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

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

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

Neural Network Control of Robot Formations Using RISE Feedback

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 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. Theoretical results are demonstrated using numerical simulations

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 Nonholonomic Mobile Robot Formations Using Neural Networks

In this paper the control of formations of multiple nonholonomic mobile robots is attempted by integrating a kinematic controller with a neural network (NN) computed-torque controller. 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. The NN is introduced 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 uniformly ultimately bounded, and numerical results are provided

Control of Nonholonomic Mobile Robot Formations: Backstepping Kinematics into Dynamics

In this paper, we seek to expand framework developed to control a single nonholonomic mobile robot 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. The asymptotic stability of the entire formation is guaranteed using Lyapunov theory, and numerical results are provided The kinematic controller is developed around control strategies for single mobile robots and the idea of virtual leaders. The virtual leader is replaced with a physical mobile robot leader and the assumption of constant reference velocities is removed An auxiliary velocity control is developed allowing the asymptotic stability of the followers to be proved without the use of Barbalat\u27s Lemma which simplifies proving the entire formation is asymptotically stable. A novel approach is taken in the development of the dynamical controller such that the torque control inputs for the follower robots include the dynamics of the follower robot as well as the dynamics of its leader, and the case when all robot dynamics are known is considered

Neural Network Output Feedback Control of a Quadrotor UAV

A neural network (NN) based output feedback controller for a quadrotor unmanned aerial vehicle (UAV) is proposed. The NNs are utilized in the observer and for generating virtual and actual control inputs, respectively, where the NNs learn the nonlinear dynamics of the UAV online including uncertain nonlinear terms like aerodynamic friction and blade flapping. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semi-globally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle

Neural Network Control of Nonholonomic Robot Formations Using Limited Communication with Reliability Assessment

Architectures for the control of mobile robot formations are often described by three levels of abstraction: an intelligence layer for task planning, a network layer for relaying commands and information throughout the formation, and finally, at the lowest level of abstraction is a robot model layer where each robot is locally controlled to be consistent with the current formation task. In this work, the network and robot model layers are considered, and an output feedback control law for leader-follower based formation control is developed using neural networks (NN) and limited communication. A NN is introduced to approximate the dynamics of the follower as well as its leader using online weight tuning while a novel NN observer is designed to estimate the linear and angular velocities of both the follower robots and its leader. Thus, each robot can achieve its control objective with limited knowledge of its leader\u27s states and dynamics while simultaneously reducing the communication load required in the network layer. It is shown using Lyapunov theory that the errors for the entire formation are uniformly ultimately bounded while relaxing the separation principle. Numerical results are provided to verify the theoretical conjectures, and the reliability of the scheme is evaluated by introducing processing and communication delays, as well as communication failures

Discrete-time Optimal Control of Nonholonomic Mobile Robot Formations Using Linearly Parameterized Neural Networks

In this paper, the infinite horizon optimal tracking control problem is solved online and forward-in-time for leader-follower based formation control of nonholonomic mobile robots. Using the backstepping approach and the kinematic controller developed in our previous work, the dynamical controller inputs for the robots are approximated from nonlinear optimal control techniques to track the designed control velocities. The proposed adaptive dynamic programming approach uses neural networks (NNs) to solve the optimal formation control problem in discrete-time in the presence of unknown internal dynamics and a known control coefficient matrix. All NNs are tuned online using novel weight update laws, and the stability of the entire formation is demonstrated using Lyapunov methods. Numerical simulations are also provided to demonstrate the effectiveness of the proposed approach