Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

Nonlinear systems identification and control via dynamic multitime scales neural networks

This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.

Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay

This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov-Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.

Neural-adaptive control of single-master-multiple-slaves teleoperation for coordinated multiple mobile manipulators with time-varying communication delays and input uncertainties

In this paper, adaptive neural network control is investigated for single-master-multiple-slaves teleoperation in consideration of time delays and input dead-zone uncertainties for multiple mobile manipulators carrying a common object in a cooperative manner. Firstly, concise dynamics of teleoperation systems consisting of a single master robot, multiple coordinated slave robots, and the object are developed in the task space. To handle asymmetric time-varying delays in communication channels and unknown asymmetric input dead zones, the nonlinear dynamics of the teleoperation system are transformed into two subsystems through feedback linearization: local master or slave dynamics including the unknown input dead zones and delayed dynamics for the purpose of synchronization. Then, a model reference neural network control strategy based on linear matrix inequalities (LMI) and adaptive techniques is proposed. The developed control approach ensures that the defined tracking errors converge to zero whereas the coordination internal force errors remain bounded and can be made arbitrarily small. Throughout this paper, stability analysis is performed via explicit Lyapunov techniques under specific LMI conditions. The proposed adaptive neural network control scheme is robust against motion disturbances, parametric uncertainties, time-varying delays, and input dead zones, which is validated by simulation studies.

Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation

A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.

Trajectory Planning and Optimized Adaptive Control for a Class of Wheeled Inverted Pendulum Vehicle Models

In this paper, we investigate optimized adaptive control and trajectory generation for a class of wheeled inverted pendulum (WIP) models of vehicle systems. Aiming at shaping the controlled vehicle dynamics to be of minimized motion tracking errors as well as angular accelerations, we employ the linear quadratic regulation optimization technique to obtain an optimal reference model. Adaptive control has then been developed using variable structure method to ensure the reference model to be exactly matched in a finite-time horizon, even in the presence of various internal and external uncertainties. The minimized yaw and tilt angular accelerations help to enhance the vehicle rider's comfort. In addition, due to the underactuated mechanism of WIP, the vehicle forward velocity dynamics cannot be controlled separately from the pendulum tilt angle dynamics. Inspired by the control strategy of human drivers, who usually manipulate the tilt angle to control the forward velocity, we design a neural-network-based adaptive generator of implicit control trajectory (AGICT) of the tilt angle which indirectly "controls" the forward velocity such that it tracks the desired velocity asymptotically. The stability and optimal tracking performance have been rigorously established by theoretic analysis. In addition, simulation studies have been carried out to demonstrate the efficiency of the developed AGICT and optimized adaptive controller.

Output feedback trajectory stabilization of the uncertainty DC servomechanism system

This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.

Adaptive dynamic output feedback neural network control of uncertain MIMO nonlinear systems with prescribed performance

An adaptive dynamic output feedback neural network controller for a class of multi-input/multi-output affine in the control uncertain nonlinear systems is designed, capable of guaranteeing prescribed performance bounds on the system's output as well as boundedness of all other closed loop signals. It is proved that simply guaranteeing a boundedness property for the states of a specifically defined augmented closed loop system is necessary and sufficient to solve the problem under consideration. The proposed dynamic controller is of switching type. However, its continuity is guaranteed, thus alleviating any issues related to the existence and uniqueness of solutions. Simulations on a planar two-link articulated manipulator illustrate the approach.