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

Robust Adaptive Cooperative Control for Formation-Tracking Problem in a Network of Non-Affine Nonlinear Agents

In this chapter, a decentralized cooperative control protocol is proposed with application to any network of agents with non-affine nonlinear multi-input-multi-output (MIMO) dynamics. Here, the main purpose of cooperative control protocol is to track a time-variant reference trajectory while maintaining a desired formation. The reference trajectory is defined to a leader, which has at least one information connection with one of the agents in the network. The design procedure includes a robust adaptive law for estimating the unknown nonlinear terms of each agent’s dynamics in a model-free format, that is, without the use of any regressors. Moreover, an observer is designed to have an approximation on the values of control parameters for the leader at the agents without connection to the leader. The entire design procedure is analysed successfully for the stability using Lyapunov stability theorem. Finally, the simulation results for the application of the proposed method on a network of nonholonomic wheeled mobile robots (WMR) are presented. Desirable leader-following tracking and geometric formation control performance have been successfully demonstrated through simulated group of wheeled mobile robots

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

Stability and String Stability Analysis of Formation Control Architectures for Platooning.

This thesis presents theoretical results for stability and string stability of formation control architectures for platooning. We consider three important interconnection topologies for vehicles travelling in a straight line as a string: leader following, cyclic and bidirectional. For the leader following topology we discuss modifications that allow reduced coordination requirements. In the first case we consider the use of the leader velocity as the state to be broadcast to the followers, rather than the standard use of the leader position. This selection yields a formation control architecture that achieves string stability even under time delays in the state broadcast, while reducing typical coordination requirements of leader following architectures. For the second modification we change the way in which the leader position is sent across the string to every follower. This technique keeps some of the good transient properties of the standard leader following architecture but eliminates most of the coordination requirements for the followers. However, we show that this technique does not provide string stability when time delays are present in the communication. The second topology that we discuss is a cyclic one, where the first member of the platoon is forced to track the last one. We discuss two strategies: one where the inter-vehicle spacings may follow a constanttime headway spacing policy and one where an independent leader broadcasts its position to every member of a cyclic platoon. For both strategies we obtain closed form expressions for the transfer functions from disturbances to inter-vehicle spacings. These expressions allow us to show that if the design parameters are not properly chosen, the vehicle platoon may become unstable when the string size is greater than a critical number. On the contrary, if the design parameters are well chosen, both architectures can be made stable and string stable for any size of the platoon. The final topology that we consider is bidirectional, where every member of the platoon, with the exception of the first and last, use measurements of the two nearest neighbours to control their position within the string. Although the derivations are more complex than in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in the form of simple transfer functions from disturbances to vehicles. They allow us to obtain stability results for any size of the platoon and understand the behaviour of the least stable pole location as the string size increases. All of the results obtained are illustrated by numerical examples and ad-hoc simulations