Masood Ghasemi

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of fully actuated agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network.

Finite-time tracking using sliding mode control

Abstract Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler–Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.

Sliding mode coordination control for multiagent systems with underactuated agent dynamics

In this paper, we develop a new integrated coordinated control and obstacle avoidance approach for a general class of underactuated agents. We use graph-theoretic notions to characterise communication topology in the network of underactuated agents as determined by the information flow directions and captured by the graph Laplacian matrix. Obstacle avoidance is achieved by surrounding the stationary as well as moving obstacles by elliptical or other convex shapes that serve as stable periodic solutions to planar systems of ordinary differential equations and using transient trajectories of those systems to navigate the agents around the obstacles. Decentralised controllers for individual agents are designed using sliding mode control approach and are only based on data communicated from the neighbouring agents. We demonstrate the efficacy of our theoretical approach using an example of a system of wheeled mobile robots that reach and maintain a desired formation. Finally, we validate our results experimentally.

Sliding Mode Cooperative Control for Multirobot Systems: A Finite-Time Approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. We consider a group of agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. We further extend these results to multiagent systems involving underactuated dynamical agents such as mobile wheeled robots. For this case, we show that while the position variables can be coordinated in finite time, the orientation variables converge to the steady states asymptotically. Finally, we validate our results experimentally using a wheeled mobile robot platform.

Formation Control Protocols for Nonlinear Dynamical Systems Via Hybrid Stabilization of Sets

In this paper, we develop a hybrid control framework for addressing multiagent formation control protocols for general nonlinear dynamical systems using hybrid stabilization of sets. The proposed framework develops a novel class of fixed-order, energy-based hybrid controllers as a means for achieving cooperative control formations, which can include flocking, cyclic pursuit, rendezvous, and consensus control of multiagent systems. These dynamic controllers combine a logical switching architecture with the continuous system dynamics to guarantee that a system generalized energy function whose zero level set characterizes a specified system formation is strictly decreasing across switchings. The proposed approach addresses general nonlinear dynamical systems and is not limited to systems involving single and double integrator dynamics for consensus and formation control or unicycle models for cyclic pursuit. Finally, several numerical examples involving flocking, rendezvous, consensus, and circular formation protocols for standard system formation models are provided to demonstrate the efficacy of the proposed approach. [DOI: 10.1115/1.4027501]

Flocking and rendezvous control protocols for nonlinear dynamical systems via hybrid stabilization of sets

In this paper, we develop a hybrid control framework for addressing flocking and rendezvous formation control protocols for general nonlinear dynamical systems using stabilization of sets. The proposed framework develops a novel class of fixed-order, energy-based hybrid controllers as a means for achieving cooperative control formations. These dynamic controllers combine a logical switching architecture with the continuous system dynamics to guarantee that a system generalized energy function whose zero level set characterizes a specified system formation is strictly decreasing across switchings. The proposed approach addresses general nonlinear dynamical systems and is not limited to systems involving double integrator dynamics for formation control.

Finite-Time Tracking Using Sliding Mode Control

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In various tasks that the real world systems have to perform, the execution time is critical, and thus, it is important to enforce that the system trajectories that converge to a desired state do so in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler-Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. Specifically, we develop feedback controllers using sliding mode approach that guarantee finite-time tracking. The approach is based on designing non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader.Copyright

Output reversibility in linear discrete-time dynamical systems☆

Output reversibility involves dynamical systems where for every initial condition and the corresponding output there exists another initial condition such that the output generated by this initial condition is a time-reversed image of the original output with the time running forward. Through a series of necessary and sufficient conditions, we characterize output reversibility in linear discrete-time dynamical systems in terms of the geometric symmetry of its eigenvalue set with respect to the unit circle in the complex plane. Furthermore, we establish that output reversibility of a linear continuous-time system implies output reversibility of its discretization. In addition, we present a control framework that allows to alter the system dynamics in such a way that a discrete-time system, otherwise not output reversible, can be made output reversible. Finally, we present numerical examples involving a discretization of a Hamiltonian system that exhibits output reversibility and an example of a controlled system that is rendered output reversible.

Output Reversibility in Linear Discrete-Time Dynamical Systems

Output reversibility involves dynamical systems where for every initial condition and the corresponding output there exists another initial condition such that the output generated by this initial condition is a time-reversed image of the original output with the time running forward. Through a series of necessary and sufficient conditions, we characterize output reversibility in linear single-output discrete-time dynamical systems in terms of the geometric symmetry of its eigenvalue set with respect to the unit circle in the complex plane. Furthermore, we establish that output reversibility of a linear continuous-time system implies output reversibility of its discretization regardless of the sampling rate. Finally, we present a numerical example involving a discretization of a Hamiltonian system that exhibits output reversibility.Copyright

Sliding Mode Coordination Control Design for Multiagent Systems

In this paper, we develop a coordination control technique for a group of agents described by a general class of underactuated dynamics. The objective is for the agents to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized controllers for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Finally, we show the efficacy of our theoretical results on the example of a system of wheeled mobile robots that reach and maintain the desired formation.Copyright