Generalized algorithm for computing the 4-3-4 N-axis robotic trajectory

A generalized inversion technique and algorithm is presented for the purpose of computing the 9n coefficients pertaining to the three segments—i.e., liftoff, transitory, and setdown—of a motion trajectory of an n-axis robot manipulator. The technique and the computer program presented is general enough to be immediately applicable to an n-axis robot manipulator if only the desired initial and final position, velocity, acceleration, as well as the intermediate “via” positions are given. A number of examples are presented for a wide spectrum of these constraint conditions on the desired motion trajectories.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Design and Control of a Hydraulic Simulator for a Flexible-Joint Robot

For the first time, a novel experimental hydraulic system that simulates joint flexibility of a single-rigid-link flexible-joint robot manipulator, with the ability of changing the joint flexibility's parameters, was designed and implemented in this study. Such a system could facilitate future control studies of robot manipulators by reducing investigation time and implementation cost of research. It could also be used to test the performance of different strategies to control the movement of flexible-joint manipulators. A hydraulic rotary servo motor was used to simulate the action of a flexible-joint robot manipulator, which was a challenging task, since the control of angular acceleration was required. In this study, a single-rigid-link elastic-joint robot manipulator was mathematically modeled and implemented in which joint flexibility parameters such as stiffness and damping could be easily changed. This simulation is referred to as a 'function generator' to drive a hydraulic robot manipulator. In this study the desired angular acceleration of the manipulator was used as the input to the hydraulic rotary motor and the objective was to make the hydraulic system follow the desired acceleration in the frequency range specified. A hydraulic actuator robot was built and tested. The results indicated that if the input signal had a frequency in the range of 5–15 Hz and damping ratio of 0.1 (typical values for flexible joints), the experimental setup was able to reproduce the input signal with acceptable accuracy. Owing to the inherent noise associated with the measurement of acceleration and some severe nonlinearities in the rotary motor, control of the experimental test system using classical methods was a challenging task that had not been anticipated.     

Linearized dynamic models of robot manipulators in cartesian space

This article presents development of the linearized dynamic models of robot manipulators in Cartesian space. A clever method is proposed to formulate the linearized dynamic models of robot manipulators in Cartesian space. Efficient methods are developed to compute various matrices involved in the models (or the manipulator sensitivity matrices in Cartesian space), such as the Jacobian matrix and the first and second derivatives of it with respect to time as well as the manipulator sensitivity matrices in joint space. The proposed methods are simple and systematic and have computational complexity of the order O(n²) only, where n is the number of degrees-of-freedom of the manipulator.     

Effect of gravity on the static behavior of manipulators

The gravity-induced forces on revolute robot links dominate over the dynamic induced forces, particularly at low speeds. These forces, however, are generally ignored in conceptual analysis works due to the ensuing simplifications that their omission bring about. The force ellipsoid, the dynamic manipulability ellipsoid, and the generalized ellipsoid of inertia introduced by some researchers are but a few examples. For robot-arm control applications, the effect of gravity is usually isolated from the dynamic equations and then compensated for by the robot controller.This study presents a method to introduce the effect of gravity in the static analysis of robot arms. Using the concept of fields, the gravity-induced forces acting on individual links are replaced by a single force, called here the generalized weight of the arm. The generalized weight is a force that acts at the endpoint, and its magnitude and direction are functions of the configuration of the robot arm. The generalized weight field is then integrated with the force ellipsoid to result in the true force that a manipulator can apply to its environment. Since the system is conservative, the generalized weight is considered to be the gradient of a potential field called the generalized potential field. This field alone can illustrate the overall effect of gravity on the manipulator throughout its work volume.     

作业型飞行机器人动态滑翔抓取的鲁棒自适应控制

作业型飞行机器人是指将多自由度机械臂固连在飞行机器人上的一类新型机器人系统,它能够对周围环境施加主动影响,同时也存在较为复杂的动力学性能.本文针对作业型飞行机器人滑翔抓取物体时所受到的摩擦力和接触力问题以及在飞行过程中产生的转动惯量变化问题,设计了一种整体式鲁棒自适应控制策略.首先在作业型飞行机器人系统动力学建模中引入摩擦力和接触力模型,考虑飞行机器人转动惯量为有界变量,提高了建模和抓取的精度.然后,为减弱滑翔抓取产生的剧烈扰动对飞行控制性能的影响,设计了一种抗扰动的鲁棒自适应控制器,并使用区间矩阵法对转动变量变化进行补偿控制.接着,通过Lyapunov稳定性理论证明了系统的稳定性.最后通过仿真对比实验,验证了所提出方法的有效性和优势.     

Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

Path planning with obstacle avoidance based on visibility binary tree algorithm

In this paper, a novel method for robot navigation in dynamic environments, referred to as visibility binary tree algorithm, is introduced. To plan the path of the robot, the algorithm relies on the construction of the set of all complete paths between robot and target taking into account inner and outer visible tangents between robot and circular obstacles. The paths are then used to create a visibility binary tree on top of which an algorithm for shortest path is run. The proposed algorithm is implemented on two simulation scenarios, one of them involving global knowledge of the environment, and the other based on local knowledge of the environment. The performance are compared with three different algorithms for path planning.     

An adaptive friction compensator for global tracking in robot manipulators

A novel adaptive friction compensator based on a dynamic model recently proposed in the literature is presented in this paper. The compensator ensures global position tracking when applied to an n degree of freedom robot manipulator perturbed by friction forces with only measurements of position and velocity, and all the system parameters (robot and friction model) unknown. Instrumental for the solution of the problem is the observation that friction compensation can be recasted as a disturbance rejection problem. The control signal is then designed in two steps, first a classical adaptive robot controller that (strictly) passifies the system, and then a relay-based outer-loop that rejects the disturbance.     

力矩输入有界的柔性关节机器人轨迹跟踪控制

为解决柔性关节机器人在关节驱动力矩输出受限情况下的轨迹跟踪控制问题,提出一种基于奇异摄动理论的有界控制器.首先,利用奇异摄动理论将柔性关节机器人动力学模型解耦成快、慢两个子系统.然后,引入一类平滑饱和函数和径向基函数神经网络非线性逼近手段,依据反步策略设计了针对慢子系统的有界控制器.在快子系统的有界控制器设计中,通过关节弹性力矩跟踪误差的滤波处理加速系统的收敛.同时,在快、慢子系统控制器中均采用模糊逻辑实现控制参数的在线动态自调整.此外,结合李雅普诺夫稳定理论给出了严格的系统稳定性证明.最后,通过仿真对比实验验证了所提出控制方法的有效性和优越性.     

Simulation of Industrial Manipulators Based on the UDU T Decomposition of Inertia Matrix

The UDU ^T – U and D are respectively the upper triangular and diagonal matrices – decomposition of the generalized inertia matrix of an n-link serial manipulator, introduced elsewhere, is used here for the simulation of industrial manipulators which are mainly of serial type. The decomposition is based on the application of the Gaussian elimination rules to the recursive expressions of the elements of the inertia matrix that are obtained using the Decoupled Natural Orthogonal Complement matrices. The decomposition resulted in an efficient order n, i.e., O(n), recursive forward dynamics algorithm that calculates the joint accelerations. These accelerations are then integrated numerically to perform simulation. Using this methodology, a computer algorithm for the simulation of any n degrees of freedom (DOF) industrial manipulator comprising of revolute and/or prismatic joints is developed. As illustrations, simulation results of three manipulators, namely, a three-DOF planar manipulator, and the six-DOF Stanford arm and PUMA robot, are reported in this paper.     

Type-2 fuzzy control for a flexible-joint robot using voltage control strategy

Type-1 fuzzy sets cannot fully handle the uncertainties. To overcome the problem, type-2 fuzzy sets have been proposed. The novelty of this paper is using interval type-2 fuzzy logic controller (IT2FLC) to control a flexible-joint robot with voltage control strategy. In order to take into account the whole robotic system including the dynamics of actuators and the robot manipulator, the voltages of motors are used as inputs of the system. To highlight the capabilities of the control system, a flexible joint robot which is highly nonlinear, heavily coupled and uncertain is used. In addition, to improve the control performance, the parameters of the primary membership functions of IT2FLC are optimized using particle swarm optimization (PSO). A comparative study between the proposed IT2FLC and type-1 fuzzy logic controller (T1FLC) is presented to better assess their respective performance in presence of external disturbance and unmodelled dynamics. Stability analysis is presented and the effectiveness of the proposed control approach is demonstrated by simulations using a two-link flexible-joint robot driven by permanent magnet direct current motors. Simulation results show the superiority of the IT2FLC over the T1FLC in terms of accuracy, robustness and interpretability.     

A Recursive Algorithm for On-line Clustering Obstacles Cluttered in Dynamic Environments

In some applications of industrial robots, the robot manipulator must traverse a pre-specified Cartesian path with its hand tip while links of the robot safely move among obstacles cluttered in the robot's scene (environment). In order to reduce the costs of collision detection, one approach is to reduce the number of collision checks by enclosing a few real obstacles with a larger (artificial) bounding volume (a cluster), e.g., by their convex hull [4, 14], without cutting the specified path.In this paper, we propose a recursive algorithm composed of four procedures to tackle the problem of clustering convex polygons cluttered around a specified path in a dynamic environment. A key fact observed is that the number k of clusters is actually determined by the specified path not by any criterion used in clustering. Based on this fact, an initial set of k clusters could be rapidly generated. Then, the initial set of clusters and its number is further refined for satisfying the minimum Euclidean distance criterion imposed in clustering. Compared to the heuristic algorithm in [14], complexity of the proposed algorithm is reduced by one order with respect to the number n of obstacles. Simulation are performed in both static and dynamic environments, which show that the recursive algorithm is very efficient and acquires less number k of clusters.     

A force–impedance controlled industrial robot using an active robotic auxiliary device

A strategy to improve the performance of current commercial industrial robots is presented in this paper. This strategy involves cooperation of two robotic manipulators: the robotic controlled impedance device (RCID) and a commercial industrial robot. The RCID is a small six degrees-of-freedom (DOF) high bandwidth force–impedance controlled parallel manipulator, developed at the School of Engineering of the University of Porto (Portugal). The RCID works attached in series with a position controlled commercial industrial robot. Combination of the two manipulators behaves as a single manipulator having the impedance and force control dynamic performance of the RCID, as well as the workspace and trajectory tracking bandwidth of the industrial robot. Force–impedance control of the RCID, and experimental results on typical tasks that involve end-effector contact with uncertain environments of unknown stiffness are presented.     

Dynamic motion learning for multi-DOF flexible-joint robots using active–passive motor babbling through deep learning

This paper proposes a learning strategy for robots with flexible joints having multi-degrees of freedom in order to achieve dynamic motion tasks. In spite of there being several potential benefits of flexible-joint robots such as exploitation of intrinsic dynamics and passive adaptation to environmental changes with mechanical compliance, controlling such robots is challenging because of increased complexity of their dynamics. To achieve dynamic movements, we introduce a two-phase learning framework of the body dynamics of the robot using a recurrent neural network motivated by a deep learning strategy. The proposed methodology comprises a pre-training phase with motor babbling and a fine-tuning phase with additional learning of the target tasks. In the pre-training phase, we consider active and passive exploratory motions for efficient acquisition of body dynamics. In the fine-tuning phase, the learned body dynamics are adjusted for specific tasks. We demonstrate the effectiveness of the proposed methodology in achieving dynamic tasks involving constrained movement requiring interactions with the environment on a simulated robot model and an actual PR2 robot both of which have a compliantly actuated seven degree-of-freedom arm. The results illustrate a reduction in the required number of training iterations for task learning and generalization capabilities for untrained situations.     

Reducing the Complexity of Robot's Scene for Faster Collision Detection

In many real-life industrial applications such as welding and painting, the hand tip of a robot manipulator must follow a desired Cartesian curve while its body avoids collisions with obstacles in its environment. Collision detection is an absolutely essential task for any robotic manipulators in order to operate safely and effectively in cluttered environments. A significant factor that influences the complexity of the collision detection problem is the obstacles' density, i.e., the total number of obstacles in the robot's environment.In this paper, a heuristic algorithm for approximating the collision detection problem into a simpler one is presented. The algorithm reduces the number of obstacles that must be examined during the robot's motion by applying efficient techniques from computational geometry. The algorithm runs in time O(max(n ² log m, n m)) , and uses O(n ² + m n) space; with n being the number of obstacles in the robot's workspace, and m the total number of obstacles' vertices. Both costs are worst-case bounds.     

Trajectory tracking control of flexible-joint robots

Inverse dynamics control of flexible-joint robots is addressed. It is shown that, in a flexible-joint robot, the acceleration level inverse dynamic equations are singular because the control torques do not have an instantaneous effect on the end-effector accelerations due to the elastic media. Implicit numerical integration methods that account for the higher order derivative information are utilized for solving the singular set of differential equations. The trajectory tracking control law presented linearizes and decouples the system and yields an asymptotically stable fourth order error dynamics for each end-effector degree of freedom. A 3R spatial robot with all joints flexible is simulated to illustrate the performance of the proposed algorithm.     

An Efficient Algorithm for Identification of Robot Parameters Including Drive Characteristics

A procedure for estimating the dynamic model parameters of an n degree-of-freedom (DOF) robot is presented. The characteristics of the drive dynamics are included in the modelling process. In this manner, the estimated dynamic model can facilitate the design of control laws for actual implementation. Due to a regrouping procedure, the estimation model for the model parameters is formulated in an upper block triangular form. This special structure can be exploited to obtain a computational efficient estimation algorithm for the model parameters. An integral form of the estimation algorithm is then developed to eliminate the need of using joint accelerations which tend to be noisy. The complete procedure does not require prior knowledge of the manipulator's geometric parameters. Furthermore the robot manipulator needs not follow some restrictive test trajectories. The experimental results obtained from a 4-DOF SCARA robot are presented to illustrate the practical application of the method.     

Position and stiffness analysis of a new asymmetric 2PRR–PPR parallel CNC machine

In this paper, structural stiffness analysis of a new 3-axis asymmetric planar parallel manipulator, a 2 P RR–P P R structural kinematic chain, is investigated. The manipulator is proposed as a tool holder for a 5-axis hybrid computer numerical control (CNC) machine. First, the structure of the robot is introduced and inverse kinematics solution is presented. Secondly, stiffness matrix of the robot is determined using a continuous method based on Castigliano’s theorem and calculation of strain energy of the robot components. This method removes the need for commonly used simplifying assumptions and, therefore, results in good accuracy. For this purpose, force and strain energy for each segment of the robot are analyzed. Finally, to verify the analytical results, commercial FEM software is used to simulate the physical structure of the manipulator. A numerical example is presented which confirms the correctness of the analytical formulations.