Analysis and Verification of Repetitive Motion Planning and Feedback Control for Omnidirectional Mobile Manipulator Robotic Systems

Mobile manipulator robotic systems (MMRSs) composed of a manipulator and a mobile platform are investigated in this paper. In order for the mobile manipulator robotic system (MMRS) to return to its initial state when the manipulator’s end-effector is requested to execute cyclical tasks, a quadratic program (QP) based repetitive motion planning and feedback control (RMPFC) scheme is proposed and analyzed. Such an RMPFC scheme can not only mix motion planning and reactive control, but also consider the physical limits of the robotic system. Mathematically, the efficacy of the RMPFC scheme is verified via gradient dynamics analysis. To further demonstrate the effectiveness of the RMPFC scheme, a kinematically redundant MMRS composed of a three degrees-of-freedom (DOF) planar manipulator and an omnidirectional mobile platform is designed, modeled and analyzed. Then, repetitive motion planning and feedback control for the designed omnidirectional MMRS is studied. Besides, a numerical algorithm is developed and presented to solve the QP and resolve the redundancy of the robotic system. Moreover, computer simulations are comparatively performed on such an omnidirectional MMRS, and simulation results substantiate the effectiveness, accuracy and superiority of the proposed RMPFC scheme.     

冗余机器人系统的自运动控制

研究冗余机器人系统的自运动控制问题，给出一种非连续切换控制算法。该算法可以在保持机器人手端任务向量不变的情况下，使关节构形收敛到期望位置。与以往的算法相比，所提出的算法可以跳出局部最小点，并使关节收敛到期望构形。对三杆平面机器人系统进行的计算机仿真证实了算法的有效性。     

A closed-loop jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists

The solution of the inverse kinematic problem is of the utmost importance in robotic manipulator control. This article proposes a closed-loop scheme for solving the inverse kinematic problem for nonredundant and redundant wrists based on the computation of the Jacobian transpose. The manipulability measure is suitably introduced as a constraint for redundant wrists, by taking advantage of the null space of the Jacobian matrix. The resulting algorithm provides a computational tool to solve a specified orientation trajectory into a joint trajectory. Numerical results with two spherical wrists show the excellent performance of the scheme.     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

考虑驱动系统动态的机械手神经网络控制及应用

针对结构和参数均未知的机械手控制问题, 提出了考虑驱动系统动态的机械手神经网络控制方法, 采用稳定的径向基(Radial basis function, RBF)神经网络辨识机械手未知动态, 而附加的鲁棒控制可以保证存在神经网络的建模误差和外部干扰时系统的稳定性和性能, 并且该方法使机械手闭环系统一致最终有界. 同时开发了基于半实物仿真技术的机械手控制系统, 最后, 将本文方法与经典的PD控制器和自适应控制器在同一机械手平台上进行了实验验证与分析, 实验结果表明该方法具有良好的控制性能.     

Lane-keeping assistance control algorithm using differential braking to prevent unintended lane departures

This paper describes a hierarchical lane keeping assistance control algorithm for a vehicle. The proposed control strategy consists of a supervisor, an upper-level controller and a lower-level controller. The supervisor determines whether lane departure is intended or not, and whether the proposed algorithm is activated or not. To detect driver′s lane change intention, the steering behavior index has been developed incorporating vehicle speed and road curvature. To validate the detection performance on the lane change intention, full-scale simulator tests on a virtual test track (VTT) are conducted under various driving situations. The upper-level controller is designed to compute the desired yaw rate for the lane departure prevention, and for the guidance with ride comfort. The lower-level controller is designed to compute the desired yaw moment in order to track the desired yaw rate, and to distribute it into each tire′s braking force in order to track the desired yaw moment. The control allocation method is adopted to distribute braking forces under the actuator’s control input limitation. The proposed lane keeping assistance control algorithm is evaluated with human driver model-in-the-loop simulation and experiments on a real vehicle.     

An Adaptive Regulator of Robotic Manipulators in the Task Space

This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.     

Robust Interaction Control of a Mobile Manipulator – Dynamic Model Based Coordination

This paper discusses the modeling and control of a spatial mobile manipulator which consists of a robotic manipulator mounted upon a wheeled mobile platform. The nonholonomic model, which assumes perfect contact between the wheels and the ground, is obtained using the Lagrange–d'Alembert formulation. Also, the dynamic model, which considers slip of the platform's tires, is developed using the Newton–Euler method and incorporates Dugoff's tire friction model. The complexity of the model is increased by introducing kinematic redundancy which is created when a multi-linked manipulator is used. The kinematic redundancy is resolved by decomposing the mobile manipulator into two subsystems; the mobile platform and the manipulator. Based on the coordination scheme used to resolve the kinematic redundancy, a robust interaction control algorithm, in which suitable controllers are designed for the two subsystems, is developed and applied. The adverse effect of the wheel slip on the tracking of commanded motion is discussed in the simulation. For the dynamic model, a robust control approach is employed to minimize the harmful effect of the wheel slip on the tracking performance. Simulation results show the promise of the developed algorithm.     

Aerial cooperative transporting and assembling control using multiple quadrotor–manipulator systems

In this paper, a fully distributed control scheme for aerial cooperative transporting and assembling is proposed using multiple quadrotor–manipulator systems with each quadrotor equipped with a robotic manipulator. First, the kinematic and dynamic models of a quadrotor with multi-Degree of Freedom (DOF) robotic manipulator are established together using Euler–Lagrange equations. Based on the aggregated dynamic model, the control scheme consisting of position controller, attitude controller and manipulator controller is presented. Regarding cooperative transporting and assembling, multiple quadrotor–manipulator systems should be able to form a desired formation without collision among quadrotors from any initial position. The desired formation is achieved by the distributed position controller and attitude controller, while the collision avoidance is guaranteed by an artificial potential function method. Then, the transporting and assembling tasks request the manipulators to reach the desired angles cooperatively, which is achieved by the distributed manipulator controller. The overall stability of the closed-loop system is proven by a Lyapunov method and Matrosov's theorem. In the end, the proposed control scheme is simplified for the real application and then validated by two formation flying missions of four quadrotors with 2-DOF manipulators.     

基于QR分解的冗余度机械臂雅可比矩阵求逆方法

针对冗余度机械臂在轨操作实时性的需求,提出一种基于QR分解的冗余度机械臂雅克比矩阵求逆方法。根据具体的冗余度机械臂的构型特点,将运动学逆解过程划分为多个模块,采用修正施密特QR分解方法计算机械臂雅可比矩阵的伪逆,利用硬件描述语言在FPGA上对各个模块进行了实现。以机械臂直线运动为例,通过仿真实验与利用Matlab解算的方法进行了对比,并研究了定点数长度对硬件资源和误差的影响。实验结果验证了所提出雅克比矩阵求逆方法的可行性及有效性。     

Stabilization of second-order nonholonomic systems in canonical chained form

Stabilization of a class of second-order nonholonomic systems in canonical chained form is investigated in this paper. First, the models of two typical second-order nonholonomic systems, namely, a three-link planar manipulator with the third joint unactuated, and a kinematic redundant manipulator with all joints free and driven by forces/torques imposing on the end-effector, are presented and converted to second-order chained form by transformations of coordinate and input. A discontinuous control law is then proposed to stabilize all states of the system to the desired equilibrium point exponentially. Computer simulation is given to show the effectiveness of the proposed controller.     

Control strategies for rodotic contact tasks: An experimental study

In this article, we study the contact instability problem encountered in robotic manipulators while trying to make contact with an environment, such as grasping or pushing against objects, and propose a unified control strategy capable of achieving a stable contact against both stiff and compliant environments. The problem has three distinct stages of the contact task. In the first stage, free-space motion, the robot is approaching the environment; in the second stage, post-contact force regulation; in the third, impact stage, the transition from the first stage to the second. We make an experimental comparison of the control schemes that may be used for the three stages. For example, during impact, the manipulator should not lose contact with the environment, nor exert high impulsive forces on the environment, and in the post-impact phase, the robot should have a fast force trajectory tracking. The best strategies for the above stages are experimentally determined and then combined into a single unified controller that can achieve stable contact as well as a fast force trajectory tracking response for surfaces of variable stiffnesses. This control scheme does not require a priori knowledge of the stiffness of the environment, and is able to estimate the environmental stiffness and tune gains accordingly so as to achieve the best response. Also experimentally compared is the use of such a scheme with impedance control, another method proposed in the literature for robotic contact task control. © 1995 John Wiley & Sons, Inc.     

Coordination control of an active pneumatic deburring tool

An efficient robotic deburring method was developed based on a new active pneumatic tool. The developed method considers the interaction among the tool, the manipulator and the workpiece and couples the tool dynamics and a control design that explicitly considers deburring process information. The new active pneumatic tool was developed based on a single pneumatic actuator with a passive chamber to provide compliance and reduce the chatter caused by air compressibility. A coordination control method was developed for efficient control of the system, which adopts two-level hierarchical control structure based on a coordination scheme. Robust feedback linearization was utilized to minimize the undesirable effect of external disturbances such as static and Coulomb friction and nonlinear compliance of the pneumatic cylinder stemming from the compressibility of air. The developed coordination control method demonstrated its efficacy in terms of deburring accuracy and speed.     

Real-time adaptive control for haptic telemanipulation with Kalman active observers

This paper discusses robotic telemanipulation with Kalman active observers and online stiffness estimation. Operational space techniques, feedback linearization, discrete state space methods, augmented states, and stochastic design are used to control a robotic manipulator with a haptic device. Stiffness estimation only based on force data (measured, desired, and estimated forces) is proposed, avoiding explicit position information. Stability and robustness to stiffness errors are discussed, as well as real-time adaptation techniques. Telepresence is analyzed. Experiments show high performance in contact with soft and hard surfaces.     

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on the hand position and orientation vectors usually adopted to describe motion in the task space. The analysis of the computational burden is performed by taking the Stanford arm as a reference. Finally a case study is developed via numerical simulations.     

Visual servoing tracking control of uncalibrated manipulators with a moving feature point

The paper is concerned with the problem of uncalibrated visual servoing robots tracking a dynamic feature point along with the desired trajectory. A nonlinear observer and a nonlinear controller are proposed, which allow the considered uncalibrated visual servoing robotic system to fulfil the desired tracking task. Based on this novel control method, a dynamic feature point with unknown motion parameters can be tracked effectively along with the desired trajectory, even with multiple uncertainties existing in the camera, the kinematics and the manipulator dynamics. By the Lyapunov theory, asymptotic convergence of the image errors to zero with the proposed control scheme is rigorously proven. Simulations have been conducted to verify the performance of the proposed control scheme. The results demonstrated good convergence of the image errors.     

Redundant grasps,redundant manipulators,and their dual relationships

This article presents a meaningful, practical, and theoretically sound solution that solves the problem of grasping a rigid object with a hand that has redundant (>6) grasping contacts. This is accomplished by introducing compliance at each contact point in such a way as to provide the engineer with the capabilities of object manipulation via controlled forces at the contact points. This method of solution is adapted straight-away to compute the static forces generated in the legs of a redundant in-parallel manipulator that equilibrates a wrench applied to the moving/platform or end-effector. In a way similar to the redundant grasping problem, this is accomplished by introducing the knowledge of the compliances that exist in the legs. The solution thus obtained stems from physical parameters that model the in-parallel manipulator. The in-depth study of the duality between the statics of in-parallel manipulators and the kinematics of serial manipulators reveals a meaningful, practical, and theoretically sound solution for the inverse kinematics of a redundant serial manipulator. This is accomplished by incorporating the knowledge of the compliances that exist or are desired to exist in the joints of the manipulator. (For instance, the torsional compliance in revolute joints or the linear compliance in prismatic joints.) Such information provides a physically meaningful model of the serial manipulator that in turn yields a physically meaningful set of joint increments for a given end-effector twist. © 1992 John Wiley & Sons, Inc.