受约束空间机器人降阶自适应神经网络滑模控制

为了实现受约束空间机器人的高精度控制,提出了一种基于U-K(Udwadia-Kalaba)方程的降阶自适应神经网络滑模控制算法;基于U-K方程,同时考虑受约束空间机器人各个关节的理想约束力与非理想约束力,推导得到详细的动力学方程;考虑到非理想约束力具有不确定性且单独采用滑模控制会出现抖振现象,提出了自适应神经网络滑模控制算法,实现各关节角度、角速度以及非理想约束力的高精度跟踪;针对系统受约束模型,对动力学方程和滑模控制器进行了降阶求解,减少了变量并简化了计算过程;为了验证所提算法的正确性与合理性,以2自由度受约束空间机器人为例进行了仿真验证;仿真结果表明：受约束空间机器人的各关节角度、角速度以及非理想约束力的跟踪误差均低于10^-4量级。     

受限柔性机器人臂的鲁棒变结构混合位置/力控制

针对一类平面双连杆受限柔性机器人臂提出一种混合位置/力控制方案,采用鲁棒变 结构控制策略对控制方案进行修正,以改善该柔性机器人系统的鲁棒性,控制机器人终端执行 器的位置和接触力.通过引入变结构鲁棒控制器,可确保输出跟踪误差在有限时间内收敛到零, 或一致终结有界.计算机仿真结果证明了这种控制方案的可行性和有效性.     

Control of constrained robots including effects of joint flexibility and actuator dynamics

We consider mathematical representations of constrained robot systems in which the effects of joint flexibility and actuator dynamics are significant. The objective is to design a feedback control law so that the position output variables and the force output variables of the robot follows the desired position and the desired force trajectories respectively despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. The development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility. Thus using the force/position control law developed in this paper one can achieve better tracking performance in cases where such effects are significant.     

High Precision Constrained Grasping with Cooperative Adaptive Handcontrol

A method for high precision constrained object manoeuvering for non-redundant rigid multifinger hands is proposed. A passivity-based adaptive cooperative control scheme carries out compensation of all uncertain inertial and dynamic friction forces to guarantee asymptotic tracking of all contact forces and joint position-orientation trajectories over orthogonal force- and position-based impedance error manifolds. Optimal internal and external force trajectories are obtained to minimize the contact forces onto the constrained object while exerting a given desired contact force onto the environment. The simulation study of two robot fingers manipulating a constrained object for combined fast and slow velocity regimes shows that when the dynamic friction compensation is turned on tracking errors decrease tenfold.     

Adaptive Jacobian force/position tracking for space free-flying robots with prescribed transient performance

This paper presents a tracking control with guaranteed prescribed performance (PP) for space free-flying robots with uncertain kinematics (Jacobian matrix) and dynamics, uncertain normal force parameter, and bounded disturbances in a compliant contact with a planar surface. Given the orientation of the surface and a nonlinear model of the elastic force, a controller is designed requiring no information on the robot parameters and the disturbances. This controller will guarantee that the tracking errors satisfy PP indexes such as the maximum steady-state errors and overshoots, and the minimum convergence rates. Thus, contact maintenance can be ensured as prescribed. An approximation of the Jacobian is utilized in the presence of uncertain robot kinematics, and PP position/attitude tracking of the free-flying base is achieved in addition to the PP force/position tracking of the manipulator’s fingertip. The proposed controller is based on an error transformation technique, and a directly tunable gain for the transformed error feedback is introduced in the control to trade off between the tracking performance and control effort. Numerical simulations and comparisons demonstrate the effectiveness and superiority of the proposed controller.     

Perfect position/force tracking of robots with dynamical terminal sliding mode control

According to a given performance criteria, perfect tracking is defined as the performance of zero tracking error in finite time. It is evident that robotic systems, in particular those that carry out compliant task, can benefit from this performance since perfect tracking of contact forces endows one or many constrained robot manipulators to interact dexterously with the environment. In this article, a dynamical terminal sliding mode controller that guarantees tracking in finite‐time of position and force errors is proposed. The controller renders a dynamic sliding mode for all time and since the equilibrium of the dynamic sliding surface is driven by terminal attractors in the position and force controlled subspaces, robust finite‐time convergence for both tracking errors arises. The controller is continuous; thus chattering is not an issue and the sliding mode condition as well the invariance property are explicitly verified. Surprisingly, the structure of the controller is similar with respect to the infinite‐time tracking case, i.e., the asymptotic stability case, and the advantage becomes more evident because terminal stability properties are obtained with the same Lyapunov function of the asymptotic stability case by using more elaborate error manifolds instead of a more complicated control structure. A simulation study shows the expected perfect tracking and a discussion is presented. © 2001 John Wiley & Sons, Inc.     

受动态约束的谐波传动式可重构模块机器人分散积分滑模控制

针对受外界动态约束的谐波传动式可重构模块机器人轨迹跟踪问题, 提出一种基于关节力矩反馈的分散积分滑模控制方法. 在无力/力矩传感器且存在耦合模型不确定性的条件下即能获得良好的控制品质. 基于谐波传动模型, 仅采用位置测量数据估计关节力矩, 并建立机器人子系统动力学模型. 基于可变增益超螺旋算法(VGSTA) 设 计分散积分滑模控制器, 补偿模型不确定性并削弱控制器抖振. 采用Lyapunov 理论对系统的渐近稳定性进行了证明. 值仿真结果验证了所设计的控制器的优越性.

     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

Adaptive sliding mode dynamic controller with integrator in the loop for nonholonomic wheeled mobile robot trajectory tracking

In this paper, novel adaptive sliding mode dynamic controller with integrator in the loop is proposed for nonholonomic wheeled mobile robot (WMR). The modified kinematics controller is used to generate kinematics velocities of WMR which are subsequently used as the input to adaptive dynamic controller. Actuator dynamics are also derived to generate actuator voltage of WMR through torque and velocity vectors. Stability of both kinematics and dynamic controller is presented using Lyapunov stability analysis. The proposed scheme is verified and validated using computer simulations for tracking the desired trajectory of WMR. The performance of proposed scheme is compared with standard backstepping kinematics controller and classical sliding mode control. In addition, the performance is further compared with standard backstepping kinematics controller with adaptive sliding mode controller without integrator. It is shown that the proposed scheme exhibits zero steady state error, fast error convergence and robustness in the presence of continuous disturbances and uncertainties.     

An exponentially convergent adaptive sliding mode control of robot manipulators

A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.     

Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.     

神经网络自适应滑模控制的不确定机器人轨迹跟踪控制

提出一种针对机器人跟踪控制的神经网络自适应滑模控制策略。该控制方案将神经网络的非线性映射能力与滑模变结构和自适应控制相结合。对于机器人中不确定项,通过RBF网络分别进行自适应补偿,并通过滑模变结构控制器和自适应控制器消除逼近误差。同时基于Lyapunov理论保证机器手轨迹跟踪误差渐进收敛于零。仿真结果表明了该方法的优越性和有效性。     

Experimental evaluation of a variable structure controller for constrained robots

In this paper, a variable structure control scheme for constrained robots is developed. This control law ensures the asymptotic convergence of the position errors to zero and also the boundedness of the force tracking error. The control scheme requires a few online computations and thus can be easily implemented. The proposed control law does not require measurements of the joint accelerations or the estimation of the derivative of the force. Experimental results are presented to verify the theoretical developments.     

Feedback control for robotic manipulator with an uncertain Jacobian matrix

In most applications of robots, a desired path for the end‐effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end‐effector path and the Jacobian matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.     

轮式移动机器人瞬态模型鲁棒自适应同步终端滑模编队控制

在轮式移动机器人协同编队问题中,如何保证移动机器人在追踪自身期望轨迹的同时,又能实现与其他机器人运动同步的问题对控制算法的设计提出了更高的要求.本文提出一种基于图论的鲁棒自适应同步终端滑模控制算法来解决这一问题.首先介绍了轮式移动机器人非线性运动学瞬态模型,该模型避免了一般运动学模型多输入耦合互相干扰的问题.然后根据交叉耦合误差设计同步控制算法实现运动同步,通过鲁棒控制对系统外部干扰进行抑制,自适应律保证切换增益实时调节.运用Lyapunov方法进行了稳定性分析,证明了系统追踪误差的收敛性.最后通过MATLAB仿真验证了所设计算法的有效性.     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

Robust Motion Control for Robotic Assembly Tasks using Variable Structure Control Scheme

The success of robot assembly tasks depends heavily on its ability to handle the interactions which take place between the parts being assembled. In this paper, a robust motion-control method is presented for robot manipulators performing assembly tasks in the presence of dynamic constraints from the environment. Using variable structure model reaching control concept, the control objectives is first formulated as a performance model in the task space. A dynamic compensator is then introduced to form the switching function such that the sliding-mode matches the desired model. A simple variable structure control law is suggested to force the system to reach and stay on the sliding mode so that the specified model is achieved.The proposed method is applied to control the prismatic joint of a selective compliance assembly robot-arm type robot for the insertion of printed circuit board into an edge connector socket. Various amounts of interaction forces are generated during the operation. Experimental and simulation results demonstrated the performance of the variable structure model reaching control approach. In comparison, it is shown that the popular position controllers such as proportional plus derivative control and proportional plus derivative with model-based feedforward control are not suitable for achieving good trajectory tracking accuracy in assembly tasks which experience potential interaction force.     

基于三步法的机械臂轨迹跟踪控制

考虑机械臂末端轨迹跟踪控制问题,以跟踪逆运动学求解出的末端期望轨迹对应的各关节期望角度为控制目标.设计了一种基于三步法的控制器,该控制器由类稳态控制、可变参考前馈控制和误差反馈控制3部分组成.证明了该控制器可以通过控制机械臂的各关节力矩实现各关节实际角度对期望角度的状态跟踪,进而使得末端轨迹渐近跟踪期望轨迹,并且跟踪误差是输入到状态稳定的.仿真表明基于三步法控制器的空间机械臂末端可以渐近跟踪期望轨迹,并且该算法可以克服系统的末端负载质量变化等不确定性的影响.     

具有时滞的柔性关节多机械臂协同自适应位置/力控制

由于关节机械臂长期运行后,齿轮间隙扩大产生的时间滞后将使得系统跟踪性能降低.针对此问题,本文提出了一种自适应位置/力控制策略来保证闭环系统稳定性以及位置/力跟踪性能.首先,对多机械臂和物体系统进行任务空间动力学建模.随后,利用Pade理论将时间滞后近似为二阶有理分式.同时,利用神经网络自适应算法克服模型建模误差对系统稳定性的影响,利用同时包含位置误差和力误差的线性滑模项,设计位置/力控制器.通过李雅普诺夫稳定性理论,证明控制策略能实现位置误差和内力误差的渐近收敛.最后,仿真验证证明所设计控制策略的有效性.     

Robust Sliding Control of Robotic Manipulators Based on a Heuristic Modification of the Sliding Gain

A task space robust trajectory tracking control is developed for robotic manipulators. A second order linear model, which defines the desired impedance for the robot, is used to generate the reference position, velocity and acceleration trajectories under the influence of an external force. The control objective is to make the robotic manipulator’s end effector track the reference trajectories in the task space. A sliding mode based robust control is used to deal with system uncertainties and external perturbations. Thus, a sliding manifold is defined by a linear combination of the tracking errors of the system in the task space built from the difference between the real and the desired position, velocity and acceleration trajectories in comparison with previous works where the sliding manifold was defined by the desired impedance and the external force. Moreover, the ideal relay has been substituted by a relay with a dead-zone in order to fit in with the actual way in which a real computational device implements the typical sign function in sliding mode control. Furthermore, a higher level supervision algorithm is proposed in order to reduce the amplitude of the high frequency components of the output associated to an overestimation of the system uncertainty bounds. Then, the robust control law is applied to the case of a robot with parametric uncertainty and unmodeled dynamics. The closed-loop system is proved to be robustly stable with all signals bounded for all time while the control objective is fulfilled in practice. Finally, a simulation example which shows the usefulness of the proposed scheme is presented.