基于末端圆周运动的可变形臂旋量参数快速标定算法

针对家庭服务机器人工作的非结构化环境,设计了一种可以根据任务需求相应地调整连杆形状的可变形操作臂．该操作臂工作空间易于拓展、灵活度较高且成本低廉．但臂形的改变也给操作臂的建模和控制带来了困难．首先,可变形臂的运动学参数发生了巨大且无规律的变化,使得固结在连杆上的坐标系脱离连杆本体,变得不可测量．其次,为适应不同任务需求,可变形臂的连杆形状需要经常改变,而传统标定方法往往追求更高的标定精度而非标定效率,因而需要开发一种耗时较短的标定方法．最后,可变形臂的标定方法必须简便而易于在家庭环境中实施．针对上述问题,本文提出了一种基于末端圆周运动的可变形臂旋量参数快速标定算法．对于任意一个旋转关节,单独转动该关节时,操作臂末端的轨迹形成了一个圆弧,且该关节轴垂直于圆弧所在平面（旋转平面）并经过圆弧的圆心．基于该性质,利用随机抽样一致性（RANSAC）算法和最小二乘算法来拟合操作臂末端轨迹,从而获取操作臂的旋量参数初值．在获取到初值的基础上,提出了一种扩展卡尔曼滤波（EKF）算法进一步优化旋量参数,提高标定精度．仿真和实验结果验证了本文方法的有效性．     

Multidirectional compliance and constraint for improved robotic deburring. Part 1: improved positioning

This two-part paper presents a method for both improving the positioning capability and increasing the effective stiffness (bracing) of a robotic manipulator through multidirectional compliance and constraint. Improved relative positioning and increased stiffness are obtained through the use of: (1) an end-effector mounted jig capable of establishing a workpart-based reference frame through multipoint contact with the workpart, and (2) a manipulator compliance designed to provide a specified form of directional coupling in its mapping of forces to deflections. The directional coupling in the compliance is shown to be important in establishing multipoint contact (during insertion) and in maintaining contact (while edge tracking) despite finite positional errors. Improved manipulator positioning is demonstrated in the context of workpart edge deburring.     

A New Calibration Method for a Directly Driven 3<Emphasis Type="Underline">P</Emphasis>RR Positioning System

Calibration is one of the most important works for the parallel manipulator. The manufacturing and assembling errors will modify the designed parameters of the parallel mechanism, leading to the positioning errors. Calibration is an effective method for improving the accuracy of the parallel mechanism. It is vital to identify the parameters and calibrate the system aiming at improving the positioning accuracy. In order to build an object stage of the micro/nano operation system, a 3 degree-of-freedoms (DOFS) parallel mechanism has been designed and constructed, with combination of legs of the PRR type (the underline of the P represent the actuated joint), P and R representing prismatic and revolute pairs respectively (3PRR). Due to the space constraint, this 3PRR mechanism is built without the end-effector feedback, and must be calibrated for high accuracy positioning. The error model of the 3PRR mechanism has been derived and analyzed, and the error distribution mappings of the 3PRR mechanism are obtained. The calibration method based on the error model is investigated. Since some parameters are difficult to be identified by using the decoupling error model, the assistant measurements are proposed and utilized to compensate for this calibration method. Numerical simulations and experiments are carried out. The simulation results show that it is not enough to calibrate this system by using the calibration method based on error model only, and the experimental results demonstrate that the combined assistant measurements will achieve a better effect for calibration.     

Compensation of Robot joint variables using special Jacobian matrices

In dealing with an industrial manipulator, the end-effector accuracy is a major concern. The positioning of the end effector is determined by the controller that utilizes the data from a closed-form kinematic inversion. The closed-form inversion uses nominal, i.e., manufacturer specified, values of link lengths, twists, and offsets. Due to manufacturing tolerances, set-up, and usage, these nominal parameters may be inaccurate. If the nominal parameters contain built-in error values, the closed-form kinematic inversion will yield incorrect joint values, and the actual end-effector position will deviate from its desired position. One may use a parameter identification method to identify the position-independent error parameter values. This article assumes that this has been done and it presents an iterative compensation algorithm (ICA) through which the identified position-independent parameter error values may be used to correct the joint values obtained through the closed-form kinematic inversion. The Denavit and Hartenberg (D-H) parameters (θsαa) are used to model the given M-jointed manipulator, and a set of four special Jacobian matrices ( J _θ, J _s, J _α, and J _a) are formulated. The iterative compensation algorithm allows one to determine the M unknown position-dependent joint error values by using these four special Jacobian matrices. The improvements obtained through the use of the compensation algorithm will be presented for regular trajectories, as well as when the robot nears certain singularity conditions. Since it is important to know a priori a definite number of iterations that must be performed, the level of compensation after a fixed number of iterations is also studied. Through the presentation of numerous examples, it is shown that the proposed compensation algorithm is simple and straightforward to implement, and it increases the end-effector accuracy.     

In-field self-calibration of robotic manipulator using stereo camera: application to Humanitarian Demining Robot

A robotic manipulator using a stereo camera mounted on one of its links requires a precise kinematic transformation calibration between the manipulator and the camera coordinate frames, the so-called hand–eye calibration, to achieve high-accuracy end-effector positioning. This paper introduces a new method that performs simultaneous joint angle and hand–eye calibration, based on a traditional method that uses a sequence of pure rotations of the manipulator links. The new method considers an additional joint angle constraint, which improves the calibration accuracy when the circular arc that can be measured by the stereo camera is very limited. Experimental results using a manipulator developed for humanitarian demining demonstrate that relative errors between the end effector and the external points mapped by the stereo camera are greatly reduced compared to traditional methods.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

A passive mechanism that improves robotic positioning through compliance and constraint

This paper presents the design of a passive robotic wrist that is capable of establishing and maintaining an accurate position relative to a workpart edge through compliance and constraint (force guidance).In previous work, we have shown that, through proper selection of a manipulator's impedance, a manipulator's end-effector can be guided to its desired relative position despite errors in its commanded position. The selected proper impedance is attained here through the design of a passive micromanipulator that is mounted on the end-effector of a conventional manipulator. The micromanipulator consists of three linkages connected by revolute joints and torsional springs. The outermost linkage contacts the workpart at multiple locations providing multidirectional unilateral kinematic constraint. This kinematic constraint in conjunction with the compliance provided by the torsional springs causes the linkage to be re-positioned so that any existing misalignment (that inevitably occurs) is eliminated and a unique planar position/orientation with respect to the workpart edge is attained.Here, we present the procedure used in the parametric design of this mechanism. The desired compliant properties identified in task space (using Cartesian variables (x, y, and θ) for force and motion) are extended here to joint space (using joint variables (θ₁, θ₂), and θ₃) for torque and motion). The appropriate micromanipulator link lengths, initial linkage angles, and the appropriate torsional spring constants are selected using an optimization procedure. Computer simulation of the constrained manipulator/workpart interaction demonstrates that the desired force guidance behavior is attained.     

Workspace Determination of General 6-d.o.f. Cable Manipulators

This paper addresses workspace determination of general 6-d.o.f. cable-driven parallel manipulators with more than seven cables. The workspace under study is called force-closure workspace, which is defined as the set of end-effector poses satisfying the force-closure condition. Having force-closure in a specific end-effector pose means that any external wrench applied to the end-effector can be balanced through a set of non-negative cable forces under any motion condition of the end-effector. In other words, the inverse dynamics problem of the manipulator always has a feasible solution at any pose in the force-closure workspace. The workspace can be determined by the Jacobian matrix and, thus, it is consistent with the usual definition of workspace in the robotics literature. A systematic method of determining whether or not a given end-effector pose is in the workspace is proposed. Based on this method, the shape, boundary, dimensions and volume of the workspace of a 6-d.o.f., eight-cable manipulator are discussed.     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

Prediction of geometric errors of robot manipulators with Particle Swarm Optimisation method

This paper reports on the prediction of the expected positioning errors of robot manipulators due to the errors in their geometric parameters. A Swarm Intelligence (SI) based algorithm, which is known as Particle Swarm Optimization (PSO), has been used to generate error estimation functions. The experimental system used is a Motoman SK120 manipulator. The error estimation functions are based on the robot position data provided by a high precision laser measurement system. The functions have been verified for three test trajectories, which contain various configurations of the manipulator. The experimental results demonstrate that the positioning errors of robot manipulators can be effectively predicted using some constant coefficient polynomials whose coefficients are determined by employing the PSO algorithm. It must be emphasized that once the estimation functions are obtained, there may be no need of any further experimental data in order to determine the expected positioning errors for a subsequent use in the error correction process.     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

Casting Manipulation—Midair Control of a Gripper by Impulsive Force

We have developed a casting manipulator that includes a flexible light string in the link mechanism to enlarge the workspace of the manipulator. In the casting manipulation, an end-effector is launched to its target by releasing the string connected to it, and its trajectory is controlled by the tension of the string. In this paper, we present the midair control of the end-effector. As a simple way, we propose the braking technique to apply impulsive force to the end-effector by braking the movement of the string. Examining dynamic characteristics of the string when an impulsive force applies to it, we show that the midair motion of the end-effector can be controlled by the braking technique. Then, we apply the braking technique to the multiple braking control of the trajectory. We confirm the effectiveness of the proposed method through simulations and experiments using casting manipulator hardware.     

A New Cable-Based Parallel Robot with Three Degrees of Freedom

In this paper, a new cable-based parallel robot is introduced. In this robot, the cables are used to not only actuate the end-effector but apply the necessary kinematic constrains to provide three pure translational degrees of freedom. In order to maintain tension in the cables, a collapsible element called “spine” is used between the end-effector and the robot’s base. The kinematic analysis of this robot is similar to that of a rigid link parallel manipulator as long as the cables are in tension. The rigidity of this robot which corresponds to having all cables in tension is studied thoroughly and it is proved that a single spine with a finite force is sufficient to guarantee rigidity for any external load at any position of the workspace.     

受限机器人运动的自适应控制

本文基于[4]中对受限机器人运动方程的变换,给出了一种自适应控制方案,使得在系统某些参数未知的情况下,机器人末端操纵器的位置运动及其与刚性、无摩擦的工作环境之间的接触力渐近趋于期望值,本文中的仿真例子验证了给出的自适应控制方案的有效性。     

Feedback linearization control of flexible joint robots

In this paper, the control of a two link, flexible joint manipulator is examined. Among external forces, an exogenous constraint force acting on the end-effector is included. The manipulator dynamics are described by:

. On the assumption that f(x), g(x) and J^T f_e(x) are smooth vector fields, it is shown that the inner loop control u is of the form:

u=1/dT_n,g(v−dT_n,(ƒ(x)+J^Tƒ_e(x)))

where u is an outer loop control signal and y = T(x) is a diffleomorphism that transform (a) into linear system. As the position control scheme is adopted, the value of the contact force is not controlled.

The results for the inner loop control are substantiated by simulation of a two-link robot model. The robustness of the control method is examined and a Lyapunov-based control correction, similar to that of the free motion case, is implemented. Results are obtained for parametric errors of up to 50%. In the simulation, the manipulator is required to follow a specified joint trajectory such that the end-effector traces a sinusoidal path along a constraint surface. The results obtained illustrate the tracking of the link reference trajectory and indicate that the inner loop corrections are valid.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

A direct algorithm for continuous path control of manipulators

This paper presents an algorithm for positioning and orientation of the hand for a redundant or non-redundant manipulator along a continuous path in space. This algorithm minimizes the distance between the actual position of the tip of the end-effector and the desired path. The algorithm does not use the Jacobian matrix for the inverse kinematics of the robot. It takes full advantage of the resolution of the joint drives, avoids singularity problems, and can be used for both redundant manipulators. The algorithm can be used in any situation where continuus motion of the end-effector is required in an open loop mode.     

Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator

In general, the manipulator's end-effector can be located in a desired position and orientation in its work-space through angular and/or linear displacements of its joints. These joint coordinates can be obtained by solving the loop-closure equation of the manipulator's kinematic model. The most common method for obtaining this equation is based on the point coordinates 4×4 homogeneous transformation matrix. This method uses a special set of frames which are adapted to the manipulator's configuration. Within the last few years there has been some interest in the use of screw operators (line transformations) to model the kinematic configuration of manipulators and to form the loop-closure equation. In this article, a kinematic model of a general (6 DOF) manipulator is obtained through the application of a screw operator (dual-unit quaternion) to represent the screw displacements of the line coordinates of the manipulator link and joint axes. The loop-closure equation of the closed kinematic chain is obtained by introducing a hypothetical link/joint at the manipulator's end-effector location. The resultant non-linear loop-closure equation is then solved for the joint coordinates using a numerical technique. The method is illustrated with an example.