This dissertation addresses the design and stability analysis of decentralized, cooperative control laws for multivehicle systems. Advances in communication, navigation, and surveillance systems have enabled greater autonomy in multivehicle systems, and there is a shift toward decentralized, cooperative systems for computational efficiency and robustness. In a decentralized control scheme, control inputs are determined onboard each vehicle; therefore, decentralized controllers are more efficient for large numbers of vehicles, and the system is more robust to communication failures and reconfiguration. The design of decentralized, cooperative control laws is explored for a nonlinear vehicle model that can be represented in a double-integrator form. Cooperative controllers are functions of spacing errors with respect to other vehicles in the system, where the communication structure defines the information that is available to each vehicle. Control inputs are selected to achieve internal stability, or zero steady-state spacing errors, between vehicles in the system. Closed-loop equations of motion for the cooperative system can be written in a structural form, where damping and stiffness matrices contain control gains acting on the velocity and positions of the vehicles, respectively. The form of the stiffness matrix is determined by the communication structure, where different communication structures yield different control forms. Communication structures are compared using two structural analysis tools: modal cost and frequency-response functions, which evaluate the response of the multivehicle systems to disturbances. The frequency-response information is shown to reveal the string stability of different cooperative control forms. The effects of time delays in the feedback states of the cooperative control laws on system stability are also investigated. Closed-loop equations of motion are modeled as delay differential equations, and two stability notions are presented: delay-independent and delay-dependent stability. Lastly, two additional cooperative control forms are investigated. The first control form spaces vehicles along an arbitrary path, where distances between vehicles are constant for a given spacing parameter. This control form shows advantages over spacing vehicles using control laws designed in an inertial frame. The second control form employs a time-based spacing scheme, which spaces vehicles at constant-time intervals at a desired endpoint. The stability of these control forms is presented.

To reduce complexity of system analysis and control design, simplified models that capture the behavior of interest in the original system can be obtained. These simplified models, called abstractions, can be analyzed more easily than the original complex model. Hierarchies of consistent abstractions can significantly reduce the complexity in determining the reachability properties of nonlinear systems. Such consistent hierarchies of reachability-preserving nonlinear abstractions are considered for the robotic car. Not only can these abstractions be analyzed with respect to some behavior of interest, they can also be used to transfer control design for the complex model to the simplified model. In this work, the abstraction is applied to the car/unicycle system. Working towards control design, it is seen that there are certain classes of trajectories that exist in the rolling disk system that cannot be achieved by the robotic car. In order to account for these cases, the new concepts of traceability and &#949-traceability are introduced. This work also studies the relationship between the evolution of uncertain initial conditions in abstracted control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. Abstracted control systems with stochastic initial conditions show the same behavior as systems with deterministic initial conditions. A conservation law is applied to the probability density function (pdf) requiring that the area under it be unity. Application of the conservation law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system. / Ph. D.

This thesis addresses the pose stabilization of a car-like vehicle using omnidirectional visual feedback. The presented method allows a vehicle to servo to a pre-learnt target pose based on feature bearing angle and range discrepancies between the vehicle's current view of the environment and that seen at the learnt location. The best example of such a task is the use of visual feedback for autonomous parallel-parking of an automobile. Much of the existing work in pose stabilization is highly theoretical in nature with few examples of implementations on 'real' vehicles, let alone vehicles representative of those found in industry. The work in this thesis develops a suitable test platform and implements vision-based pose stabilization techniques. Many of the existing techniques were found to fail due to vehicle steering and velocity loop dynamics, and more significantly, with steering input saturation. A technique which does cope with the characteristics of 'real' vehicles is to divide the task into predefined stages, essentially dividing the state space into sub-manifolds. For a car-like vehicle, the strategy used is to stabilize the vehicle to the line which has the correct orientation and contains the target location. Once on the line, the vehicle then servos to the desired pose. This strategy can accommodate velocity and steering loop dynamics, and input saturation. It can also allow the use of linear control techniques for system analysis and tuning of control gains. To perform pose stabilization, good estimates of vehicle pose are required. A simple, yet robust, method derived from the visual homing literature is to sum the range vectors to all the landmarks in the workspace and divide by the total number of landmarks--the Improved Average Landmark Vector. By subtracting the IALV at the target location from the currently calculated IALV, an estimate of vehicle pose is obtained. In this work, views of the world are provided by an omnidirectional camera, while a magnetic compass provides a reference direction. The landmarks used are red road cones which are segmented from the omnidirectional colour images using a pre-learnt, two-dimensional lookup table of their colour profile. Range to each landmark is estimated using a model of the optics of the system, based on a flat-Earth assumption. A linked-list based method is used to filter the landmarks over time. Complementary filtering techniques, which combine the vision data with vehicle odometry, are used to improve the quality of the measurements.

<p>This work is concerned with the dynamics and stability of nonlinear systems that roll in a single track, including holonomic and nonholonomic systems. First the classic case of Euler's disk is introduced as an example of a nonholnomic system in three dimensions, and the methodology for deriving equations of motion that is used throughout this work is demonstrated, including use of Lagrange's equations, accommodating constraints with both Lagrange multipliers and with Gauss's Principle. </p><p>Next, a disk in two dimensions with an eccentric center of mass is explored. The disk is assumed to roll on a cubic curve, creating the possibility of well-escape behavior, which is examined analytically and numerically, showing regions of multi-periodicity and chaos. This theoretical system is compared to an experiment designed</p><p>to demonstrate the same behavior.</p><p>The remainder of the present document is concerned with the stability of a bicycle, both on flat ground, and on a type of trainer known as "rollers." The equations of motion are derived using Lagrange's equations with nonholonomic constraints, then the equations are linearized about a constant forward velocity, and a straight path, yielding a two degree of freedom system for the roll and steer angles. Stability is then determined for a variety of different parameters, exploring the roll of bicycle geometry and rider position, along with the effect of adding a steering torque, taking the form of different control laws.</p><p>Finally, the system is adapted to that of a bicycle on rollers, and the related equations of motion are derived and linearized. Notable differences with the classic bicycle case are detailed, a new eigenvalue behavior is presented, and configurations for optimal drum spacing are recommended.</p> / Dissertation

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 / In this work, a position controller for ground vehicles is developed. The algorithm takes into account the constraints of both Ackermann and differential drive platforms. A simplistic model is used for the initial development of this control algorithm, and more rigid constraints are added based on the intended platform. 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. Throughout this work, we present the theoretical development as well as simulation and experiments to verify the efficacy of our approach. 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.

The recent technological advances in the field of autonomous vehicles have resulted in a growing impetus for researchers to improve the current framework of mission planning and execution within both the military and civilian contexts. Many recent efforts towards this direction emphasize the importance of replacing the so-called monolithic paradigm, where a mission is planned, monitored, and controlled by a unique global decision maker, with a network centric paradigm, where the same mission related tasks are performed by networks of interacting decision makers (autonomous vehicles). The interest in applications involving teams of autonomous vehicles is expected to significantly grow in the near future as new paradigms for their use are constantly being proposed for a diverse spectrum of real world applications. One promising approach to extend available techniques for addressing problems involving a single autonomous vehicle to those involving teams of autonomous vehicles is to use the concept of Voronoi diagram as a means for reducing the complexity of the multi-vehicle problem. In particular, the Voronoi diagram provides a spatial partition of the environment the team of vehicles operate in, where each element of this partition is associated with a unique vehicle from the team. The partition induces, in turn, a graph abstraction of the operating space that is in a one-to-one correspondence with the network abstraction of the team of autonomous vehicles; a fact that can provide both conceptual and analytical advantages during mission planning and execution. In this dissertation, we propose the use of a new class of Voronoi-like partitioning schemes with respect to state-dependent proximity (pseudo-) metrics rather than the Euclidean distance or other generalized distance functions, which are typically used in the literature. An important nuance here is that, in contrast to the Euclidean distance, state-dependent metrics can succinctly capture system theoretic features of each vehicle from the team (e.g., vehicle kinematics), as well as the environment-vehicle interactions, which are induced, for example, by local winds/currents. We subsequently illustrate how the proposed concept of state-dependent Voronoi-like partition can induce local control schemes for problems involving networks of spatially distributed autonomous vehicles by examining different application scenarios.