General Projection Neural Network Research Articles

Cooperation and Coordination Transportation for Nonholonomic Mobile Manipulators: A Distributed Model Predictive Control Approach

This article addresses the problem of cooperation and coordination transportation for decoupling nonholonomic mobile manipulators (NMMs) in a workspace with obstacles. We propose a distributed model predictive control (MPC) approach for a team of NMMs to transport a target object while satisfying significant constraints and limitations, such as the feasible state and control input constraints, parameter synchronization constraints, and obstacles within the workspace. First, under the framework of the decoupling dynamics, an auxiliary dynamics model for task-space end-effectors and null-space mobile bases is obtained by the nonlinear feedback technique based on the Euler–Lagrange description of the NMMs. Using the modified virtual structure method, the cooperation and coordination transportation problem for NMMs is simplified as two independent synchronization tracking control problems for task-space end-effectors and null-space mobile bases. A distributed constrained optimization problem is established by taking the parameter synchronization and system constraints into the cost function. A general projection neural network (GPNN) approach is employed to solve the optimization problem and obtain the optimal control input. Moreover, a sufficient condition that guarantees the stability of the closed-loop system is further developed. Simulation results show that the proposed cooperation and coordination transportation strategy is feasible and effective.

Trajectory tracking of multi-legged robot based on model predictive and sliding mode control

To address the problem of achieving accurate tracking control of multi-legged robots, which is difficult due to their strong coupling structure, this paper decomposes the trajectory tracking of the whole-body into body-level and limb-level sub-control systems. First, a tracking controller based on the model predictive control strategy is designed for the body-level subsystem, and the general projection neural network method is used to quickly solve for the optimal control signal that satisfies stride constraints. Then, a robust adaptive terminal sliding mode controller is designed for the limb-level subsystem to resist the influence of model uncertainties and external disturbances on tracking performance. The designed gait mode generator and stride solver modules serve as two bridges connecting the body- and limb-level subsystems, thus coalescing the entire control system into a closed loop, which greatly improves the tracking accuracy of the whole system. Finally, two cases, the directed curved-trajectory tracking with tripod gait and the undirected polyline-trajectory tracking with quadruped gait, are given to illustrate the omnidirectional mobility of the multi-legged robot, and to demonstrate the effectiveness and practicability of the proposed control strategy.

Incremental Updating Multirobot Formation Using Nonlinear Model Predictive Control Method With General Projection Neural Network

In this paper, an incremental centralized formation system is developed for controlling the multirobot formation with joining robots, and a nonlinear model predictive control (NMPC) method is implemented as the controller. The incremental updating method is used to update the system's state in real time, when there is a new robot joining during the formation process. Then, an NMPC approach is developed to reformulate the formation system into a convex nonlinear minimization problem, which can be further transformed into a quadratic programming (QP) with constraints. Then, a general projection neural network (GPNN) is implemented for solving this QP problem online to get the optimal inputs. In the end, two examples of incremental multirobot formation are demonstrated to verify the effectiveness of this method.

Leader-Follower Consensus Multi-Robot Formation Control Using Neurodynamic-Optimization-Based Nonlinear Model Predictive Control

This paper investigates a nonlinear-model-predictive-control (NMPC)-strategy-based distributed leader-follower consensus multi-robot formation system. The control objective of this system is to design a group of nonholonomic robots to converge into the desired geometric pattern and to track a designed path. A directed graph that specifies communication topology for the formation is given. A leader-follower consensus formation problem based on the mobile robot kinematic model is obtained, which is further reformulated into a constrained nonlinear minimization problem through the NMPC strategy. A general projection neural network (GPNN) is implemented to efficiently derive the optimal control inputs for the robots. The simulation results verify the effectiveness of the proposed formation algorithm.

General Projection Neural Network Based Nonlinear Model Predictive Control for Multi-Robot Formation and Tracking

For controlling the multi-robot formation system, a general projection neural network based nonlinear model predictive control (NMPC) strategy is proposed in this paper. The multi-robot formation system consists of the trajectory tracking of leader robot and the leader-follower formation controlling. Their kinematic error systems can be reformulated as a convex nonlinear minimization problem by the NMPC method and can be transformed into a constrained quadratic programming (QP) optimization problem. To solve this QP problem online efficiently, a general projection neural network (GPNN) is applied to obtain the optimal solution, which includes the optimal inputs of the formation system. Compare to other existing leader-follower approaches, the proposed nonlinear MPC method can take the input and state constraints of system into consideration. In the end of this work, simulations of the trajectory tracking and multi-robot formation are performed to verify the effectiveness of the developed strategy.

Model Predictive Control of Nonholonomic Chained Systems Using General Projection Neural Networks Optimization

In this paper, a class of nonholonomic chained systems is first converted into two subsystems, and then an explicit exponential decaying term is introduced into the input of the first subsystem to guarantee its controllability. After a state-scaling transformation, a model predictive control (MPC) scheme is proposed for the nonholonomic chained systems. The proposed MPC scheme employs a general projection neural network (GPN) to iteratively solve a quadratic programming (QP) problem over a finite receding horizon. The GPN employed in this paper is proved to be stable in the sense of Lyapunov, and its global convergence to the optimal solution is guaranteed for the reformulated QP. A simulation study is performed to show stable and convergent control performance under the proposed method, irrespective of whether the control input $\boldsymbol {u_{1}}$ vanishes or not.

A Recurrent Neural Network Based on Projection Operator for Extended General Variational Inequalities

Based on the projection operator, a recurrent neural network is proposed for solving extended general variational inequalities (EGVIs). Sufficient conditions are provided to ensure the global convergence of the proposed neural network based on Lyapunov methods. Compared with the existing neural networks for variational inequalities, the proposed neural network is a modified version of the general projection neural network existing in the literature and capable of solving the EGVI problems. In addition, simulation results on numerical examples show the effectiveness and performance of the proposed neural network.

Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints

Extended linear-quadratic programming (ELQP) is an extension of the conventional linear programming and quadratic programming, which arises in many dynamic and stochastic optimization problems. Existing neural network approaches are limited to solve ELQP problems with bound constraints only. In the paper, I consider solving the ELQP problems with general polyhedral sets by using recurrent neural networks. An existing neural network in the literature, called general projection neural network (GPNN) is investigated for this purpose. In addition, based on different types of constraints, different approaches are utilized to lower the dimensions of the designed GPNNs and consequently reduce their structural complexities. All designed GPNNs are stable in the Lyapunov sense and globally convergent to the solutions of the ELQP problems under mild conditions. Numerical simulations are provided to validate the results.

Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks

Generalized linear variational inequality (GLVI) is an extension of the canonical linear variational inequality. In recent years, a recurrent neural network (NN) called general projection neural network (GPNN) was developed for solving GLVIs with simple bound (often box-type or sphere-type) constraints. The aim of this paper is twofold. First, some further stability results of the GPNN are presented. Second, the GPNN is extended for solving GLVIs with general linear equality and inequality constraints. A new design methodology for the GPNN is then proposed. Furthermore, in view of different types of constraints, approaches for reducing the number of neurons of the GPNN are discussed, which results in two specific GPNNs. Moreover, some distinct properties of the resulting GPNNs are also explored based on their particular structures. Numerical simulation results are provided to validate the results.

A general projection neural network for solving monotone variational inequalities and related optimization problems.

Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.