mouvement conjugué du mandrin et des bobines permet aux fils de former une tresse autour du mandrin. Le procédé est automatisé donc répétable et la déposition de dizaines, voire de centaines de fils simultanément lui confère une excellente productivité. Le textile tressé dispose aussi d’une excellente résistance à l’impact. Les caractéristiques mécaniques sont dépendantes de l’angle de tressage formé par les fils. La connaissance du comportement du tressage et, plus particulièrement du lien entre la vitesse d’avance du mandrin et angle de tressage est limité dans la littérature. Les travaux présentés dans ce mémoire visent à modéliser ce lien et à réaliser l’implémentation dans un laboratoire recherche. De nombreux travaux disponibles dans la littérature ont cherché à établir le lien entre l’angle de tressage et la vitesse d’avance du mandrin. Pour les mandrins circulaires, des relations analytiques existent. Pour les mandrins complexes, des modèles ont été publiés mais sont limités soit par leur précision, soit par leur temps de mise en œuvre. L’objectif principal est de développer une nouvelle approche pour résoudre le problème inverse de prédiction des paramètres de fabrication fonction l’angle de tressage désiré en ayant une meilleure précision tout en limitant le temps de mise en œuvre. Le second objectif est de développer et d’implémenter, chez le partenaire industriel, le post- processeur permettant de faire le lien entre le modèle informatique et l’outil réel de production. Grâce à cela, les essais de tressages ont pu être réalisés afin de valider la modélisation. Les résultats montrent la validité de l’approche. En effet, l’erreur entre l’angle de tressage cible et celui mesuré est limité à 0.87° sur l’ensemble des mesures effectuées alors que la référence de qualité est généralement fixée à 1° dans l’industrie.----------ABSTRACT Braiding is a textile preforming process used in the aeronautical industry. Carriers arranged on the circular track of the braiding machine rotate in opposite directions while in the braiding machine center, the mandrel representing the counterpart of the part to be manufactured advances. The combined movement of the mandrel and the carriers allows the yarns to be braided over the mandrel. The process is automated and therefore repeatable, and the deposition of tens or even hundreds of yarns simultaneously gives excellent productivity. The braided textile also has excellent impact resistance. The mechanical properties of the braided parts are function of the braiding angle formed by the yarns. The knowledge of the braiding behaviour and the link between the take-off speed and braiding angle is sparse in the literature. The work presented in this thesis aims to model this link and to implement it in a research laboratory context. Numerous researches available in the literature have tried to model the link between the braiding angle and the take-off speed of the mandrel. For circular mandrels, analytical relationships exist. For complex mandrels though, models have been published but they have limitations either in accuracy or in processing time. The primary objective is to develop a new approach to solve the inverse problem which aims at identifying the manufacturing parameters that result in the targeted braiding angle with better accuracy while reducing the processing time. The second objective is to develop and implement, at the industrial partner's lab, the post-processor enabling the link between the computer model and the production tool. Thanks to this, the experiments can be carried out in order to validate the model. The results show the validity of the approach and the error between the targeted braiding angle and the measured angle limited to 0.87° on all the measurements carried out while the quality threshold is generally set at 1° in the industry

Path planning for robotic truss assembly

A new Potential Fields approach to the robotic path planning problem is proposed and implemented. Our approach, which is based on one originally proposed by Munger, computes an incremental joint vector based upon attraction to a goal and repulsion from obstacles. By repetitively adding and computing these 'steps', it is hoped (but not guaranteed) that the robot will reach its goal. An attractive force exerted by the goal is found by solving for the the minimum norm solution to the linear Jacobian equation. A repulsive force between obstacles and the robot's links is used to avoid collisions. Its magnitude is inversely proportional to the distance. Together, these forces make the goal the global minimum potential point, but local minima can stop the robot from ever reaching that point. Our approach improves on a basic, potential field paradigm developed by Munger by using an active, adaptive field - what we will call a 'flexible' potential field. Active fields are stronger when objects move towards one another and weaker when they move apart. An adaptive field's strength is individually tailored to be just strong enough to avoid any collision. In addition to the local planner, a global planning algorithm helps the planner to avoid local field minima by providing subgoals. These subgoals are based on the obstacles which caused the local planner to fail. A best-first search algorithm A* is used for graph search