Temporal Circular Formation Control with Bounded Trajectories in a Uniform Flowfield
01 Jul 2019-pp 189-194
TL;DR: Control laws are derived that achieves objectives of circular formation control of multi-vehicle systems, modeled with unicycle dynamics, in a uniform flowfield with different temporal phase arrangements, while assuring that the trajectories of the vehicles remains bounded within a region.
Abstract: This paper studies circular formation control of multi-vehicle systems, modeled with unicycle dynamics, in a uniform flowfield with different temporal phase arrangements, while assuring that the trajectories of the vehicles remains bounded within a region. Using the idea of Barrier Lyapunov function in conjunction with temporal phase potential functions, we derive control laws that achieves our objectives, under a mild assumption on the initial states of the vehicles. We further obtain bounds on the various signals in the post-design analysis and show that these depends on the initial conditions and controller gains. Simulations are provided to illustrate the theoretical findings.
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TL;DR: In this article, a null-space-based behavioral control architecture is built by defining the priorities of the basic tasks and computing the corresponding velocity vectors to avoid obstacle/collision and maintain the formation configuration, and the adaptive coordinated tracking control algorithm is designed such that the states satisfy the time-varying constraints, even subject to uncertainties and unknown disturbances.
Abstract: The problem of the relative position coordinated control for spacecraft formation flying with a leader spacecraft under the obstacle environment is the focus of this paper. To avoid obstacle/collision and maintain the formation configuration, the Null-Space-Based behavioral control architecture is built by defining the priorities of the basic tasks and computing the corresponding velocity vectors. Through the null-space projection, the desired velocity of each follower spacecraft can be calculated by merging the basic tasks. Moreover, due to the partial access to the dynamic leader spacecraft’s states, the distributed estimators are presented for each follower spacecraft. Then, based on the desired velocity, the adaptive coordinated tracking control algorithm incorporated with the barrier Lyapunov function is designed such that the states satisfy the time-varying constraints, even subject to uncertainties and unknown disturbances. Finally, numerical simulations are performed to illustrate the main results.
16 citations
Proceedings Article•
13 Jun 2023
TL;DR: In this article , the authors proposed a control scheme using the concept of the Barrier Lyapunov Function (BLF), which helps in restricting the agents' trajectories within a predefined boundary.
Abstract: This paper aims to stabilize agents (or vehicles) on a commonly desired circle with bounded trajectories in an external flow field. We consider the formation in a balanced or synchronized phase pattern. In a balanced phase pattern, all agents symmetrically move on a desired common circle. In contrast, in a synchronized phase pattern, all agents move together with the same phase angle on a desired common circle. We propose the control scheme using the concept of the Barrier Lyapunov Function (BLF), which helps in restricting the agents’ trajectories within a predefined boundary. Simulations are provided to support the theoretical developments.
References
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TL;DR: This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions.
Abstract: In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on a Quadratic Lyapunov Function, and we show that our control requires less restrictive initial conditions. A numerical example is provided to illustrate the performance of the proposed control.
1,999 citations
"Temporal Circular Formation Control..." refers background or methods in this paper
...The potential S(r,γ) is positive semidefinite and continuously differentiable for |ek| < δ, ∀k and becomes zero whenever ek = 0 for all k [18]....
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...In this paper, we use the idea of Logarithmic BLF as introduced in [18] to solve the problem considered in this paper....
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...The paper is organized as follows: Section II describes the vehicle model in a uniform flowfield and reviews some preliminary results related to BLF. Section III introduces potential functions to stabilize collective circular motion with temporal phase arrangements....
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...Two types of BLFs are generally seen in the literature−Logarithmic BLF [18] and Tangent BLF [19]....
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...2) By exploiting the idea of BLF, we propose the stabilizing controllers that asymptotically stabilize a fleet of vehicles to a desired common circle in temporal phase patterns of two-types, namely temporal phase synchronization and balancing....
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TL;DR: The first evidence for collective memory is presented in such animal groups (where the previous history of group structure influences the collective behaviour exhibited as individual interactions change) during the transition of a group from one type of collective behaviour to another.
Abstract: We present a self-organizing model of group formation in three-dimensional space, and use it to investigate the spatial dynamics of animal groups such as fish schools and bird flocks. We reveal the existence of major group-level behavioural transitions related to minor changes in individual-level interactions. Further, we present the first evidence for collective memory in such animal groups (where the previous history of group structure influences the collective behaviour exhibited as individual interactions change) during the transition of a group from one type of collective behaviour to another. The model is then used to show how differences among individuals influence group structure, and how individuals employing simple, local rules of thumb, can accurately change their spatial position within a group (e.g. to move to the centre, the front, or the periphery) in the absence of information on their current position within the group as a whole. These results are considered in the context of the evolution and ecological importance of animal groups.
1,906 citations
"Temporal Circular Formation Control..." refers background in this paper
...Foraging ants around a sugar piece, a swirlingly growing epiphyte colony, and schooling of fish around a predator are some of the examples from natural systems [2]....
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TL;DR: A survey of formation control of multi-agent systems focuses on the sensing capability and the interaction topology of agents, and categorizes the existing results into position-, displacement-, and distance-based control.
Abstract: We present a survey of formation control of multi-agent systems. Focusing on the sensing capability and the interaction topology of agents, we categorize the existing results into position-, displacement-, and distance-based control. We then summarize problem formulations, discuss distinctions, and review recent results of the formation control schemes. Further we review some other results that do not fit into the categorization.
1,751 citations
"Temporal Circular Formation Control..." refers background in this paper
...INTRODUCTION Formation control of multi-agent systems has been a widely researched topic in the last decade [1]....
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05 Mar 2007
TL;DR: This paper addresses the design of mobile sensor networks for optimal data collection by using a performance metric, used to derive optimal paths for the network of mobile sensors, to define the optimal data set.
Abstract: This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored
920 citations
"Temporal Circular Formation Control..." refers background in this paper
...Examples from engineering applications are tracking, source seeking, capturing, monitoring and securing a target or a search region [3]–[9]....
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01 Dec 2014
TL;DR: A control methodology that unifies control barrier functions and control Lyapunov functions through quadratic programs is developed, which allows for the simultaneous achievement of control objectives subject to conditions on the admissible states of the system.
Abstract: This paper develops a control methodology that unifies control barrier functions and control Lyapunov functions through quadratic programs. The result is demonstrated on adaptive cruise control, which presents both safety and performance considerations, as well as actuator bounds. We begin by presenting a novel notion of a barrier function associated with a set, formulated in the context of Lyapunov-like conditions; the existence of a barrier function satisfying these conditions implies forward invariance of the set. This formulation naturally yields a notion of control barrier function (CBF), yielding inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the simultaneous achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). These formulations are illustrated in the context of adaptive cruise control, where the control objective of achieving a desired speed is balanced by the minimum following conditions on a lead car and force-based constraints on acceleration and braking.
703 citations
"Temporal Circular Formation Control..." refers background in this paper
...The concept of Control Barrier Function (CBF) is one of the modern control design tools for solving the problem of stabilization, without violating the system’s constraints [12], [13]....
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