Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

基于分解动量的仿人机器人手臂高速运动实时平衡控制

本文面向仿人机器人7自由度手臂高速动态作业运动需求,提出了基于分解动量的仿人机器人实时平衡控制方法,给出了作业臂运动用末端执行器速度向量表示下的机器人总动量计算公式,分析了动量控制维度的择优选取原则,给出了基于分解动量控制的辅助臂关节速度实时计算优化方法.仿真实验表明,经过改进优化的分解动量控制方法对于仿人机器人手臂高速作业运动下的平衡控制具有较高的可行性和实时性,不仅所控制维度的分解动量完全达到了预期的效果,而且其他维度的分解动量也有所降低或基本维持不变,所生成辅助臂运动平滑且在关节运动性能上有较大裕度,机器人总体具有优秀的零力矩点(zero-moment point,ZMP)稳定性.     

Numerical filtering for the operation of robotic manipulators through kinematically singular configurations

The loss of independent degrees of freedom at singular configurations is an inherent characteristic of robotic manipulators. Due to the unavoidable singularity of mechanical wrists, singular configurations cannot be avoided by simply restricting the bounds of the workspace. Techniques for operating at singular configurations without inducing unacceptably high joint velocities or end effector tracking errors are presented. Extensions to the damped least-squares formulation which incorporate estimates of the proximity to singularities and selective filtering of singular components are illustrated. The generality of the technique presented is illustrated in a computer simulation of a commercially available manipulator operating through singular configurations.     

Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator’s elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.     

Tracking human-like natural motion by combining two deep recurrent neural networks with Kalman filter

The Kinect skeleton tracker can achieve considerable performance with human body tracking in a convenient and low-cost manner. However, the tracker often captures unnatural human poses, such as discontinuous and vibrational movement when self-occlusions occur. In this study, we propose an advanced post-processing method to improve the Kinect skeleton using a single Kinect sensor, in which a combination of probabilistic filtering techniques and supervised learning techniques is employed to correct unnatural tracking movements. Specifically, two deep recurrent neural networks are used to improve joint velocities, as well as joint positions produced by the Kinect skeleton tracker. Moreover, a classic Kalman filter further refines positions and velocities. In addition, we propose a novel measure to evaluate the naturalness of captured joint trajectories. We evaluated the proposed approach by comparing it to ground truth obtained using a commercial optical maker-based motion capture system.     

Learning from hint for the conservative motion of the constrained industrial redundant manipulators

A neural network (NN)-based kinematic inversion of industrial redundant arms is developed in this paper to conserve the joint configuration in cyclic trajectories. In the developed approach, the Widrow–Hoff NN with an online adaptive learning algorithm derived by applying Lyapunov approach is introduced. Since this kinematic inversion has an infinite number of joint angle vectors, a fuzzy neural network system is designed to provide an approximate value for that vector. Feeding this vector as an additional hint input vector to the NN limits and guides the output of the NN within the self-motion of the manipulator. The derivation of the candidate Lyapunov function, which is designed to achieve the joint configurations conservation in addition to the joint limits avoidance, leads to a computationally efficient online learning algorithm of the NN. Simulations are conducted for the PA-10 redundant manipulator to bear out the efficacy of the developed approach for tracking closed trajectories.     

Classification and characterization of inverse kinematics solutions for anthropomorphic manipulators

Topological properties of the kinematics map are exploited to develop a novel method for redundancy parameterization and extremely fast inverse kinematics solutions for 7-DOF anthropomorphic manipulators and animation characters. The method consists of generating joint angles vectors (configurations) and determining their associated hand position/orientation (pose) via the known forward kinematics. The generated data are classified into various inverse kinematics solutions manifolds. These manifolds are subsequently segmented so that the redundancy can be parameterized and the solutions can be represented by simple equations whose parameters are stored for rapid online computation. During the online phase, given the desired hand pose, the appropriate stored parameters are retrieved and various inverse kinematics solutions are computed. The online time to provide various solutions is of the order of several microseconds, which allow real-time inverse kinematics evaluations for fast moving animation characters or manipulators.     

二自由度SCARA机器人位置的端口受控哈密顿与反步法协调控制

针对二自由度SCARA机器人系统使用单一控制方法难以实现快速、精准的位置跟踪控制的问题,设计了基于端口受控哈密顿(PCH)与反步法的协调控制.PCH用于保证系统稳态性能,反步法用于保证系统快速性.采用指数函数作为协调函数以实现协调控制策略,从而适应二自由度SCARA机器人的轨迹跟踪控制.该SCARA机器人系统,既能够实现系统快速的跟踪位置信号,又能够提高系统的输出信号的稳态性能.仿真实验表明,当存在干扰时,采用PCH与反步法的协调控制的二自由度SCARA机器人位置跟踪系统能够有效地结合两者的优点,系统的动态性能和稳态性能优良,且能够很好地抵抗外部干扰.     

柔性关节机器人高精度自适应反步法控制

为实现多连杆柔性关节机器人的高精度运动控制,首先对其建立完整的动力学模型,包含了连杆和关节动力学的耦合项、LuGre动态摩擦模型和关节回差等因素．然后针对该模型设计带观测器的自适应反步法控制器,对不可测项进行在线估计和补偿．理论分析证明了观测器的收敛性和闭环系统的稳定性．该方法在一个3DOF（degree of freedom）柔性关节机器人上进行仿真,仿真结果验证了观测器的有效性,并表明该控制器能够降低连杆跟踪误差,实现良好的轨迹跟踪效果．     

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.     

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

A hybrid control scheme is proposed to stabilize the vibration of a two-link flexible manipulator while 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.     

Determination of optimum robot base location considering discrete end-effector positions by means of hybrid genetic algorithm

The performance of a robot manipulator during a process depends on its position relative to the corresponding path. An ill-placed manipulator risks inefficient operation as well as blocks due to singularities. The paper deals with an optimization algorithm to determine the base position and the joint angles of a spatial robot, when the end-effector poses are prescribed, avoiding the singular configurations. The optimization problem is solved through a hybrid heuristic method that combines the advantages of a genetic algorithm, a quasi-Newton algorithm and a constraints handling method. Six cases of a 6-DOF manipulator are studied to verify the feasibility of the proposed algorithm.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Overview of damped least-squares methods for inverse kinematics of robot manipulators

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility.The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described.Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.     

基于PD-ADRC的四旋翼控制器设计

针对四旋翼无人机强耦合、非线性的控制难点,研究设计了一种基于自抗扰控制和比例微分控制的双闭环控制器。首先,分析了小型四旋翼飞行器动力学模型,确定四旋翼无人机的六自由度方程。然后,利用自抗扰控制技术对强耦合、非线性的姿态模型进行了解耦,设计扩张状态观测器对其总扰动进行观测与补偿。其次,设计比例微分控制器对解耦后的系统进行位置跟踪,从而与姿态控制器组成双闭环系统。最后,通过仿真及试飞实验测试系统性能。仿真和试飞结果表明该系统能够完成对控制指令的实时跟踪,并且对干扰具有极强的抑制力。     

Swing-up control of a 3-DOF acrobot using an evolutionary approach

We present a control method for a 3-DOF acrobot which is a model of a gymnast on a horizontal bar with three links, two active joints, and a passive joint. This robot is a nonholonomic and underactuated system. We propose two control methods for the 3-DOF acrobot. First, swing-up control is performed by genetic programming (GP), and stabilizing control is handled by a linear quadratic regulator (LQR). GP can search widely for the optimum input torques for swing-up so that the acrobot is able to reach a near balancing point. The LQR is then switched on to stabilize the system. In the simulation results, the 3-DOF acrobot could swing up to the desired position, and the proposed method could control the acrobot effectively.     

On the adaptive control of robot manipulators with velocity observers

To achieve accurate tracking control of robot manipulators many schemes have been proposed. A common approach is based on adaptive control techniques, which guarantee trajectory tracking under the assumption that the robot model structure is perfectly known and linear in the unknown parameters, while joint velocities are available. Despite tracking errors tend to zero, parameter errors do not unless some persistent excitation condition is fulfilled. There are few works dealing with velocity observation in conjunction with adaptive laws. In this note, an adaptive control/observer scheme is proposed for tracking position of robot manipulators. It is shown that tracking and observation errors are ultimately bounded, with the characteristic that when a persistent excitation condition is matched then they, as well as the parameter errors, tend to zero. Simulation results are in good agreement with the developed theory.     

Fast and robust numerical method for inverse kinematics with prioritized multiple targets for redundant robots

In this paper, a new numerical method for inverse kinematics with prioritized multiple targets is proposed. The proposed method is constructed based on the virtual spring model and joint-based damping control. The targets are prioritized by adjusting the effect of the virtual springs. The proposed method has the following three features. First, it does not require complex calculations such as a Jacobian matrix projection into the null space. Second, it can solve prioritized inverse kinematics problems in the position level without integrating the joint velocity. Third, it is robust to parameter variations and singular configurations. The second feature is motivated by the background that most industrial robots in factories are used as position-controlled robots. Simulation experiments using a 9-DOF redundant robot show that the proposed method is faster and more robust than the conventional method. The proposed method is expected to be useful for helping to avoid collisions between links and obstacles using the redundancy.     

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。     

线驱动模块化七自由度机器人轨迹跟踪控制

阐述了一种线驱动与常规串联驱动相结合的混合设计方法．这种设计方法融合了线驱动并联机构和模块化串联机构的优点,而且混合驱动机器人的工作空间大于完全线驱动机器人的工作空间．文章首先介绍了混合驱动机器人的机构设计,也就是机器人的肩关节采用模块化串联结构,而肘、腕关节采用线驱动结构．然后利用几何分析的方法来解机器人前向运动学问题．在分析驱动线长与关节角之间变换关系的基础上,分别利用速度法和关节角增量法来计算机器人逆向运动学解．最后,使用VC++实现混合驱动机器人对直线运动轨迹进行跟踪的仿真,从而证明了文章所描述的设计方法的正确性．