Quasi-linearization approach for the under-actuated robots

A novel technique to reduce energy consumption for industrial robots by using redundancy and under-actuated configurations is introduced in this paper. The study concentrates on kinematics including a passive axis which causes a highly nonlinear coupling of the Coriolis and centrifugal forces and high inertia coupling. The challenge of meeting the requirements of position accuracy, precision, and repeatability combined with the requirements for the speed, acceleration, and torque is coped with by solving a sequence of linear two point boundary value problems for controlling the movement of the end effector between two points. The advantages of this method are the ability of reducing the computation time dramatically, computer storage, and linearizing the nonlinear model. Furthermore the optimal trajectories are identified with minimizing energy consumption and enabling high speed capability. Numerical simulations are conducted to validate the theoretical analysis

Bahnplanung und Steuerungsentwicklung für unteraktuierte Manipulatoren durch eine Modellierung der Kinematik und Dynamik

Robotic handling operations cover a diversity of applications. Pick and place, palletizing or depalletizing, loading on machines or unloading from machines, storage/retrieval, and feeding the production lines are some examples. A manifold of different applications inspires the development of industrial robot types. The advantages of industrial robots can be summarized in different aspects: worker’s protection in dangerous working conditions, higher working quality, higher productivity rate, and cost saving. Due to concerns about resource efficiency, energy consumption has become an issue for robotic development. The System Applying Momentum Transfer for Acceleration of an End Effector with the Redundant Axis (SAMARA) is a robotic prototype of an industrial robot for pick and place applications. This prototype uses redundant, under-actuated configurations and an evolutionary algorithm (EA) to minimize energy consumption. Enabling for applications with relatively large displacement tasks, higher than one meter and high payload of up to 5.5 kilograms, the effectiveness of handling can be increased. Energy saving in specified cycle time has been achieved for this robotic kinematics. Reducing the cycle time and energy consumption are conflicting goals. However, actually, the computation time for the trajectory planning is too long. PID (proportional–integral–derivative) control is not adequate for a robust under-actuated motion (UAM). The uncertainty of payload causes unacceptable effects on accuracy, repeatability, and precision of the under-actuated robot. Using the Quasi-Linearization (QL) is an approach for trajectory planning with minimizing energy consumption and reducing computation time. The QL is focused on reducing the cycle time to increase the productivity of the handling operations to achieve an optimal performance for the robot to meet the industrial requirements. The suggested control scheme uses the adaptive model predictive control (AMPC). The AMPC is classified as an advance optimal control technique; it has the ability to minimize the input torque, and the error between the actually achieved response and the desired response of the manipulator. The model has the inherent ability to deal naturally with constraints on the inputs and has the capability of updating the linearized dynamic model at each current operating point, which solves the problem of nonlinearity in dynamic equations of the robot. Evaluations for the control scheme and for the trajectory planning are tested for SAMARA prototype. The concepts have been verified using several criteria, e.g., by comparing the results between the simulation power consumption and the actual power consumption measured from the physical prototype, comparing the performance of the QL approach with EA as trajectory planning algorithm for the under-actuated motion, and comparing the performance of SAMARA with other industrial robots from several perspectives. The applicability of under-actuated robotic kinematics for practical applications has been approved by examples from food industry, and press lines industry, with their respective requirements.Roboterbasierte Handhabungsoperationen sind in unterschiedlichen Anwendungsbereichen relevant. Beispiele sind Pick-und-Place Operationen, Palettierungen, Be- und Entladen von Maschinen sowie die Bereitstellung von Fertigungslinien mit Werkstücken. Die Entwicklung von Industrierobotern wird von einer Vielfalt unterschiedlicher Anwendungsbereiche inspiriert. Vorteile von Industrierobotern sind hohe Arbeitsgenauigkeit, hohe Produktivität, Kostenreduktion und der mögliche Einsatz in gefährlichen Produktionsumgebungen. Vorbehalte gegenüber Industrierobotern ergeben sich aus ihrer oft geringen Ressourceneffizienz, weswegen der Energieverbrauch in den Fokus aktueller Entwicklungsarbeiten tritt. Das „System Applying Momentum Transfer for Acceleration of an End Effector with the Redundant Axis“ (SAMARA) ist der Prototyp eines Industrieroboters für Pick-und-Place Operationen. Unter Verwendung redundanter, unteraktuierter Konfigurationen und Evolutionärer Algorithmen (EA) kann der Energieverbrauch reduziert werden. Für Anwendungen mit verhältnismäßig größeren Handhabungsweglängen und hohen Traglasten von bis zu 5,5kg kann die Effektivität der Handhabungsoperation verbessert werden. Für diese Roboterkinematik konnten bereits Energieeinsparungen erreicht werden. Es hat sich gezeigt, dass die Verringerung der Zykluszeit bei gleichzeitiger Reduktion des Energieverbrauches ein Zielkonflikt darstellt. Gleichermaßen ist die Berechnungszeit zur Planung der Trajektorie der Endeffektoren zu hoch. PID Control eignet sich nicht für robuste unteraktuierte Bewegungen (UAM). Unsicherheiten über die Höhe der Traglast beeinflussen die Ablagegenauigkeit sowie die Wiederholgenauigkeit bei der Handhabung. Der Ansatz einer Quasi-Linearization (QL) dient der Planung von Trajektorien bei gleichzeitiger Reduktion von Energieverbrauch und Rechenzeit. QL ist auf die Reduktion der Zykluszeit und damit auf die Erhöhung der Produktivität von Handhabungsoperationen durch die Entwicklung eines verbesserten Controllers gerichtet, um die aktuellen industriellen Anforderungen zu erfüllen. Die Control-Strategie verwendet ein sog. Adaptive Model Predictive Control (AMPC). Das AMPC ist eine verbesserte Control-Strategie mit der Eigenschaft, das Eingansdrehmoment und den Fehler zwischen Soll- und Istposition des Manipulators zu minimieren. Das Modell hat darüber hinaus die Fähigkeiten mit Randbedingungen der Eingänge umzugehen und das linearisierte dynamische Modell zu aktualisieren, wodurch das Problem der Nichtlinearität der dynamischen Gleichungen des Roboters umgangen werden kann. Eine Bewertung des Control-Vorganges und der Trajektorieplanung wurde für SAMARA durchgeführt. Die Konzepte wurden unter Berücksichtigung mehrerer Kriterien verifiziert. Hierzu zählen der Vergleich der Ergebnisse von simuliertem Energieverbrauch mit dem tatsächlichen im Betrieb gemessenen, der Leistung des QL-Ansatzes mit EA als Algoritmus zur Planung von Trajektorien und der Leistung von SAMARA mit anderen Industrierobotern. Sowohl in der Lebensmittel- als auch in der Druckindustrie konnten unteraktuierte Roboter ihre Anwendbarkeit unter Beweis stellen

Using Adaptive Model Predictive Technique to Control Underactuated Robot and Minimize Energy Consumption

AbstractThis paper presents an adaptive model predictive control scheme to control the underactuated and redundant robot, the robot has highly nonlinear coupling because of the existence of a passive axis. Adaptive model predictive control provides a framework to solve optimal discrete control problem for a nonlinear system under input saturation and state constraints. The optimal reference trajectory is computed by using Quasi-linearization (QL) approach to minimize the energy consumption for underactuated motion between two points. The challenge is to meet the performance requirements e.g. position accuracy, repeatability, and precision, combined with high speed capability. Numerical simulations are conducted to validate the control scheme. Simulation results show very good comparison and prove the adequateness of this control technique for underactuated industrial robots

Modeling, Identification, and Control of a Discrete Variable Stiffness Actuator (DVSA)

A branch of robotics, variable impedance actuation, along with one of its subfields variable stiffness actuation (VSA) targets the realization of complaint robotic manipulators. In this paper, we present the modeling, identification, and control of a discrete variable stiffness actuator (DVSA), which will be developed for complaint manipulators in the future. The working principle of the actuator depends on the involvement of series and parallel springs. We firstly report the conceptual design of a stiffness varying mechanism, and later the details of the dynamic model, system identification, and control techniques are presented. The dynamic parameters of the system are identified by using the logarithmic decrement algorithm, while the control schemes are based on linear quadratic control (LQR) and computed torque control (CTC), respectively. The numerical simulations are performed for the evaluation of each method, and results showed the good potentialities for the system. Future work includes the implementation of the presented approach on the hardware

Modeling, Control, and Numerical Simulations of a Novel Binary-Controlled Variable Stiffness Actuator (BcVSA)

This research work aims at realizing a new compliant robotic actuator for safe human-robotic interaction. In this paper, we present the modeling, control, and numerical simulations of a novel Binary-Controlled Variable Stiffness Actuator (BcVSA) aiming to be used for the development of a novel compliant robotic manipulator. BcVSA is the proof of concept of the active revolute joint with the variable recruitment of series-parallel elastic elements. We briefly recall the basic design principle which is based on a stiffness varying mechanism consisting of a motor, three inline clutches, and three torsional springs with stiffness values (K0, 2K0, 4K0) connected to the load shaft and the motor shaft through two planetary sun gear trains with ratios (4:1, 4:1 respectively). We present the design concept, stiffness and dynamic modeling, and control of our BcVSA. We implemented three kinds of Multiple Model Predictive Control (MPC) to control our actuator. The main motivation of choosing this controller lies in the fact that working principle of multiple MPC and multiple states space representation (stiffness level) of our actuator share similar interests. In particular, we implemented Multiple MPC, Multiple Explicit MPC, and Approximated Multiple Explicit MPC. Numerical simulations are performed in order to evaluate their effectiveness for the future experiments on the prototype of our actuator. The simulation results showed that the Multiple MPC, and the Multiple Explicit MPC have similar results from the robustness point of view. On the other hand, the robustness performance of Approximated Multiple Explicit MPC is not good as compared to other controllers but it works in the offline framework while having the capability to compute the sub-optimal results. We also performed the comparison of MPC based controllers with the Computed Torque Control (CTC), and Linear Quadratic Regulator (LQR). In future, we are planning to test the presented approach on the hardware prototype of our actuator