Adaptive Neural Control for Robotic Manipulators With Output Constraints and Uncertainties

Summary The distributed formation‐containment (DFC) problem under a directed graph is addressed for networked Euler‐Lagrange systems. First, using a leader‐follower framework, the DFC problem is properly defined. For the leaders and the followers, respectively, a DFC control law is next proposed without using velocity information. Based on the artificial potential function, all the agents can achieve the control objective satisfactorily while avoiding collisions with others as well as the obstacles in the environment. By the Lyapunov stability theory, the boundedness of the error signals is guaranteed. Simulations are finally given to show the feasibility of this approach.

“…In the case of without velocity measurements, we estimate the immeasurable state z 2 i using a high‐gain observer

{\hat{z}}_{2 i} = \frac{π_{2 i}}{ε_{i}} - α_{1 i}, i \in 𝒱,

and the dynamics of π 2 i is given as

\begin{align} ε_{i} {\overset{π}{true}}_{1 i} = π_{2 i}, \end{align}

\begin{align} ε_{i} {\overset{π}{true}}_{2 i} & = prefix- {\overset{λ}{true}}_{1 i} π_{2 i} prefix- π_{1 i} + q_{i}, \end{align}

where

{\overline{λ}}_{1 i}

is picked as long as the polynomial

s^{2} + {\overline{λ}}_{1 i} s + 1

is Hurwitz, and ε i is a small positive constant. Then, the following property holds:

\begin{align} ξ_{2 i} = \frac{π_{2 i}}{ε_{i}} prefix- {\overset{q}{true}}_{i} = prefix- ε_{i} {ψ_{i}}^{((), 2)}, \end{align}

…”

Section: Dfc Control With Collision Avoidance Via Output Feedbackmentioning

confidence: 99%

“…where 1i is picked as long as the polynomial s 2 + 1i s + 1 is Hurwitz, and i is a small positive constant. Then, the following property holds: 45,46…”

Section: Dfc Control With Collision Avoidance Via Output Feedbackmentioning

confidence: 99%

Formation‐containment control of networked collision‐free Lagrangian systems

et al. 2020

“…"> iii.Assumption suggests that the initial outputs of all the agents are required to satisfy constraint k , which is known and available to each agent. It is emphasized that this assumption is commonly needed in the output‐constrained control literature; see, for instance, the control of single output‐constrained nonlinear systems and consensus control of output‐constrained multiagent systems . Besides, as remarked by Zhang et al, this assumption can be easily satisfied by choosing a large k .…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

Wang

Cai

2020

Summary This paper presents a novel distributed adaptive control algorithm for uncertain higher‐order nonlinear multiagent systems subject to output constraints and unknown control directions. Regarding the latter, a generic class of cases is considered, allowing completely unknown and even nonidentical control directions. Furthermore, the communication topology is only required to contain a fixed directed spanning tree. To guarantee the output constraints and address the asymmetric directed communication topology, a new reference output using the transformation strategy is introduced for each agent, benefiting from which the consensus problem of the multiagent system is recast as local tracking control problems of single agents. Then, the distributed control algorithm is recursively established based on the backstepping technique and the Nussbaum‐type function. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that, under the proposed distributed algorithm, uniform boundedness of all closed‐loop signals can be ensured, and asymptotic consensus is achieved without violation of the output constraints. Finally, simulation studies on the angle control of single‐link robots are given to verify the effectiveness of the proposed algorithm.

“…A survey on different neural networks structures used in control of robot manipulators has been presented in Reference . To fill the gap between theoretical and practical results, input/state constrained problems in neural control of robot manipulators have been studied in recent years …”

Section: Introductionmentioning

confidence: 99%

Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

Izadbakhsh

Khorashadizadeh

2020

This article presents a robust adaptive controller for electrically driven robots using Bernstein polynomials as universal approximator. The lumped uncertainties including unmodeled dynamics, external disturbances, and nonimplemented control signals (they assumed as a function of time, instead a function of several variables) are represented with this powerful mathematical tool. The polynomial coefficients are then tuned based on the adaptation law obtained in the stability analysis. A comprehensive approach is adopted to include the saturated and unsaturated areas and also the transition between these areas in the stability analysis. As a result, the stability and the performance of the proposed controller have been improved considerably in dealing with actuator saturation. Also, in comparison with a recent paper based on uncertainty estimation using Taylor series, the proposed controller is less computational due to reducing the size of the matrix of convergence rate. A performance evaluation has been carried out to verify satisfactory performance of transient response of the controller.Simulation results on a Puma560 manipulator actuated by geared permanent magnet dc motors have been presented to guarantee its satisfactory performance. K E Y W O R D Sactuator saturation, adaptive uncertainty estimation, Bernstein polynomials, electrically driven robots, stability analysis 1 Int J Robust Nonlinear Control. 2020;30:2719-2735.wileyonlinelibrary.com/journal/rnc