On the Modulus Consensus of Multi-agent Systems with Double-Integrator Kinematics in Three-Dimensional Space under Linear Control

In this paper, we consider the problem of formation control of multi-agent systems in three-dimensional (3D) space, where the desired formation is dynamic. This is motivated by applications where the formation size and/or geometric shape needs to vary in time. Using a single-integrator model and rigid graph theory, we propose a new control law that exponentially stabilizes the origin of the nonlinear, interagent distance error dynamics and ensures tracking of the desired, 3D time-varying formation. Extensions to the formation maneuvering problem and double-integrator model are also discussed. The formation control is illustrated with a simulation of eight agents forming a dynamic cube.

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Cooperative Localization of Vehicles in Three-Dimensional Space

Volume 2: Intelligent Transportation/Vehicles; Manufacturing; Mechatronics; Engine/After-Treatment Systems; Soft Actuators/Manipulators; Modeling/Validation; Motion/Vibration Control Applications; Multi-Agent/Networked Systems; Path Planning/Motion Control; Renewable/Smart Energy Systems; Security/Privacy of Cyber-Physical Systems; Sensors/Actuators; Tracking Control Systems; Unmanned Ground/Aerial Vehicles; Vehicle Dynamics, Estimation, Control; Vibration/Control Systems; Vibrations ◽

10.1115/dscc2020-3206 ◽

2020 ◽

Author(s):

Juan Carlos Oliveros ◽

Hashem Ashrafiuon

Keyword(s):

Cooperative Control ◽

Ad Hoc ◽

Dimensional Space ◽

Three Dimensional ◽

Euler Angle ◽

Cooperative Localization ◽

Multi Agent Systems ◽

Agent Systems ◽

Accurate Localization ◽

Multi Agent

Abstract Effective trajectory planning and cooperative control of multi-agent systems require accurate localization of the agents to perform collaborative missions. Accurate localization may be achieved by Global Positioning System (GPS) and simultaneous localization and mapping. However, GPS signals and fixed features may not be readily available, particularly in remote and unstructured environments. Under these circumstances, Cooperative Localization (CL) has been proposed as a short-term solution that can significantly improve vehicle pose estimation. CL algorithms have been developed and tested mainly on mobile robots and planar vehicles due to complexities of three-dimensional (3D) motion. In this paper, we present a CL algorithm for multi-agent systems comprised of 3D vehicles. Each vehicle’s pose is represented by three position and three orientation variables. Quaternions are employed to represent orientation and avoid singularities associated with Euler angle. Vehicle kinematic velocity relations are used to model vehicle dynamics with respect to a fixed reference frame. It is assumed a vehicle can take relative pose measurements of other neighboring vehicles within an ad hoc network of agents. We then designate the observed as target vehicles and the observers as base vehicles and determine the linearized output matrix of the relative measurements for Extended Kalman Filter (EKF) application. Simulations are presented to discuss the advantages and shortcomings of the algorithm.

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