Closed-Form Inverse Kinematics for Continuum Manipulators

This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.     

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution corresponding to the Jacobian pseudo inverse is non-integrable, while that associated with the extended Jacobian is integrable. Two methods of devising the approximating extended Jacobian algorithm are examined. The first method is referred to as differential geometric, and relies on the approximation of a non-integrable distribution (in fact: a codistribution) by an integrable one. As an alternative, the approximation problem has been formulated as the minimization of an approximation error functional, and solved using the methods of the calculus of variations. Performance of the obtained extended Jacobian inverse kinematics algorithms has been compared by means of computer simulations involving the kinematics model of the 7 dof industrial manipulator POLYCRANK. It is concluded that the differential geometric method offers a rapid, while the variational method a systematic tool for solving inverse kinematic problems.     

机器人运动控制的两种模型

以六自由度模块化机器人为对象,利用D-H坐标变换方法进行运动学分析,计算出各杆之间的齐次坐标变换矩阵,建立求解机器人逆运动学问题的两种模型。并根据两种模型应用vc＋＋程序对机器人进行控制,验证了两种模型的有效性,并对这两种模型进行了比较。     

Application of Fuzzy Logic for the Solution of Inverse Kinematics and Hierarchical Controls of Robotic Manipulators

In this paper, hierarchical control techniques is used for controlling a robotic manipulator. The proposed method is based on the establishment of a non-linear mapping between Cartesian and joint coordinates using fuzzy logic in order to direct each individual joint. The hierarchical control will be implemented with fuzzy logic to improve the robustness and reduce the run time computational requirements. Hierarchical control consists of solving the inverse kinematic equations using fuzzy logic to direct each individual joint. A commercial Microbot with three degrees of freedom is utilized to evaluate this methodology. A decentralized fuzzy controller is used for each joint, with a Fuzzy Associative Memories (FAM) performing the inverse kinematic mapping in a supervisory mode. The FAM determines the inverse kinematic mapping which maps the desired Cartesian coordinates to the individual joint angles. The individual fuzzy controller for each joint generates the required control signal to a DC motor to move the associated link to the new position. The proposed hierarchical fuzzy controller is compared to a conventional controller. The simulation experiments indeed demonstate the effectiveness of the proposed method.     

机械手的模糊逆模型鲁棒控制

提出一种基于模糊聚类和滑动模控制的模糊逆模型控制方法,并将其应用于动力学方程未知的机械手轨迹控制.首先,采用C均值聚类算法构造两关节机械手的高木-关野(T-S)模糊模型,并由此构造模糊系统的逆模型.然后,在提出的模糊逆模型控制结构中,离散时间滑动模控制和时延控制(TDC)用于补偿模糊建模误差和外扰动,保证系统的全局稳定性并改进其动态和稳态性能.系统的稳定性和轨迹误差的收敛性可以通过稳定性定理来证明.最后,以两关节机械手的轨迹跟随控制为例,揭示了该设计方法的控制性能.     

Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions

This study offers the solution at the control feedback level to the inverse kinematics problem subject to state equality and inequality constraints for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers generating the mobile manipulator trajectory whose attractor attained in a finite time, fulfills the above state constraints. The problem of both holonomic manipulability enforcement and collision avoidance is solved here based on an exterior penalty function approach which results in continuous mobile manipulator velocities near obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.     

Inverse Kinematics of Binary Manipulators Using a Continuum Model

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. The major benefits of binary actuation are that extensive feedback control is not required, reliability and task repeatability are very high, and two-state actuators are generally very inexpensive, resulting in low cost robotic mechanisms. These manipulators have great potential for use in both the manufacturing and service sectors, where the cost of high performance robotic manipulators is often difficult to justify. The most difficult challenge with a binary manipulator is to achieve relatively continuous end-effector trajectories given the discrete nature of binary actuation. Since the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, calculation of inverse kinematics by direct enumeration of joint states and calculation of forward kinematics is not feasible in the highly actuated case. This paper presents an efficient method for performing binary manipulator inverse kinematics and trajectory planning based on having the binary manipulator shape adhere closely to a time-varying curve. In this way the configuration of the arm does not exhibit drastic changes as the end effector follows a discrete trajectory.     

Stability Analysis for Prioritized Closed-Loop Inverse Kinematic Algorithms for Redundant Robotic Systems

Stability analysis of priority-based kinematic control algorithms for redundant robotic systems is approached in this paper. Starting from the classical applications in position control of manipulators, the kinematic-based approaches have lately been applied to, e.g., visual servoing and quadruped or multirobot coordination control. A common approach consists in the definition of several tasks properly combined in priority. In this paper, by resorting to a Lyapunov-based stability discussion for several prioritized inverse kinematics algorithms, sufficient conditions for the control gains and the tasks' design are given for the regulation problem. Two case studies show the practical implementation of the results.     

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.     

An Artificial Neural Network Approach for Inverse Kinematics Computation and Singularities Prevention of Redundant Manipulators

In this article an Artificial Neural Network (ANN) approach for fast inverse kinematics computation and effective singularities prevention of redundant robot manipulators is presented. The approach is based on establishing some characterizing matrices, representing some geometrical concepts, in order to yield a simple performance index and a null space vector for singularities avoidance/prevention and safe path generation. Here, this null space vector is computed using a properly trained ANN and included in the computation of the inverse kinematics being performed also by another properly trained ANN.     

Geometrically Exact Models for Soft Robotic Manipulators

Unlike traditional rigid linked robots, soft robotic manipulators can bend into a wide variety of complex shapes due to control inputs and gravitational loading. This paper presents a new approach for modeling soft robotic manipulators that incorporates the effect of material nonlinearities and distributed weight and payload. The model is geometrically exact for the large curvature, shear, torsion, and extension that often occur in these manipulators. The model is based on the geometrically exact Cosserat rod theory and a fiber reinforced model of the air muscle actuators. The model is validated experimentally on the OctArm V manipulator, showing less than 5% average error for a wide range of actuation pressures and base orientations as compared to almost 50% average error for the constant-curvature model previously used by researchers. Workspace plots generated from the model show the significant effects of self-weight on OctArm V.      

Optimal Motion Planning of Robotic Manipulators Removing Mobile Objects Grasped in Motion

The following study deals with motion optimization of robot arms having to transfer mobile objects grasped when moving. This approach is aimed at performing repetitive transfer tasks at a rapid rate without interrupting the dynamics of both the manipulator and the moving object. The junction location of the robot gripper with the object, together with grasp conditions, are partly defined by a set of local constraints. Thus, optimizing the robot motion in the approach phase of the transfer task leads to the statement of an optimal junction problem between the robot and the moving object. This optimal control problem is characterized by constrained final state and unknown traveling time. In such a case, Pontryagin"s maximum principle is a powerful mathematical tool for solving this optimization problem. Three simulated results of removing a mobile object on a conveyor belt are presented; the object is grasped in motion by a planar three-link manipulator.     

面向灵活工作空间的血管外科手术机器人设计

在分析医生显微缝合与打结动作和操作空间布置的基础上，采用向两个方向投影的方法，对医生的动作进行了记录和量化分析．分析了测量数据与机器人灵活度的关系，并以该关系作为整个设计分析的基础．根据投影几何以及显微手术数据得到了从手末端工具准确的三维灵活操作空间．根据测量得到的灵活空间运用逆运动学原理，对机器人的机构参数和关节的运动范围进行了计算．在理论分析和设计的基础之上，加工出了一台显微手术样机(MicroHand)．     

Trajectory Planning with Collision Avoidance for Redundant Robots Using Jacobian and Artificial Potential Field-based Real-time Inverse Kinematics

This study proposes an algorithm for combining the Jacobian-based numerical approach with a modified potential field to solve real-time inverse kinematics and path planning problems for redundant robots in unknown environments. With an increase in the degree of freedom (DOF) of the manipulator, however, the problems in realtime inverse kinematics become more difficult to solve. Although the analytical and geometrical inverse kinematics approach can obtain the exact solution, it is considerably difficult to solve as the DOF increases, and it necessitates recalculations whenever the robot arm DOF or Denavit-Hartenberg (D-H) parameters change. In contrast, the numerical method, particularly the Jacobian-based numerical method, can easily solve inverse kinematics irrespective of the aforementioned changes including those in the robot shape. The latter method, however, is not employed in path planning for collision avoidance, and it presents real-time calculation problems. This study accordingly proposes the Jacobian-based numerical approach with a modified potential field method that can realize real-time calculations of inverse kinematics and path planning with collision avoidance irrespective of whether the case is redundant or non-redundant. To achieve this goal, the use of a judgment matrix is proposed for obstacle condition identification based on the obstacle boundary definition; an approach for avoiding the local minimum is also proposed. After the obstacle avoidance path is generated, a trajectory plan that follows the path and avoids the obstacle is designed. Finally, the proposed method is evaluated by implementing a motion planning simulation of a 7-DOF manipulator, and an experiment is performed on a 7-DOF real robot.

     

机械臂自适应鲁棒轨迹跟踪控制

针对具有外界干扰和不确定性的机械臂轨迹跟踪控制问题,提出了一种自适应鲁棒补偿控制算法,将计算转矩法用于系统标称模型,鲁棒控制用于消除系统不确定性的影响,并通过自适应算法自动调节不确定项,保证系统存在建模误差和外部干扰时的稳定性和动态性能。给出了具体的控制算法设计和系统稳定性、收敛性证明,最后通过仿真实验,表明系统具有跟踪误差快速收敛性以及良好的鲁棒性。     

Modeling of Flexible Beams for Robotic Manipulators

This work treats the problem of modeling robotic manipulators withstructural flexibility. A mathematical model of a planarmanipulator with a single flexible link is developed. This modelis capable of reproducing nonlinear dynamic effects, such as thebeam stiffening due to the centrifugal forces induced by therotation of the joints, giving it the capability to predictreliable dynamic behaviors for a wide range of applications. Onthe other hand, the model complexity is reduced, in order to keepit amenable for analysis and controller design. The models foundin current literature for control design of flexible manipulatorarms present dynamic limitations for the sake of real timeimplementation in a control scheme. These limitations are theresult of premature linearizations in the formulation of thedynamics equations. In this paper, these common linearizations arepresented and their dynamic limitations uncovered. An alternativereliable model is then presented. The model is founded on twobasic assumptions: inextensibility of the neutral fiber, andmoderate rotations of the cross sections in order to account forthe foreshortening of the beam due to bending. Simulation andexperimental results show that the proposed model has the closestdynamic behavior to the real beam.     

Modified Transpose Effective Jacobian Law for Control of Underactuated Manipulators

Underactuated manipulators consist of active and passive joints, and developing a control technique that can manage such systems is an attractive, challenging problem. Most works in this area present model-based control laws that require a full dynamics model, and are consequently affected from uncertainties and time delays due to massive computations. Non-model-based control approaches provide an efficient alternative for practical implementation. The Modified Transpose Jacobian (MTJ) algorithm is one of these controllers that has been recently proposed for fully actuated manipulators with a square matrix Jacobian. Based on an approximated feedback linearization approach, the MTJ does not need a priori knowledge of the plant dynamics. In this paper, this scheme is extended to the complicated control problem of underactuated robots in Cartesian space. To this end, the notion of the Transpose Effective Jacobian (TEJ) is presented and so the proposed algorithm is called the Modified TEJ (MTEJ) algorithm. The MTEJ control law employs stored data of the control command in the previous time step, as a learning tool to yield an improved performance. Therefore, the proposed law needs just to a portion of mass matrix that corresponds to passive joint(s), and it is much less affected by inaccuracies in system properties. The gains of the proposed MTEJ can be selected more systematically and do not need to be large; hence, the noise rejection characteristics of the algorithm are improved. Also, no need for the pseudo-inversion of the Jacobian matrix in the proposed controller makes further convenience in the underactuated cases. In addition, the relationship between kinematic and dynamic manipulability measures is discussed for underactuated manipulators. Obtained results show its superior performance even compared to that of the model-based algorithms that need full dynamics models, while the proposed MTEJ requires much lower computation effort.     

机械手自适应模糊控制器设计

本文提出了一种自适应模糊控制器用于机械手轨迹跟踪控制,该控制器通过对训练数据的聚类分析提取典型数据送入神经网络学习,得到的控制规则更加适用,在线控制时可以自动调整神经网络的结构以及隶属函数的参数。仿真实验表明该控制器能够对机械手实时控制,而且精度较高。     

机器人的鲁棒预测控制

本文提出基于误差预测的机器人鲁棒控制器。考虑到机器人的动力学建模误差影响其控制性能,本文建立机器人的误差模型,给出预测建模误差对运动轨迹偏差的作用的有效方法,并提出建模误差的鲁棒性补偿。本文分别在关节空间和直角空间针对冗余机器人和非冗余机器人提出鲁棒预测控制器设计,其有效性由仿真例子检验。     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.