Reactive Control Of Autonomous Dynamical Systems

This thesis mainly consists of five independent papers concerning the reactive control design of autonomous mobile robots in the context of target tracking and cooperative formation keeping with obstacle avoidance in the static/dynamic environment. Technical contents of this thesis are divided into three parts. The first part consists of the first two papers, which consider the target-tracking and obstacle avoidance in the static environment. Especially, in the static environment, a fundamental issue of reactive control design is the local minima problem(LMP) inherent in the potential field methods(PFMs). Through introducing a state-dependent planned goal, the first paper proposes a switching control strategy to tackle this problem. The control law for the planned goal is presented. When trapped into local minima, the robot can escape from local minima by following the planned goal. The proposed control law also takes into account the presence of possible saturation constraints. In addition, a time-varying continuous control law is proposed in the second paper to tackle this problem. Challenges of finding continuous control solutions of LMP are discussed and explicit design strategies are then proposed. The second part of this thesis deals with target-tracking and obstacle avoidance in the dynamic environment. In the third paper, a reactive control design is presented for omnidirectional mobile robots with limited sensor range to track targets while avoiding static and moving obstacles in a dynamically evolving environment. Towards this end, a multiiii objective control problem is formulated and control is synthesized by generating a potential field force for each objective and combining them through analysis and design. Different from standard potential field methods, the composite potential field described in this paper is time-varying and planned to account for moving obstacles and vehicle motion. In order to accommodate a larger class of mobile robots, the fourth paper proposes a reactive control design for unicycle-type mobile robots. With the relative motion among the mobile robot, targets, and obstacles being formulated in polar coordinates, kinematic control laws achieving target-tracking and obstacle avoidance are synthesized using Lyapunov based technique, and more importantly, the proposed control laws also take into account possible kinematic control saturation constraints. The third part of this thesis investigates the cooperative formation control with collision avoidance. In the fifth paper, firstly, the target tracking and collision avoidance problem for a single agent is studied. Instead of directly extending the single agent controls to the multiagents case, the single agent controls are incorporated with the cooperative control design presented in [1]. The proposed decentralized control is reactive, considers the formation feedback and changes in the communication networks. The proposed control is based on a potential field method, its inherent oscillation problem is also studied to improve group transient performance

Coordinated path following: A nested invariant sets approach

In this thesis we study a coordinated path following problem for multi-agent systems. Each agent is modelled by a smooth, nonlinear, autonomous, deterministic control-affine ordinary differential equation. Coordinated path following involves designing feedback controllers that make each agent's output approach and traverse a pre-assigned path while simultaneously coordinating its motion with the other agents. Coordinated motion along paths includes tasks like maintaining formations, traversing paths at a common speed and more general tasks like making the positions of some agents obey functional constraints that depend on the states of other agents. The coordinated path following problem is viewed as a nested set stabilization problem. In the nested set stabilization approach, stabilization of the larger set corresponds to driving the agents to their assigned paths. This set, under suitable assumptions, is an embedded, controlled invariant, product submanifold and is called the multi-agent path following manifold. Stabilization of the nested set, contained in the multi-agent path following manifold, corresponds to meeting the coordination specification. Under appropriate assumptions, this set is also an embedded controlled invariant submanifold which we call the coordination set. Our approach to locally solving nested set stabilization problems is based on feedback equivalence of control systems. We propose and solve two local feedback equivalence problems for nested invariant sets. The first, less restrictive, solution gives necessary and sufficient conditions for the dynamics of a system restricted to the larger submanifold and transversal to the smaller submanifold to be linear and controllable. This normal form facilitates designing controllers that locally stabilize the coordination set relative to the multi-agent path following manifold. The second, more restrictive, result additionally imposes that the transversal dynamics to the larger submanifold be linear and controllable. This result can simplify designing controllers to locally stabilize the multi-agent path following manifold. We propose sufficient conditions under which these normal forms can be used to locally solve the nested set stabilization problem. To illustrate these ideas we consider a coordinated path following problem for a multi-agent system of dynamic unicycles. The multi-agent path following manifold is characterized for arbitrary paths. We show that each unicycle is feedback equivalent, in a neighbourhood of its assigned path, to a system whose transversal and tangential dynamics to the path following manifold are both double integrators. We provide sufficient conditions under which the coordination set is nonempty. The effectiveness of the proposed approach is demonstrated experimentally on two robots

Control Of Nonh=holonomic Systems

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\u27 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

Autonomous Behaviors With A Legged Robot

Over the last ten years, technological advancements in sensory, motor, and computational capabilities have made it a real possibility for a legged robotic platform to traverse a diverse set of terrains and execute a variety of tasks on its own, with little to no outside intervention. However, there are still several technical challenges to be addressed in order to reach complete autonomy, where such a platform operates as an independent entity that communicates and cooperates with other intelligent systems, including humans. A central limitation for reaching this ultimate goal is modeling the world in which the robot is operating, the tasks it needs to execute, the sensors it is equipped with, and its level of mobility, all in a unified setting. This thesis presents a simple approach resulting in control strategies that are backed by a suite of formal correctness guarantees. We showcase the virtues of this approach via implementation of two behaviors on a legged mobile platform, autonomous natural terrain ascent and indoor multi-flight stairwell ascent, where we report on an extensive set of experiments demonstrating their empirical success. Lastly, we explore how to deal with violations to these models, specifically the robot\u27s environment, where we present two possible extensions with potential performance improvements under such conditions

Incorporation of acoustic sensors in the regulation of a mobile robot

This article introduces the incorporation of acoustic sensors for the localization of a mobile robot. The robot is considered as a sound source and its position is located applying a Time Delay of Arrival (TDOA) method. Since the accuracy of this method varies with the microphone array, a navigation acoustic map that indicates the location errors is built. This map also provides the robot with navigation trajectories point-to-point and the control is capable to drive the robot through these trajectories to a desired configuration. The proposed localization method is thoroughly tested using both a 900 Hz square signal and the natural sound of the robot, which is driven near the desired point with an average error of 0:067 m.This is an Accepted Manuscript of an article published by Taylor & Francis in Advanced Robotics on 01/01/2019, available online: http://www.tandfonline.com/10.1080/01691864.2019.1573703.”Peer ReviewedPostprint (author's final draft

Synchronized closed path following for a differential drive and manipulator robot

Li, Y., & Nielsen, C. (2017). Synchronized Closed Path Following for a Differential Drive and Manipulator Robot. IEEE Transactions on Control Systems Technology, 25(2), 704–711. https://doi.org/10.1109/TCST.2016.2562578We locally solve a synchronized path-following problem for a heterogeneous multiagent system consisting of a differential drive robot and a serial manipulator. Each is assigned a simple, regular, and closed curve in its output space. The outputs of the systems must approach and traverse their assigned curves while synchronizing their motions along the paths. We use the notion of path-following outputs to facilitate a solution and present a novel synchronization controller and a novel singularity avoidance controller. The controllers are all given in closed form making their implementation straightforward. A numerical simulation is presented, which includes modeling uncertainty to demonstrate the utility of this approach.Partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC