Coverage control has many applications such as security patrolling, land mine detectors, and automatic vacuum cleaners. This Thesis presents an analytical approach for generation of control inputs for a non-holonomic mobile robot in coverage control. Neural Network approach is used for complete coverage of a given area in the presence of stationary and dynamic obstacles. A complete coverage algorithm is used to determine the sequence of points. Once the sequences of points are determined a smooth trajectory characterized by fifth order polynomial having second order continuity is generated. And the slope of the curve at each point is calculated from which the control inputs are generated analytically. Optimal trajectory is generated using a method given in research literature and a qualitative analysis of the smooth trajectory is done. Cooperative sweeping of multirobots is achieved by dividing the area to be covered into smaller areas depending on the number of robots. Once the area is divided into sub areas, each robot is assigned a sub area for cooperative sweeping.

In this thesis, four robots will be used to implement a collision-free trajectory planning/replanning algorithm. The existence of a chained form transformation so that the robot's model can be control in canonical form will be analyzed and proved. A trajectory generation for obstacles avoidance will be derived, simulated, and implemented. A specific PC based control algorithm will be developed. Chapter two describes two wheels differential drive robot modeling and existence of controllable canonical chained form. Chapter 3 describes criterion for avoiding dynamic objects, a feasible collision-free trajectory parameterization, and solution to steering velocity. Chapter 4 describes robot implementation, pc wireless interface, and strategy to send and receive information wirelessly. The main robot will be moving in a dynamically changing environment using canonical chained form. The other three robots will be used as moving obstacles that will move with known piecewise constant velocities, and therefore, with known trajectories. Their initial positions are assumed to be known as well. The main robot will receive the command from the computer such as how fast to move and to turn in order to avoid collision. The robot will autonomously travel to the desired destination collision-free.

In this dissertation, a novel and generic solution of trajectory generation is developed and evaluated for ground and aerial vehicles in a dynamic environment. By explicitly considering a kinematic model of the ground vehicles, the family of feasible trajectories and their corresponding steering controls are derived in a closed form and are expressed in terms of one adjustable parameter for the purpose of collision avoidance. A collision-avoidance condition is developed for the dynamically changing environment, which consists of a time criterion and a geometrical criterion. By imposing this condition, one can determine a family of collision-free paths in a closed form. Then, optimization problems with respect to different performance indices are setup to obtain optimal solutions from the feasible trajectories. Among these solutions, one with respect to the near-shortest distance and another with respect to the near-minimal control energy are analytical and simple. These properties make them good choices for real-time trajectory planning. Such optimal paths meet all boundary conditions, are twice differentiable, and can be updated in real time once a change in the environment is detected. Then this novel method is extended to 3D space to find a real-time optimal path for aerial vehicles. After that, to reflect the real applications, obstacles are classified to two types: "hard" obstacles that must be avoided, and "soft" obstacles that can be run over/through. Moreover, without losing generality, avoidance criteria are extended to obstacles with any geometric shapes. This dissertation also points out that the emphases of the future work are to consider other constraints such as the bounded velocity and so on. The proposed method is illustrated by computer simulations.

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles' kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs.

Yes / This paper proposes a novel trajectory tracking control approach for nonholonomic wheeled mobile robots. In this approach, the integration of feed-forward and feedback controls is presented to design the kinematic controller of wheeled mobile robots, where the control law is constructed on the basis of Lyapunov stability theory, for generating the precisely desired velocity as the input of the dynamic model of wheeled mobile robots; a proportional-integral-derivative based membrane controller is introduced to design the dynamic controller of wheeled mobile robots to make the actual velocity follow the desired velocity command. The proposed approach is defined by using an enzymatic numerical membrane system to integrate two proportional-integral-derivative controllers, where neural networks and experts’ knowledge are applied to tune parameters. Extensive experiments conducted on the simulated wheeled mobile robots show the effectiveness of this approach. / The work of XW and GZ is supported by the National Natural Science Foundation of China (61170016, 61373047). The work of MG, FI and RL was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI (project number: PN-II-ID-PCE-2011-3-0688).

A nonholonomic tracking controller is designed and adapted to work with both differential steering and Ackermann steering based platforms whose dynamics are represented using a unicycle model. The goal of this work is to find a relatively simple approach that offers a practical alternative to bulky and expensive algorithms, but still bolsters applicability where many other lightweight algorithms are too lax. The hope is that this alternative will offer a straightforward approach for groups interested in autonomous vehicle research but who do not have the resources or personnel to implement more complex solutions. In the first phase of this work, saturation constraints based on differential drive kinematics are added to ensure that the vehicle behaves intuitively and does not exceed user defined limitations. A new strategy for mapping commands back into a viable envelope is introduced, and the restrictions are accounted for using Lyapunov stability criteria. This stage of work is validated through simulation and experimentation. Following the development of differential drive methods, similar techniques are applied to Ackermann steering kinematic constraints. An additional saturation algorithm is presented, which likewise is accounted for using Lyapunov stability criteria. As with the differential case, the Ackermann design is validated through simulation and experimentation. Overall, the results presented in this work demonstrate that the developed algorithms show significant promise and offer a lightweight, practical solution to the problem of vehicle tracking control. / Master of Science

No / We analyze the possibility and efficiency of nonholonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary units of arbitrary physical nature, and can be employed efficiently for universal quantum computations and simulation of quantum-field dynamics. As an example we describe a toy device that can perform Toffoli-gate transformations and discrete Fourier transform on 9 qubits.

This thesis describes the current state of development of the Flexible Low-cost Automated Scaled Highway (FLASH) laboratory at the Virginia Tech Transportation Institute (VTTI). The FLASH lab and the scale model cars contained therein provide a testbed for the small scale development stage of intelligent transportation systems (ITS). In addition, the FLASH lab serves as a home to the prototype display being developed for an educational museum exhibit. This thesis also gives details of the path following lateral controller implemented on the FLASH car. The controller was developed using the kinematic model for a wheeled robot. The global model is converted into the path coordinate model so that only local variables are needed. then the path coordinate model is converted into chained form and a controller is given to perform path following. The path coordinate model introduces a new parameter to the system: the curvature of the path. Thus, it is necessary to provide the path's curvature value to the controller. Because of the environment in which the car is operating, the curvature values are known a priori. Several online methods for determining the curvature are developed. A MATLAB simulation environment was created with which to test the above algorithms. The simulation uses the kinematic model to show the car's behavior and implements the sensors and controller as closely as possible to the actual system. The implementation of the lateral controller in hardware is discussed. The vehicle platform is described and the harware and software architecture detailed. The car described is capable of operating manually and autonomously. In autonomous mode, several sensors are utilized including: infrared, magnetic, ultrasound, and image based technology. The operation of each sensor type is described and the information received by the processor from each is discussed. / Master of Science

Differential-algebraic equations (DAEs) consist of mixed systems of ordinary differential equations (ODEs) coupled with linear or nonlinear equations. Such systems may be viewed as ODEs with integral curves lying in a manifold. DAEs appear frequently in applications such as classical mechanics and electrical circuits. This thesis concentrates on systems of index 2, originally index 3, and mixed index 2 and 3. Fast and efficient numerical solvers for DAEs are highly desirable for finding solutions. We focus primarily on the class of Gauss-Lobatto SPARK methods. However, we also introduce an extension to methods proposed by Murua for solving index 2 systems to systems of mixed index 2 and 3. An analysis of these methods is also presented in this thesis. We examine the existence and uniqueness of the proposed numerical solutions, the influence of perturbations, and the local error and global convergence of the methods. When applied to index 2 DAEs, SPARK methods are shown to be equivalent to a class of collocation type methods. When applied to originally index 3 and mixed index 2 and 3 DAEs, they are equivalent to a class of discontinuous collocation methods. Using these equivalences, (s,s)--Gauss-Lobatto SPARK methods can be shown to be superconvergent of order 2s. Symplectic SPARK methods applied to Hamiltonian systems with holonomic constraints preserve well the total energy of the system. This follows from a backward error analysis approach. SPARK methods and our proposed EMPRK methods are shown to be Lagrange-d'Alembert integrators. This thesis also presents some numerical results for Gauss-Lobatto SPARK and EMPRK methods. A few problems from mechanics are considered.

Courses in analytical mechanics for undergraduate students are often limited to treatment of holonomic constraints, which are constraints on coordinates. The concept of nonholonomic constraints, constraints on velocities, is usually only mentioned briefly and it is easy to get a wrongful idea of what they are and how to treat them. This text explains and compares the methods of deriving the Euler-Lagrange equations and the consequences when imposing different kinds of constraints. One way to properly treat both holonomic and nonholonomic constraints is given, pinpointing the difficulties and common errors. Along the way, the treatment in local coordinates is also put in more modern terms, in the language of differential geometry, which is the language most commonly used in modern texts on the subject.