An adaptive sliding mode backstepping control for the mobile manipulator with nonholonomic constraints

To solve disturbances, nonlinearity, nonholonomic constraints and dynamic coupling between the platform and its mounted robot manipulator, an adaptive sliding mode controller based on the backstepping method applied to the robust trajectory tracking of the wheeled mobile manipulator is described in this article. The control algorithm rests on adopting the backstepping method to improve the global ultimate asymptotic stability and applying the sliding mode control to obtain high response and invariability to uncertainties. According to the Lyapunov stability criterion, the wheeled mobile manipulator is divided into several stabilizing subsystems, and an adaptive law is designed to estimate the general nondeterminacy, which make the controller be capable to drive the trajectory tracking error of the mobile manipulator to converge to zero even in the presence of perturbations and mathematical model errors. We compare our controller with the robust neural network based algorithm in nonholonomic constraints and uncertainties, and simulation results prove the effectivity and feasibility of the proposed method in the trajectory tracking of the wheeled mobile manipulator.     

Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

In this paper, the developed model of an N-flexible-link mobile manipulator with revolute-prismatic joints is presented for the cooperative flexible multi mobile manipulator. In this model, the deformation of flexible links is calculated by using the assumed modes method. In additions, non-holonomic constraints of the robots’ mobile platforms that bound its locomotion are considered. This limitation is alleviated through the concurrent motion of revolute and prismatic joints, although it results in computational complexity and changes the final motion equations to time-varying form. Not only is the proposed dynamic model implemented for the multi-mobile manipulators with arms having independent motion, but also for multi-mobile manipulators in cooperation after defining gripper's kinematic constraints. These constraints are imported to the dynamic equations by defining Lagrange multipliers. The recursive Gibbs–Appell formulation is preferred over other similar approaches owing to the capability of solving the equations without the need to use Lagrange multipliers for eliminating non-holonomic constraints in addition to the novel optimized process of obtaining system equations. Hence, cumbersome simultaneous computations for eliminating the constraints of platform and arms are circumvented. Therefore, this formulation is improved for the first time by importing Lagrange multipliers for solving kinematic constrained systems. In the simulation section, the results of forward dynamics solution for two flexible single-arm manipulators with revolute-prismatic joints while carrying a rigid object are presented. Inverse dynamics equations of the system are also presented to obtain the maximum dynamic load-carrying capacity of the two-rigid-link mobile manipulators on a predefined path. Two constraints, namely the capacity of joint motors torque and robot motion stability are considered as the limitation criteria. The concluded motion equations are used to accurately control the movement of sensitive bodies, which is not achievable through the use of one platform.     

Computed torque control of an under-actuated service robot platform modeled by natural coordinates

The paper investigates the motion planning of a suspended service robot platform equipped with ducted fan actuators. The platform consists of an RRT robot and a cable suspended swinging actuator that form a subsequent parallel kinematic chain and it is equipped with ducted fan actuators. In spite of the complementary ducted fan actuators, the system is under-actuated. The method of computed torques is applied to control the motion of the robot.The under-actuated systems have less control inputs than degrees of freedom. We assume that the investigated under-actuated system has desired outputs of the same number as inputs. In spite of the fact that the inverse dynamical calculation leads to the solution of a system of differential–algebraic equations (DAE), the desired control inputs can be determined uniquely by the method of computed torques.We use natural (Cartesian) coordinates to describe the configuration of the robot, while a set of algebraic equations represents the geometric constraints. In this modeling approach the mathematical model of the dynamical system itself is also a DAE.The paper discusses the inverse dynamics problem of the complex hybrid robotic system. The results include the desired actuator forces as well as the nominal coordinates corresponding to the desired motion of the carried payload. The method of computed torque control with a PD controller is applied to under-actuated systems described by natural coordinates, while the inverse dynamics is solved via the backward Euler discretization of the DAE system for which a general formalism is proposed. The results are compared with the closed form results obtained by simplified models of the system. Numerical simulation and experiments demonstrate the applicability of the presented concepts.     

Mathematical modeling and computer simulation of a robotic rat pup

In this paper, we describe the mathematics and computer implementation of a robotic rat pup simulation. Our goal is to understand neurobehavioral principles in a mammalian model organism—the Norway rat pup (Rattus norvegicus). Our approach is unique in that animal, simulation, and robot studies occur in parallel and inform each other. Behavior is dependent on the nervous system, body morphology, physiology, environment, and the interactions among these elements. Autonomous robotics hardware models and their associated simulations allow the possibility of systematically manipulating variables in each of these elements in ways that would be impossible using live animals. Specifically, we describe the development and validation of a Newtonian-dynamics-based simulation of a robotic rat pup, including mathematical formulation and computer implementation. The computer simulation consists of three distinct components that interact to simulate robotic behavior: (1) dynamics of the robotic rat pup itself, including sensors and actuators, (2) environmental coupling dynamics of the robot arena with the robotic rat pup, and (3) the robot control algorithms as implemented on the physical robot. The mathematical formulation, software implementation, model identification, model validation, and an application example are all described.     

Sequentially switched fuzzy-model-based control for wheeled mobile robot with visual odometry

This study focused on the Takagi–Sugeno (T–S) fuzzy-model-based control design for the differentially-driven wheeled mobile robot with visual odometry. The position and posture of the mobile robot are estimated by visual odometry. The polar kinematic model of the mobile robot is exactly converted to the T–S fuzzy model and then the fuzzy control design is synthesized to the fuzzy model. The sequentially switched fuzzy control design includes turning, forward motion as well as position and posture control modes. The stabilization is guaranteed based on the Lyapunov stability criterion. The practical constraints on the visual odometry are also satisfied in the control design. Finally, the experiment results demonstrate the effectiveness of the fuzzy-model-based control design for the mobile robot with visual odometry.     

Full forward kinematics of redundant kinematic hybrid manipulator

A unified recursive mathematic model is established for full forward kinematics analysis of various redundant kinematic hybrid manipulators which are formed by several different parallel manipulators connected in series. In the established model, the relationships between the general input velocity/acceleration and the general output velocity/acceleration are discovered. The Jacobian matrices for mapping the general output velocities to the general input velocity and the Hessian matrices for mapping the general output velocities to the general input acceleration are derived. The unified iteration recursive formulae are derived for solving the general output velocity/acceleration of the end moving platform of the redundant kinematic hybrid manipulator by only giving the general input velocity/acceleration of every parallel manipulator. A 3D model of a novel (4SPS + SPR )+ (4SPS/SP) + 3SPR type hybrid manipulator is constructed and its full forward velocity/acceleration formulae are derived from the established unified recursive mathematic model and are proved to be correct by utilizing a simulation solution of the novel redundant kinematic hybrid manipulator.     

Modelling,simulation and control of a redundant parallel robotic manipulator based on invariant manifolds

In this article a systematic approach of modelling and control for a parallel robotic manipulator is presented. Regarding the framework of structured analysis of dynamical systems the derivation of a differential-algebraic model of the mechanical system is straightforward. Using some differential-geometric considerations based on invariant manifolds and the definition of fictitious additional input and output variables a suitable state feedback can be constructed which transforms the differential-algebraic representation into a state-space model for the robotic manipulator. On this basis a classical two-degree-of-freedom (2-DOF) control structure has been designed using the well-known input–output linearization and a linear time-variant Kalman filter-based output feedback. Finally, the control structure including a friction compensation is applied to the robotic system in the laboratory which shows the practical applicability of the proposed procedure.     

Modelling of closed-chain manipulators on an excavator vehicle

The main focus of this paper is to develop a physics-based model for a closed-chain manipulator in an excavator vehicle. The derivation of closed-chain manipulator dynamic equations with a structure similar to open-chain manipulator equations is an important research problem, particularly with reference to controller design. In this paper, an approach for deriving closed-chain manipulator equations with an open-chain structure, based on trigonometric t-formulae, is presented. Holonomic loop closure constraints are employed in order to derive the closed-chain mechanism dynamics from the reduced system dynamics. The closed-chain equations, with a structure similar to serial link equations, are presented. The model incorporates the dynamic properties of the manipulator and bucket. The dynamic model for the excavation system is validated against measured data obtained from a full-scale closed-chain excavator vehicle. A dynamic model is important for the design of control strategies for trajectory tracking, a key requirement for automating the excavation task. It is noted that even though the results presented in this paper are focused on a particular excavator vehicle, the research is generic and can be adapted to any closed-chain manipulator.     

Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints

This paper is concerned with mathematical modeling and optimal motion designing of flexible mobile manipulators. The system is composed of a multiple flexible links and flexible revolute joints manipulator mounted on a mobile platform. First, analyzing on kinematics and dynamics of the model is carried out then; open-loop optimal control approach is presented for optimal motion designing of the system. The problem is known to be complex since combined motion of the base and manipulator, non-holonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of the flexible nature of both links and joints are taken into account. In the proposed method, the generalized coordinates and additional kinematic constraints are selected in such a way that the base motion coordination along the predefined path is guaranteed while the optimal motion trajectory of the end-effector is generated. This method by using Pontryagin’s minimum principle and deriving the optimality conditions converts the optimal control problem into a two point boundary value problem. A comparative assessment of the dynamic model is validated through computer simulations, and then additional simulations are done for trajectory planning of a two-link flexible mobile manipulator to demonstrate effectiveness and capability of the proposed approach.     

Stabilization of the motion of a spherical robot using feedbacks

The paper is concerned with the problem of stabilizing a spherical robot of combined type during its motion. The focus is on the application of feedback for stabilization of the robot which is an example of an underactuated system. The robot is set in motion by an internal wheeled platform with a rotor placed inside the sphere. The results of experimental investigations for a prototype of the spherical robot are presented.     

Kinematic and dynamic analysis of the Gantry-Tau,a 3-DoF translational parallel manipulator

This paper deals with the mathematical modeling of kinematics and dynamics of the 3-degrees-of-freedom Gantry-Tau manipulator. Compared to many other parallel robots, Gantry-Tau offers a large accessible workspace and high stiffness. The kinematics of Gantry-Tau is presented which includes inverse kinematics formulation for the position, velocity and acceleration of the mechanism. Also, based on the obtained Jacobin matrices, singular configurations of the robot are studied. Afterwards, the equations of the inverse dynamic model of the Gantry-Tau are obtained through two different methods, i.e., virtual work and Newton–Euler. Finally, a case study is performed to verify the correctness of the derived models and investigate their computational efficiency.     

Algoritmo compensador neuronal discreto de dinámica en robots móviles usando filtro de Kalman extendido

This paper presents the design of an algorithm based on neural networks in discrete time for its application in mobile robots. In addition, the system stability is analyzed and an evaluation of the experimental results is shown.The mobile robot has two controllers, one addressed for the kinematics and the other one designed for the dynamics. Both controllers are based on the feedback linearization. The controller of the dynamics only has information of the nominal dynamics (parameters). The neural algorithm of compensation adapts its behaviour to reduce the perturbations caused by the variations in the dynamics and the model uncertainties. Thus, the differences in the dynamics between the nominal model and the real one are learned by a neural network RBF (radial basis functions) where the output weights are set using the extended Kalman filter. The neural compensation algorithm is efficient, since the consumed processing time is lower than the one required to learning the totality of the dynamics. In addition, the proposed algorithm is robust with respect to failures of the dynamic controller. In this work, a stability analysis of the adaptable neural algorithm is shown and it is demonstrated that the control errors are bounded depending on the error of approximation of the neural network RBF. Finally, the results of experiments performed by using a mobile robot are shown to test the viability in practice and the performance for the control of robots.     

Stability of steady motions of a mobile robot with roller-carrying wheels and a displaced centre of mass

The motion of a mobile three-wheel robotic vehicle on a horizontal surface is investigated. Passive rollers are fastened along the rim of each wheel, enabling each wheel not only to roll in the usual manner, but also to move perpendicular to its plane. Each of these wheels, as well as the ordinary wheels, is equipped with one drive, which rotates the wheel about its axis. The vehicle equipped with roller-carrying wheels can move in any direction with any orientation. The motion of the robot on a horizontal surface is studied in the case where the centre of mass of the robot deviates from the geometric centre of the triangular platform, and there is no slip at the points of contact of the rollers with the supporting surface. In the case of free motion of the robot, an additional first integral is pointed out and the exact solution found is analysed. An equation for specifying steady motions, under which a constant voltage is supplied to the DC motors that drive the wheels, is constructed. The stability of the rectilinear motion of the robot is investigated.     

Motion control of mobile wheeled robots

A vector-matrix formalism of nonholonomic mechanics is set up, which is used to construct mathematical models of mobile wheeled robots. The properties of free (ballistic) motions of mobile robots, which can be the basis of natural motion control modes, are studied. The analysis of uncontrollable motions is carried out, taking transients in circuits of the electric drive into consideration. The problem of determining voltages supplied to drives of the robot that ensure implementation of program motions is discussed. One candidate solution of a problem of planning a pathway of the robot in an ordered medium is presented. A mobile single-wheeled robot with a gyroscopic stabilization system is described—the “Gyrowheel” robot, capable of moving autonomously along a straight-line (rectilinear motion), as well as along a curvilinear pathway. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 29–80, 2005.     

基于冗余任务的轮式机器人巡检方法

针对配电室电力设备智能化巡检工作中,存在巡检方式单一等问题,基于轮式巡检机器人结构及系统、路径优化和通信等关键技术,研究了一种基于冗余任务的轮式机器人巡检方法.针对目前配电室巡检环境和轮式巡检机器人结构及系统特性,建立配电室巡检过程模型.分析顺序巡检方法的速度、位姿和节点关系,建立机器人巡检过程的路程-时间模型和奖惩模型,根据能耗约束得到目标函数.最后,通过设计方法实验流程图,依次分析顺序巡检、任务巡检和冗余任务巡检的效益值.实验结果表明,冗余任务巡检方式在保证单位时间和单位行程能耗比率不变的前提下,降低了控制系统能耗,有效提高了人机交互的巡检效益,且更好地兼容远程监测人员经验与机器人巡检优势,为智能化巡检技术的研究和推广提供了思路和方法.     

Spatial impedance control of two cooperative industrial manipulators

Nowadays robotic manipulators are considered to perform a wide range of tasks. Since robotic systems consisting of multiple manipulators are capable of handling a variety of tasks that cannot be executed by single manipulators, cooperation of multiple manipulators is becoming increasingly interesting in particular for industrial applications. The interaction with other manipulators, respectively the environment, requires an extension of the conventional position control in order to achieve a desired compliance, and thus to limit the interaction wrench so to avoid damaging the involved objects. In this contribution the cooperation of two industrial manipulators, a Stäubli RX130L (6-DOF) and a Stäubli TX90L mounted on a linear axis (constituting a redundant 7-DOF manipulator), is addressed applying an impedance control scheme. The manipulation task is to grasp an object with both manipulators and to follow a prescribed trajectory by simultaneously limiting the contact forces between the manipulators and the object and ensuring a compliant behavior towards the environment. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the mobile platform motion optimal control at energy performance index

The paper presents a method of optimal control of the mobile robot on example of the 2-wheel mobile platform. The robot investigated has non-holonomic constraints. Mathematical model of 2-wheel mobile platform is characterized by finite number of nonlinear differential equations. The presented method of control is minimizing velocity and position errors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Geometric Approach to Actuator Failure in Robotic Manipulators

The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effect that passive joints have on the mobility of the mechanism. Then, if the mobility, considering passive joints only, is not zero we find a condition for which the parallel manipulator is conditionally equilibrated with respect to a specific external force. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

递推牛顿——欧拉动力学算法的推广及其应用

将固定底座的串联机器人的递推牛顿——欧拉动力学算法推广到运动底座 ,给出了不考虑连杆重力和考虑连杆重力两种情况下的递推牛顿——欧拉动力学算法 .然后用数学方法证明了后一种情况下的递推牛顿——欧拉动力学算法是由前一种情况下的递推牛顿——欧拉动力学算法通过改动初始值得到的 .这种通过改动初始值而得到的算法具有较好的计算效率 ,将此算法应用到由清华大学设计的一种新型混联机床的动力学分析上 .