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This article studies a distributed average tracking (DAT) problem, in which a collection of agents work collaboratively, subject to local communication, to track the average of a set of reference signals, each of which is available to a single agent. Our primary objective is to seek a design methodology for DAT under possibly weight-unbalanced directed networks—the most general and thus most challenging case from the network topology perspective, which has few results in the literature. For this purpose, we propose a distributed algorithm based on a chain of two integrators that are coupled with a distributed estimator. It is found that the convergence depends on not only the network topology but also the deviations among the reference signal accelerations. Another primary interest of this article stems from the dynamics perspective—a point perceived as a main source of control design difficulty for multiagent systems. Indeed, we devise a nonlinear algorithm that is capable of achieving DAT under weight-unbalanced directed networks for agents subject to high-order integrator dynamics. The results show that the convergence to the vicinity of the average of the reference signals is guaranteed as long as the signals’ states and control inputs are all bounded. Both algorithms are robust to initialization errors, i.e., DAT is insured even if the agents are not correctly initialized, enabling the potential applications in a wider spectrum of application domains. [ABSTRACT FROM AUTHOR]

Modern applications of robotics typically involve a robot control system with an inner proportional–integral (PI) or proportional–integral–derivative (PID) control loop and an outer user-specified control loop for specifying the velocity (or position) command. Most existing outer loop controllers, however, do not take into consideration the dynamic effects of robots and their effectiveness relies on the ad hoc assumption that the inner PI or PID control loop is fast enough, and other torque-based controllers cannot be implemented in robots with closed architecture. This paper investigates the adaptive control of robotic systems with an inner/outer loop structure, taking into account the effects of the dynamics and uncertainties, and both the task-space control and joint-space control are considered. We propose a dynamic modularity approach to resolve this issue, and a class of adaptive outer loop control schemes is proposed and their role is to dynamically generate the joint velocity (or position) command for the low-level joint servoing loop. Without relying on the ad hoc assumption that the joint servoing loop is fast enough or modification of the low-level joint controller structure, we show that the proposed outer loop controllers can ensure stability and convergence of the closed-loop system. The formulated dynamic modularity approach is validated by the experimental results using different generations of the UR10 robots. [ABSTRACT FROM AUTHOR]

This paper studies the distributed time-varying convex optimization problem for a class of nonlinear multiagent systems. An auxiliary system is first designed to estimate the global optimal state and its high-order derivatives by means of a distributed algorithm. Relying on this auxiliary system, the solution of the distributed time-varying convex optimization problem is converted into that of a tracking problem for a class of nonlinear systems. A tracking control scheme is then proposed based on the back-stepping strategy. Simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the constraint sets are not required to be bounded. For continuous-time multiagent systems, a distributed continuous algorithm is first introduced where the stepsizes and the convex constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the constraint sets are unbounded. After that, the obtained results are extended to discrete-time multiagent systems and then the case where each agent remains in a corresponding convex constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions. [ABSTRACT FROM AUTHOR]

This paper addresses distributed average tracking of physical second-order agents with heterogeneous unknown nonlinear dynamics, where there is no constraint on input signals and there is no need for correct initialization. The unknown nonlinear terms in agents’ dynamics are heterogeneous, satisfying a Lipschitz-like condition that will be defined later and is more general than the Lipschitz condition. In the proposed algorithm, a control input and a filter are designed for each agent. Each agent's filter has two outputs and the idea is that the first output estimates the average of the input signals, and the second output estimates the average of the input velocities asymptotically. In parallel, each agent's position and velocity are driven to track, respectively, the first and the second outputs. Having an unknown term in agents’ dynamics necessitates designing the filters for agents. Since the nonlinear terms in agents’ dynamics can be unbounded and the input signals are arbitrary, novel time-varying gains are employed in agents’ filters and control inputs to overcome these unboundedness effects. Finally, the results are improved to achieve the distributed average tracking for a group of double-integrator agents, where there is no constraint on input signals and the filter is not required anymore. Numerical simulations are also presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for continuous-time multi-agent systems with single-integrator dynamics. The objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains, finite-time convergence, and a common convex constraint set. First, a distributed nonsmooth algorithm is introduced for a special class of convex objective functions that have a quadratic-like form. It is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Second, a distributed algorithm is presented for general differentiable convex objective functions, in which the interaction gains of each agent can be self-adjusted based on local states. A corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically. Third, a distributed optimization algorithm with state-dependent gradient gains is given for general differentiable convex objective functions. It is shown that the distributed continuous-time optimization problem can be solved even though the gradient gains are not identical. Fourth, a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable convex objective functions. It is shown that all agents reach a consensus while minimizing the team objective function in finite time. Fifth, as an extension of the previous results, a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite-time optimization algorithm are given. It is shown that both algorithms can be used to solve a distributed continuous-time optimization problem with a common convex constraint set. Numerical examples are included to illustrate the obtained theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. The objective is to minimize the sum of local time-varying cost functions, each of which is known to only an individual agent, through local interaction. Here, the optimal point is time varying and creates an optimal trajectory. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. In both cases, a centralized approach is first introduced to solve the optimization problem. Then, this problem is solved in a distributed manner and a discontinuous algorithm based on the signum function is proposed in each case. In the case of single-integrator (respectively, double-integrator) dynamics, each agent relies only on its own position and the relative positions (respectively, positions and velocities) between itself and its neighbors. A gain adaption scheme is introduced in both algorithms to eliminate certain global information requirement. To relax the restricted assumption imposed on feasible cost functions, an estimator based algorithm using the signum function is proposed, where each agent uses dynamic average tracking as a tool to estimate the centralized control input. As a tradeoff, the estimator-based algorithm necessitates communication between neighbors. Then, in the case of double-integrator dynamics, the proposed algorithms are further extended. Two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. To account for interagent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics. It is shown that the center of the agents tracks the optimal trajectory, the connectivity of the agents is maintained, and interagent collision is avoided. [ABSTRACT FROM AUTHOR]

In this technical note, the distributed average tracking (DAT) problem for reference signals with bounded accelerations is considered. A sliding-mode surface is designed such that trajectories on the surface will achieve DAT. A discontinuous control algorithm is then proposed to guarantee that the surface can be reached in finite time. It is shown that if the switching network topology is connected at all time, then DAT can be solved by properly choosing a gain parameter of the algorithm. [ABSTRACT FROM PUBLISHER]

Under an extended proportional-integral (PI) control scheme, a new class of distributed average tracking (DAT) algorithms has been developed for three different kinds of references: references with steady states, references with bounded derivatives, and references with a common derivative. The class of DAT algorithms are further applied to solve the DAT problem for Euler-Lagrange (EL) systems. [ABSTRACT FROM AUTHOR]

We present a distributed discontinuous control algorithm for a team of agents to track the average of multiple time-varying reference signals with bounded derivatives. We use tools from nonsmooth analysis to analyze the stability of the system. For time-invariant undirected connected network topologies, we prove that the states of all agents will converge to the average of the time-varying reference signals with bounded derivatives in finite time provided that the control gain is properly chosen. The validity of this result is also established for scenarios with switching undirected connected network topologies. For time-invariant directed network topologies with a directed spanning tree, we show that all agents will still reach a consensus in finite time, but the convergent value is generally not the average of the time-varying reference signals with bounded derivatives. Simulation examples are presented to show the validity of the above results. [ABSTRACT FROM AUTHOR]

This note studies the distributed containment control problem for a group of autonomous vehicles modeled by double-integrator dynamics with multiple dynamic leaders. The objective is to drive the followers into the convex hull spanned by the dynamic leaders under the constraints that the velocities and the accelerations of both the leaders and the followers are not available, the leaders are neighbors of only a subset of the followers, and the followers have only local interaction. Two containment control algorithms via only position measurements of the agents are proposed. Theoretical analysis shows that the followers will move into the convex hull spanned by the dynamic leaders if the network topology among the followers is undirected, for each follower there exists at least one leader that has a directed path to the follower, and the parameters in the algorithm are properly chosen. Numerical results are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept. [ABSTRACT FROM PUBLISHER]

In this note, we study a distributed coordinated tracking problem for multiple networked Euler–Lagrange systems. The objective is for a team of followers modeled by full-actuated Euler–Lagrange equations to track a dynamic leader whose vector of generalized coordinates is time varying under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. We consider two cases: i) The leader has a constant vector of generalized coordinate derivatives, and ii) The leader has a varying vector of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and an adaptive control law to account for parametric uncertainties. In the second case, we propose a model-independent sliding mode control algorithm. Simulation results on multiple networked two-link revolute joint arms are provided to show the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]