An official website of the United States government
This work analyzes and develops some fundamental results for attitude consensus control of a network of rigid-body vehicles, considered a multi-agent rigid body system (MARBS). The system is analyzed using a full rigid body dynamics model on TSO(3) for each vehicle (agent) in the network. Therefore, the state space of the system is TSO(3)^N, where N is the number of vehicles. Attitude synchronization control laws for each vehicle to reach a consensus attitude with zero angular velocity for a particular type of network are obtained, using a Morse-Lyapunov function. Some fundamental results on equilibria of the network under these attitude consensus control laws are obtained. We show that unlike cooperative control of multi-agent systems with highly simplified dynamics models for agents, like point particles or unicycles where the state space of the dynamics is modeled as a vector space, there are multiple equilibrium solutions possible for attitude consensus control laws for a MARBS with dynamics on TSO(3)^N. Further, the number of equilibria depends on the network graph topology. This is followed by numerical simulation results for two different network graphs, which show this network control framework to be effective in obtaining attitude consensus.
more »
« less
Finite-time Attitude Consensus Control of a Multi-Agent Rigid Body System
In this paper, finite-time attitude consensus control laws for multi-agent rigid body systems are presented using rotation matrices. The control objective is to stabilize the relative configurations in a finite convergence time. First, the control design is done on the kinematic level where the angular velocities are the control signals. Next, the design is conducted on the dynamic level in the framework of the tangent bundle TSO(3) associated with SO(3), where the torques implement the feedback control of relative attitudes and angular velocities. The Lyapunov-based almost global finite-time stability of the consensus subspace is demonstrated for both cases. Finally, numerical simulations are provided to verify the effectiveness of the proposed consensus control algorithms.
more »
« less
- Award ID(s):
- 1739748
- PAR ID:
- 10195658
- Date Published:
- Journal Name:
- 2020 American Control Conference (ACC)
- Page Range / eLocation ID:
- 877 to 882
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract In this paper, we consider the problem of tracking noisy two-dimensional level curves using only the instantaneous measurements of the field, taken by two mobile agents, without the need of estimating the field gradient. To do this, we propose a dual-control-module structure consisting of the formation control and curve tracking modules. The former uses the linear velocity of the agents to generate the angular velocities, which are then used to maintain a constant distance between the two agents. The latter uses the instantaneous field measurements to generate the linear velocities of the two agents to successfully track level curves. The modular approach decouples the problems of formation control and curve tracking, thus allowing the seamless design of the two modules. We show that the proposed dual-module control structure allows fast and accurate tracking of planar level curves.more » « less
-
null (Ed.)This paper proposes a finite-time event-triggered secondary frequency and voltage control for islanded AC microgrids (MGs) in a distributed fashion. The proposed control strategy can effectively perform frequency restoration and voltage regulations, while sharing the active and reactive power among the distributed generators (DGs) based on their power ratings. The finite-time control enables a system to reach consensus in a finite period of time enhanced from the asymptotic convergence. The event-triggered communication is utilized to reduce the communication burden among the DG controllers by transmitting data among DGs if an event-triggering condition is satisfied. The performance of the proposed finite-time event-triggered frequency control is verified utilizing a hardware-in-the-loop experimental testbed which simulates an AC MG in Opal-RT.more » « less
-
We consider distributed consensus in networks where the agents have integrator dynamics of order two or higher (n>=2). We assume all feedback to be localized in the sense that each agent has a bounded number of neighbors and consider a scaling of the network through the addition of agents in a modular manner, i.e., without re-tuning controller gains upon addition. We show that standard consensus algorithms, which rely on relative state feedback, are subject to what we term scale fragilities, meaning that stability is lost as the network scales. For high-order agents (n>=3), we prove that no consensus algorithm with fixed gains can achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge, it causes instability if the network grows beyond a certain finite size. This holds in families of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network size (e.g. all planar graphs). For second-order consensus (n=2) we prove that the same scale fragility applies to directed graphs that have a complex Laplacian eigenvalue approaching the origin (e.g. directed ring graphs). The proofs for both results rely on Routh–Hurwitz criteria for complex-valued polynomials and hold true for general directed network graphs. We survey classes of graphs subject to these scale fragilities, discuss their scaling constants, and finally prove that a sub-linear scaling of nodal neighborhoods can suffice to overcome the issue.more » « less
-
Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second-order integrator systems under a parameterized family of controllers (homotopy), that continuously trade between relative and absolute feedback interconnections, in terms of the H 2 norm of an appropriately defined input-output system. Our approach extends the previous H 2 norm-based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H 2 norm, but purely relative feedback can only achieve finite norms when the measurement error is not exciting the subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of absolute feedback in double integrator systems smoothly decreases the system performance (increases the H 2 norm) and that this performance degradation is more rapid in systems with relative feedback in only the first state (position).more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC45564.2020.9147639
