SUMMARY This paper addresses the design of low‐level controllers for leader–follower formations of nonholonomic vehicles in the presence of bounded measurement delays. The concept of input‐to‐state stability is extended to encompass the effect of bounded delays and restrictions on the input. A method is proposed to integrate a Smith predictor in a backstepping design on the basis of nested saturations and nonlinear small‐gain assignment, which allows for time delays in the feedback loop. Robustness analysis under uncertain bounded time delays is provided, and design tradeoffs resulting from the use of bounded controls are discussed. Illustrative simulations are shown to validate the design and robustness analysis in the context of a simple leader–follower trailing control problem. Copyright © 2012 John Wiley & Sons, Ltd.

As in any control system, the presence of small delays in the feedback channel may severely affect the performance of the closed-loop system, and prevent a the successful application of established nonlinear control methodologies. In order to make a control law robust with respect to small time delay, we first extend Input-to-State Stability (ISS) concepts to encompass the effect of bounded delays and restrictions on the input. Then, a method is proposed to integrate the presence of a Smith predictor in a backstepping design based on nonlinear small gain assignment, when small time delays is present in the feedback loop. The method is applied to a leader-follower trailing control problem. Simulation results confirm the validity of the control design and the robustness analysis.

The focus of this paper is on the design of a control architecture of decentralized type for controlling a leader/follower pair of autonomous non-holonomic vehicles. A fundamental constraint in this trailing control requires that each agent employs local sensor information to process data on the relative position and velocity between its neighbouring vehicles, without relying on global communication with mission control. This constraint poses a challenge in the design of the control system because the reference trajectory to be tracked, which in the case considered in this paper is related to the motion of the leader, is not known a priori. It is shown in the paper that this specific control problem can be approached from the point of view of the internal model paradigm. In particular, once models of the autonomous dynamics of the leader are embedded in a decentralized dynamic controller, the design of the controller can be completed with a robust stabilizer, obtained by using ISS-gain-assignment techniques. It is shown that asymptotic convergence of the follower to an arbitrarily small neighbourhood of the desired steady-state configuration is achieved, despite the presence of possibly large parameter uncertainties, while the motion of each agent remains confined into specified 'sectors' to avoid possible collision between neighbouring vehicles during transients. Simulation results are presented to illustrate the design methodology. Copyright (C) 2006 John Wiley & Sons, Ltd.

Formation control of multiple autonomous agents has gained intense interest from the control community due to its importance in military and civilian applications. Leader/follower trailing control, which drives a follower to a prescribed relative position with respect to its leader, is one of the most fundamental building blocks of formation control. The focus of this dissertation is on the design of a decentralized trailing control architecture for pairs of autonomous non-holonomic vehicles based on generic vehicle models. A fundamental constraint in trailing control requires that each agent employs local sensor information to process data on the relative position and velocity between its neighboring vehicles, possibly without relying on communication with mission control. This constraint poses a challenge to the design of the control system because the reference trajectory to be tracked may not be known a priori. The lack of the leader reference trajectory can be overcome by resorting to the "internal model paradigm". It is shown how a controller can be designed by embedding a model of the autonomous dynamics of the leader in a robust stabilizer obtained by using nonlinear gain assignment techniques. A benefit of the proposed design is that each agent can be confined into specified "sectors" to avoid possible collision even during transients. An important aspect in assessing the stability of a multi-layered formation is the analysis of the internal dynamics of intermediate leaders. Although this aspect is often neglected in the literature, it is shown that the internal dynamics need to be well behaved, not only at the desired formation in steady-state but also during transients, to prevent agents from erratic motion which may lead to potential collisions. An important tool for the design of robust trailing control architecture is the nonlinear small-gain theorem. The use of saturated controller with tunable gains has been shown to be instrumental in building controllers robust with respect to small slow-varying measurement errors for arbitrary initial conditions, or even small time delay. Sufficient conditions guaranteeing asymptotic stability of closed-loop systems are given and practical guidelines on how to tune those control parameters are provided for implementation.