Article

Towards consensus in networked non-holonomic systems [Brief Paper]

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

The authors study the consensus problem in networked non-holonomic systems (NHSs). Based on Brockett's stabilisability condition, the stabilisation of NHSs is usually considered by using time-varying or discontinuous control (including switching control). Observing that the consensus problem has more flexibility than the stabilisation one, the authors aim to establish time-invariant continuous state feedbacks for the problem at hand.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... It is worthy of considering whether Brockett s condition is also effective in the cooperative control of multiple nonholonomic systems. Consensus for networked nonholonomic unicycles has been realized using time invariant continuous feedback controllers in [30] without group reference. Results obtained in [30] have shown that Brockett s condition is not a barrier in consensus of nonholonomic unicycles. ...
... Consensus for networked nonholonomic unicycles has been realized using time invariant continuous feedback controllers in [30] without group reference. Results obtained in [30] have shown that Brockett s condition is not a barrier in consensus of nonholonomic unicycles. Different from the work of [30] where the consensus value cannot be specified, the consensus problem of networked multiple nonholonomic mobile robots with groups reference trajectory will be considered in this paper. ...
... Results obtained in [30] have shown that Brockett s condition is not a barrier in consensus of nonholonomic unicycles. Different from the work of [30] where the consensus value cannot be specified, the consensus problem of networked multiple nonholonomic mobile robots with groups reference trajectory will be considered in this paper. ...
Article
Consensus problems of multiple nonholonomic mobile robots are considered in this paper. These problems are simplified into consensus problems of two subsystems based on structure of nonholonomic mobile robots. Linear distributed controllers are constructed respectively for these two subsystems thanks to the theory of nonautonomous cascaded systems. Consensus of multiple nonholonomic mobile robots has been realized using the methodology proposed in this paper no matter whether the group reference signal is persistent excitation or not. Different from previous research on cooperative control of nonholonomic mobile robots where the consensus problem under persistent exciting reference has received a lot of attention, this paper reports the first consensus result for multiple nonholonomic mobile robots whose group reference converges to zero. Simulation results using Matlab illustrate the effectiveness of the proposed controllers in this paper.
... Lin et al. (2005), Dimarogonas and Kyriakopoulos (2007), Xie and Ma (2014), Zhihua Qu and Ann Weitnauer (2015) for unicycle robots, Wang et al. (2016) for type (1,2) nonholonomic mobile robots, Dong and Farrell (2008b) and Xie et al. (2018) for underactuated surface vessels with second-order nonholonomic constraint. The second approach to overcome nonholonomic constraint was to make the common vector not necessarily constant, so that smooth time-invariant static distributed controllers could be developed to reach asymptotic leaderless consensus control of chained systems (Xie & Ma, 2017;Zhai et al., 2010). ...
... The above reviews demonstrate that the leaderless consensus/formation control problem of high-order nonholonomic chained systems has not been solved by a smooth time-invariant static distributed control law, and deserves a further investigation. To be more precise, the controllers in Yu-Ping Tian and Chen (2015) and Cao et al. (2018) are not global, the one in Guanghui Wen et al. (2016) is discontinuous leading to chattering trajectories of states, and the ones in Zhai et al. (2010) and Xie and Ma (2017) are effective only for low-order scenarios. Note that, the chattering states may destroy the hardware of system and the high-order chained structure can describe more mechanical systems than low-order case, such as tricycle-type mobile robots, cars towing several trailers, the knife-edge, and so on Jiang and Nijmeijer (1999). ...
... The construction of P in low-order case with P ∈ R 3×3 is much easier, because only nine entries of P are needed determined, which was done by combining trial and error method and LaSalle invariance principle in Zhai et al. (2010) and Xie and Ma (2017). However, as the size of P becomes larger, more entries are required computed, and the trial and error approach becomes unapplicable for n ≥ 3. ...
Article
This paper investigates the leaderless consensus control problem of high-order nonholonomic chained systems. Based on the relationship between state and consensus error, a novel Lyapunov function is defined for the networked systems, which is proved positive definite and radially unbounded. The first control law is constructed to make the Lyapunov function non-increasing. The Lyapunov method, graph theory and LaSalle invariance principle are applied to analyze the system stability, where some skillful mathematical calculations are conducted to overcome the difficulties caused by nonholonomic constraint and high-order structure, and the explicit expression and the conditions of control parameter matrix are calculated. It is proved that under the first control law, the consensus error is globally asymptotically convergent to zero. Then, the second control law is designed by extending the results to the input saturation case by using a saturation function. Both of the two controllers are smooth, time-invariant, static, distributed, and able to achieve global asymptotic consensus of nonholonomic chained systems over connected undirected graph. Numerical simulation examples are implemented to demonstrate the effectiveness of the proposed control schemes.
... Nevertheless, consensus control without leader only requires all the system state vectors converge to a common configuration, regardless of whether the common one is time-varying or not. Thus, asymptotic leaderless consensus control of nonholonomic systems can be achieved by smooth time-invariant static distributed control, not necessarily by time-varying or discontinuous control [16,17], which however is not suitable to higher-order nonholonomic chained systems. Thus, it is deserved to derive smooth timeinvariant distributed static control law for asymptotic leaderless consensus control of high-order nonholonomic chained systems. ...
... Since Assumption 1 shows that L is symmetric positive semidefinite, hence so is L ⊗ P , and V is a positive semidefinite function with respect to Z [16]. Unlike [16], we further present in the next Lemma that V is positive definite with respect to the consensus errors (i.e., the state errors Z i − Z j ). ...
... Since Assumption 1 shows that L is symmetric positive semidefinite, hence so is L ⊗ P , and V is a positive semidefinite function with respect to Z [16]. Unlike [16], we further present in the next Lemma that V is positive definite with respect to the consensus errors (i.e., the state errors Z i − Z j ). (8) is positive definite and radially unbounded with respect to consensus errors, provided that Assumption 1 holds and P = P T 0. ...
... However, the Lyapunov-like function candidate in the study by Zhai et al. 30 is only shown to be positive semidefinite, and hence, the system stability requires further analysis. Moreover, Zhai et al. 30 do not take into account the input saturation. Therefore, it is deserved to develop a new smooth time-invariant static distributed control law for leaderless consensus control of multiple nonholonomic systems subject to input saturation. ...
... For multiple leaderless consensus case, most of the published references still focus on the design of time-varying, discontinuous, or dynamic controller, see the literatures [19][20][21][22][23][24][25][26][27][28][29] which achieve the leaderless consensus/formation control of multiple nonholonomic systems. In addition, it was reported in the study by Zhai et al. 30 that the smooth time-invariant static distributed control law can realize the asymptotic leaderless ...
... For the second control scheme, the size of the control inputs u i1 and u i2 can be tuned artificially by adjusting k. Compared to the one in the study by Zhai et al., 30 our second control scheme is effective in the case of input saturation and can achieve a quick convergence rate in the small neighborhood of zero consensus errors. ...
Article
Full-text available
This article studies the leaderless consensus control problem of multiple nonholonomic chained systems. Two smooth time-invariant static distributed controllers are derived based on Lyapunov method, graph theory, and LaSalle invariance principle. Both of the proposed controllers guarantee that the states of the multiple nonholonomic systems globally asymptotically converge to a common vector, provided that the interconnection topology is undirected and connected. In particular, the second control scheme can reduce the size of the control inputs via saturated control and is more applicable in real engineering. Several numerical simulations are implemented for kinematic models of four nonholonomic unicycle mobile robots, demonstrating the effectiveness of the proposed control schemes.
... Solutions to leaderless consensus control problem of nonholonomic chained systems in Xu et al. [21], Du et al. [22], Zhai et al. [23], Xie and Ma [24], and Xie et al. [25] can also solve the full-state formation control problem of unicycle vehicles, since their models can be transformed into each other. In Xu et al. [21], graph decomposition and input-to-sate stability theory were combined to design a dynamic control law that realized semi-global output consensus control of nonholonomic chained systems, and the choice of controller parameters relied upon initial states of systems. ...
... In Du et al. [22], a discontinuous control law was derived based on recursive design method and the first-order consensus theory, reaching global finite-time consensus of nonholonomic systems with high-order chained structure. Based on Laplacian based Lyapunov function, smooth time-invariant static distributed controllers were developed in Zhai et al. [23], Xie and Ma [24], and Xie et al. [25] to globally asymptotically steer the consensus error of chained systems to zero with time-varying common configuration. ...
... The above reviews show that the full-state formation control problem of unicycle vehicles has not been well solved so far. To be more precise, among the related works, Lin et al. [8], Yu et al. [9], Zheng and Sun [10], Xie and Ma [11], Chen et al. [12], Roza et al. [13], Khaledyan et al. [14], Ajorlou et al. [15], Ajorlou and Aghdam [16], and Li et al. [17] only considered position rendezvous/fomation control; Cao et al. [5], Dimarogonas and Kyriakopoulos [18], and Xu et al. [21] only obtained local results; Jafarian, [19] Maghenem et al. [20], Du et al. [22], Zhai et al. [23], Xie and Ma [24], and Xie et al. [25] relied on undirected connected information flow for ensuring the Laplacian based Lyapunov function positive (semi-) definite; and all of them did not consider convergence rate. The guarantee of decay rate is crucial for control performance, which has been researched for consensus control of linear systems [26,27], and is worth investigating for formation control of unicycle vehicles. ...
Article
Full-text available
This paper studies the full‐state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time‐varying output‐like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time‐varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.
... Since real life mobile agents have dynamics more complicated than the single or double integrator models commonly used, some authors have expanded the field to include the problem of cooperation of non holonomic agents. The works of Zhai et al. [14], Listman [15] and Ghommam [16] present different approaches to solve this problem. However, very few works, besides that of Dong and Farrell [17], have treated the consensus or formation control problems for non-holonomic agents under time delayed communications. ...
... It is well known that (14) does not satisfy Brockett's condition [26], and therefore there is no continuous, linear time invariant feedback law that can stabilize the system. The consensus protocol (1) cannot be directly applied. ...
Article
This document considers the formation control problem for a group of non-holonomic mobile robots under time delayed communications. The agents are assumed to be working under a directed and fixed communication topology. A recently developed formation control technique, based on a consensus protocol for linear systems is revisited. The stability analysis of this control technique, in the domain of the time delays, is performed using the CTCR paradigm under the SDS domain approach. This analysis leads to an exact declaration of the stability boundaries in the domain of the delays. This linear control law is adapted to the nonlinear dynamics of the non-holonomic carts by means of feedback linearization. Simulation results show the applicability of this method to the class of agents considered here.
... Under undirected topologies or balanced topologies, novel control laws were found. A time-invariant continuous consensus law was established for multiple nonholonomic systems with low orders [13], and the potential field based consensus algorithm was proposed for a team of unicycles [14]. In [15], output synchronization of systems in chained form was considered by means of the backstepping design. ...
... Compared with results in [2,12], the analysis procedure formulated in this paper may be extended to analyze a class of nonlinear consensus protocols. Compared with results in [13,14,15], the consensus controller is developed and analyzed under the directed topology rather than the undirected or balanced one. ...
Article
In this paper, the problem of output consensus for multiple non-holonomic systems in chained form has been investigated. First, an output consensus controller under the strongly connected communication topology is devised by two steps, where a time-varying control strategy and the backstepping design technique are employed. Then, the results are extended to the general directed topology case via graph decomposition, in which the input-to-state stability theory plays a critical role. We prove that the proposed controller can achieve the semi-global output consensus among multiple non-holonomic systems, provided that the interaction graph contains a spanning tree. Finally, numerical examples are provided to illustrate the effectiveness of the designed controller.
... In the last two decades, there has been great interest in cooperative control of multi-agent systems [1][2][3] , where all agents are connected by a network (described by a graph), and they communicate to neighbor agents for necessary information such that the whole group could achieve a collective behavior. The specification for collective behavior includes flocks and swarms, sensor fusion, random networks, synchronization of coupled oscillators, formation control of multi robots, optimization-based cooperative control, etc. ...
... And, consensus problems in cooperative control have been studied extensively, and there are many important papers which have made great contribution in consensus problems for multi-agent systems with directed topologies [24][25][26][27][28][29] . The approaches of achieving consensus for general linear agents have been obtained in [2,3,[30][31][32] , and in [33] the authors proved that the hierarchical network organization can achieve the best performance in terms of convergence rates and established that the connections between the leader and the followers have effective impacts on increasing the convergence rates by presenting a novel analysis on the efficiency of the hierarchical topology among the leader-following systems. However, the obtained consensus results of multi-agent systems with directed topologies cannot be extended to handle formation problem directly. ...
... His work includes discussions on the stability of the controlled dynamics, as well as the abilities of rejection of disturbances, using linear models of holonomic robots. In the real world, robots possess dynamics that can be more complicated than those linear representations commonly used, so some authors like Zhai et al. [20], Listmann [15] and Ghommam [11] have included the problem of cooperation with non-holonomic robots. The approaches presented here offered clarity in some of the concepts related to conflict resolution and its application to the tasks and scenarios that were implemented. ...
Article
Full-text available
This paper presents the development of a cooperation scheme among unmanned aerial vehicle (UAV). Sliding mode control technique is used to guarantee that the set of robots can follow a reference trajectory and, in addition, will guarantee collision-free navigation of these autonomous vehicles. The analytical approach of the control strategy is shown, and the necessary conditions to guarantee the stability and governability of the multi-robot system are derived. The strategy and the derived conditions are tested using simulations, to demonstrate their effectiveness for collision-free navigation of an UAV fleet.
... The interconnection graph considered in [12] is undirected, and thus, the discussion can not be extended to directed interconnection cases. Moreover, an approach of achieving consensus for more general linear agents in the framework of matrix inequalities and stabilization was proposed in [13], and the extension to the consensus problem for networked nonholonomic systems was dealt with in [14]. For multi-agent systems with switching interconnection graphs, [15] adopted a combination of connected and disconnected graphs to achieve desired consensus, where the basic idea was inspired by switched systems analysis. ...
Article
We deal with a consensus control problem for a group of third order agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control input. The problem is reduced to designing Hurwitz polynomials with real or complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition can be obtained for designing the consensus algorithm. Since the condition is both necessary and sufficient, we provide a kind of parametrization for all the weighting coefficients achieving consensus. Moreover, the condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively decreased computation burden. The result is also extended to the case where communication delay exists in the control input.
... The consensus problem of third-order nonlinear multi-agent systems with a fixed communication topology is discussed, and a consensus algorithm is proposed with several sufficient conditions in [11]. Moreover, the approach of achieving consensus for more general linear agents in the framework of matrix inequalities and stabilization is proposed in [12], and the extension to the This research has been supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) 21560471 consensus problem for networked nonholonomic systems is dealt with in [13]. For multi-agent systems with switching interconnection graphs, [14] adopted the idea of switched systems analysis to propose using combination of connected and disconnected graphs so as to achieve desired consensus. ...
... There are several important papers which have made great contribution to the consensus problem for self-organizing networked systems (Fax and Murray, 2004;Jadbabaie et al., 2003;Moreau, 2005;Ren and Beard, 2005;Cai and Ishii, 2012;Priolo et al., 2014). The approach of achieving consensus for general linear agents in the framework of matrix inequalities and stabilization is proposed by Zhai et al. (2009), and the extension to the consensus problem for networked nonholonomic systems is dealt with in another work of Zhai et al. (2010). ...
Article
Full-text available
In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.
Article
In this paper, we propose a new consensus protocol for networks of multiple mobile robots with fixed communication topology using a strategy based on an invariant manifold technique. The agents are subjected to non-holonomic constraints and transformed into Brockett integrator form. The objective is to asymptotically stabilize the non-holonomic model for each agent about a group decision value using distributed protocol. This approach solves the consensus problem in two cases: leader–follower consensus problem when the leader is static and leaderless consensus problem. Then, a design of test-bed is fully described for testing distributed protocols. The setup consists of a group of non-holonomic mobile robots moving on a platform with different ArUco markers on their tops, an overhead camera to determine the poses (positions and orientations) of these markers, and a desktop computer to provide the interaction between the robots. The design of this test-bed has relied on ROS framework as a software platform for offering ROS network architecture a solution for distributed communication. Finally, results were presented to show the performance of this design by applying the proposed protocol.
Article
Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.
Article
This work investigates the position centroid rendezvous/formation problems of multiple unicycle agents for the first time. By constructing a new output, the unicycle model is converted to canonical normal form via feedback linearisation approach. Then, we propose the centroid rendezvous and the centroid formation control laws, respectively, guaranteeing that all the agents globally meet at the common initial centroid location and the desired geometric pattern centred at the initial centroid. The proposed control laws are distributed, smooth and time-varying, ensuring the internal orientation states and the velocity inputs convergent to some fixed values and zero, respectively. All the results are proved under the communication scenarios of fixed directed balanced graph with a spanning tree. Simulation results verify the effectiveness and the robustness of the proposed control schemes.
Article
Practical formation stabilization control problems of multiple nonholonomic mobile robots have been considered in this paper. Cascaded structure of nonholonomic mobile robot system has been incorporated in the design of formation controllers. Some external perturbing signals have been injected into the consensus protocols of each robot's direction to overcome the uncontrollability of nonholonomic mobile robots when their reference target dose not satisfy the popular condition of persistent excitation. Simulation results using Matlab have illustrated the effectiveness of the formation stabilization controllers presented in this paper.
Article
Rendezvous problem of nonholonomic unicycles has been considered in this paper and nonlinear distributed controllers based on backstepping are constructed to guarantee the consensus of both position and direction simultaneously. Cascaded theory of nonlinear system is utilised to reduce the rendezvous problem of nonholonomic unicycles to consensus problem of moving direction and consensus problem of position, respectively. The uncontrollable challenge of position system after consensus of moving direction has been successfully removed through dilated coordinate transformation. Then, a modified backstepping methodology based on the coupling structure of position system is derived to guarantee the consensus of each unicycle's position. In the end, not only consensus of position but also consensus of direction has been realised for multiple nonholonomic unicycles using the controllers proposed in this paper. Simulation results using Matlab illustrate the effectiveness of the results of this paper.
Article
Cooperative path following control problem of multiple nonholonomic mobile robots has been considered in this paper. Based on the framework of decomposition, the cooperative path following problem has been transformed into path following problem and cooperative control problem; Then cascaded theory of non-autonomous system has been employed in the design of controllers without resorting to feedback linearization. One time-varying coordinate transformation based on dilation has been introduced to solve the uncontrollable problem of nonholonomic robots when the whole group's reference converges to stationary point. Cooperative path following controllers for nonholonomic robots have been proposed under persistent reference or reference target that converges to stationary point respectively. Simulation results using Matlab have illustrated the effectiveness of the obtained theoretical results.
Article
The paper investigates the consensus problem of multiple nonholonomic systems. Two event-triggered control strategies, one centralized and the other distributed, are developed, which can reduce the frequency of control updating. Under the proposed protocols, the multiple nonholonomic systems can achieve consensus, and the bound of inter-event time intervals is provided to illustrate that no Zeno behavior exists. Finally, numerical simulations are also provided to demonstrate the effectiveness of the proposed control strategies.
Chapter
In this work, we study the distributed cooperative control problem of multiple nonholonomic unicycle robots with a time-varying reference trajectory. Under the mild assumptions that the communication topology is bidirectional connected, the reference trajectory is bounded and known for at least one robot and the velocity of the reference trajectory is bounded but unknown for all robots, a novel distributed cooperative control protocol is proposed guaranteeing that all the robots follow the reference trajectory with an arbitrarily small ultimate tracking errors. Simulation examples are given to verify the proposed distributed cooperative scheme.
Article
In this paper, the global consensus problem of ring-networked nonholonomic systems with saturated input is considered. Based on the Lyapunov method and appropriate related technologies, the stabilization of the nonholonomic systems is achieved towards consensus. Assuming that each agent has its own position informa- tion available in the global coordinates and can obtain the position information of its neighbors, global consensus is achieved asymptotically by using the designed distribut- ed saturated controllers. Subject-predicate-complement, a wireless local area network is set up with a local com- puter as the controller, having data transmitted through the wireless network so that the movement of the robots can be controlled. Consistent simulation and experiment results are presented to illustrate the practical design and theoretical analysis.
Article
In this study, we have considered the cooperative output synchronisation problem of non-linear multi-agent system. The dynamic of each agent in the network is a class of genuinely non-linear system, named as high-order power integrator that may be uncontrollable after linearisation around the origin. Disturbance is considered in the input channel of each agent as well. Combined Graph theory with the method of adding a power integrator, a distributed controller is designed recursively for each agent to achieve the control objective. The distributed controller of each agent has three parts: state feedback of itself, output information of its neighbours and an adaptive disturbance compensator. It is proved that when the undirected graph is connected, all agents' outputs in the network can be synchronised, that is, cooperative output synchronisation is achieved. Simulation result is presented to verify its effectiveness.
Article
Full-text available
In this paper, we consider a hybrid control strategy for stabilization of nonholonomic systems. In particular, we deal with a typical nonholonomic system, namely a two-wheeled vehicle. We first rewrite the system in a chained form, and then transform it into a nonholonomic integrator (NHI) system. Finally, we apply and modify the hybrid control method for the NHI system, so that the entire system is exponentially stable. We provide a simulation example to demonstrate the effectiveness of the transformation and the control, and give some analysis together with an example for the case where there are constraints on control inputs. We also extend the discussion to the case of four-wheeled vehicles.
Conference Paper
Full-text available
In this paper, we study an extended consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The concept extended consensus means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, we propose to reduce the problem to a stabilization problem with an appropriate transformation, and thus obtain a strict matrix inequality with respect to a Lyapunov matrix and a structured controller gain matrix. We then utilize a homotopy based method for solving the matrix inequality effectively, and show validity of the result by an example. The feature of the present algorithm is that it can deal with various additional control requirements such as convergence rate specification and actuator limitations.
Article
Full-text available
This paper presents the experimental results of the tracking control of a car-trailer system. The proposed scheme involves three steps: 1) generate a path off-line using a path space iterative algorithm; 2) linearize the kinematic model about a trajectory which is constructed using the path; and 3) apply a time-varying linear quadratic regulator to track the trajectory. Experiments presented include parallel parking a car, docking a tractor-trailer vehicle, and parallel parking a double tractor-trailer vehicle
Article
This paper considers feedback control of a group of nonholonomic dynamic systems with uncertainty. Decentralized cooperative controllers are proposed with the aid of Lyapunov techniques, results of graph theory, and backstepping techniques. Robustness of the control laws with respect to communication delays is analyzed. An application of the proposed results is discussed. Simulation results show the effectiveness of the proposed controllers.
Article
This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of comple
Article
. This paper demonstrates how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic. Results concerning stability and performance of the resulting hybrid system are derived. One of the main advantages of this type of controller is that the stability analysis can be made using fairly straightforward arguments. The methodology used is generalizable to a larger class of control problems related to nonholonomic systems. Keywords. Switching algorithms; Supervisory control; Nonlinear systems; Stability analysis; Performance analysis. 1. INTRODUCTION Over the last decade there has been a great deal of research on the problem of stabilizing systems which are locally null controllable but fail to meet Brockett's condition for smooth stabilizability (Brockett 1983): Given the system x = f(x; u) ; x(t 0 ) = x 0 ; f(0; 0) = 0 (1) with f : R n Theta R m ! R n continuously differentiable. If (1) is smoothly stabilizable, i.e. there exists a continu...
Article
This paper considers two cooperative control problems for nonholonomic mobile agents. In the first problem, we discuss the design of cooperative control laws such that a group of nonholonomic mobile agents cooperatively converges to some stationary point under various communication scenarios. Dynamic control laws for each agent are proposed with the aid of sigma-processes and results from graph theory. In the second problem, we discuss the design of cooperative control laws such that a group of mobile agents converges to and tracks a target point which moves along a desired trajectory under various communication scenarios. By introducing suitable variable transformations, cooperative control laws are proposed. Since communication delay is inevitable in cooperative control, in each of the above cooperative control problems, we analyze the effect of delayed communication on the proposed controllers. As applications of the proposed results, formation control of wheeled mobile robots is discussed. It is shown that our results can be successfully used to solve formation control problem. To show effectiveness of the proposed approach, simulation results are included.
Article
In this note, a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced. The proposed nonholonomic control law is discontinuous and time-invariant and using tools from nonsmooth Lyapunov theory and graph theory the stability of the overall system is examined. Similarly to the linear case, the convergence of the multi-agent system relies on the connectivity of the communication graph that represents the inter-agent communication topology. The control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph. Moreover, the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework
Nonholonomic behaviour in free-floating space manipulators and its utilization
  • E Papadopoulos
  • Z Li
  • J F Canny
The Laplacian spectrum of graphs
  • B Mohar
  • Y Alavi
  • G Chartrand
  • O Ollermann
  • A Schwenk