Optimal control of nonlinear partially-unknown systems with unsymmetrical input constraints and its applications to the optimal UAV circumnavigation problem

Aimed at solving the optimal control problem for nonlinear systems with unsymmetrical input constraints, we present an online adaptive approach for partially unknown control systems/dynamics. The designed algorithm converges online to the optimal control solution without the knowledge of the internal system dynamics. The optimality of the obtained control policy and the stability for the closed-loop dynamic optimality are proved theoretically. The proposed method greatly relaxes the assumption on the form of the internal dynamics and input constraints in previous works. Besides, the control design framework proposed in this paper offers a new approach to solve the optimal circumnavigation problem involving a moving target for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our method is compared with that of the existing circumnavigation control law in a numerical simulation and the simulation results validate the effectiveness of our algorithm

Least-Squares Based Adaptive Source Localization with Biomedical Applications

In this thesis, we study certain aspects of signal source/target localization by sensory agents and their biomedical applications. We first focus on a generic distance measurement based problem: Estimation of the location of a signal source by a sensory agent equiped with a distance measurement unit or a team of such a sensory agent. This problem was addressed in some recent studies using a gradient based adaptive algorithm. In this study, we design a least-squares based adaptive algorithm with forgetting factor for the same task. Besides its mathematical background, we perform some simulations for both stationary and drifting target cases. The least-squares based algorithm we propose bears the same asymptotic stability and convergence properties as the gradient algorithm previously studied. It is further demonstrated via simulation studies that the proposed least-squares algorithm converges significantly faster to the resultant location estimates than the gradient algorithm for high values of the forgetting factor, and significantly reduces the noise effects for small values of the forgetting factor. We also focus on the problem of localizing a medical device/implant in human body by a mobile sensor unit (MSU) using distance measurements. As the particular distance measurement method, time of flight (TOF) based approach involving ultra wide-band signals is used, noting the important effects of the medium characteristics on this measurement method. Since human body consists of different organs and tissues, each with a different signal permittivity coefficient and hence a different signal propagation speed, one cannot assume a constant signal propagation speed environment for the aforementioned medical localization problem. Furthermore, the propagation speed is unknown. Considering all the above factors and utilizing a TOF based distance measurement mechanism, we use the proposed adaptive least-square algorithm to estimate the 3-D location of a medical device/implant in the human body. In the design of the adaptive algorithm, we first derive a linear parametric model with the unknown 3-D coordinates of the device/implant and the current signal propagation speed of the medium as its parameters. Then, based on this parametric model, we design the proposed adaptive algorithm, which uses the measured 3-D position of the MSU and the measured TOF as regressor signals. After providing a formal analysis of convergence properties of the proposed localization algorithm, we implement numerical tests to analyze the properties of the localization algorithm, considering two types of scenarios: (1) A priori information regarding the region, e.g quadrant (among upper-left, upper-right, lower-left, lower-right of the human body), of the implant location is available and (2) such a priori information is not available. In (1), assuming knowledge of fixed average relative permittivity for each region, we established that the proposed algorithm converges to an estimate with zero estimation error. Moreover, different white Gaussian noises are added to emulate the TOF measurement disturbances, and it is observed that the proposed algorithm is robust to such noises/disturbances. In (2), although perfect estimation is not achieved, the estimation error is at a low admissible level. In addition, for both cases (1) and (2), forgetting factor effects have been investigated and results show that use of small forgetting factor values reduces noise effects significantly, while use of high forgetting factor values speeds up convergence of the estimation

Least-Squares Based Adaptive Source Localization with Biomedical Applications

In this thesis, we study certain aspects of signal source/target localization by sensory agents and their biomedical applications. We first focus on a generic distance measurement based problem: Estimation of the location of a signal source by a sensory agent equiped with a distance measurement unit or a team of such a sensory agent. This problem was addressed in some recent studies using a gradient based adaptive algorithm. In this study, we design a least-squares based adaptive algorithm with forgetting factor for the same task. Besides its mathematical background, we perform some simulations for both stationary and drifting target cases. The least-squares based algorithm we propose bears the same asymptotic stability and convergence properties as the gradient algorithm previously studied. It is further demonstrated via simulation studies that the proposed least-squares algorithm converges significantly faster to the resultant location estimates than the gradient algorithm for high values of the forgetting factor, and significantly reduces the noise effects for small values of the forgetting factor. We also focus on the problem of localizing a medical device/implant in human body by a mobile sensor unit (MSU) using distance measurements. As the particular distance measurement method, time of flight (TOF) based approach involving ultra wide-band signals is used, noting the important effects of the medium characteristics on this measurement method. Since human body consists of different organs and tissues, each with a different signal permittivity coefficient and hence a different signal propagation speed, one cannot assume a constant signal propagation speed environment for the aforementioned medical localization problem. Furthermore, the propagation speed is unknown. Considering all the above factors and utilizing a TOF based distance measurement mechanism, we use the proposed adaptive least-square algorithm to estimate the 3-D location of a medical device/implant in the human body. In the design of the adaptive algorithm, we first derive a linear parametric model with the unknown 3-D coordinates of the device/implant and the current signal propagation speed of the medium as its parameters. Then, based on this parametric model, we design the proposed adaptive algorithm, which uses the measured 3-D position of the MSU and the measured TOF as regressor signals. After providing a formal analysis of convergence properties of the proposed localization algorithm, we implement numerical tests to analyze the properties of the localization algorithm, considering two types of scenarios: (1) A priori information regarding the region, e.g quadrant (among upper-left, upper-right, lower-left, lower-right of the human body), of the implant location is available and (2) such a priori information is not available. In (1), assuming knowledge of fixed average relative permittivity for each region, we established that the proposed algorithm converges to an estimate with zero estimation error. Moreover, different white Gaussian noises are added to emulate the TOF measurement disturbances, and it is observed that the proposed algorithm is robust to such noises/disturbances. In (2), although perfect estimation is not achieved, the estimation error is at a low admissible level. In addition, for both cases (1) and (2), forgetting factor effects have been investigated and results show that use of small forgetting factor values reduces noise effects significantly, while use of high forgetting factor values speeds up convergence of the estimation

Adaptive Formation Control of Cooperative Multi-Vehicle Systems

The literature comprises many approaches and results for the formation control of multi-vehicle systems; however, the results established for the cases where the vehicles contain parametric uncertainties are limited. Motivated by the need for explicit characterization of the effects of uncertainties on multi-vehicle formation motions, we study distributed adaptive formation control of multi-vehicle systems in this thesis, focusing on different interrelated sub-objectives. We first examine the cohesive motion control problem of minimally persistent formations of autonomous vehicles. Later, we consider parametric uncertainties in vehicle dynamics in such autonomous vehicle formations. Following an indirect adaptive control approach and exploiting the features of the certainty equivalence principle, we propose control laws to solve maneuvering problem of the formations, robust to parametric modeling uncertainties. Next, as a formation acquisition/closing ranks problem, we study the adaptive station keeping problem, which is defined as positioning an autonomous mobile vehicle $A$ inside a multi-vehicle network, having specified distances from the existing vehicles of the network. In this setting, a single-integrator model is assumed for the kinematics for the vehicle $A$, and $A$ is assumed to have access to only its own position and its continuous distance measurements to the vehicles of the network. We partition the problem into two sub-problems; localization of the existing vehicles of the network using range-only measurements and motion control of $A$ to its desired location within the network with respect to other vehicles. We design an indirect adaptive control scheme, provide formal stability and convergence analysis and numerical simulation results, demonstrating the characteristics and performance of the design. Finally, we study re-design of the proposed station keeping scheme for the more challenging case where the vehicle $A$ has non-holonomic motion dynamics and does not have access to its self-location information. Overall, the thesis comprises methods and solutions to four correlated formation control problems in the direction of achieving a unified distributed adaptive formation control framework for multi-vehicle systems

Distributed formation control for autonomous robots

This thesis addresses several theoretical and practical problems related to formation-control of autonomous robots. Formation-control aims to simultaneously accomplish the tasks of forming a desired shape by the robots and controlling their coordinated collective motion. This kind of robot performance is a cornerstone in the emerging field of swarm robotics, in particular with applications in precision agriculture, coverage of sport/art events, communication networks, area surveillance or vehicle platooning for energy efficiency and many others. One of the most important outcomes of this thesis is that the provided algorithms are completely distributed. This means that there is no central unit commanding the robots, but they have their own intelligence which allows them to make their own decisions based only on the local information. A distributed scheme entails a striking feature about the scalability and maintenance of a team of robots. Moreover, we also address the scenario of having wrongly calibrated sensors, which has a profound impact in the performance of the robots. The provided algorithms make the robots robust against such a practical and very common problem in real applications

Circumnavigation using distance measurements

Consider a stationary agent A at an unknown location and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in som