Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory
01 Jun 2015-International Journal of Systems Science (Taylor & Francis)-Vol. 46, Iss: 8, pp 1447-1457
TL;DR: A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem with rigorous proofs provided by using graph, matrix, and Lyapunov theories.
Abstract: In this paper, the distributed formation control problem for multiple nonholonomic mobile robots using consensus-based approach is considered. A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Distributed control laws are developed for achieving the formation control objectives: a group of nonholonomic mobile robots at least exponentially converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. Rigorous proofs are provided by using graph, matrix , and Lyapunov theories. Simulations are also given to verify the effectiveness of the theoretical results.
Citations
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TL;DR: A neural networks (NNs) enhanced telerobot control system is designed and tested on a Baxter robot and guaranteed performance is achieved at both kinematic and dynamic levels.
Abstract: In this paper, a neural networks (NNs) enhanced telerobot control system is designed and tested on a Baxter robot. Guaranteed performance of the telerobot control system is achieved at both kinematic and dynamic levels. At kinematic level, automatic collision avoidance is achieved by the control design at the kinematic level exploiting the joint space redundancy, thus the human operator would be able to only concentrate on motion of robot’s end-effector without concern on possible collision. A posture restoration scheme is also integrated based on a simulated parallel system to enable the manipulator restore back to the natural posture in the absence of obstacles. At dynamic level, adaptive control using radial basis function NNs is developed to compensate for the effect caused by the internal and external uncertainties, e.g., unknown payload. Both the steady state and the transient performance are guaranteed to satisfy a prescribed performance requirement. Comparative experiments have been performed to test the effectiveness and to demonstrate the guaranteed performance of the proposed methods.
269 citations
Cites background from "Distributed consensus-based formati..."
...The internal uncertainties mainly come from the unmodeled dynamics [8]–[11]....
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TL;DR: The stability of the closed-loop multiagent system is proven by using the Lyapunov theory by investigating practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders using adaptive neural networks.
Abstract: Practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders are investigated using adaptive neural networks (NNs), where the time-varying formation tracking error caused by time-varying external disturbances can be arbitrarily small. Different from the previous work, there exists a predefined time-varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the dynamics of each agent has both matched/mismatched heterogeneous nonlinearities and disturbances simultaneously. First, a practical time-varying formation tracking protocol using adaptive NNs is proposed, which is constructed using only local neighboring information. The proposed control protocol can process not only the matched/mismatched heterogeneous nonlinearities and disturbances, but also the unknown control inputs of the leaders. Second, an algorithm with three steps is introduced to design the practical formation tracking protocol, where the parameters of the protocol are determined, and the practical time-varying formation tracking feasibility condition is given. Third, the stability of the closed-loop multiagent system is proven by using the Lyapunov theory. Finally, a simulation example is showed to illustrate the effectiveness of the obtained theoretical results.
111 citations
Cites methods from "Distributed consensus-based formati..."
...In [23], the feedback linearization method was introduced to tackle the consensus tracking problems of second-order nonlinear multiagent systems....
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TL;DR: A force sensorless control scheme based on neural networks (NNs) is developed for interaction between robot manipulators and human arms in physical collision and an error transformation algorithm is integrated into the controller to achieve the prescribed tracking precision.
Abstract: In this paper, a force sensorless control scheme based on neural networks (NNs) is developed for interaction between robot manipulators and human arms in physical collision. In this scheme, the trajectory is generated by using geometry vector method with Kinect sensor. To comply with the external torque from the environment, this paper presents a sensorless admittance control approach in joint space based on an observer approach, which is used to estimate external torques applied by the operator. To deal with the tracking problem of the uncertain manipulator, an adaptive controller combined with the radial basis function NN (RBFNN) is designed. The RBFNN is used to compensate for uncertainties in the system. In order to achieve the prescribed tracking precision, an error transformation algorithm is integrated into the controller. The Lyapunov functions are used to analyze the stability of the control system. The experiments on the Baxter robot are carried out to demonstrate the effectiveness and correctness of the proposed control scheme.
100 citations
Cites background from "Distributed consensus-based formati..."
...However, due to existence of uncertainties, it is hard for us to obtain an accurate dynamic model of a robot [18] [19]....
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TL;DR: In this paper, a variable transformation is proposed to convert the formation control problem into a state consensus problem, and the distributed kinematic controllers and neural network torque controllers are derived for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern along the specified reference trajectory.
Abstract: This paper investigates the distributed formation control problem for multiple nonholonomic wheeled mobile robots. A variable transformation is first proposed to convert the formation control problem into a state consensus problem. Then, when the dynamics of the mobile robots are considered, the distributed kinematic controllers and neural network torque controllers are derived for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Moreover, the neural network torque controllers proposed in this work can tackle the dynamics of robots with unmodeled bounded disturbances and unstructured unmodeled dynamics. Some sufficient conditions are derived for accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers.
95 citations
TL;DR: First, the formation control problem is converted into a state consensus problem by the aid of a variable transformation, and distributed kinematic controllers and adaptive dynamic controllers are developed for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern with its centroid moving along the specified reference trajectory.
91 citations
References
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TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations
"Distributed consensus-based formati..." refers background in this paper
...In Jadbabaie, Lin, and Morse (2003), a formal mathematical analysis for consensus is first presented....
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TL;DR: It is shown that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
Abstract: This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. This note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
6,135 citations
"Distributed consensus-based formati..." refers background in this paper
...Lately, the research on consensus problems for multiple systems was also extended to the case of directed topology (Ren and Beard 2005; Lu and Chen 2009; Wu, Zhou, and Xiang 2012; Yu and Wang 2012; Wen, Peng, Rahmani, and Yu 2013)....
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TL;DR: A theoretical framework for design and analysis of distributed flocking algorithms, and shows that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders."
Abstract: In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
4,693 citations
"Distributed consensus-based formati..." refers background in this paper
...Email: zhaoxiapeng1986@gmail.com Pappas 2003a,b; Olfati-Saber 2006; Shi, Wang, and Chu 2009) and graph theory (Fax and Murray 2002, 2004), have been emerged for the formation control of multiple mobile robots....
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TL;DR: A Nyquist criterion is proved that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability, and a method for decentralized information exchange between vehicles is proposed.
Abstract: We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.
4,377 citations
"Distributed consensus-based formati..." refers background in this paper
...Email: zhaoxiapeng1986@gmail.com Pappas 2003a,b; Olfati-Saber 2006; Shi, Wang, and Chu 2009) and graph theory (Fax and Murray 2002, 2004), have been emerged for the formation control of multiple mobile robots....
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01 Dec 1998
TL;DR: New reactive behaviors that implement formations in multirobot teams are presented and evaluated and demonstrate the value of various types of formations in autonomous, human-led and communications-restricted applications, and their appropriateness in different types of task environments.
Abstract: New reactive behaviors that implement formations in multirobot teams are presented and evaluated. The formation behaviors are integrated with other navigational behaviors to enable a robotic team to reach navigational goals, avoid hazards and simultaneously remain in formation. The behaviors are implemented in simulation, on robots in the laboratory and aboard DARPA's HMMWV-based unmanned ground vehicles. The technique has been integrated with the autonomous robot architecture (AuRA) and the UGV Demo II architecture. The results demonstrate the value of various types of formations in autonomous, human-led and communications-restricted applications, and their appropriateness in different types of task environments.
3,008 citations
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...2002; Mariottini, Morbidi, Prattichizzo, Pappas, and Daniilidis 2007; Consolini, Morbidi, Prattichizzo, and Tosques 2008; Liu and Tian 2009; Wang and Wu 2012; Peng, Wen, Rahmani, and Yu 2013), behaviour-based approach (Balch and Arkin 1998; Lawton, Beard, and Young 2003; Brunete, Hernando, Gambao, and Torres 2012), virtual structure (Tan and Lewis 1996; Lewis and Tan 1997; Egerstedt and Hu 2001; Do and Pan 2007; Ghommam, Mehrjerdi, Saad, and Mnif 2010), artificial potential (Tanner, Jadbabaie, and...
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