On the motion planning & control of nonlinear robotic systems

In the last decades, we saw a soaring interest in autonomous robots boosted not only by academia and industry, but also by the ever in- creasing demand from civil users. As a matter of fact, autonomous robots are fast spreading in all aspects of human life, we can see them clean houses, navigate through city traffic, or harvest fruits and vegetables. Almost all commercial drones already exhibit unprecedented and sophisticated skills which makes them suitable for these applications, such as obstacle avoidance, simultaneous localisation and mapping, path planning, visual-inertial odometry, and object tracking. The major limitations of such robotic platforms lie in the limited payload that can carry, in their costs, and in the limited autonomy due to finite battery capability. For this reason researchers start to develop new algorithms able to run even on resource constrained platforms both in terms of computation capabilities and limited types of endowed sensors, focusing especially on very cheap sensors and hardware. The possibility to use a limited number of sensors allowed to scale a lot the UAVs size, while the implementation of new efficient algorithms, performing the same task in lower time, allows for lower autonomy. However, the developed robots are not mature enough to completely operate autonomously without human supervision due to still too big dimensions (especially for aerial vehicles), which make these platforms unsafe for humans, and the high probability of numerical, and decision, errors that robots may make. In this perspective, this thesis aims to review and improve the current state-of-the-art solutions for autonomous navigation from a purely practical point of view. In particular, we deeply focused on the problems of robot control, trajectory planning, environments exploration, and obstacle avoidance.

Modulation of peritoneal macrophage activity by the saturation state of the fatty acid moiety of phosphatidylcholine

To determine the effects of saturated and unsaturated fatty acids in phosphatidylcholine (PC) on macrophage activity, peritoneal lavage cells were cultured in the presence of phosphatidylcholine rich in saturated or unsaturated fatty acids (sat PC and unsat PC, respectively), both used at concentrations of 32 and 64 µM. The treatment of peritoneal macrophages with 64 µM unsat PC increased the production of hydrogen peroxide by 48.3% compared to control (148.3 ± 16.3 vs 100.0 ± 1.8%, N = 15), and both doses of unsat PC increased adhesion capacity by nearly 50%. Moreover, 64 µM unsat PC decreased neutral red uptake by lysosomes by 32.5% compared to the untreated group (67.5 ± 6.8 vs 100.0 ± 5.5%, N = 15), while both 32 and 64 µM unsat PC decreased the production of lipopolysaccharide-elicited nitric oxide by 30.4% (13.5 ± 2.6 vs 19.4 ± 2.5 µM) and 46.4% (10.4 ± 3.1 vs 19.4 ± 2.5 µM), respectively. Unsat PC did not affect anion production in non-stimulated cells or phagocytosis of unopsonized zymosan particles. A different result pattern was obtained for macrophages treated with sat PC. Phorbol 12-miristate 13-acetate-elicited superoxide production and neutral red uptake were decreased by nearly 25% by 32 and 64 µM sat PC, respectively. Sat PC did not affect nitric oxide or hydrogen peroxide production, adhesion capacity or zymosan phagocytosis. Thus, PC modifies macrophage activity, but this effect depends on cell activation state, fatty acid saturation and esterification to PC molecule and PC concentration. Taken together, these results indicate that the fatty acid moiety of PC modulates macrophage activity and, consequently, is likely to affect immune system regulation in vivo.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Complexity of human postural control in young and older adults during prolonged standing

Aging is known to have a degrading influence on many structures and functions of the human sensorimotor system. The present work assessed aging-related changes in postural sway using fractal and complexity measures of the center of pressure (COP) dynamics with the hypothesis that complexity and fractality decreases in the older individuals. Older subjects (68 +/- 4 years) and young adult subjects (28 +/- 7 years) performed a quiet stance task (60 s) and a prolonged standing task (30 min) where subjects were allowed to move freely. Long-range correlations (fractality) of the data were estimated by the detrended fluctuation analysis (DFA); changes in entropy were estimated by the multi-scale entropy (MSE) measure. The DFA results showed that the fractal dimension was lower for the older subjects in comparison to the young adults but the fractal dimensions of both groups were not different from a 1/f noise, for time intervals between 10 and 600 s. The MSE analysis performed with the typically applied adjustment to the criterion distance showed a higher degree of complexity in the older subjects, which is inconsistent with the hypothesis that complexity in the human physiological system decreases with aging. The same MSE analysis performed without adjustment showed no differences between the groups. Taken all results together, the decrease in total postural sway and long-range correlations in older individuals are signs of an adaptation process reflecting the diminishing ability to generate adequate responses on a longer time scale.

Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type-zero sadle-node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type-zero saddle-node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation value is presented in this paper. Copyright (C) 2010 John Wiley & Sons, Ltd.

Robust STATCOM control for the stabilisation of fixed-speed wind turbines during low voltages

This paper presents a robust voltage control scheme for fixed-speed wind generators using a static synchronous compensator (STATCOM) controller. To enable a linear and robust control framework with structured uncertainty, the overall system is represented by a linear part plus a nonlinear part that covers an operating range of interest required to ensure stability during severe low voltages. The proposed methodology is flexible and readily applicable to larger wind farms of different configurations. The performance of the control strategy is demonstrated on a two area test system. Large disturbance simulations demonstrate that the proposed controller enhances voltage stability as well as transient stability of induction generators during low voltage ride through (LVRT) transients and thus enhances the LVRT capability. (C) 2011 Elsevier Ltd. All rights reserved.

Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures

This paper deals with the application of the lumped dissipation model in the analysis of reinforced concrete structures, emphasizing the nonlinear behaviour of the materials The presented model is based on the original models developed by Cipollina and Florez-Lopez (1995) [12]. Florez-Lopez (1995) [13] and Picon and Florez-Lopez (2000) [14] However, some modifications were introduced in the functions that control the damage evolution in order to improve the results obtained. The efficiency of the new approach is evaluated by means of a comparison with experimental results on reinforced concrete structures such as simply supported beams, plane frames and beam-to-column connections Finally, the adequacy of the numerical model representing the global behaviour of framed structures is investigated and the limits of the analysis are discussed (C) 2009 Elsevier Ltd All rights reserved

Modeling, control and experimental validation of a novel actuator based on shape memory alloys

The paper presents the development of a mechanical actuator using a shape memory alloy with a cooling system based on the thermoelectric effect (Seebeck-Peltier effect). Such a method has the advantage of reduced weight and requires a simpler control strategy as compared to other forced cooling systems. A complete mathematical model of the actuator was derived, and an experimental prototype was implemented. Several experiments are used to validate the model and to identify all parameters. A robust and nonlinear controller, based on sliding-mode theory, was derived and implemented. Experiments were used to evaluate the actuator closed-loop performance, stability, and robustness properties. The results showed that the proposed cooling system and controller are able to improve the dynamic response of the actuator. (C) 2009 Elsevier Ltd. All rights reserved.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

Valve friction and nonlinear process model closed-loop identification

Among several process variability sources, valve friction and inadequate controller tuning are supposed to be two of the most prevalent. Friction quantification methods can be applied to the development of model-based compensators or to diagnose valves that need repair, whereas accurate process models can be used in controller retuning. This paper extends existing methods that jointly estimate the friction and process parameters, so that a nonlinear structure is adopted to represent the process model. The developed estimation algorithm is tested with three different data sources: a simulated first order plus dead time process, a hybrid setup (composed of a real valve and a simulated pH neutralization process) and from three industrial datasets corresponding to real control loops. The results demonstrate that the friction is accurately quantified, as well as ""good"" process models are estimated in several situations. Furthermore, when a nonlinear process model is considered, the proposed extension presents significant advantages: (i) greater accuracy for friction quantification and (ii) reasonable estimates of the nonlinear steady-state characteristics of the process. (C) 2010 Elsevier Ltd. All rights reserved.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.