Modeling and control of formations of nonholonomic mobile robots

Desai, Jaydev P.; Ostrowski, James; Kumar, Vijay

doi:10.1109/70.976023

Cited by 1,027 publications

(537 citation statements)

References 13 publications

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“…A promising alternative approach is to leverage the interactions between nodes by controlling only a relatively small subset of nodes (leaders), which act as external inputs and influence the remaining nodes (followers). The leader-follower architecture has been implemented in initial studies of unmanned vehicles [41], in which the leader nodes are controlled by remote operators and the remaining nodes follow the trajectory defined by the leaders. Anchor nodes in localization and time synchronization has also been studied within the leader-follower framework [11].…”

Section: Introductionmentioning

confidence: 99%

Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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Submodularity in Dynamics and Control of Networked Systems Andrew ClarkCo-Chairs of the Supervisory Committee:Radha Poovendran Electrical Engineering Linda Bushnell Electrical EngineeringControlling a networked dynamical system to reach a desired state is a fundamental challenge in applications including transportation, energy, social, and biological systems. One scalable approach to controlling such systems is to directly control the states of a subset of leader nodes, while relying on local interactions to steer the remaining nodes towards their desired states. The choice of leader nodes is known to affect system metrics including robustness to noise, rate of convergence to a desired state, and controllability of the system.Selecting an optimal subset of leader nodes, however, is inherently a combinatorial problem, making optimal leader node selection intractable in general.This thesis presents a submodular optimization framework to selecting leader nodes for control of networked systems. We investigate the problem of selecting a subset of leader nodes in order to minimize node state errors due to noise in the communication links between nodes. We prove that the error due to link noise is a supermodular function of the set of leader nodes, leading to the first polynomial-time algorithms for minimizing error due to link noise with provable optimality bounds. We develop our approach for networks with static topologies, as well as dynamic topologies due to random link failures, switching between predefined topologies, and arbitrary mobility.We study selecting leader nodes in order to minimize convergence error, defined as the error in the intermediate node states prior to reaching their desired values. We derive upper bounds for a class of convergence error metrics based on the hitting time of random walk on the network, which we prove to be a supermodular function of the set of input nodes.We present polynomial-time algorithms for minimizing convergence error with provable optimality bounds, for static as well as dynamic networks.Efficient algorithms have recently been proposed for selecting leader nodes to satisfy controllability, defined as the ability to drive the non-input nodes from any initial state to any desired state in finite time. These algorithms, however, do not incorporate performance criteria including robustness to noise and convergence rate. We study the problem of leader selection for joint performance and controllability, and prove that controllability can be formulated as a matroid constraint on the set of leader nodes. We propose efficient algorithms with provable optimality gap for selecting leader nodes for joint performance and controllability, and characterize the submodular structure of the largest controllable subgraph of a network.We also investigate selecting input nodes for guaranteeing synchronization in networked systems. Using the widely-studied Kuramoto model of nonlinear phase-coupled oscillators, we develop novel threshold-based conditions for a set of input nodes to ...

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Section: Introductionmentioning

confidence: 99%

Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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“…The obstacle avoidance method considered is also insufficient in dealing with more complex obstacles and may cause robots to be trapped behind obstacles. Formation control with both one-leader and two-leaders constraints was presented in [3]. Their work focuses on how transitions between formations can be realized via a transition matrix.…”

Section: Introductionmentioning

confidence: 99%

“…Several investigations on this issue have been considered [2,3]. Shao et al [2] consider a one-leader constraint formation control, which produces a non-rigid formation control graph.…”

Section: Introductionmentioning

confidence: 99%

Distributed formation control of networked mobile robots in environments with obstacles

2014

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A distributed control mechanism for ground moving nonholonomic robots is proposed. It enables a group of mobile robots to autonomously manage formation shapes while navigating through environments with obstacles. The formation can be maintained without the need of any inter-robot communication. Obstacle avoidance is designed to be performed by the individual robots themselves. Formation scaling is implemented to ensure the formation shape is maintained for as long as possible. If the formation fails to hold its shape when navigating through environments with obstacles, formation morphing has been incorporated to preserve the interconnectivity of the robots, thus reducing the possibility of losing robots from the formation.The algorithm has been implemented on a nonholonomic multi-robot system for empirical analysis. Experimental results demonstrate formations completing an obstacle course within 12 seconds with zero collisions. Furthermore, the system is capable of withstanding up to 25% sensor noise.

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“…Applications include master-slave synchronisation of robot manipulators in [21], leader-follower synchronisation for control of mobile robots in [2,11,23,10], and for formation control of marine vessels in [7]. For these applications the models are either fully actuated or formulated only at the kinematic level.…”

Section: Introductionmentioning

confidence: 99%

Leader–Follower Synchronisation for a Class of Underactuated Systems

Belleter

Pettersen

2016

Nonlinear Systems

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In this work leader-follower synchronization is considered for underactuated followers in an inhomogeneous multi-agent system. The goal is to synchronise the motion of a leader and an underactuated follower. Measurements of the leader's position, velocity, acceleration, and jerk are available, while the dynamics of the leader is unknown. The leader velocities are used as input for a constant bearing guidance algorithm to assure that the follower synchronises its motion to the leader. It is also shown that the proposed leader-follower scheme can be applied to multi-agent systems that are subjected to unknown environmental disturbances. Furthermore, the trajectory of the leader does not need to be known. The closed-loop dynamics are analysed and it is shown that under certain conditions all solutions remain bounded and the synchronisation error kinematics are shown to be integral input-to-state stable with respect to changes in the unactuated sway velocity. For straight-line motions, i.e. where the desired yaw rate and sway velocity go to zero, synchronisation is achieved. Simulation results are presented to validate the proposed control strategy.

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Modeling and control of formations of nonholonomic mobile robots

Cited by 1,027 publications

References 13 publications

Submodularity in Dynamics and Control of Networked Systems

Submodularity in Dynamics and Control of Networked Systems

Distributed formation control of networked mobile robots in environments with obstacles

Leader–Follower Synchronisation for a Class of Underactuated Systems

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