In this paper, new distributed adaptive methods are proposed for solving both leaderless and leader–follower consensus problems in networks of uncertain robot manipulators, by estimating only the gravitational torque forces. Comparing with the existing adaptive methods, which require the estimation of the whole dynamics, presented methods reduce the excitation levels required for efficient parameter search, the convergence time, and the complexity of the regressor. Additionally, proposed schemes eliminate the need for velocity information exchange between the agents. Global asymptotic synchronization is shown by introducing new Lyapunov functions. Simulation results are provided for a network of 10 4-DOF robot manipulators.

This paper proposes a fully distributed continuous region-reaching controller for multi-robot systems which can effectively eliminate the chattering issues and the negative effects caused by discontinuities. The adaptive control gain technique is employed to solve the distributed region-reaching control problem. By performing Lyapunov function-based stability analysis, it is shown that all the robots can move cohesively within the desired region under the proposed distributed control algorithm. In addition, collision avoidance and velocity matching within the moving region can be guaranteed under properly designed control gains. Simulation examples are given to verify the capabilities of the proposed control method.

The paper presents a distributed cooperative control law for autonomous deployment of a team of heterogeneous agents. Deployment problems deal with the coordination of groups of agents in order to cover one or more assigned areas of the operational space. In particular, we consider a team composed by agents with different dynamics, sensing capabilities, and resources available for the deployment. Sensing heterogeneity is addressed by means of the descriptor function framework, an abstraction that provides a set of mathematical tools for describing both agent sensing capabilities and the desired deployment. A distributed cooperative control law is then formally derived finding a suboptimal solution of a cooperative differential game, where the agents are interested in achieving the requested deployment, while optimizing the resources usage according to their dynamics. The control law effectiveness is proven by theoretical arguments, and supported by numerical simulations.

This paper presents an adaptive distributed control strategy for n-serial-flexible-link manipulators. The proposed adaptive controller is used for flexible-link-manipulators: (1) to solve the tracking control problem in the joint space, and (2) to reduce vibrations of the links. The dynamical model of flexible link manipulators is reorganized to take the form of n interconnected subsystems. Each subsystem has a one-joint and one-link pair. The system parameters are deemed to be unknown. The adaptive distributed strategy controls one subsystem in each step, starting from the last one. The nth subsystem is controlled by assuming that the remaining subsystems are stable. Then, proceeding backward to the (n-1)th system, the same strategy is applied, and so on, until the first subsystem is reached. The gradient-based estimator is used to estimate the parameters of each subsystem. The control law of the ith subsystem uses its own estimated parameters and the estimated parameters of all upper level subsystems. The global stability of the error dynamics is proved using Lyapunov approach. This algorithm was implemented in real time on a two-flexible-link manipulator, and a comparison with the non-adaptive version shows the effectiveness of this approach.

In this paper, we present a novel algorithm for exploring an unknown environment using a team of mobile robots. The suggested algorithm is a grid-based search method that utilizes a triangular pattern which covers an area so that exploring the whole area is guaranteed. The proposed algorithm consists of two stages. In the first stage, all the members of the team make a common triangular grid of which they are located on the vertices. In the second stage, they start exploring the area by moving between vertices of the grid. Furthermore, it is assumed that the communication range of the robots is limited, and the algorithm is based on the information of the nearest neighbours of the robots. Moreover, we apply a new mapping method employed by robots during the search operation. A mathematically rigorous proof of convergence with probability 1 of the algorithm is given. Moreover, our algorithm is implemented and simulated using a simulator of the real robots and environment and also tested via experiments with Adept Pioneer 3DX wheeled mobile robots.

A distributed coverage control scheme based on the state space model predictive control, which is known as receding horizon control (RHC) for decoupled systems, is presented. An optimal control problem is formulated for a set of decoupled robotic systems where a cost function couples the dynamical behavior of the robots. The coupling is described through a connected graph using a Voronoi diagram, where each robot is a node and the cost and constraints of the optimization problem associated with each robot are a function of its state and of the states of its neighbors. The complexity of the problem is addressed by breaking a centralized receding horizon controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and it computes the local control inputs based only on the position of the robot and that of its neighbors. The stability of the distributed scheme is analyzed and its properties compared with the linear quadratic regulator (LQR) design which has been proposed in the literature. Moreover, the proposed coverage algorithm is also applied to deploy a group of mobile robots in a desired formation pattern. The simulation results are used to illustrate the good performance of the proposed coverage control scheme.

In this article, we propose and analyse a sparse grid collocation method to solve an optimal control problem involving an elliptic partial differential equation with random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive an optimality system. A Galerkin approximation in physical space and a sparse grid collocation in the probability space is used. Error estimates for a fully discrete solution using an appropriate norm are provided, and we analyse the computational efficiency. Computational evidence complements the present theory, to show the effectiveness of our stochastic collocation method.

This paper presents a nonlinear distributed control strategy for flexible-link manipulators to solve the tracking control problem in the joint space and cancel vibrations of the links. First, the dynamic of an n-flexible-link manipulator is decomposed into n subsystems. Each subsystem has a pair of one joint and one link. The distributed control strategy is applied to each subsystem starting from the last subsystem. The strategy of control consists in controlling the nth joint and stabilizing the nth link by assuming that the remaining subsystems are stable. Then, going backward to the (n − 1)th subsystem, the same control strategy is applied to each corresponding joint-link subsystem until the first. Sliding mode technique is used to develop the control law of each subsystem and the global stability of the resulting tracking errors is proved using the Lyapunov technique. This algorithm was tested on a two-flexible-link manipulator and gave effective results, a good tracking performance, and capability to eliminate the links' vibrations.

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order O(h2+k2) is obtained for the numerical solution in a discrete L2-norm. A numerical experiment is presented to test the theoretical result.

In an interdisciplinary field on mathematics and physics, we examine a physical problem, fluid flow in porous media, which is represented by a stochastic partial differential equation (SPDE). We first give a priori error estimates for the solutions to an optimization problem constrained by the physical model under lower regularity assumptions than the literature. We then use the concept of Galerkin finite element methods to establish a new numerical algorithm to give approximations for our stochastic optimal physical problem. Finally, we develop original computer programs based on the algorithm and use several numerical examples of various situations to see how well our solver works by comparing its outputs to the priori error estimates.

The goal of this paper is to derive some error estimates for thenumerical discretization of some optimal control problems governedby semilinear elliptic equations with bound constraints on thecontrol and a finitely number of equality and inequality stateconstraints. We prove some error estimates for the optimalcontrols in the L ∞ norm and we also obtain error estimatesfor the Lagrange multipliers associated to the state constraintsas well as for the optimal states and optimal adjoint states.