Robust formation tracking control of mobile robots via one-to-one time-varying communication

We solve the formation tracking control problem for mobile robots via linear control, under the assumption that each agent communicates only with one ‘leader’ robot and with one follower, hence forming a spanning-tree topology. We assume that the communication may be interrupted on intervals of time. As in the classical tracking control problem for non-holonomic systems, the swarm is driven by a fictitious robot which moves about freely and which is a leader to one robot only. Our control approach is decentralised and the control laws are linear with time-varying gains; in particular, this accounts for the case when position measurements may be lost over intervals of time. For both velocity-controlled and force-controlled systems, we establish uniform global exponential stability, hence consensus formation tracking, for the error system under a condition of persistency of excitation on the reference angular velocity of the virtual leader and on the control gains.     

Adaptive control for robot manipulators using multiple parameter models

In this paper, we propose multiple parameter models based adaptive switching control system for robot manipulators. We first uniformly distribute the parameter set into a finite number of smaller compact subsets. Then, distributed candidate controllers are designed for each of these smaller compact subsets. Using Lyapunov inequality, a candidate controller is identified from the finite set of distributed candidate controllers that best estimates the plant at each instant of time. The design reduced the observer-controller gains by reducing modeling errors and uncertainties via identifying an appropriate control/model via choosing largest guaranteed decrease in the value of the Lyapunov function energy function. Compared with CE based CAC design, the proposed design requires smaller observer-controller gains to ensure stability and tracking performance in the presence of large-scale modeling errors and disturbance uncertainties. In contrast with existing adaptive method, multiple model based distributed hybrid design can be used to reduce the energy consumption of the industrial robotic manipulator for large scale industrial automation by reducing actuator input energy. Finally, the proposed hybrid adaptive control design is experimentally tested on a 3-DOF Phantom^TM robot manipulator to demonstrate the theoretical development for real-time applications.

     

Transient performance analysis in robust nonlinear adaptive control

This paper deals with the problem of controlling unknown linear systems in the presence of strictly proper unmodelled dynamics and bounded disturbances. Adaptive controllers that ensure the closed-loop global (uniform) stability and asymptotic performances can be designed following either the backstepping approach or the certainty-equivalence method. The main shortcoming of the involved controllers is that they do not allow quantification of the closed-loop transient behaviour. In this paper, the transient issue is addressed for backstepping adaptive controllers. A L_∞ bound on the tracking error is explicitly given as a function of the design parameters. This shows that the error can be made arbitrarily small by sufficiently increasing the design gains.     

Global positioning of robot manipulators with mixed revolute and prismatic joints

The existing controllers for robot manipulators with uncertain gravitational force can globally stabilize only robot manipulators with revolute joints. The main obstacles to the global stabilization of robot manipulators with mixed revolute and prismatic joints are unboundedness of the inertia matrix and the Jacobian of the gravity vector. In this note, a class of globally stable controllers for robot manipulators with mixed revolute and prismatic joints is proposed. The global asymptotic stabilization is achieved by adding a nonlinear proportional and derivative term to the linear proportional-integral-derivative (PID) controller. By using Lyapunov's direct method, the explicit conditions on the controller parameters to ensure global asymptotic stability are obtained.     

Contact Stability Analysis of a One Degree-of-Freedom Robot

The aim of this note is to examine the conditions of stability of a simple robotic task: we consider a one degree-of-freedom (dof) robot that collides with a spring-like environment with stiffness k, the goal being to stabilize the system in contact with the environment. We study conditions on the feedback gains that guarantee quadratic Lyapunov stability of the task with a well-conditioned solution to the Lyapunov equation. It is shown that when the environment's stiffness k grows unbounded, those conditions yield unbounded values of the gains. Motivated by the stability analysis of the impact Poincaré map in the perfectly rigid case ( ), we propose an analysis that is independent of k. It enables us to conclude on global asymptotic convergence of the system's state towards the equilibrium point. This work can also be seen as the study of stability of a contact (force control) phase, taking into account the unilateral feature of the constraint.     

Nonlinear generalization of scaled ℋ︁∞ control: global robustification against nonlinearly bounded uncertainties

This paper proposes a novel approach to the problem of ??₂ disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state‐dependent scaling adapted to dynamic uncertainties and nonlinear‐gain bounded uncertainties that do not necessarily have finite linear‐gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ??^∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial‐state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state‐dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd.     

Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.     

Joint stick-slip friction compensation of robot manipulators by using smooth robust controllers

In this article, two new smooth robust nonlinear compensators have been developed, respectively, for positional regulation and trajectory tracking of rigid robot manipulators with internal joint stick-slip friction. The proposed controllers can improve not only the positioning accuracy but also the smoothness of motion. No exact knowledge of the friction models is required for the design of the controllers. Furthermore, the tracking controller is also robust with respect to the uncertain link parameters. Using Lyapunov's direct method, we can show that the time-invariant positional regulation controller guarantees the global boundedness stability of the closed-loop system, while the time-varying positional tracking controller guarantees the global asymptotic stability of the closed-loop system. The numerical simulations of the controllers on a two-link robot are presented as illustrations. © 1994 John Wiley & Sons, Inc.     

Finite‐time tracking control of a nonholonomic mobile robot

In this paper, the finite‐time tracking problem is investigated for a nonholonomic wheeled mobile robot in a fifth‐order dynamic model. We consider the whole tracking error system as a cascaded system. Two continuous global finite‐time stabilizing controllers are designed for a second‐order subsystem and a third‐order subsystem respectively. Then finite‐time stability results for cascaded systems are employed to prove that the closed‐loop system satisfies the finite‐time stability. Thus the closed‐loop system can track the reference trajectory in finite‐time when the desired velocities satisfy some conditions. In particular, we discuss the control gains selection for the third‐order finite‐time controller and give sufficient conditions by using Lyapunov and backstepping techniques. Simulation results demonstrate the effectiveness of our method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A tool to analyze robust stability for model predictive controllers

A strategy based on Nonlinear Programming (NLP) sensitivity is developed to establish stability bounds on the plant/model mismatch for a class of optimization-based Model Predictive Control (MPC) algorithms. By extending well-known nominal stability properties for these controllers, we derive a sufficient condition for robust stability of these controllers. This condition can also be used to assess the extent of model mismatch that can be tolerated to guarantee robust stability. In this derivation we deal with MPC controllers with final time constraints or infinite time horizons. Also for this initial study we concentrate only on discrete time systems and unconstrained state feedback control laws with all of the states measured. To illustrate this approach we give two examples: a linear first-order dynamic system and a nonlinear SISO system involving a first order reaction. ©     

Robust Adaptive Control of Robots Using Neural Network: Global Stability

A desired compensation adaptive law‐based neural network (DCAL‐NN) controller is proposed for the robust position control of rigid‐link robots. The NN is used to approximate a highly nonlinear function. The controller can guarantee the global asymptotic stability of tracking errors and boundedness of NN weights. In addition, the NN weights here are tuned on‐line, with no offline learning phase required. When compared with standard adaptive robot controllers, we do not require linearity in the parameters, or lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of rigid robots without any modifications. A comparative simulation study with different robust and adaptive controllers is included.     

New tuning conditions for a class of nonlinear PID global regulators of robot manipulators

Several nonlinear proportional-integral-derivative (PID) controllers for robot manipulators that ensure global asymptotic stability have been proposed in the literature. However, the tuning criteria obtained are expressed in terms of conditions so restrictive that they have avoided, until now, carrying out experimental tests with such controllers. Tuning criteria of some PID controllers for robot manipulators with conditions more relaxed than those presented previously in the literature have been proposed in two recent works by the authors. This was achieved by setting the tuning conditions individually for each joint instead of general conditions for the whole robot. In this paper we extend these results to a class of nonlinear PID global regulators for robot manipulators. The obtained tuning criteria are given in terms of conditions so relaxed that they have allowed to carry out, for the first time, experimental essays with these controllers. Such experiments are presented in this paper using a two-degrees-of-freedom robot manipulator.     

Polynomial family of PD-type controllers for robot manipulators

This paper addresses the problem of position control for robot manipulators. A new polynomial family of PD-type controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the proposed polynomial family. The classical PD controller can be found among this large class of controllers when its proportional gain is a diagonal matrix. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the proposed family of controllers is globally asymptotically stable in agreement with Lyapunov's direct method and LaSalle's invariance principle. Besides the theoretical results, a real-time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD and PID schemes on a three degrees of freedom direct-drive arm.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

全局稳定的PD+前馈机器人鲁棒自适应控制

研究应用PD+前馈控制结构的不确定性机器人轨迹跟踪问题.在忽略摩擦力和外部扰动情况下,设计了一大类综合的自适应控制策略,能保证系统全局的渐近稳定;在摩擦力和外部扰动存在时,提出两种新颖的鲁棒自适应混合控制方法,不仅可以保证闭环系统的全局稳定性,同时还能给出系统清晰的暂态性能.严格的理论证明和二自由度机器人的仿真验证了控制器的有效性.     

Finite-time H∞ control of periodic piecewise linear systems

In this paper, the finite-time stability, stabilisation, L₂-gain and H_∞ control problems for a class of continuous-time periodic piecewise linear systems are addressed. By employing a time-varying control scheme in which the time interval of each subsystem constitutes a number of basic time segments, the finite-time controllers can be developed with periodically time-varying control gains. Based on a piecewise time-varying Lyapunov-like function, a sufficient condition of finite-time stability and the relevant time-varying controller are proposed. Considering the finite-time boundedness of the closed-loop periodic system, the L₂-gain criterion with continuous time-varying Lyapunov-like matrix function is studied. A finite-time H_∞ controller is proposed based on the L₂-gain analysis. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed criteria.     

Stable computed-torque control of robot manipulators via fuzzyself-tuning

Computed-torque control is a well-known motion control strategy for manipulators which ensures global asymptotic stability for fixed symmetric positive definite (proportional and derivative) gain matrices. In this paper, we show that global asymptotic stability also holds for a class of gain matrices depending on the manipulator state. This feature increases the potential of the computed-torque control scheme to handle practical constraint in actual robots such as presence of friction in the joints and actuators with limited torque capabilities. We illustrate this potential by means of a fuzzy self-tuning algorithm to select the proportional and derivative gains according to the actual tracking position error. Experiments on a two degrees of freedom robot arm show the usefulness of the proposed approach.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

Output feedback hierarchical control for nonlinear systems

In this paper, we address the problem of hierarchical control for nonlinear systems and design two dynamic output feedback hierarchical control laws in a semiglobal sense and in a global sense, respectively. With the controllers applied to a class of nonlinear systems, some transient and steady properties of the system output trajectories can be satisfied simultaneously. Furthermore, the corresponding result in the global sense for linear systems is naturally derived. Finally, the effectiveness of our approach is illustrated by a single‐link robot arm system. Copyright © 2017 John Wiley & Sons, Ltd.     

Global positioning of robot manipulators via PD control plus aclass of nonlinear integral actions

Deals with the position control of robot manipulators. Proposed is a simple class of robot regulators consisting of a linear proportional-derivative (PD) feedback plus an integral action of a nonlinear function of position errors. By using Lyapunov's direct method and LaSalle's invariance principle, the authors characterize a class of such nonlinear functions, and they provide explicit conditions on the regulator gains to ensure global asymptotic stability. These regulators offer an attractive alternative to global regulation compared with the well-known partially model-based PD control with gravity compensation and PD control with desired gravity compensation