Adaptive control of robotic manipulators with unified motion constraints

In this paper, we present an adaptive control of robotic manipulators with parametric uncertainties and motion constraints. Position and velocity constraints are considered and they are unified and converted into the constraint of the nominal input. An adaptive neural network control is developed to achieve trajectory tracking, while the problems of motion constraints are addressed by considering the saturation effect of the nominal input. The uniform boundedness of all closed-loop signals is verified through Lyapunov analysis. Simulation and experiment results on a 2 DOF robotic manipulator demonstrate the effectiveness of the proposed method

Approximate hybrid model predictive control for multi-contact push recovery in complex environments

Feedback control of robotic systems interacting with the environment through contacts is a central topic in legged robotics. One of the main challenges posed by this problem is the choice of a model sufficiently complex to capture the discontinuous nature of the dynamics but simple enough to allow online computations. Linear models have proved to be the most effective and reliable choice for smooth systems; we believe that piecewise affine (PWA) models represent their natural extension when contact phenomena occur. Discrete-time PWA systems have been deeply analyzed in the field of hybrid Model Predictive Control (MPC), but the straightforward application of MPC techniques to complex systems, such as a humanoid robot, leads to mixed-integer optimization problems which are not solvable at real-time rates. Explicit MPC methods can construct the entire control policy offline, but the resulting policy becomes too complex to compute for systems at the scale of a humanoid robot. In this paper we propose a novel algorithm which splits the computational burden between an offline sampling phase and a limited number of online convex optimizations, enabling the application of hybrid predictive controllers to higher-dimensional systems. In doing so we are willing to partially sacrifice feedback optimality, but we set stability of the system as an inviolable requirement. Simulation results of a simple planar humanoid that balances by making contact with its environment are presented to validate the proposed controller

Stabilizing nonlinear model predictive control in presence of disturbances and off - line approximations of the control law

2009/2010One of the more recent and promising approaches to control is the Receding Horizon one. Due to its intrinsic characteristics, this methodology, also know as Model Predictive Control, allows to easily face disturbances and model uncertainties: indeed at each sampling instant the control action is recalculated on the basis of the reached state (closed loop). More in detail, the procedure consists in the minimization of an adequate cost function with respect to a control input sequence; then the first element of the optimal sequence is applied. The whole procedure is then continuously reiterated. In this thesis, we will focus in particular on robust control of constrained systems. This is motivated by the fact that, in practice, every real system is subjected to uncertainties, disturbances and constraints, in particular on state and input (for instance, plants can work without being damaged only in a limited set of configurations and, on the other side, control actions must be compatible with actuators' physical limits). With regard to the first aspect, maintaining the closed loop stability even in presence of disturbances or model mismatches can result in an essential strategy: moreover it can be exploited in order to design an approximate stabilizing controller, as it will be shown. The control input values are obtained recurring to a Nearest Neighbour technique or, in more favourable cases, to a Neural Network based approach to the exact RH law, which can be then calculated off line: this implies a strong improvement related to the applicability of MPC policy in particular in terms of on line computational burden. The proposed scheme is capable to guarantee stability even for systems that are not stabilizable by means of a continuous feedback control law. Another interesting framework in which the study of the influence of uncertainties on stability can lead to significant contributions is the networked MPC one. In this case, due to the absence of physical interconnections between the controller and the systems to be controlled, stability can be obtained only taking into account of the presence of disturbances, delays and data losses: indeed this kind of uncertainties are anything but infrequent in a communication network. The analysis carried out in this thesis regards interconnected systems and leads to two distinct procedures, respectively stabilizing the linear systems with TCP protocol and nonlinear systems with non-acknowledged protocol. The core of both the schemes resides in the online solution of an adequate reduced horizon optimal control problem.Una delle strategie di controllo emerse più recentemente, più promettenti e di conseguenza più studiate negli ultimi anni è quella basata sull'approccio Receding Horizon. Grazie alle caratteristiche che contraddistinguono questa tecnica, cui si fa spesso riferimento anche col nome di Model Predictive Control, risulta piuttosto agevole trattare eventuali disturbi e incertezze di modellazione; tale metodo prevede infatti il calcolo di un nuovo ingresso di controllo per ciascun istante di campionamento, in seguito alla minimizzazione ad ogni passo di un'opportuna funzione di costo rispetto ad una sequenza di possibili futuri ingressi, inizializzata sulla base del valore dello stato del sistema all'istante considerato. Il controllo è dato dal primo elemento di tale sequenza ottima; tutto questo viene continuamente ripetuto, il che comporta un aggiornamento costante del segnale di controllo. Gli inconvenienti di questa tecnica risiedono nelle elevate risorse computazionali e nei tempi di calcolo richiesti, così da ridurne drasticamente l'applicabilità specie nel caso di sistemi con elevata dinamica. In questa tesi ci si concentrerà sulle caratteristiche di robustezza del controllore: l'importanza di quest'analisi risiede nel fatto che ogni sistema reale è soggetto a incertezze e disturbi di varia origine cui bisogna far fronte durante le normali condizioni di funzionamento. Inoltre, la capacità di gestire errori di modellazione, come si vedrà, può essere sfruttata per ottenere un notevole incremento delle prestazioni nella stima del valore da fornire in ingresso all'impianto: si tratta di ripartire l'errore complessivo in modo da garantirsi dei margini che consentano di lavorare con un'approssimazione della legge di controllo, come specificato più avanti. In tutto il lavoro si considereranno sistemi vincolati: l'interesse per questa caratteristica dipende dal fatto che nella pratica vanno sempre tenuti in considerazione eventuali vincoli su stato e ingressi: basti pensare al fatto che ogni impianto è progettato per lavorare solo all'interno un determinato insieme di configurazioni, determinato ad esempio da vincoli fisici su attuatori, sensori e così via: non riporre sufficiente attenzione in tali restrizioni può risultare nel danneggiamento del sistema di controllo o dell'impianto stesso. Le caratteristiche di stabilità di un sistema controllato mediante MPC dipendono in modo determinante dalla scelta dei parametri e degli attributi della funzione di costo da minimizzare; nel seguito, con riferimento al caso dei sistemi non lineari, saranno forniti suggerimenti e strumenti utili in tal senso, al fine di ottenere la stabilità anche in presenza di disturbi (che si assumeranno opportunamente limitati). Successivamente tale robustezza verrà sfruttata per la progettazione di controllori stabilizzanti approssimati: si dimostrerà infatti che, una volta progettato adeguatamente il sistema di controllo “esatto” basato su approccio RH e conseguentemente calcolati off-line i valori ottimi degli ingressi su una griglia opportunamente costruita sul dominio dello stato, il ricorso a una conveniente approssimazione di tali valori non compromette le proprietà di stabilità del sistema complessivo, che continua per di più a mantenere una certa robustezza. Da notare che ciò vale anche per sistemi non stabilizzabili mediante legge di controllo feedback continua: la funzione approssimante può essere ottenuta in questo caso con tecniche di tipo Nearest Neighbour; qualora invece la legge di controllo sia sufficientemente regolare si potrà far ricorso ad approssimatori smooth, quali ad esempio le reti neurali. Tutto ciò comporta un notevole miglioramento delle prestazioni del controllore RH sia dal punto di vista del tempo di calcolo richiesto che (nel secondo caso) della memoria necessaria ad immagazzinare i parametri del controllore, risultando nell'applicabilità dell'approccio basato su MPC anche al caso di sistemi con elevata dinamica. Un altro ambito in cui lo studio dell'influenza delle incertezze e dei disturbi sulla stabilità richiede una notevole attenzione è quello dei sistemi networked; anche in questo caso il ricorso all'MPC può portare a ottimi risultati di stabilità robusta, a patto di individuare un' opportuna struttura per il sistema complessivo ed effettuare scelte adeguate per il problema di ottimizzazione. In particolare, si considererà il caso di trasmissione di dati tra un controllore centralizzato e le varie parti dell'impianto in assenza di collegamento fisico diretto. Lo studio della stabilità dovrà allora tenere in considerazione la presenza di perdite di pacchetti o ritardi di trasmissione, condizioni tutt'altro che infrequenti per le reti. Saranno quindi proposte due distinte procedure, che si dimostreranno essere in grado di garantire robustezza a sistemi rispettivamente lineari comunicanti con protocolli di tipo TCP e non lineari in presenza di protocolli UDP. Questo secondo caso è senz'altro il più complesso ma allo stesso tempo il più concreto tra i due. Il nucleo del controllo è ancora basato su una tecnica MPC, ma stavolta il controllore è chiamato a risolvere il problema di ottimizzazione su un orizzonte “ridotto”, che consente la gestione dei ritardi e di eventuali perdite di pacchetto su determinati canali. La lunghezza dell'orizzonte dipenderà dalla presenza o meno dei segnali di ricezione del pacchetto (acknowledgement).XXIII Ciclo197

Design of Adaptive Sliding Mode Fuzzy Control for Robot Manipulator Based on Extended Kalman Filter

In this work, a new adaptive motion control scheme for robust performance control of robot manipulators is presented. The proposed scheme is designed by combining the fuzzy logic control with the sliding mode control based on extended Kalman filter. Fuzzy logic controllers have been used successfully in many applications and were shown to be superior to the classical controllers for some nonlinear systems. Sliding mode control is a powerful approach for controlling nonlinear and uncertain systems. It is a robust control method and can be applied in the presence of model uncertainties and parameter disturbances, provided that the bounds of these uncertainties and disturbances are known. We have designed a new adaptive Sliding Mode Fuzzy Control (SMFC) method that requires only position measurements. These measurements and the input torques are used in an extended Kalman filter (EKF) to estimate the inertial parameters of the full nonlinear robot model as well as the joint positions and velocities. These estimates are used by the SMFC to generate the input torques. The combination of the EKF and the SMFC is shown to result in a stable adaptive control scheme called trajectory-tracking adaptive robot with extended Kalman (TAREK) method. The theory behind TAREK method provides clear guidelines on the selection of the design parameters for the controller. The proposed controller is applied to a two-link robot manipulator. Computer simulations show the robust performance of the proposed scheme

Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.Comment: 32 pages, 5 figure

Explicit feedback synthesis for nonlinear robust model predictive control driven by quasi-interpolation

We present QuIFS (Quasi-Interpolation driven Feedback Synthesis): an offline feedback synthesis algorithm for explicit nonlinear robust minmax model predictive control (MPC) problems with guaranteed quality of approximation. The underlying technique is driven by a particular type of grid-based quasi-interpolation scheme. The QuIFS algorithm departs drastically from conventional approximation algorithms that are employed in the MPC industry (in particular, it is neither based on multi-parametric programming tools and nor does it involve kernel methods), and the essence of its point of departure is encoded in the following challenge-answer approach: Given an error margin $\varepsilon>0$, compute in a single stroke a feasible feedback policy that is uniformly $\varepsilon$-close to the optimal MPC feedback policy for a given nonlinear system subjected to constraints and bounded uncertainties. Closed-loop stability and recursive feasibility under the approximate feedback policy are also established. We provide a library of numerical examples to illustrate our results.Comment: 31 Page

Integral sliding mode fault tolerant control allocation for a class of affine nonlinear system

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper develops novel fault tolerant integral sliding mode control allocation schemes for a class of over-actuated affine nonlinear system. The proposed schemes rely on an existing baseline controller and the objective is to retain the nominal (fault-free) closed-loop performance in the face of actuator faults/failures by effectively utilizing actuator redundancy. The online control allocation reroutes the control effort to the healthy actuators using knowledge of the actuator effectiveness level estimates. One of the proposed schemes is tested in simulation using a well known high fidelity model of a large civil transport aircraft (B747) from the literature. Good simulation results show the efficacy of the scheme

Precision Control of a Sensorless Brushless Direct Current Motor System

Sensorless control strategies were first suggested well over a decade ago with the aim of reducing the size, weight and unit cost of electrically actuated servo systems. The resulting algorithms have been successfully applied to the induction and synchronous motor families in applications where control of armature speeds above approximately one hundred revolutions per minute is desired. However, sensorless position control remains problematic. This thesis provides an in depth investigation into sensorless motor control strategies for high precision motion control applications. Specifically, methods of achieving control of position and very low speed thresholds are investigated. The developed grey box identification techniques are shown to perform better than their traditional white or black box counterparts. Further, fuzzy model based sliding mode control is implemented and results demonstrate its improved robustness to certain classes of disturbance. Attempts to reject uncertainty within the developed models using the sliding mode are discussed. Novel controllers, which enhance the performance of the sliding mode are presented. Finally, algorithms that achieve control without a primary feedback sensor are successfully demonstrated. Sensorless position control is achieved with resolutions equivalent to those of existing stepper motor technology. The successful control of armature speeds below sixty revolutions per minute is achieved and problems typically associated with motor starting are circumvented.Research Instruments Ltd