Use of coherence analysis for the evaluation and adjustment of robot gear performance

Previous work by our group has demonstrated that it is possible to use the robot joint excitation technique and coherence analysis function to adjust robot joint gears for maximum robot precision. A robot joint gear box equipped with gear adjustment mechanism was instrumented so that the gap between the teeth of a pair of gears (backlash) could be measured. The translational and rotational components of robot link motion were decoupled using multiple sensors so that the relationship between the coherence analysis function of each type of motion and gear backlash could be investigated. The sensitivity of the adjustment technique to various input signals and sensor positions was also examined. Results show that coherence analysis can be used as a measurement technique to determine the precision with which the robot joint link responds to control signal input.     

Ground adaptive and optimized locomotion of snake robot moving with a novel gait

In this paper, we present a novel gait, forward head serpentine (FHS), for a two dimensional snake robot. The advantage of this new gait is that the head link remains in the forward direction during motion. This feature significantly improves snake robot potential applications. Genetic Algorithm (GA) is used to find FHS gait parameters. Relationship between FHS gait parameters and friction coefficients of the ground are developed. Next, robot speed is considered in the optimization. A fitness function covering robot speed and head link angular changes is defined. A general sinusoidal wave form is applied for each joint. GA is used to find gait parameters resulting in maximum speed while head link angular changes remain in an acceptable range. Optimal gait parameters are also calculated for different friction coefficients and relationships between them are developed. Experiments are also performed using a 5-link snake robot. It is shown that experimental and theoretical results closely agree.     

Adaptive Tracking Controller for Rigid-Link Elastic-Joint Robots with Link Acceleration Estimation

This paper presents a adaptive switching control scheme for elastic joint robot manipulators. The characteristics of both flexible and rigid subsystems are assumed unknown except the joint stiffness. An adaptive estimator compensates the uncertainty due to the unknown robot characteristics. The actuators and links position, velocity and an estimation of the link acceleration are used as feedback to the control law. A filter is designed to estimate the links acceleration and its accuracy is insured by the linear control theory. Lyapunov theory is used to verify the asymptotic stability of the control law. The performance of the proposed control method is tested using a simulated planar robot with two rotational degrees of freedom for high and low joint stiffness.     

Efficient robot arm modeling for computer control

This article presents a comparative study of the required number of arithmetic operations necessary for computing robot arm models using the Denavit-Hartenberg symbolic notation and a proposed one. The proposed notation is based on the idea of describing the motion of a robot joint by a pair matrix and the geometry of a link by a shape matrix. This notation needs the use of two coordinate systems for each joint or link. The results prove that the proposed notation reduces the computation time of robot models. For a 6-degrees of freedom robot arm, the computation times of kinematic position, velocity, and dynamic models are reduced respectively by 20%, 5%, and 2%, respectively. The two notations have the same effects on computing the inverse models. © 1993 John Wiley & Sons, Inc.     

具有力矩传感器的柔性关节的振动抑制

针对具有谐波减速器的柔性关节机器人容易产生振动的问题,设计了一种轮辐式力矩传感器,该力矩传感器安装于谐波减速器输出端和机器人臂杆之间,用于反馈机械臂反作用于关节的扭转力矩,从而能够直接获得关节的振动状态信息.基于该力矩传感器信息和计算的关节名义输出力矩,提出了一种新的振动抑制方法,在传统力矩负反馈PD控制器基础上通过增...     

Adaptive tracking control of flexible‐joint manipulators without overparametrization

In this paper, an adaptive controller is designed for rigid‐link flexible‐joint robot manipulators based on link and actuator position measurements only. It is based on the adaptive integrator backstepping method and the link and actuator velocity filters are used to estimate the unknown velocity terms. Moreover, the proposed controller exploits the estimate of the joint stiffness matrix inverse to overcome the overparametrization problem, which has been a significant drawback in adaptive partial state feedback controllers. It achieves asymptotic tracking of link positions while keeping all states and signals bounded. The tracking capability of the presented method is shown through simulation results of one‐ and two‐link flexible joint manipulators. © 2004 Wiley Periodicals, Inc.     

Evolutionary Minimum Cost Trajectory Planning for Industrial Robots

A general method for computing minimum cost trajectory planning for industrial robot manipulators is presented. The aim is minimization of a cost function with constraints namely joint positions, velocities, jerks and torques by considering dynamic equations of motion. A clamped cubic spline curve is used to represent the trajectory. This is a non-linear constrained optimization problem with five objective functions, 30 constraints and 144 variables. The cost function is a weighted balance of transfer time, mean average of actuators efforts and power, singularity avoidance, joint jerks and joint accelerations. The problem is solved by two evolutionary techniques such as Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Differential Evolution (DE). Numerical applications for a six link robotic manipulator – STANFORD robot (pick and place operation) and a two link planar manipulator (motion in the presence of obstacles) are illustrated. The results obtained from the Proposed techniques (NSGA-II and DE) are compared for different values of weighting coefficients. The influences of the algorithm parameters and weight factors on algorithm performance are analyzed. The DE algorithm converges quickly than NSGA-II. Also DE algorithm gives better results than NSGA-II in majority of cases. A comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal solutions of any complex problem using DE algorithm.     

A geometric method for determining joint rotations in the inverse kinematics of robotic manipulators

An inverse‐kinematics algorithm has been developed to evaluate the joint rotations of a robotic manipulator given the orientation of its hand link. The method mimics the way a person would determine the joint rotations by assembling the links comprising the robot mechanism and making adjustments in the joint displacements until the hand link is in the desired situation. An example is given where it is shown that the method is reasonably robust, can be applied to any design of robot, and is competitive with alternative highly‐mathematical, specific‐robot specialized, computational‐intensive schemes. ©2000 John Wiley & Sons, Inc.     

Performance measures for locomotion robots

We design two performance measures for a planar locomotion robot, modeled closely after the Platonic Beast. The first measure is proportional to the total motion of all joints during locomotion of the robot. This is a rough approximation to the energy consumption of the robot. The second measure determines the maximal speed of locomotion, for given limits on the joint speeds. We compute optimal modes of locomotion on different slopes for various designs. The results indicate that a variable link length can greatly improve the ability of the robot to walk on steep slopes. © 1997 John Wiley & Sons, Inc.     

An improved method for on-line calculation and compensation of the static deflection at a robot end-effector

Traditionally, robotic deflection analysis for a low-weight robot has been performed based on an assumption that each link is treated as a cantilever beam, which leads to no angular deflection at a joint. In practice, a robotic intermediate joint is linearly and angularly deflected when a load is applied at the end-effector. It is found in this study that the additional link deflection resulting from the angular deflection of a robotic revolute joint substantially contributes to the end-effector's total deflection. This article presents an improved method via a combination of classical beam theory, energy methods and the concepts of differential relationships to more accurately calculate the static deflection at the end-effector. A systematic approach to deflection calculation through three different Jacobians are presented. The study also shows that the end-effector's deflection heavily depends on robotic arm configurations. The deflection is then compensated based on the selected optimum configuration. The theoretical deflection analysis is verified by experimental results. A planar two-link robot and a six-degree-of-freedom Elbow Manipulator are used for numerical illustration and calculation procedure.     

工业机器人的工作空间综合

根据机器人工作位姿要求确定其自由度数，关节类型及排列，杆件尺寸，关节运动范围，机器人的位置等过程称为机器人的工作空间综合过程，本文侧重对已知的机器人结构提出了进行工作空间综合的优化方法。     

A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints

In the present study, for the first time, flexible multibody dynamics for a three-link serial robot with two flexible links having active prismatic joints is presented using an approximate analytical method. Transverse vibrations of flexible links/beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the links. In this study, first, vibration analysis of a flexible link sliding through an active prismatic joint having translational motion is considered. A rigid-body coordinate system is used, which aids in obtaining a new and rather simple form of the kinematic differential equation without the loss of generality. Next, the analysis is extended to include dynamic forces for a three-link planar serial robot called PPP (Prismatic, Prismatic, Prismatic), in which all joints are prismatic and active. The robot has a rigid first link but flexible second and third links. To model the prismatic joint, time-variant constraints are written, and a motion equation in a form of virtual displacement and virtual work of forces/moments is obtained. Finally, an approximate analytical method called the “constrained assumed modes method” is presented for solving the motion equations. For a numerical case study, approximate analytical results are compared with finite element results, which show that the two solutions closely follow each other.     

Modelling the dynamic characteristics of a robot arm joint

The dynamic behavior of a robot arm has been modelled, taking into account the elasticity and damping of the joints and the backlash introduced by the gear pairs of the transmission mechanism. The links of the robot arm are considered to be rigid and its joints rotational. A technique for automatic formulation of the differential equations of the lumped mass dynamic model of the gear train, incorporating the backlash nonlinearity, has been developed. Each link and the accompanying joint comprise a module. The dynamic equations of the manipulator are formulated through an iterative technique. The algorithm will provide automatic formulation of the dynamic equations of the model of the arm including the referenced nonlinearities of the joint drives. Finally, an application of the algorithm to a planar manipulator arm with two links and two rotational joints is presented.     

Error-model-based robot calibration using a modified CPC model

Selection of a proper robot kinematic model is a critical step in error-model-based robot calibration. The Denavit-Hartenberg (DH) model exhibits singularities in calibration of robots having consecutive parallel joint axes. The complete and parametrically continuous (CPC) modeling technique is one of the more versatile alternative modeling conventions designated to fit the needs of manipulator calibration. No modeling convention is, however, perfect. One “user-unfriendly” aspect of the CPC model is a condition handling technique needed, when constructing the error model, to avoid model singularities due to the adoption of the direction vectors of the joint axes as link parameters.This paper presents a modification to the CPC model which brings the model closer to the DH model. Rather than using the direction vectors of joint axes, the modified CPC (MCPC) model employs angular parameters to acommodate the required rotations for each link transformation. This modification results in a much simplified error model. The model, like the CPC model, is capable of completely describing the geometry and motion of the manipulator in a reference coordinate frame. Its error model possesses a minimum number of parameters to span the entire geometric error space and it can be made singularity-free by proper selection of the tool axis. This paper presents a calibration study of the PUMA robot using the MCPC model. A moving stereo camera system was employed for end-effector pose measurements. The MCPC error model was then used for kinematic identification. Results on the PUMA arm show that the MCPC performs well for robot calibration. The well-defined structure and user friendliness of the MCPC model may facilitate the implementation of robot calibration techniques on the factory floor.     

基于连杆力矩传感器动态补偿的机器人灵巧手笛卡儿阻抗控制

为了对连杆空间力矩传感器进行动态补偿,提出了适用于求取串联机器人任意连杆中任意一点处所受的内力和内力矩的算法.该算法采用连杆假想截断原理利用牛顿-欧拉方程推导而出.推导过程综合考虑了串联机器人是否处于静态以及末端是否受外力作用的情况,以及串联机器人的关节是否是回转关节的情况.然后利用该算法计算动态补偿值,构建了基于连杆力矩传感器动态补偿的笛卡儿阻抗控制器.最后在HIT/DLR Hand II五指灵巧手上进行了实验验证.实验结果一方面验证了该算法的有效性,另一方面也验证了本文所构建的笛卡儿阻抗控制器的有效性.     

质心坐标系的牛顿-欧拉动力学方程

在机器人的运动学和动力学分析中,杆的附件坐标系通常是建立在关节轴线上的.本文采用在机器人各杆的质心建立杆附体坐标系的方法,推导了机器人的牛顿-欧拉动力学递推方程.并以平面两杆机械手为例给出这种方法的结果.     

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided.      

Compliance measurement for the Mitsubishi PA-10 robot

In this study, we measure the compliance characteristics of the 7-degree-of-freedom (DOF) vertical multiarticulated Mitsubishi PA-10 robot. To determine the compliance characteristics of the robot, numerical values of joint compliance are identified by a partial simultaneous measurement method using a force/torque sensor and a 3-D measurement system. The identified compliance is derived from an extended 10-DOF link model that comprises three additional virtual joints and seven actual joints. The virtual joints, which can be handled in the same manner as the actual joints, can be used for more accurate identification. The modeling error derived from link flexibility may be compensated by introducing the extended link model with additional virtual joints. To investigate the accuracy of the compliances identified with the extended link model, verification experiments were conducted. The results show that precise compliance characteristics are obtained from the extended link model. Finally, we reveal the compliance model of the Mitsubishi PA-10 robot, which comprises the numerical values of the joint compliance and a simple kinematic modeling.     

Cooperative Strategy for a Wheelchair and a Robot to Climb and Descend a Step

This paper discusses a cooperative strategy that enables a wheelchair and a wheeled robot to climb and descend a step. In this method, not only does the robot assist the wheelchair user, but also the user assists the robot to overcome the step. The research indicates the feasibility of this new cooperative strategy between a physically disabled person and a personal robot that is not designed for high-level performance. The two vehicles (the wheelchair and the wheeled robot) are connected by a simple link mechanism, the two connecting positions of which are free joints. This method is especially affected by the link positions. A numerical calculation clarifies the combinations of the two link positions to avoid a collision between each vehicle and to overcome a step at the same time. The result of the simulations indicate that it is necessary to change the link positions to climb and descend a step safely. The experimental results show that this method is effective.