Nonlinear control of nonholonomic mobile robot formations

In this thesis, the framework developed to control a single nonholonomic mobile robot is expanded to include the control of formations of multiple nonholonomic mobile robots. A combined kinematic/torque control law is developed for leader-follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers typically found in literature --Abstract, page iv

Neural Network Observer-Based Finite-Time Formation Control of Mobile Robots

This paper addresses the leader-following formation problem of nonholonomic mobile robots. In the formation, only the pose (i.e., the position and direction angle) of the leader robot can be obtained by the follower. First, the leader-following formation is transformed into special trajectory tracking. And then, a neural network (NN) finite-time observer of the follower robot is designed to estimate the dynamics of the leader robot. Finally, finite-time formation control laws are developed for the follower robot to track the leader robot in the desired separation and bearing in finite time. The effectiveness of the proposed NN finite-time observer and the formation control laws are illustrated by both qualitative analysis and simulation results

Asymptotic Stability of Nonholonomic Mobile Robot Formations Using Multilayer Neural Networks

In this paper, a combined kinematic/torque control law is developed for leader-follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers that are widely reported in the literature. A multilayer neural network (NN) is introduced along with robust integral of the sign of the error (RISE) feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. It is shown using Lyapunov theory that the errors for the entire formation are asymptotically stable and the NN weights are bounded as opposed to uniformly ultimately bounded (UUB) stability which is typical with most NN controllers. Simulation results are included

Formation control of mobile robots and unmanned aerial vehicles

In this dissertation, the nonlinear control of nonholonomic mobile robot formations and unmanned aerial vehicle (UAV) formations is undertaken and presented in six papers. In the first paper, an asymptotically stable combined kinematic/torque control law is developed for leader-follower based formation control of mobile robots using backstepping. A neural network (NN) is introduced along with robust integral of the sign of the error (RISE) feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. Subsequently, in the second paper, a novel NN observer is designed to estimate the linear and angular velocities of both the follower and its leader robot and a NN output feedback control law is developed. On the other hand, in the third paper, a NN-based output feedback control law is presented for the control of an underactuated quad rotor UAV, and a NN virtual control input scheme is proposed which allows all six degrees of freedom to be controlled using only four control inputs. The results of this paper are extended to include the control of quadrotor UAV formations, and a novel three-dimensional leader-follower framework is proposed in the fourth paper. Next, in the fifth paper, the discrete-time nonlinear optimal control is undertaken using two online approximators (OLA\u27s) to solve the infinite horizon Hamilton-Jacobi-Bellman (HJB) equation forward-in-time to achieve nearly optimal regulation and tracking control. In contrast, paper six utilizes a single OLA to solve the infinite horizon HJB and Hamilton-Jacobi-Isaacs (HJI) equations forward-intime for the near optimal regulation and tracking control of continuous affine nonlinear systems. The effectiveness of the optimal tracking controllers proposed in the fifth and sixth papers are then demonstrated using nonholonomic mobile robot formation control --Abstract, page iv

Adaptive consensus based formation control of unmanned vehicles

Over the past decade, the control research community has given significant attention to formation control of multiple unmanned vehicles due to a variety of commercial and defense applications. Consensus-based formation control is considered to be more robust and reliable when compared to other formation control methods due to scalability and inherent properties that enable the formation to continue even if one of the vehicles experiences a failure. In contrast to existing methods on formation control where the dynamics of the vehicles are neglected, this dissertation in the form of four papers presents consensus-based formation control of unmanned vehicles-both ground and aerial, by incorporating the vehicle dynamics. First, neural networks (NN)-based optimal adaptive consensus-based formation control over finite horizon is presented for networked mobile robots or agents in the presence of uncertain robot/agent dynamics and communication. In the second paper, a hybrid automaton is proposed to control the nonholonomic mobile robots in two discrete modes: a regulation mode and a formation keeping mode in order to overcome well-known stabilization problem. The third paper presents the design of a distributed consensus-based event-triggered formation control of networked mobile robots using NN in the presence of uncertain robot dynamics to minimize communication. All these papers assume state availability. Finally, the fourth paper extends the consensus effort by introducing the development of a novel nonlinear output feedback NN-based controller for a group of quadrotor UAVs --Abstract, page iv

Formation Control of Car-like Mobile Robots: A Lyapunov Function Based Approach

In literature leader - follower strategy has been used extensively for formation control of car-like mobile robots with the control law being derived from the kinematics. This paper takes it a step further and a nonlinear control law is derived using Lyapunov analysis for formation control of car-like mobile robots using robot dynamics. Controller is split into two parts. The first part is the development of a velocity controller for the follower from the error kinematics (linear and angular). The second part involves the use of the dynamics of the robot in the development of a torque controller for both the drive and the steering system of the car-like mobile robot. Unknown quantities like friction, desired accelerations (unmeasured) are computed using an online neural network. Simulations results prove the ability of the controller to effectively stabilize the formation while maintaining the desired relative distance and bearing

Neural Network Control of Mobile Robot Formations Using RISE Feedback

In this paper, an asymptotically stable (AS) combined kinematic/torque control law is developed for leader-follower-based formation control using backstepping in order to accommodate the complete dynamics of the robots and the formation, and a neural network (NN) is introduced along with robust integral of the sign of the error feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. It is shown using Lyapunov theory that the errors for the entire formation are as and that the NN weights are bounded as opposed to uniformly ultimately bounded stability which is typical with most NN controllers. Additionally, the stability of the formation in the presence of obstacles is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation do not occur. The asymptotic stability of the follower robots as well as the entire formation during an obstacle avoidance maneuver is demonstrated using Lyapunov methods, and numerical results are provided to verify the theoretical conjectures

Control of a non-holonomic mobile robot system with parametric uncertainty

In this paper, the control of a mobile robot system via a feedback linearization controller and anti-control of chaos with parametric uncertainty is researched. Anti-control is also applied to convert non-chaotic systems to chaotic ones and to create chaos dynamic. The synchronization of system errors with a chaotic gyroscope system is researched for energy reduction and performance improvement. In the other words, control effort is based on synchronizing the error system with chaos for decreasing control cost. The combination of these techniques yields high efficiency and global convergence of trajectories, even in the presence of parametric uncertainty, which has been shown by simulation. Finally, the energy of control signals is calculated and compared for showing the energy reduction

Planning And Control Of Swarm Motion As Continua

In this thesis, new algorithms for formation control of multi agent systems (MAS) based on continuum mechanics principles will be investigated. For this purpose agents of the MAS are treated as particles in a continuum, evolving in an n-D space, whose desired configuration is required to satisfy an admissible deformation function. Considered is a specific class of mappings that is called homogenous where the Jacobian of the mapping is only a function of time and is not spatially varying. The primary objectives of this thesis are to develop the necessary theory and its validation via simulation on a mobile-agent based swarm test bed that includes two primary tasks: 1) homogenous transformation of MAS and 2) deployment of a random distribution of agents on to a desired configuration. Developed will be a framework based on homogenous transformations for the evolution of a MAS in an n-D space (n=1, 2, and 3), under two scenarios: 1) no inter-agent communication (predefined motion plan); and 2) local inter-agent communication. Additionally, homogenous transformations based on communication protocols will be used to deploy an arbitrary distribution of a MAS on to a desired curve. Homogenous transformation with no communication: A homogenous transformation of a MAS, evolving in an space, under zero inter agent communication is first considered. Here the homogenous mapping, is characterized by an n x n Jacobian matrix ( ) and an n x 1 rigid body displacement vector ( ), that are based on positions of n+1 agents of the MAS, called leader agents. The designed Jacobian ( ) and rigid body displacement vector ( ) are passed onto rest of the agents of the MAS, called followers, who will then use that information to update their positions under a pre- iv defined motion plan. Consequently, the motion of MAS will evolve as a homogenous transformation of the initial configuration without explicit communication among agents. Homogenous Transformation under Local Communication: We develop a framework for homogenous transformation of MAS, evolving in , under a local inter agent communication topology. Here we assume that some agents are the leaders, that are transformed homogenously in an n-D space. In addition, every follower agent of the MAS communicates with some local agents to update its position, in order to grasp the homogenous mapping that is prescribed by the leader agents. We show that some distance ratios that are assigned based on initial formation, if preserved, lead to asymptotic convergence of the initial formation to a final formation under a homogenous mapping. Deployment of a Random Distribution on a Desired Manifold: Deployment of agents of a MAS, moving in a plane, on to a desired curve, is a task that is considered as an application of the proposed approach. In particular, a 2-D MAS evolution problem is considered as two 1-D MAS evolution problems, where x or y coordinates of the position of all agents are modeled as points confined to move on a straight line. Then, for every coordinate of MAS evolution, bulk motion is controlled by two agents considered leaders that move independently, with rest of the follower agents motions evolving through each follower agent communicating with two adjacent agents