Nonholonomic Mobile Manipulators: Kinematics, Velocities and Redundancies

We consider nonholonomic mobile manipulators built from an n _a joint robotic arm and a nonholonomic mobile platform with two independently driven wheels. Actually, there is no efficient kinematic formalism for these systems which are generally characterized by their high number of actuators. So, kinematic modelling is presented with particular emphasis on redundancy. Whereas kinematic redundancy is well known in the holonomic case, it is pointed out that it is necessary to define velocity redundancy in the case of nonholonomic systems. Reduced velocity kinematics based on quasi-velocities are shown to provide an efficient formalism. Two examples of mobile manipulators are presented. Finally, reduced velocity kinematics and velocity redundancy are shown to be adequate tools in order to realize operational task while optimizing criteria such as manipulability.     

Further results on adaptive iterative learning control of robot manipulators

Based on a combination of a PD controller and a switching type two-parameter compensation force, an iterative learning controller with a projection-free adaptive algorithm is presented in this paper for repetitive control of uncertain robot manipulators. The adaptive iterative learning controller is designed without any a priori knowledge of robot parameters under certain properties on the dynamics of robot manipulators with revolute joints only. This new adaptive algorithm uses a combined time-domain and iteration-domain adaptation law allowing to guarantee the boundedness of the tracking error and the control input, in the sense of the infinity norm, as well as the convergence of the tracking error to zero, without any a priori knowledge of robot parameters. Simulation results are provided to illustrate the effectiveness of the learning controller.     

Virtual joint method for kinematic modeling of wheeled mobile manipulators

In this paper, we propose a virtual joint method that better utilizes quasi-velocities for the kinematic modeling of wheeled mobile manipulators. By identifying quasi-velocities as motions of imaginary revolute and prismatic kinematic pairs, our method enables one to regard a mobile manipulator as an ordinary articulated manipulator for the purposes of velocity analysis. We also propose an inverse kinematic scheme for the mobile manipulators along the line with the virtual joint based kinematic framework. Details are worked out for mobile manipulators with representative differential-drive and car-like mobile platforms.     

Design and experimental validation of a second-order sliding-mode motion controller for robot manipulators

This article presents an original motion control strategy for robot manipulators based on the coupling of the inverse dynamics method with the so-called second-order sliding mode control approach. Using this method, in principle, all the coupling non-linearities in the dynamical model of the manipulator are compensated, transforming the multi-input non-linear system into a linear and decoupled one. Actually, since the inverse dynamics relies on an identified model, some residual uncertain terms remain and perturb the linear and decoupled system. This motivates the use of a robust control design approach to complete the control scheme. In this article the sliding mode control methodology is adopted. Sliding mode control has many appreciable features, such as design simplicity and robustness versus a wide class of uncertainties and disturbances. Yet conventional sliding mode control seems inappropriate to be applied in robotics since it can generate the so-called chattering effect, which can be destructive for the controlled robot. In this article, this problem is suitably circumvented by designing a second-order sliding mode controller capable of generating a continuous control law making the proposed sliding mode controller actually applicable to industrial robots. To build the inverse dynamics part of the proposed controller, a suitable dynamical model of the system has been formulated, and its parameters have been accurately identified relying on a practical MIMO identification procedure recently devised. The proposed inverse dynamics-based second-order sliding mode controller has been experimentally tested on a COMAU SMART3-S2 industrial manipulator, demonstrating the tracking properties and the good performances of the controlled system.     

An observer-based set-point controller for robot manipulators with flexible joints

We present a globally asymptotically stable controller for point-to-point regulation of robot manipulators with flexible joints that uses only position measurement on the motor side. Existing asymptotically stable schemes for the set point regulation problem without velocity measurement address only the rigid robot case. Furthermore, these solutions ensure only local stability provided some bounds on the dynamic part of the robot model are known. Also, they require the injection of high gains into the loop to enlarge the equilibrium domain of attraction. In contrast, our solution is global, applies for robots with flexible joints and assumes only that the gravity forces are known. The underlying rationale of the design is to ‘shape’ the potential energy of the closed loop system so that it has an absolute minimum at the desired equilibrium, and add the required dampingto achieve asymptotic stability. This is attained by adding a (linear) observer that converges to the position required to compensate the gravity forces and injects the damping, and a ‘spring-like’ effect between the observer and the robot that ‘pulls’ the robot to the desired target. This approach to observer-based controller design differs from the classical certainly equivalent approach and effectively exploits the dynamic properties of the physical system.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

Learning Control of Robot Manipulators in Task Space

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end‐effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which “learns” the overall uncertainties in the robot manipulator dynamics. The stability of the closed‐loop system and asymptotic end‐effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in‐house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.     

Sliding Mode Adaptive Neural-Network Control for Nonholonomic Mobile Modular Manipulators

A general mobile modular manipulator can be defined as a m-wheeled holonomic/nonholonomic mobile platform combining with a n-degree of freedom modular manipulator. This paper presents a sliding mode adaptive neural-network controller for trajectory following of nonholonomic mobile modular manipulators in task space. Dynamic model for the entire mobile modular manipulator is established in consideration of nonholonomic constraints and the interactive motions between the mobile platform and the onboard modular manipulator. Multilayered perceptrons (MLP) are used as estimators to approximate the dynamic model of the mobile modular manipulator. Sliding mode control and direct adaptive technique are combined together to suppress bounded disturbances and modeling errors caused by parameter uncertainties. Simulations are performed to demonstrate that the dynamic modeling method is valid and the controller design algorithm is effective.     

An LMI approach to vibration control of base-isolated building structures with delayed measurements

In this article, we address a convex optimisation approach to the problem of state-feedback H _∞ control design for vibration reduction of base-isolated building structures with delayed measurements, where the delays are time-varying and bounded. An appropriate Lyapunov–Krasovskii functional and some free-weighting matrices are utilised to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities. The controller, which guarantees asymptotic stability and an H _∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.     

Predictive end-point trajectory control of elastic manipulators

This article presents an approach to end-point trajectory control of elastic manipulators based on the nonlinear predictive control theory. Although this approach is applicable to manipulators of general configuration, only planar flexible multi-link manipulators are considered. A predictive control law is derived by minimizing a quadratic function of the trajectory error of the end-points of each link, elastic modes, and control torques. This approach avoids the instability of the zero dynamics encountered in the controller design using feedback linearization and variable structure control techniques for end-point control. Furthermore, the derived predictive controller is robust to uncertainty in the system parameters. Simulation results are presented for a one-link flexible manipulator to show that in the closed-loop system accurate end-point trajectory control and vibration damping can be accomplished. © 1996 John Wiley & Sons, Inc.     

Finite‐time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite‐time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite‐time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite‐time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite‐time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite‐time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

Energy-efficient and high-precision control of hydraulic robots

In addition to high-precision closed-loop control performance, energy efficiency is another vital characteristic in field-robotic hydraulic systems as energy source(s) must be carried on board in limited space. This study proposes an energy-efficient and high-precision closed-loop controller for the highly nonlinear hydraulic robotic manipulators. The proposed method is twofold: 1) A possibility for energy consumption reduction is realized by using a separate meter-in separate meter-out (SMISMO) control set-up, enabling an independent metering (pressure control) of each chamber in hydraulic actuators. 2) A novel subsystem-dynamics-based and modular controller is designed for the system actuators, and it is integrated to the previously designed state-of-the-art controller for multiple degrees-of-freedom (n-DOF) manipulators. Stability of the overall controller is rigorously proven. The comparative experiments with a three-DOF redundant hydraulic robotic manipulator (with a payload of 475 kg) demonstrate that: 1) It is possible to design the triple objective of high-precision piston position, piston force and chamber pressure trackings for the hydraulic actuators. 2) In relation to the previous SMISMO-control methods, unprecedented motion and chamber pressure tracking performances are reported. 3) In comparison to the state-of-the-art motion tracking controller with a conventional energy-inefficient servovalve control, the actuators’ energy consumption is reduced by 45% without noticeable motion control (position-tracking) deterioration.     

多机械臂协调控制研究综述

多机械臂系统的协调控制是当今机器人领域的研究热点.针对机器人基坐标系标定,协调系统动力学建模,控制器综合方法等问题,介绍近年来多机械臂系统在协调控制上研究工作的进展,主要从系统的动力学模型建立方式和协调运动的控制综合方式两个方面进行深入介绍.全面系统地介绍多机械臂系统协调控制问题的研究现状与发展方向,并指明未来工作的研究方向.     

Posture measure and control for robot compliance tasks

Various measures have been proposed for evaluating the compatibility of manipulator postures with respect to task requirements from kinematic and dynamic standpoints. In most previous studies, the measures were used to determine optimal postures for manipulators in advance, and their effects on system performance were generally examined statically. When posture measures are applied to controlled dynamic systems, however, their effects are usually not evident, because deficiencies (merits) caused by bad (good) postures can be compensated for by the controller. On the other hand, postures determined according to proper measures can still alleviate the controller's load and be helpful in control strategy realization. In this paper, we propose that planned compliant motion trajectories should be accompanied by proper postures for compliance tasks. Thus, we analyze manipulator dynamic behavior by using postures specified according to various measures. And, because different postures are used in different phases of the compliance task, a posture selection and control scheme is also proposed to govern the sequence of postures selected according to task requirements and environments. Redundant robot manipulators were used for investigation because of their better manipulability. Simulations that demonstrate the effectiveness of the proposed scheme are described. © 1998 John Wiley & Sons, Inc.     

Noncertainty equivalent adaptive control of robot manipulators without velocity measurements

This paper presents a noncertainty equivalent adaptive motion control scheme for robot manipulators in the absence of link velocity measurements. A new output feedback adaptation algorithm, based on the attractive manifold design approach, is developed. A proportional-integral adaptation is selected for the adaptive parameter estimator to strengthen the passivity of the system. In order to relieve velocity measurements, an observer is designed to estimate the velocities. The controller guarantees semiglobal asymptotic motion tracking and velocity estimation, as well as L_∞ and L₂ bounded parameter estimation error. The effectiveness of the proposed controller is verified by simulations for a two-link robot manipulator and a four-bar linkage. The results are further compared with the earlier certainty-equivalent adaptive partial and full state feedback controller to highlight potential closed-loop performance improvements.     

Output tracking control for networked control systems with time delay and packet dropout

This article studies the problems of H _∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By using linear matrix inequality (LMI)-based method, H _∞ output tracking performance analysis and controller design are presented for NCSs with constant sampling period. For NCSs with time-varying sampling period, a multi-objective optimisation methodology in terms of LMIs is used to deal with H _∞ output tracking performance analysis and controller design. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The simulation results illustrate the effectiveness of the proposed H _∞ output tracking controller design.     

Robustness improvement of a nonlinear H∞ controller for robot manipulators via saturation functions

In this paper, previous works on nonlinear H_∞ control for robot manipulators are extended. In particular, integral terms are considered to cope with persistent disturbances, such as constant load at the end‐effector. The extended controller may be understood as a computed‐torque control with an external PID, whose gain matrices vary with the position and velocity of the robot joints. In addition, in order to increase the controller robustness, an extension of the algorithms with saturation functions has been carried out. This extension deals with the resulting nonlinear equation of the closed‐loop error. A modified expression for the required increment in the control signal is provided, and the local closed‐loop stability of this approach is discussed. Finally, simulation results for a two‐link robot and experimental results for an industrial robot are presented. The results obtained with this technique have been compared with those attained with the original controllers to show the improvements achieved by means of the proposed method. © 2005 Wiley Periodicals, Inc.     

Decentralized stabilization of Markovian jump interconnected systems with unknown interconnections and measurement errors

This paper investigates the decentralized output feedback control problem for Markovian jump interconnected systems with unknown interconnections and measurement errors. Different from some existing results, the global operation modes of all subsystems are not required to be completely accessible for the decentralized control system. A decentralized dynamic output feedback controller is constructed using neighboring mode information and local outputs, where the measurement errors between actual and measured outputs are considered. Subsequently, a new design method is developed such that the resultant closed‐loop system is stochastically stable and satisfying an L_∞‐norm constraint. Sufficient conditions are formulated by linear matrix inequalities, and the controller gains are characterized in terms of the solution of a convex optimization problem. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

Passivity based adaptive Jacobian tracking for free-floating space manipulators without using spacecraft acceleration

Most research so far on trajectory tracking of free-floating space manipulators has assumed that the kinematics of the space manipulator is exactly known. However, when a space manipulator picks up different tools of unknown lengths or unknown gripping points, its kinematics and dynamics change and are difficult to derive exactly. Thus, in this paper, we have proposed a passivity based adaptive Jacobian controller for free-floating space manipulators. The proposed controller consists of a transposed Jacobian feedback and a dynamic compensation term, and the parameter adaptation laws are derived by Lyapunov-like stability analysis tools. It is shown that the end-effector motion tracking errors converge asymptotically. To avoid using spacecraft acceleration, we define a new reference velocity, which is called spacecraft reference velocity. In addition, we have also conducted passivity interpretation of the proposed controller to obtain some physical insight into its properties. Simulation results are presented to show the performance of the proposed controller.