工作空间坐标下操作器的运动规划与控制

本文针对操作器的工作空间坐标下轨线跟踪,提出了直接利用跟踪误差进行规划和控制的设计方案.这一规划方案基于速度矢量的线性合成原理.同时借助于定义一个偏差超平面,利用滑动模控制的思想,将原非线性规划问题转化为线性规划问题,特别适用于具有冗余自由度的操作器,并且不再要求操作器参数、定位等非常精确;而这一控制方案将规划过程统一于控制器之中,直接对跟踪误差进行控制,可以得到更加优秀的外部品质.     

Position and force tracking of a two‐manipulator system manipulating a flexible beam

This article discusses the issue of hybrid position and force control of a two‐manipulator system manipulating a flexible beam in trajectory tracking. Unlike our previous approach of set‐point position control in the trajectory tracking, the system coordinates are hard to be regulated to the desired states with nonzero tracking velocities under continuous feedback control. In this study, we design a hybrid position and force tracking controller while using saturation control to compensate for the effect of beam vibration dynamics on the tracking performance. All parameters and states used in the controller are readily available so that the proposed method is feasible to implement. Under the proposed controller, the tracking error asymptotically converges to a predetermined boundary. Simulation results demonstrate the validity of the proposed approach. © 2001 John Wiley & Sons, Inc.     

Operator-based robust nonlinear optimal vibration control for an L-shaped arm driven by linear pulse motor

An L-shaped arm driven by a linear pulse motor is considered in this paper, an operator-based robust nonlinear control approach is proposed to reduce the vibration of the arm. First, by separating the arm into two parts, its vibration dynamics is modelled based on Euler-Bernoulli beam theory. Second, by using operator-based robust right coprime factorization approach, two control schemes are designed, one for controlling the linear pulse motor move to the desired destination and reducing the vibration of the arm with optimal trajectory, another one is to control vibration of the arm by using a piezoelectric actuator, where a tracking compensator is designed to compensate the hysteresis of the piezoelectric actuator and make the arm vibration track to the reference values. Finally, simulation results are demonstrated to verify the effectiveness of the proposed control scheme.     

Joint space trajectory planning for flexible manipulators

A trajectory planning approach for controlling flexible manipulators is proposed. It is demonstrated that choosing actual joint angles as the generalized rigid coordinates is the key to applying the proposed approach. From the observation of the special structure of the input matrix, the concepts of motion-induced vibration and inverse dynamics under a specified motion history of the joints are formed naturally. Based on the above concepts, trajectory planning in joint space is proposed by using the optimization technique to determine the motion of joints along a specified path in joint space or work space and for general point-to-point motion. The motion for each joint is assumed to be in a class consisting of a fifth-order polynomial and a finite terms of Fourier series. This parameterization of motion allows the optimal trajectory planning to be formulated as a standard nonlinear programming problem, which avoids the necessity of solving a two-point-boundary-value problem and using dynamic programming. Setting the accelerations to zero at the initial and the final times is used to obtain smoother motion to reduce the spillover energy into unmodeled high-frequency dynamics. A penalty term on vibration energy contained in the performance index is used to minimize the vibration of the system modeled by lower frequency only. The final simulation results show the effectiveness of the proposed approach and the advantage for proper trajectory planning. © 2995 John Wiley & Sons, Inc.     

基于坐标补偿的自动泊车系统无模型自适应控制

针对自动泊车系统,提出了无模型自适应控制(Model-free adaptive control, MFAC)方案.控制方案的设计仅利用泊车系统的前轮转角输入数据和车身角输出数据,不包含车辆模型信息.因此,针对不同车型的自动泊车系统,该方案均能实现无模型自适应控制.为了改善期望轨迹的坐标跟踪误差,进一步提出基于坐标补偿的无模型自适应控制方案,该方案由控制算法、参数估计算法、参数重置算法和坐标补偿算法构成.针对不同车型不同泊车速度的仿真结果表明,基于坐标补偿的MFAC方案和原型MFAC方案均能较好地完成自动泊车过程,且基于坐标补偿的MFAC方案相比原型MFAC方案和PID控制方案,在轨迹坐标和车身角等方面均具有更小的跟踪误差和更快的响应速度.     

On adaptive trajectory tracking of a robot manipulator usinginversion of its neural emulator

This paper is concerned with the design of a neuro-adaptive trajectory tracking controller. The paper presents a new control scheme based on inversion of a feedforward neural model of a robot arm. The proposed control scheme requires two modules. The first module consists of an appropriate feedforward neural model of forward dynamics of the robot arm that continuously accounts for the changes in the robot dynamics. The second module implements an efficient network inversion algorithm that computes the control action by inverting the neural model. In this paper, a new extended Kalman filter (EKF) based network inversion scheme is proposed. The scheme is evaluated through comparison with two other schemes of network inversion: gradient search in input space and Lyapunov function approach. Using these three inversion schemes the proposed controller was implemented for trajectory tracking control of a two-link manipulator. Simulation results in all cases confirm the efficacy of control input prediction using network inversion. Comparison of the inversion algorithms in terms of tracking accuracy showed the superior performance of the EKF based inversion scheme over others.     

PD-based trajectory tracking control in automatic cell injection system

Trajectory tracking technology has been the focus of industrial manipulatory applications for many years, and its research has been found in micromanipulation in bioengineering recently. In this paper, a hybrid vision and force control method is applied to the automatic cell injection. The three-dimensional cell injection process involves the trajectory tracking in free space and the force control in contact space. A PD plus feedforward compensation control method is applied to the trajectory tracking in 3D space. Further, a PD-based robust controller is introduced into trajectory tracking while the systemic uncertainty of the cell injection is additionally considered. Both of the two control methods are theoretically proved to be exponential convergent. Finally, the effectiveness of the proposed method is verified as compared with other control methods by its application to trajectory tracking problem.     

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.     

Model-based control of redundantly actuated parallel manipulators in redundant coordinates

Model-based control of parallel kinematics machines (PKM) relies on computationally efficient formulations in terms of a set of independent joint coordinates. Since PKM models are commonly expressed in terms of actuator or end-effector coordinates the models are not valid at input- or output-singularities, respectively. Moreover input-singularities limit the motion range of PKM. Actuation redundancy is a means to increase the singularity-free range of motion. However, due to the redundancy only a subset of the actuator coordinates constitute independent coordinates. This subset corresponds to the actuator coordinates of the non-redundant PKM, which does generally not constitute proper minimal coordinates for the entire workspace. Hence a redundantly actuated PKM (RA-PKM) controlled by a model-based controller in terms of minimal coordinates would exhibit the same limitations as the non-redundant PKM. One approach to tackle this problem is to switch between different minimal coordinates, i.e., different motion equations are used within the controller.In this contribution a computed torque and augmented PD control scheme in redundant coordinates is proposed, as an alternative to coordinate switching, and applied to the control of redundantly actuated PKM. That is, no minimal coordinates are selected. This novel formulation is numerically robust and does not suffer from input- or output-singularities. Even more the formulation is always valid except at configuration space singularities. For the redundancy resolution within the inverse dynamics the pseudoinverse of a rank deficient matrix is required, for which an explicit formulation is presented. For both controllers exponential trajectory tracking is shown. Experimental results are reported for a planar 2 DOF RA-PKM.     

Inverse dynamics of articulated flexible structures: Simultaneous trajectory tracking and vibration reduction

This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. For such flexible structures, closed loop passive joint based controllers have been shown to be effective in trajectory control by Paden et al. Crucial to the development of such closed loop controllers, which are robust to external perturbations, is the problem of dynamic inversion which yields the nominal state trajectories and the feedforward inputs. In this paper we propose a new inverse dynamics scheme for computing the nominal lumped and distributed feedforward inputs for tracking a prescribed trajectory.     

An iterative linear quadratic regulator based trajectory tracking controller for wheeled mobile robot

We present an iterative linear quadratic regulator(ILQR) method for trajectory tracking control of a wheeled mobile robot system.The proposed scheme involves a kinematic model linearization technique,a global trajectory generation algorithm,and trajectory tracking controller design.A lattice planner,which searches over a 3D(x,y,θ) configuration space,is adopted to generate the global trajectory.The ILQR method is used to design a local trajectory tracking controller.The effectiveness of the proposed method is demonstrated in simulation and experiment with a significantly asymmetric differential drive robot.The performance of the local controller is analyzed and compared with that of the existing linear quadratic regulator(LQR) method.According to the experiments,the new controller improves the control sequences(v,ω) iteratively and produces slightly better results.Specifically,two trajectories,’S’ and ’8’ courses,are followed with sufficient accuracy using the proposed controller.     

Robust adaptive control for mobile manipulators

This paper addresses the trajectory tracking control of a nonholonomic wheeled mobile manipulator with parameter uncertainties and disturbances. The proposed algorithm adopts a robust adaptive control strategy where parametric uncertainties are compensated by adaptive update techniques and the disturbances are suppressed. A kinematic controller is first designed to make the robot follow a desired end-effector and platform trajectories in task space coordinates simultaneously. Then, an adaptive control scheme is proposed, which ensures that the trajectories are accurately tracked even in the presence of external disturbances and uncertainties. The system stability and the convergence of tracking errors to zero are rigorously proven using Lyapunov theory. Simulations results are given to illustrate the effectiveness of the proposed robust adaptive control law in comparison with a sliding mode controller.     

Exponential trajectory tracking control in the workspace of a class of flexible robots

In this paper, we present a control strategy that ensures the exponential stability of the tracking error in the virtual joint space of a class of mechanical systems made up of rigid links that form a chain that ends with a flexible beam. Virtual joints are defined so as to be related kinematically to the workspace. Thus, when the inverse kinematics is nonsingular, trajectory tracking in the virtual joint space is equivalent to trajectory tracking in the workspace. The method proposed in this paper calls for the transformation of the trajectory from the virtual joint space to the joint and deformation space. The robot is a non-minimum-phase system in the virtual joint space. However, this transformation, which involves the dynamics of the flexible part, can be solved using a causal–anticausal iterative approach. The controller is then designed using an input–output feedback linearization scheme, with regard to the joints, and two linear control laws with regard to the joint and to the deformation variable tracking errors. Analysis based on the passivity theorem, hierarchical systems stability, and linear matrix inequalities then allows us to determine the controller gains that ensure that the tracking errors in the virtual joint space are well damped and exponentially stable. Finally, the strategy is validated by simulating a controller that incorporates the proposed laws and that drives a two-link manipulator that has one rigid and one flexible link. The simulation results demonstrate the good performance of the proposed control system. © 1998 John Wiley & Sons, Inc.     

Robust trajectories following control of a 2-link robot manipulator via coordinate transformation for manufacturing applications

A common idea concerning trajectory control of robot manipulators is to tackle the motion of the end-effector. According to traditional trajectory designs, a prescribed profile in a work space is first decomposed into independent joint positions such that the success in a contouring task lies with good tracking capability of individual joints. To advance trajectory control precision without relying on high tracking performance, a contour control strategy for a robot manipulator is presented in this paper. Different from the traditional concept of trajectory control, a contour following control strategy is developed via a coordinate transformation scheme. The main advantage of the proposed control architecture is that the final contouring accuracy will not be degraded in case the tracking performance of the robot manipulator is not good enough. Moreover, using a concept of variable structure control theory, a smooth robust control algorithm is realized in the form of proportional control plus an integration term. The robustness of the control algorithm is also demonstrated. A number of experiments are conducted to demonstrate the advantage of the trajectories following control framework and validate the feasibility of the proposed controller.     

Adaptive neural network output feedback control for flexible multi-link robotic manipulators

In this paper, a novel approach for adaptive control of flexible multi-link robots in the joint space is presented. The approach is valid for a class of highly uncertain systems with arbitrary but bounded dimension. The problem of trajectory tracking is solved through developing a stable inversion for robot dynamics using only joint angles measurement; then a linear dynamic compensator is utilised to stabilise the tracking error for the nominal system. Furthermore, a high gain observer is designed to provide an estimate for error dynamics. A linear in parameter neural network based adaptive signal is used to approximate and eliminate the effect of uncertainties due to link flexibilities and vibration modes on tracking performance, where the adaptation rule for the neural network weights is derived based on Lyapunov function. The stability and the ultimate boundedness of the error signals and closed-loop system is demonstrated through the Lyapunov stability theory. Computer simulations of the proposed robust controller are carried to validate on a two-link flexible planar manipulator.     

Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertainties and input saturation

A novel robust state error port controlled Hamiltonian (PCH) trajectory tracking controller of an unmanned surface vessel (USV) subject to time-varying disturbances, dynamic uncertainties and control input saturation is presented. The proposed control scheme combines the advantages of the high robustness and energy minimization of the state error PCH approach and the approximation capability of adaptive radial basis function neural networks (RBFNNs). Adaptive RBFNNs are used to the time-varying disturbances of the environment and unknown dynamics uncertainties of the USV model. The state error PCH control approach is designed such that the system can optimize energy consumption, and the state error PCH technique makes the designed trajectory tracking controller be easy to implement in practice. To handle the effect of the control input saturation, a Gaussian error function model is employed. It has been demonstrated that the proposed approach can maintain the USV's trajectory at the desired trajectory, while the closed-loop control system can guarantee the uniformly ultimate boundedness. The energy consumption model of the USV is constructed to reveal to the energy consumption. Simulation results demonstrate the effectiveness of the proposed controller.     

Robust maneuvering of autonomous underwater vehicle: an adaptive fuzzy PI sliding mode control

The control issues in nonlinear trajectory tracking of an autonomous underwater vehicle (AUV) are a challenging task due to the complex oceanic environment, highly nonlinear coupled dynamics, imprecise hydrodynamic coefficients and unpredictable external disturbances such as ocean waves, current fluctuations and tides. This paper addresses an adaptive fuzzy PI sliding mode control (AFPISMC) for trajectory tracking control of AUV to achieve high precise maneuvering in undersea environment. An AFPISMC is basically comprised of an equivalent control based on approximately known inverse dynamic model output and continuous adaptive PI term is designed to eliminate chattering effect. Furthermore, it does not require a priori knowledge of upper bounds on uncertainties in the dynamic parameters of an AUV. In this approach, decoupled single input fuzzy PI control strategy is employed along with a reduced rule base and self-tuning control law is derived to modify hitting gain in order to enhance tracking response. The overall control scheme guarantees the global asymptotic stability based on Lyapunov theory. Finally, the effectiveness and robustness of the proposed approach are demonstrated through simulation and comparison studies.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Robust adaptive trajectory tracking independent of models for robotic manipulators

This article proposes a robust adaptive trajectory control scheme for robotic trajectory tracking under uncertainties. The control scheme is globally exponentially convergent without the knowledge of the robotic dynamics and is simple in structure with a small computation. It can make the trajectory error convergent to an arbitrary small region. Lyapunov approach is used to analyze the stability and the robustness of this control scheme. Experiments on a two‐link direct‐drive robotic manipulator verify the validity of the proposed control scheme. © 2001 John Wiley & Sons, Inc.     

Hybrid Control Scheme for Robust Tracking of Two-Link Flexible Manipulator

The hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while the robustness of Variable Structure Control (VSC) developed for rigid manipulators is maintained for controlling the joint angles. The VSC law alone, which is designed to accomplish only the asymptotic decoupled joint angle trajectory tracking, does not guarantee the stability of the flexible mode dynamics of the links. In order to actively suppress the flexible link vibrations, hybrid trajectories for the VSC are generated using the virtual control force concept, so that robust tracking control of the flexible-link manipulator can also be accomplished. Simulation results confirm that the proposed hybrid control scheme can achieve more robust tracking control of two-link flexible manipulator than the conventional control scheme in the presence of payload uncertainty.