Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insufficient to be captured by constant structures. Here, we propose sequential temporal networks to characterize growing networked populations, and we extend the theory of evolutionary games to these temporal networks with arbitrary structures and growth rules. We derive analytical rules under which a sequential temporal network has a higher fixation probability for cooperation than its static counterpart. Under neutral drift, the rule is simply a function of the increment of nodes and edges in each time step. But if the selection is weak, the rule is related to coalescence times on networks. In this case, we propose a mean-field approximation to calculate fixation probabilities and critical benefit-to-cost ratios with lower calculation complexity. Numerical simulations in empirical datasets also prove the cooperation-promoting effect of population growth. Our research stresses the significance of population growth in the real world and provides a high-accuracy approximation approach for analyzing the evolution in real-life systems.

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties, and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division can promote collective cooperation markedly. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.

Despite recent advances made in salient object detection using graph theory, the approach still suffers from accuracy problems when the image is characterized by a complex structure, either in the foreground or background, causing erroneous saliency segmentation. This fundamental challenge is mainly attributed to the fact that most existing graph-based methods take only the adjacently spatial consistency among graph nodes into consideration. In this paper, we tackle this issue from a coarse-to-fine perspective and propose a two-stage-graphs approach for salient object detection, in which two graphs having the same nodes but different edges are employed. Specifically, a weighted joint robust sparse representation model, rather than the commonly used manifold ranking model, helps to compute the saliency value of each node in the first-stage graph, thereby providing a saliency map at the coarse level. In the second-stage graph, along with the adjacently spatial consistency, a new regionally spatial consistency among graph nodes is considered in order to refine the coarse saliency map, assuring uniform saliency assignment even in complex scenes. Particularly, the second stage is generic enough to be integrated in existing salient object detectors, enabling improved performance. Experimental results on benchmark data sets validate the effectiveness and superiority of the proposed scheme over related state-of-the-art methods.

In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players' actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

This paper focuses on the average consensus of double-integrator networked systems based on the asynchronous periodic edge-event triggered control. The asynchronous property lies in the edge event-detecting procedure. For different edges, their event detections are performed at different times and the corresponding events occur independently of each other. When an event is activated, the two adjacent agents connected by the corresponding link sample their relative state information and update their controllers. The application of incidence matrix facilitates the transformation of control objects from the agent-based to the edge-based. Practically, due to the constraints of network bandwidth and communication distance, agents usually cannot receive the instantaneous information of some others, which has an impact on the system performance. Hence, it is necessary to investigate the presence of communication time delays. For double-integrator multiagent systems with and without communication time delays, the average state consensus can be asynchronously achieved by designing appropriate parameters under the proposed event-detecting rules. The presented results specify the relationship among the maximum allowable time delays, interaction topologies, and event-detecting periods. Furthermore, the proposed protocols have the advantages of reduced communication costs and controller-updating costs. Simulation examples are given to illustrate the proposed theoretical results.

In this brief, we consider the consensus problem of hybrid multiagent systems. First, the hybrid multiagent system is proposed, which is composed of continuous-time and discrete-time dynamic agents. Then, three kinds of consensus protocols are presented for the hybrid multiagent system. The analysis tool developed in this brief is based on the matrix theory and graph theory. With different restrictions of the sampling period, some necessary and sufficient conditions are established for solving the consensus of the hybrid multiagent system. The consensus states are also obtained under different protocols. Finally, simulation examples are provided to demonstrate the effectiveness of our theoretical results.

Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.

This paper studies the leader-following consensus problem for linear and Lipschitz nonlinear multiagent systems where the communication topology has a directed spanning tree with the leader as the root. Due to the constraints of communication bandwidth and storage space, agents can only receive uniform quantized information. We first consider the leader-following consensus problem for linear multiagent systems via quantized control. Then, in order to reduce the communication load, an event-triggered control strategy is investigated to solve the consensus problem for linear multiagent systems with uniform quantization. It is shown that leader-following practical consensus can be achieved and no Zeno behavior occurs in this case. Furthermore, the proposed control strategies are extended to investigate the leader-following consensus problem for multiagent systems with Lipschitz nonlinear dynamics. Simulation results are given to demonstrate the feasibility and effectiveness of the theoretical analysis.

In this paper, we study the consensus problem of discrete-time and continuous-time multiagent systems with distance-dependent communication networks, respectively. The communication weight between any two agents is assumed to be a nonincreasing function of their distance. First, we consider the networks with fixed connectivity. In this case, the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough. We show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound. Second, we study the networks with distance-dependent connectivity. It is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range. With the validity of some conditions related to the property of the initial communication graph, we prove that consensus can be achieved asymptotically. Third, we present some applications of the main results to opinion consensus problems and formation control problems. Finally, several simulation examples are presented to illustrate the effectiveness of the theoretical findings.In this paper, we study the consensus problem of discrete-time and continuous-time multiagent systems with distance-dependent communication networks, respectively. The communication weight between any two agents is assumed to be a nonincreasing function of their distance. First, we consider the networks with fixed connectivity. In this case, the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough. We show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound. Second, we study the networks with distance-dependent connectivity. It is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range. With the validity of some conditions related to the property of the initial communication graph, we prove that consensus can be achieved asymptotically. Third, we present some applications of the main results to opinion consensus problems and formation control problems. Finally, several simulation examples are presented to illustrate the effectiveness of the theoretical findings.

During early and middle stance of level-ground walking, the ankle joint usually rotates passively due to the locomotion of human body. Based on this passive dynamics of human locomotion, we develop an energy-efficient torque controller with hierarchical structure for a robotic prosthesis. The low-level controller generates motor current from the human locomotion and controls the motor current/torque according to the high-level command. The high-level controller consists of a forward estimator and a feedback compensator. The forward estimator estimates the motor torque according to the desired ankle torque based on the prosthesis model that represents the transmission gain between the motor torque and the ankle torque. The feedback compensator compensates for the model and low-level control errors based on the torque measurements. Step response and frequency response show that the low-level controller could reach the desired value within 0.3 seconds and had a bandwidth of 4.2 Hz. Experiments of constant and linear torque tracking achieve small RMS tracking errors, which confirm the effectiveness of the proposed high-level controller.

This paper presents a realtime locomotion mode recognition method for an active pelvis orthosis. Five locomotion modes, including sitting, standing still, level-ground walking, ascending stairs, and descending stairs, are taken into consideration. The recognition is performed with locomotion information measured by the onboard hip angle sensors and the pressure insoles. These five modes are firstly divided into static modes and dynamic modes, and the two kinds are classified by monitoring the variation of the relative hip angles of the two legs within a pre-defined period. Static states are further classified into sitting and standing still based on the absolute hip angle. As for dynamic modes, a fuzzy-logic based method is proposed for the recognition. Two event-based locomotion features, including the hip joint angle at the first foot-strike and the center of foot pressure at the first foot-strike are used to calculate the membership of different modes based on the membership function, and the mode with the maximal membership is selected as the target mode. Experimental results with three subjects achieve an average recognition accuracy of 99.87% and average recognition delay of 18.12% of one gait cycle.

This paper presents a fuzzy logic based terrain identification method using multi-sensor fusion for powered prosthesis control. Five locomotion features including rising time of ground reaction force, sequence of foot strike on ground, foot inclination angle during stance, shank inclination angle at toe-off and maximal shank inclination angle during swing are selected to identify different terrains. These features are measured by fusion of two gyroscopes, two accelerometers, two force sensitive resistors and a timer. Based on the features, a fuzzy logic identification method is developed to identify level-ground, stair ascent, stair descent, upslope and downslope online in real time. Average identification accuracy higher than 97.5% is obtained in experiments of five able-bodied subjects and a transtibial amputee. Continuous identification results show the prospect of using the proposed method to realize real-time terrain identification of powered prostheses.

This paper considers the consensus problem for second-order multi-agent systems with inherent nonlinear dynamics under directed topologies. A variable transformation method is used to convert the consensus problem to a partial stability problem. Both fixed and switching topologies are considered. Under the assumption that the inherent nonlinear term satisfies the Lipshitz condition, sufficient conditions on the feedback gains and the Lipschitz constant to ensure consensus are given based on a Lyapunov function method.

This paper presents a bio-inspired below-knee exoskeleton to assist human walking. Different from the passive orthotic devices, the proposed exoskeleton includes powered compliant ankle and toe joints, which can output sufficient power to help the one with exoskeleton relearn normal walking gaits. We first propose a passivity-based dynamic bipedal model to analyze the effects of segmented foot and compliant joints on energetic efficiency and stability of bipedal walking. Starting from the results of theoretical analysis, we construct a below-knee exoskeleton prototype with ankle and toe joints driven by two series-elastic actuators. Experimental results validate the effectiveness of the proposed exoskeleton.

This paper presents an underwater cooperative box-pushing scenario in which three autonomous robotic fish that sense, plan and act on their own move an elongated box from some initial location to a goal location. With the onboard monocular camera, the robotic fish can estimate the pose of the object in the swimming tank. Considering the complexity of the underwater environment and the limited capability of a single robotic fish, we address the task by decomposing it into three subtasks and assigning them to capable robotic fish. With one robotic fish observing the box at the goal location and two robotic fish pushing the left and right ends of the box, the box can be moved gradually towards the goal location. The subtask consists a series of behaviors, each designed to fulfill one step of the subtask. The robotic fish coordinate through explicit communications and distribute the subtasks with a market-based dynamic task allocation method. Task reallocation mechanism that permits robotic fish to auction its assigned task to capable ones is used to cope with unexpected changes in the environment and the limited sensing range of the robotic fish. Experiments are conducted to verify the feasibility of the proposed methods.

This paper presents a seven-link dynamic walking model that is more close to human beings. We add hip actuation, upper body, flat feet and compliant ankle joints to the model. Walking sequence of the flat-foot walker has several sub-streams that form bipedal walking with dynamic series of phases, which is different with the motion of round-foot and point-foot models. We investigate the characteristics of three different walking gaits with different step lengths. Comparison of these walking gaits in walking velocity, efficiency and stability reveals the relation between step length and walking performance. Experimental results indicate that the gait which is more close to human normal walking achieves higher stability and energetic efficiency.

This paper deals with maneuver issues of a multilink biomimetic robotic fish, particularly focusing on turning control in free swimming. The characteristic parameters determining turning performance involve magnitude, position, and time of the deflections applied to the links, which are discussed via a series of simulation calculations and actual experiments.

This paper is concerned with cooperative control of a kind of multiple fish-like microrobots. Most of previous work on multi-robot cooperation is focused on the terrestrial robots and seldom deals with underwater applications. In fact, the tasks in hydro-environment is more challenging than those in ground circumstances and need the cooperation of robots much more. In this paper, we investigate this problem in the framework of an adversarial game with several underwater microrobots. A fuzzy reinforcement learning approach is adopted to acquire cooperative behavior and a behavioral hierarchical architecture is proposed. We conduct extensive experiments to verify the effectiveness of the proposed algorithms

This paper considers the flocking problem of a group of autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighboring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighboring agents and the external reference signal (or "virtual leader"). Then we prove that, if the acceleration input of the virtual leader is known, then each agent can follow the virtual leader, and moreover, the convergence rate of the center of mass (CoM) can be estimated; if the acceleration input is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, and thus the flocking motion can be obtained, however in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to further illustrate our theoretical results

This paper describes the design of a biologically inspired robotic fish which is capable of three-dimensional locomotion, and presents its depth control method. The mechanical design of the pectoral fins improves both the waterproof capability and the control precision. By adjusting the rotation angles of the pectoral fins, the robotic fish can fulfill up-and-down motion. Due to the uncertainty of the depth information measured by the pressure sensor, fuzzy logic method is applied to the depth control of the robotic fish. The experimental results on the designed prototype verify that the given method is effective in design and implementation.

This paper focuses on the design of fishlike underwater robots using an optimization approach to choose relative link lengths. Considering both ichthyologic characteristics and mechatronic constraints, the optimal link-length ratios are numerically calculated by an improved constrained cyclic variable method. Comparative results, before and after the optimization, demonstrate the enhanced performance

This paper is concerned with a novel problem of underwater cooperative transportation of multiple fishlike robots. A situation based action selection mechanism is proposed for the robots to transport a floating object to its destination. There are various control methods for cooperation of multi-robot system, but few of them deal with the underwater applications. In this paper, we first present the development of a series of biomimetic fish-like robots. Then, employing these robotic fish, we design and implement a cooperative transportation task utilizing a situation based action selection approach. We fully implement our method on three fish-like robots and make various experiments in a lab environment

This paper is concerned with the design, construction, and control of a biomimetic robotic dolphin equipped with mechanical flippers, based on a simplified engineered propulsive model. The robotic dolphin is modeled as a three-segment organism composed of rigid anterior body, flexible rear body, and an oscillating fluke. The dorsoventral movement of the tail produces the thrust, and bending of the body in the horizontal plane enables turning maneuvers. A dual-microcontroller structure is proposed to drive the oscillating multi-link rear body and the mechanical flippers. Swimming performance of the prototype robotic dolphin is tested, and the results confirm the effectiveness of the dolphin-like movement in propulsion and maneuvering

We study the coordinated motion of a group of vehicles with a leader based on nearest neighbor rules. The leader may be a special vehicle in the group or an external signal (virtual leader) to steer the vehicle group. The control law consists of two parts: a potential field force that makes the vehicles attract to each other and at the same time avoid collision in the group, and an alignment force that makes all vehicles' headings and speeds to converge respectively to common values. We assume that the interaction patterns are either fixed or switching based on the information topologies of the leader and member vehicles. Our approach is based on the Lyapunov theory and basic graph theory. We also consider the effect of noise on the collective dynamics of the group. Numerical simulations are worked out to illustrate the analytical results

This paper presents a three-dimensional, dynamic model of robotic fish which synthesizes both the carangiform and anguilliform swimming modes. The designed robotic fish is composed of three parts: stiff anterior body with a pair of pectoral fins for up-and-down motion, flexible rear body, and an oscillating lunate caudal fin. We use unsteady flow theory to analyze the motion of the anterior part and the links, and adopt experimental result from oscillating foil for the caudal fin. So the dynamic equation of each part can be obtained, and by summing up these equations, the dynamic equation for total swimming robot can be derived. The desired propulsive characteristics including forward velocity, sway velocity, pitch velocity, three velocity of Eulerian angles of the stiff anterior body, motion trajectory as well as propulsive efficiency can then be obtained by solving ordinary differential equation. The circular motion, based on asymmetrical kinematics of flexible rear body, can be achieved by adding different deflections to the oscillatory links. Comparisons between simulation results and real experiments are then conducted and discussed. A good agreement on dynamic characteristics demonstrates the validity of the proposed model

This paper presents a new method for formation control of multiple underwater fish-like robots. Considering both geometrical and mechanical constrains of the fish-like robots and based on the leader-following approach, a curvature coordinate is introduced to describe relative positions between different members within formations. Both the static and dynamic formations are concerned. We conduct simulations and physical experiments to verify effectiveness of the proposed algorithms

This paper considers a group of mobile autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the topology of the neighboring relations between agents varies with time and the coupling matrix is asymmetric. We introduce a set of switching control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its neighbors and the external reference signal (or "virtual leader"). When the velocity damping is taken into account, we can appropriately modify the control laws to generate the same stable flocking motion. Numerical simulations are worked out to further illustrate our theoretical results

This paper considers an anisotropic swarm model with an attraction/repulsion function. We study its aggregation properties and show that the swarm members aggregate and eventually form a cohesive cluster of finite size around their weighted center in a finite time. Numerical simulations demonstrate that all agents eventually enter and remain in a bounded region around the weighted center. The swarm may eventually stop moving or exhibit complex spiral motion due to asymmetry of the coupling structure. The model in this paper is more general than isotropic swarms and our results provide further insight into the effect of the interaction pattern on individual motion in a swarm system

This paper presents a novel approach for a group of vision-based autonomous robots to localize in dynamic environments. We propose a hybrid system method for localization consisted of on-line and off-line subsystems inspired by human cognition. For the on-line subsystem, we use the landmark based Markov localization method to estimate the position. When the robot does not update the probability of current position through landmarks for a certain period, we use the off-line experience subsystem to help. In addition to the hybrid system for individual localization, we propose a method of dynamic reference object for collaborative localization. By using this method, an autonomous robot can estimate and correct its position perception more accurately and effectively, taking the odometry error and other negative influence into consideration. Satisfactory experimental results are obtained in the RoboCup Four-Legged League environment

This paper deals with maneuver issues, in particular turning control of a free-swimming, multi-link biomimetic robotic fish propelled by a flexible rear body and oscillatory tail fin. Taking into account of both hydrodynamic model and engineering use, we develop a practical method to execute a circular maneuver. The turning control, based on asymmetrical kinematics and dynamics, can be achieved by adding different deflections to the oscillatory links. The characteristic parameters affecting turning performance include magnitude, position, and time of the deflections applied to the links, which are discussed with a series of simulation calculations. The experiments of circular motion with a four-link, infrared sensor-equipped robotic fish acquire a satisfactory maneuverability. Moreover, the feasibility of adding deflection angles to maneuver the robotic fish in the path planning is explored both analytically and experimentally

This paper presents the construction and motion control of a biologically inspired, multi-mode biomimetic robotic fish capable of three-dimensional locomotion. The mechanical configuration and the control system are described. The rhythmic movements of swimming are driven by the biological neural networks, called the central pattern generators (CPGs). The CPGs are modeled as nonlinear oscillators for joints and inter-joint coordination is achieved by altering the connection weights between joints. The CPG-based online gait generation method allows elegant and smooth transitions between swimming gaits, which result in multi-mode swimming to implement more lifelike locomotion. Several swimming modes can be obtained to mimic diverse actions of the real fish in nature, or designed according to special assignments by changing CPG parameters. The up-and-down motion can be implemented by adjusting the rotating angle of pectoral fins. The depth of the robotic fish is controlled utilizing a proportional-integral-derivative (PID) control algorithm according to the feedback of depth information measured by the sonar sensor installed at the bottom of the fish. The experimental results confirm the effectiveness of the control methods

In this paper we study the property of controllability for a class of interconnected systems with a leader in switching networks. We obtain necessary and sufficient conditions for the interconnected systems using neighbor rules, to be controllable by one of them acting as a leader. Here, we take the control laws to be an attractive force, and we assume the topology of the control interconnections is variant, that is, each swarm individual (agent) updates is current state based on the current information from neighboring individuals and the leader. Results show that the interconnected systems can be completely controllable even though every subsystem cannot be controllable by selecting one of the as a leader and neighbor interaction rules. Moreover, the swarm can begin from the given initial configuration and reach a desired final configuration while satisfying certain conditions. The model and results of this paper present a novel method to investigate a class of swarms via switching systems and provide further insight into the effect of the interaction pattern on self-organized motion in a swarm system. Numerical simulations are also worked out to illustrate the analytical results.

In this paper, we consider a group of mobile agents moving in the space with point mass dynamics. We investigate the dynamic properties of the group for the case where the topology of the neighboring relations between agents varies with time. Under the assumption that the neighboring graph is always connected, we show that stable flocking motion can be achieved by using a set of switching control laws. The control laws are a combination of attractive/repulsive and alignment forces. Using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between the agents, and the final tight formation minimizes all agent potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Subsequently, we study the motion of the group when the velocity damping is taken into account. In this case, we can appropriately modify the control laws to generate the same stable flocking motion. Finally, we provide some numerical simulations to further illustrate our theoretical results.

Reachability and controllability of positive discrete-time switched linear systems are firstly studied in this paper. First, a theoretic equivalent condition for reachability is addressed. A sufficient condition is also presented, but a counterexample shows that it is not necessary. A verifiable equivalent condition is given for a class of systems. Next, we show that reachability and null controllability is equivalent to complete controllability. A equivalent condition for null controllability is addressed and a verifiable one is given for a class of systems.

This paper is concerned with the parameter optimization for a simplified propulsive model of biomimetic robot fish propelled by a multiple linked mechanism. Taking account of both theoretic hydrodynamic issues and practical problems in engineering realization, the optimal link-length ratio is numerically calculated by an improved constrained cyclic variable method. The result is successfully applied to the 4-linked robot fish developed in our laboratory. The comparative experiments on forward swimming speed of the robot fish before and after parameter optimization verify the effectiveness of our method.

This paper presents a new method for controlling a group of nonholonomic mobile robots to achieve predetermined formations without using global knowledge. Based on the dynamic leader-follower model, a reactive tracking controller is proposed to make each following robot maintain a desired pose to its leader, and the stability property of this controller is discussed using Lyapunov theory. By employing such controllers, the N-robot formation control problem can be decomposed into decentralized tracking problems between N-l followers and designated leaders. Additionally, graph theory is introduced to formalize general formation patterns in a simple but effective way and two types of switching between these formations are also proposed. Numerical simulations and physical robots experiments show the effectiveness of our approach.

This paper presents a hierarchical framework for controlling a group of biomimetic fish robots to achieve cooperative tasks. Based on our previous successful work on the design and development of a robotic fish prototype, we attempt further to investigate the cooperation in groups of these fish. Employing top-down design approach, we propose a hierarchical architecture consisting of five levels: task level, role (or mode) level, behavior level, action level and controller level, to formalize the processes from task decomposition, role assignments and control performance. Two typical cases are developed to demonstrate the feasibility of the architecture and corresponding experimental results show that high efficiency and much greater capabilities are exhibited when the fish try to cooperate.

This paper considers a group of mobile autonomous agents moving in the space with point mass dynamics and with asymmetric coupling matrix. We investigate the dynamic properties of the group for the case that the topology of the neighboring relations between agents varies with time. Under the assumption that the neighboring graphs are always connected, we show that stable flocking motion can be achieved by using a set of switching control laws. The control laws are a combination of attractive/repulsive and alignment forces. By using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between the agents, and the final tight formation minimizes all agent potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Finally, we study the motion of the group when the velocity damping is taken into account. We prove that the common velocity asymptotically approaches zero. In this case, we can properly modify the control laws to generate the same stable flocking motion.

Investigation in biomimetic robotic fish is a multidisciplinary problem entirely involving hydrodynamics-based control and robotic technology. In this paper, grounded on an optimized kinematic propulsive model of fish that relate frequency to speed and joint angle bias to turns, a robotic fish and its motion control are designed. Information of multiple fishes' position and orientation, with real-time visual tracking, is then obtained for positioning in the coordinate experiment. The coordinated motions of the fishes are achieved by behavior-based strategies composed of role assignment, behavior selection and role transition. An experimental system for multiple robotic fishes' coordination is finally constructed to verify the proposed scheme and algorithms, and the running experiments of passing-hole and pushing-ball primarily show the effectiveness of the presented strategies.

This paper is concerned with the problem of motion planning for multiple robotic fish swimming together to achieve a disk-pushing task. Based on our previous successful work on the design and development of robotic fish prototypes, we attempt further to investigate how to implement cooperation in groups of these fish. The motivation of this work is that the capability of a single fish robot is always limited while there are many complex missions in practice which should be accomplished by effective cooperation of multiple fish. A disk-pushing task is employed as an example to demonstrate the design of cooperative behaviors as well as strategies. Corresponding experimental results show that higher efficiency and much greater capabilities can be obtained when these fish planning their motion properly.

The problem of stabilization of networked control systems (NCSs) with time-varying transmission period is studied. By viewing the time-varying transmission period as time-varying parameter uncertainties, sufficient conditions expressed in linear matrix inequalities are presented under which there exists constant state feedback controller proving the stabilization of NCSs. A numerical example is given to illustrate the utility of our results.

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for such feedback controllers. For second-order systems, a equivalent condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.

The problems of Extended Strict Positive Realness (ESPR) analysis and synthesis for a class of discrete-time systems with polytopic uncertainty are considered. An equivalent condition of ESPR for discrete-time systems is first given in terms of linear matrix inequalities (LMIs). Moreover, a sufficient condition for the uncertain systems to be robustly stable with ESPR is established by stability with ESPR of vertex systems. Furthermore, a condition on robust stability with ESPR for the uncertain systems is obtained in terms of linear matrix inequalities. Based on this result, a simple approach to the design of a linear state-feedback controller which stabilizes robustly the uncertain systems and achieves ESPR is proposed. A numerical example is worked out to illustrate the efficiency of the proposed approach.

We study the stabilization of discrete-time switched linear systems and discrete-time uncertain switched systems when an arbitrary switching rule is imposed on the observer-based static output feedback controllers. Several linear matrix inequality (LMI) based conditions are established to this problem with switched Lyapunov function method for both cases.

The control problem of networked control systems via output feedback is considered in this paper. In the system, a sensor is connected to a linear controller/actuator via a network. The plant is controlled alternately by an open loop controller and a closed loop controller. Necessary and sufficient conditions for the exponential stability of such systems are derived in terms of the network dwell times and the system parameters. Based on the results, a simple procedure for designing the output feedback controller is presented. Numerical simulation shows the feasibility and efficiency of the proposed method.

Switched systems are a special class of hybrid systems. Different from the existing mathematical models for switched systems, in this paper it is assumed that there are two groups of subsystems and the switching between the two groups is alternate. Based on the new model of switched linear systems under constrained switching, this paper studies the reachability of such systems. A necessary and sufficient geometric criterion for reachability of such systems is established. Finally, an example is given to illustrate the results.

This paper studies the reachability and controllability of a class of switched linear systems with state jumps at the switching instants. Necessary and sufficient geometric criteria are presented. A structural method is given to realize the reachability and controllability.

This paper studies periodic stabilization of a class of switched linear systems. The concepts of periodically asymptotical stabilizability (PAS) and periodically exponential stabilizability (PES) are first introduced. First, for the continuous-time case, a necessary and sufficient condition for PAS is established. Then, it is proved that PES is equivalent to PAS, and controllability is equivalent to PES with arbitrary decaying rate, respectively. The corresponding algorithms are given as well. Finally, a numerical examples are given to illustrate our results.

This paper investigates the /spl Lscr/;/sub 2/ gain analysis of uncertain discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function (SLF) method. The /spl Lscr/;/sub 2/ gain analysis is to characterize conditions under which an uncertain switched system is uniformly quadratically stable (UQS) with an /spl Lscr/;/sub 2/ gain smaller than a constant /spl gamma/ for all admissible uncertainties. All results in this paper are expressed in terms of LMIs, which can be easily tested with efficient LMI algorithms.

In this paper, the controllability of a class of planar piecewise linear systems is investigated. An explicit necessary and sufficient condition for null controllability of such systems is established. Moreover, it is proved that the null controllability can be realized infinite steps.