An application of lyapunov stability analysis to improve the performance of NARMAX models

Previously we presented a novel approach to program a robot controller based on system identification and robot training techniques. The proposed method works in two stages: first, the programmer demonstrates the desired behaviour to the robot by driving it manually in the target environment. During this run, the sensory perception and the desired velocity commands of the robot are logged. Having thus obtained training data we model the relationship between sensory readings and the motor commands of the robot using ARMAX/NARMAX models and system identification techniques. These produce linear or non-linear polynomials which can be formally analysed, as well as used in place of “traditional robot” control code. In this paper we focus our attention on how the mathematical analysis of NARMAX models can be used to understand the robot’s control actions, to formulate hypotheses and to improve the robot’s behaviour. One main objective behind this approach is to avoid trial-and-error refinement of robot code. Instead, we seek to obtain a reliable design process, where program design decisions are based on the mathematical analysis of the model describing how the robot interacts with its environment to achieve the desired behaviour. We demonstrate this procedure through the analysis of a particular task in mobile robotics: door traversal

Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. Although common practice in designing nested control systems is to maximize the bandwidth of the inner loop to improve tracking performance, it may not be the most suitable approach when a certain range of impedance parameters has to be rendered. In particular, it turns out that the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g. a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016

Eksplicitna regulacija sile robotskog manipulatora aktivnim prigušenjem brzine

This paper presents a new interaction control structure that generates a family of explicit force regulators for robot manipulators. The proposed structure includes a term of a class of proportional-type functions in terms of force error; the force error is defined as the difference between a desired force and the actual force measured with a force sensor located at the end-effector. Also, the structure includes a generalized active velocity damping term in order to have a control of the energy dissipation, and a term used to compensate the gravity forces of the links. The stability analysis is performed in Lyapunov sense. An experimental comparison of two new explicit force regulators and the linear proportional structure, on a three degree-of-freedom, direct-drive robot, is presented. Also, proofs of the most important properties of the Cartesian dynamic model, are presented.Ovaj rad predstavlja novu interakcijsku kontrolnu strukturu koja predstavlja skupinu exsplicitnih regulatora sile za robotske manipulatore. Predložena struktura uključuje član klase funkcija proporcionalnog tipa u smilsu pogreške sile; pogreška sile se definira kao razlika između željene sile i stvarne sile koju mjere senzori postavljeni na kraju manipulatora. Također, struktura uključuje član za generalizirano aktvino prigušenje brzine kako bi se omogućila kontrola disipacije energije i član kojim se kompenzira utjecaj sile gravitacije na članke manipulatora. Analiza stabilnosti je napravljena u smislu Lyapunova. Prikazana je eksperimentalna usporedba dva nova eksplicitna regulatora sile i linearno-proporcionalne strukture na robotu s direktnim pogonom i tri stupnja slobode. Također su prikazani dokazi najvažnijih svojstava kartezijskog dinamičnog modela

Force, impedance and trajectory learning for contact tooling and haptic identification

Humans can skilfully use tools and interact with the environment by adapting their movement trajectory, contact force, and impedance. Motivated by the human versatility, we develop here a robot controller that concurrently adapts feedforward force, impedance, and reference trajectory when interacting with an unknown environment. In particular, the robot's reference trajectory is adapted to limit the interaction force and maintain it at a desired level, while feedforward force and impedance adaptation compensates for the interaction with the environment. An analysis of the interaction dynamics using Lyapunov theory yields the conditions for convergence of the closed-loop interaction mediated by this controller. Simulations exhibit adaptive properties similar to human motor adaptation. The implementation of this controller for typical interaction tasks including drilling, cutting, and haptic exploration shows that this controller can outperform conventional controllers in contact tooling

Neural Learning of Vector Fields for Encoding Stable Dynamical Systems

Lemme A, Reinhart F, Neumann K, Steil JJ. Neural Learning of Vector Fields for Encoding Stable Dynamical Systems. Neurocomputing. 2014;141:3-14

Force Sensorless Admittance Control with Neural Learning for Robots with Actuator Saturation

© 1982-2012 IEEE. In this paper, we present a sensorless admittance control scheme for robotic manipulators to interact with unknown environments in the presence of actuator saturation. The external environment is defined as linear models with unknown dynamics. Using admittance control, the robotic manipulator is controlled to be compliant with external torque from the environment. The external torque acted on the end-effector is estimated by using a disturbance observer based on generalized momentum. The model uncertainties are solved by using radial basis neural networks (NNs). To guarantee the tracking performance and tackle the effect of actuator saturation, an adaptive NN controller integrating an auxiliary system is designed to handle the actuator saturation. By employing Lyapunov stability theory, the stability of the closed-loop system is achieved. The experiments on the Baxter robot are implemented to verify the effectiveness of the proposed method

A spatial impedance controller for robotic manipulation

Mechanical impedance is the dynamic generalization of stiffness, and determines interactive behavior by definition. Although the argument for explicitly controlling impedance is strong, impedance control has had only a modest impact on robotic manipulator control practice. This is due in part to the fact that it is difficult to select suitable impedances given tasks. A spatial impedance controller is presented that simplifies impedance selection. Impedance is characterized using ¿spatially affine¿ families of compliance and damping, which are characterized by nonspatial and spatial parameters. Nonspatial parameters are selected independently of configuration of the object with which the robot must interact. Spatial parameters depend on object configurations, but transform in an intuitive, well-defined way. Control laws corresponding to these compliance and damping families are derived assuming a commonly used robot model. While the compliance control law was implemented in simulation and on a real robot, this paper emphasizes the underlying theor

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]