Feedrate planning for machining with industrial six-axis robots

The authors want to thank Stäubli for providing the necessary information of the controller, Dynalog for its contribution to the experimental validations and X. Helle for its material contributions.Nowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology machining process demands the improvement of the overall performances of robots to achieve an accuracy level close to that realized by machine-tools. This paper presents a method of trajectory planning adapted for continuous machining by robot. The methodology used is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot

A Predictive Technique for the Real-Time Trajectory Scaling under High-Order Constraints

Modern robotic systems must be able to react to unexpected environmental events. To this purpose, planning techniques for the real-time generation/modification of trajectories have been developed in recent times. In the frequent case of applications which require following a predefined path, the assigned time-law must be inspected in real time so as to verify whether it satisfies the system constraints or, conversely, if it must be scaled in order to obtain a feasible trajectory. The problem has been addressed in several ways in the literature. One of the known approaches, based on the use of nonlinear filters, is revised in this paper in order to return feasible solutions under any circumstances. Differently from alternative strategies, it manages constraints up to the torque derivatives and has evaluation times compatible with the ones required by modern control systems. The proposed technique is validated through simulations and real experiments. Comparisons are proposed with an algorithm based on a model predictive technique and with an alternative scaling system

FIR filters for online trajectory planning with time- and frequency-domain specifications

In this paper, the use of FIR (Finite Impulse Response) filters for planning minimum-time trajectories for robots or automatic machines under constraints of velocity, acceleration, etc. is presented and discussed. In particular, the relationship between multi-segment polynomial trajectories, i.e. trajectories composed of several polynomial segments, each one possibly characterized by constraints on one or more specific derivatives (i.e. velocity, acceleration, jerk, etc.), and FIR filters disposed in a cascade configuration is demonstrated and exploited in order to design a digital filter for online trajectory planning. The connection between analytic functions and dynamic filters allows a generalization of these trajectories, usually obtained by second- or third-order polynomial functions (e.g. trapezoidal velocity and double S velocity trajectories), to a generic order with only a modest increase of the complexity. As a matter of fact, the computation of trajectories with higher degree of continuity simply requires additional FIR filters in the chain. Moreover, the modular structure of the planner provides a direct frequency characterization of the motion law. In this way, it is possible to define the trajectories by considering constraints expressed in the frequency-domain besides the classical time-domain specifications, such as bounds on velocity, acceleration, and so on. Two examples illustrate the main features of the proposed trajectory planner, in particular with respect to the problems of multi-point trajectories generation and residual vibrations suppression

High-dynamic GPS tracking

The results of comparing four different frequency estimation schemes in the presence of high dynamics and low carrier-to-noise ratios are given. The comparison is based on measured data from a hardware demonstration. The tested algorithms include a digital phase-locked loop, a cross-product automatic frequency tracking loop, and extended Kalman filter, and finally, a fast Fourier transformation-aided cross-product frequency tracking loop. The tracking algorithms are compared on their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. The measured results are shown to agree with simulation results carried out and reported previously

Online trajectory planner with constraints on velocity, acceleration and torque

A filter for trajectories smoothing is presented. The filter provides an output reproducing the input trajectory if this is compliant with given constraints on the velocity, the acceleration and the torque required for tracking it. Otherwise, the filter approximates the input profile guaranteeing that the output trajectory satisfies all the kinematic and dynamic limits. The tracking of the input signal is optimal in the sense that at each time instant the limit value of one among velocity, acceleration and torque is reached. The filter, based on a variable structure controller, is designed in the continuous-time domain but can be implemented by discretization as a sampled system. It can therefore used in mechatronic and robotic applications driven by digital controllers in order to filter trajectories planned without considering the above mentioned constraints or to generate realtime smooth trajectories by simply providing basic inputs such as step or ramp functions

Trajectory Generation for a Quadrotor Unmanned Aerial Vehicle

RÉSUMÉ Le domaine des véhicules aériens sans pilote de type multicoptères a connu une progression substantielle au cours de la dernière décennie. La génération et le contrôle des trajectoires ont été au centre des préoccupations de ce nouveau domaine, avec des méthodes qui permettent d’exécuter des manoeuvres complexes dans l’espace. Plusieurs efforts ont été faits pour exécuter ces manoeuvres en utilisant la commande non linéaire, notamment la commande par platitude différentielle. Cependant, l’absence de théorie pour l’estimation des dérivées d’ordre supérieur a empêché l’application expérimentale de plusieurs de ces techniques. Ce travail explore tout d’abord l’approche par composition séquentielle pour l’exécution de manoeuvres à travers des fenêtres étroites. Cette technique implique la combinaison de plusieurs contrôleurs théoriquement simples afin de produire un résultat complexe. Les résultats expérimentaux réalisés dans le Laboratoire de Robotique Mobile et de Systèmes Automatisés à Polytechnique Montréal démontrent la validité de cette approche, en produisant des manoeuvres précises et répétables. Cependant, on atteint rapidement les limites d’une telle méthode dans les applications du monde réel, du fait de son manque de précision initiale et l’absence d’évaluation de faisabilité. Ce mémoire se concentre ensuite sur le développement d’une architecture d’estimation d’état basée sur le filtre de Kalman linéaire afin de fournir en temps réel des estimés des 2e et 3e dérivées de la position d’un quadricoptère (appelées respectivement accélération, et àcoup ou jerk). Des filtres de complexités différentes sont développés afin d’incorporer toute l’information disponible sur le système pour améliorer l’estimé résultant. On obtient alors un estimateur d’état complet qui utilise les mesures de position et d’accélération, ainsi que les entrées de commande, et fournit des estimés pour la rétroaction. Un contrôleur du jerk augmenté basé sur la théorie de la commande optimale est ensuite développé afin de valider cet estimateur. Il est conçu de façon à utiliser le jerk, l’accélération, la vitesse et la position du drone ; sans rétroaction de chacun de ces termes, le système est alors instable. Des tests sont effectués afin d’examiner les performances de l’estimateur et du contrôleur. Tout d’abord, le quadricoptère est chargé de suivre diverses entrées de référence dans l’espace pour assurer sa stabilité. Le contrôleur permet de suivre au plus près ces références, comme réalisé en simulation. Le contrôleur doit ensuite suivre un changement de référence afin d’évaluer la précision de l’estimateur développé. Les résultats montrent que l’estimation en temps réel du jerk suit adéquatement les valeurs hors ligne. Pour autant que nous le sachions, c’est la première mise en oeuvre dans le monde réel du retour de jerk pour contrôler un multicoptère.----------ABSTRACT The field of multirotor unmanned aerial vehicles (UAVs) has seen substantial progression in the past decade. Trajectory generation and control has been a main focus in this domain, with methods that enable the performance of complex three-dimensional maneuvers through space. Efforts have been made to execute these maneuvers using concepts of nonlinear control and differential flatness. However, a lack of theory for the estimation of higher-order dérivatives of a multirotor UAV has prevented the experimental application of several of these techniques concentrated on trajectory control. This work firstly explores the existing control approach of sequential composition for the execution of quadrotor manoeuvres through narrow windows. This technique involves the combination of several theoretically simple controllers in sequence in order to produce a complex result. Experimental results conducted in the Mobile Robotics and Automated Systems Laboratory (MRASL) at Polytechnique demonstrate the validity of this approach, producing precise and repeatable manoeuvres through narrow windows. However, they also show the limitations of such a method in real world applications, notably its initial inaccuracy and lack of feasibility evaluation. This thesis then focuses on the development of a state-estimation architecture based on linear Kalman filter techniques in order to provide a real-time value of a quadrotor UAV’s second and third derivatives (referred to as acceleration and jerk, respectively). Filters of different complexities are developed with the goal of incorporating all available system information into the resulting estimate. A full-state estimator is produced that uses a quadrotor’s position and acceleration measurements as well as control inputs in order to be usable for feedback. A jerk-augmented controller based off of optimal control theory is then developed in order to validate this estimator. It is designed in such a way to use the UAV’s jerk, acceleration, velocity and position as design parameters and to be unstable without feedback in each of these terms. Tests are conducted in order to examine the performance of both the estimator and controller. Firstly, the quadrotor is commanded to track various reference inputs in 3D space to ensure its stability. The controller tracks these references very closely to simulated responses. The controller is then asked to follow a changing reference in order to evaluate the precision of the developed estimator. Results show that the real-time estimation of the jerk follows offline values adequately. To the best of our knowledge, this is the first application to implement the feedback of a multirotor UAV’s jerk in real-world experimentation

Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

Temporal models of motions and forces for Human-Robot Interactive manipulation

L'intérêt pour la robotique a débuté dans les années 70 et depuis les robots n'ont cessé de remplacer les humains dans l'industrie. L'automatisation à outrance n'apporte cependant pas que des avantages, car elle nécessite des environnements parfaitement contrôlés et la reprogrammation d'une tâche est longue et fastidieuse. Le besoin accru d'adaptabilité et de ré-utilisabilité des systèmes d'assemblage force la robotique à se révolutionner en amenant notamment l'homme et le robot à interagir. Ce nouveau type de collaboration permet de combiner les forces respectives des humains et des robots. Cependant l'homme ne pourra être inclus en tant qu'agent actif dans ces nouveaux espaces de travail collaboratifs que si l'on dispose de robots sûrs, intuitifs et facilement reprogrammables. C'est à la lumière de ce constat qu'on peut deviner le rôle crucial de la génération de mouvement pour les robots de demain. Pour que les humains et les robots puissent collaborer, ces derniers doivent générer des mouvements sûrs afin de garantir la sécurité de l'homme tant physique que psychologique. Les trajectoires sont un excellent modèle pour la génération de mouvements adaptés aux robots collaboratifs, car elles offrent une description simple et précise de l'évolution du mouvement. Les trajectoires dîtes souples sont bien connues pour générer des mouvements sûrs et confortables pour l'homme. Dans cette thèse nous proposons un algorithme de génération de trajectoires temps-réel basé sur des séquences de segments de fonctions polynomiales de degré trois pour construire des trajectoires souples. Ces trajectoires sont construites à partir de conditions initiales et finales arbitraires, une condition nécessaire pour que les robots soient capables de réagir instantanément à des événements imprévus. L'approche basée sur un modèle à jerk-contraint offre des solutions orientées performance: les trajectoires sont optimales en temps sous contraintes de sécurité. Ces contraintes de sécurité sont des contraintes cinématiques qui dépendent de la tâche et du contexte et doivent être spécifiées. Pour guider le choix de ces contraintes, nous avons étudié le rôle de la cinématique dans la définition des propriétés ergonomiques du mouvement. L'algorithme a également été étendu pour accepter des configurations initiales non admissibles permettant la génération de trajectoires sous contraintes cinématiques non constantes. Cette extension est essentielle dans le contexte des interactions physiques homme-robot, car le robot doit être capable d'adapter son comportement en temps-réel pour préserver la sécurité physique et psychologique des humains. Cependant considérer le problème de la génération de trajectoires ne suffit pas si on ne considère pas le contrôle. Le passage d'une trajectoire à une autre est un problème difficile pour la plupart des systèmes robotiques dans des contextes applicatifs réels. Pour cela, nous proposons une stratégie de contrôle réactif de ces trajectoires ainsi qu'une architecture construite autour de l'utilisation des trajectoires.It was in the 70s when the interest for robotics really emerged. It was barely half a century ago, and since then robots have been replacing humans in the industry. This robot-oriented solution doesn't come without drawbacks as full automation requires time-consuming programming as well as rigid environments. With the increased need for adaptability and reusability of assembly systems, robotics is undergoing major changes and see the emergence of a new type of collaboration between humans and robots. Human-Robot collaboration get the best of both world by combining the respective strengths of humans and robots. But, to include the human as an active agent in these new collaborative workspaces, safe and flexible robots are required. It is in this context that we can apprehend the crucial role of motion generation in tomorrow's robotics. For the emergence of human-robot cooperation, robots have to generate motions ensuring the safety of humans, both physical and physchological. For this reason motion generation has been a restricting factor to the growth of robotics in the past. Trajectories are excellent candidates in the making of desirable motions designed for collaborative robots, because they allow to simply and precisely describe the motions. Smooth trajectories are well known to provide safe motions with good ergonomic properties. In this thesis we propose an Online Trajectory Generation algorithm based on sequences of segment of third degree polynomial functions to build smooth trajectories. These trajectories are built from arbitrary initial and final conditions, a requirement for robots to be able to react instantaneously to unforeseen events. Our approach built on a constrained-jerk model offers performance-oriented solutions : the trajectories are time-optimal under safety constraints. These safety constraints are kinematic constraints that are task and context dependent and must be specified. To guide the choice of these constraints we investigated the role of kinematics in the definition of ergonomics properties of motions. We also extended our algorithm to cope with non-admissible initial configurations, opening the way to trajectory generation under non-constant motion constraints. This feature is essential in the context of physical Human-Robot Interactions, as the robot must adapt its behavior in real time to preserve both the physical and psychological safety of humans. However, only considering the trajectory generation problem is not enough and the control of these trajectories must be adressed. Switching from a trajectory to another is a difficult problem for most robotic systems in real applicative contexts. For this purpose we propose a strategy for the Reactive Control of these Trajectories as well as an architecture built around the use of trajectories

FIR filter-based online jerk-constrained trajectory generation

In the context of human-robot manipulation interaction for service or industrial robotics, the robot controller must be able to quickly react to unpredictable events in dynamic environments. In this paper, a FIR filter-based trajectory generation methodology is presented, combining the simplicity of the analytic second-order trajectory generation, i.e. acceleration-limited trajectory, with the flexibility and computational efficiency of FIR filtering, to generate on the fly smooth jerk-constrained trajectories. The proposed methodology can generate synchronized (fixed-time) and time-optimal jerk-limited trajectories from arbitrary initial velocity and acceleration conditions within 20 microsecond. Other jerk-constrained trajectories such as jerk-time fixed trajectories, which are particularly suitable for vibration reduction, can be easily generated. Experimental validations carried out on a seven axis Kuka LBR iiwa are presented

Feedrate planning for machining with industrial six-axis robots

The authors want to thank Stäubli for providing the necessary information of the controller, Dynalog for its contribution to the experimental validations and X. Helle for its material contributions.International audienceNowadays, the adaptation of industrial robots to carry out high-speed machining operations is strongly required by the manufacturing industry. This new technology machining process demands the improvement of the overall performances of robots to achieve an accuracy level close to that realized by machine-tools. This paper presents a method of trajectory planning adapted for continuous machining by robot. The methodology used is based on a parametric interpolation of the geometry in the operational space. FIR filters properties are exploited to generate the tool feedrate with limited jerk. This planning method is validated experimentally on an industrial robot