A real-time algorithm for simulation of flexible objects and hyper-redundant manipulators

Flexible objects such as a rope or snake move in a way such that their axial length remains almost constant. To simulate the motion of such an object, one strategy is to discretize the object into large number of small rigid links connected by joints. However, the resulting discretised system is highly redundant and the joint rotations for a desired Cartesian motion of any point on the object cannot be solved uniquely. In this paper, we revisit an algorithm, based on the classical tractrix curve, to resolve the redundancy in such hyper-redundant systems. For a desired motion of the `head' of a link, the `tail' is moved along a tractrix, and recursively all links of the discretised objects are moved along different tractrix curves. The algorithm is illustrated by simulations of a moving snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator. The simulations show that the tractrix based algorithm leads to a more `natural' motion since the motion is distributed uniformly along the entire object with the displacements diminishing from the `head' to the `tail'.

Redundancy resolution using a tractrix and its application to real-time simulations of hyper-redundant manipulators, snakes and tying of knots

To realistically simulate the motion of flexible objects such as ropes, strings, snakes, or human hair,one strategy is to discretise the object into a large number of small rigid links connected by rotary or spherical joints. The discretised system is highly redundant and the rotations at the joints (or the motion of the other links) for a desired Cartesian motion of the end of a link cannot be solved uniquely. In this paper, we propose a novel strategy to resolve the redundancy in such hyper-redundant systems.We make use of the classical tractrix curve and its attractive features. For a desired Cartesian motion of the `head'of a link, the `tail' of the link is moved according to a tractrix,and recursively all links of the discretised objects are moved along different tractrix curves. We show that the use of a tractrix curve leads to a more `natural' motion of the entire object since the motion is distributed uniformly along the entire object with the displacements tending to diminish from the `head' to the `tail'. We also show that the computation of the motion of the links can be done in real time since it involves evaluation of simple algebraic, trigonometric and hyperbolic functions. The strategy is illustrated by simulations of a snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator.

A Self-Organizing Neural Network Model for Redundant Sensory-Motor Control, Motor Equivalence, and Tool Use

A neural network is introduced which provides a solution of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space. To do this, the network self-organizes a mapping from motion directions in 3-D space to velocity commands in joint space. Computer simulations demonstrate that, without any additional learning, the network can generate accurate movement commands that compensate for variable tool lengths, clamping of joints, distortions of visual input by a prism, and unexpected limb perturbations. Blind reaches have also been simulated.

Redundancy resolution using tractrix -- Simulations and Experiments

Hyper-redundant robots are characterized by the presence of a large number of actuated joints, many more than the number required to perform a given task. These robots have been proposed and used for many applications involving avoiding obstacles or, in general, to provide enhanced dexterity in performing tasks. Making effective use of the extra degrees of freedom or resolution of redundancy has been an extensive topic of research and several methods have been proposed in literature. In this paper, we compare three known methods and show that an algorithm based on a classical curve called the tractrix leads to a more 'natural' motion of the hyper-redundant robot, with the displacements diminishing from the end-effector to the fixed base. In addition, since the actuators nearer the base 'see' a greater inertia due to the links farther away, smaller motion of the actuators nearer the base results in better motion of the end-effector as compared to other two approaches. We present simulation and experimental results performed on a prototype eight link planar hyper-redundant manipulator.

超冗余度机械臂的路径安全性优化研究

提出了一个对超冗余度机械臂路径规划进行安全性优化的新方法 .采用一般随机路标法得到一个表示机械臂位形空间结构信息的路标 ,计算机械臂在各个位形下与障碍物之间的最小距离 ,并把此信息加到随机路标法所求的路标上 ,从而把路标转化为网格结构 .基于此网络 ,给出了一个对路径进行安全性优化的数学模型 ,利用其对超冗余度机械臂进行路径规划 .仿真结果表明 ,相对于一般随机路标法所建模型规划的路径安全性大大提高

冗余自由度机械手的避障控制

避障碍物一直是冗余自由度机械手的主要应用 ,本文采用伪逆矩阵法 ,以障碍物和机械手之间的距离的函数作为性能指标函数来解冗余自由度机械手逆解 ,进行避障控制 ,并提出一种简单的计算机械手和障碍物之间的距离方法 ,通过对一个三自由度的平面机械手进行仿真 ,验证了算法的正确性

基于超冗余度机械臂动力学的时间最优轨迹规划

基于超冗余度机械臂的动力学方程 ,提出了一种超冗余度机械臂同时受速度和力矩约束的时间最优轨迹规划方法 .它首先采用 B样条曲线拟合无碰撞离散路径 ,得到由伪位移参数 s表示的超冗余度机械臂连续、光滑运动路径 ,然后对动力学方程和约束方程进行数学变换 ,得到由 s表示的动力学方程和约束方程 ,最后以 s和伪速度 s· 分别作为动态规划的阶段变量和状态变量 ,对超冗余度机械臂进行时间最优轨迹规划 .仿真结果表明 ,所给出的时间最优轨迹规划算法是正确的 ,所采取的解决方法是可行的

Neural Representations for Sensory-Motor Control I: Head-Centered 3-D Target Positions from Opponent Eye Commands

This article describes how corollary discharges from outflow eye movement commands can be transformed by two stages of opponent neural processing into a head-centered representation of 3-D target position. This representation implicitly defines a cyclopean coordinate system whose variables approximate the binocular vergence and spherical horizontal and vertical angles with respect to the observer's head. Various psychophysical data concerning binocular distance perception and reaching behavior are clarified by this representation. The representation provides a foundation for learning head-centered and body-centered invariant representations of both foveated and non-foveated 3-D target positions. It also enables a solution to be developed of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space.

Fault tolerance operation of cooperative manipulators

Autonomous or teleoperation of critical tasks in space applications require fault tolerant robotic manipulators. These manipulators are able to maintain their tasks even if a joint fails. If it is presumed that the manipulator is fault tolerant on its trajectory, then the next step is to provide a fault tolerant force at the end-effector of the manipulator. The problem of cooperative fault tolerant force is addressed in this paper within the operation of two manipulators. The cooperative manipulators are used to compensate the force jump which occurs on the force of the end-effector of one manipulator due to a joint failure. To achieve fault tolerant operation, the contribution of the faulty joint for the force of the end-effector of the faulty manipulator is required to be optimally mapped into the torque of the faulty and healthy manipulators. The optimal joint torque reconfigurations of both manipulators for compensating this force jump are illustrated. The proposed frameworks are deployed for two cooperative PUMA560 manipulators. The results of the case studies validate the fault tolerant cooperation strategies.

Formations of robotic swarm: an artificial force based approach

Cooperative control of multiple mobile robots is an attractive and challenging problem which has drawn considerable attention in the recent past. This paper introduces a scalable decentralized control algorithm to navigate a group of mobile robots (swarm) into a predefined shape in 2D space. The proposed architecture uses artificial forces to control mobile agents into the shape and spread them inside the shape while avoiding intermember collisions. The theoretical analysis of the swarm behavior describes the motion of the complete swarm and individual members in relevant situations. We use computer simulated case studies to verify the theoretical assertions and to demonstrate the robustness of the swarm under external disturbances such as death of agents, change of shape etc. Also the performance of the proposed distributed swarm control architecture was investigated in the presence of realistic implementation issues such as localization errors, communication range limitations, boundedness of forces etc.

Controle de Manipulador Redundante Utilizando Realimentação Visual

In conventional robot manipulator control, the desired path is specified in cartesian space and converted to joint space through inverse kinematics mapping. The joint references generated by this mapping are utilized for dynamic control in joint space. Thus, the end-effector position is, in fact, controlled indirectly, in open-loop, and the accuracy of grip position control directly depends on the accuracy of the available kinematic model. In this report, a new scheme for redundant manipulator kinematic control, based on visual servoing is proposed. In the proposed system, a robot image acquired through a CCD camera is processed in order to compute the position and orientation of each link of the robot arm. The robot task is specified as a temporal sequence of reference images of the robot arm. Thus, both the measured pose and the reference pose are specified in the same image space, and its difference is utilized to generate a cartesian space error for kinematic control purposes. The proposed control scheme was applied in a four degree-of-freedom planar redundant robot arm, experimental results are shown

An experimental study on the failure tolerant control of a redundant planar serial manipulator via pseudo-inverse approach

In this paper, fault-tolerant control of redundant planar serial manipulators has been investigated experimentally via an offline method called psuedo-inverse reconfiguration method. Minimizing the end-effector's velocity jump via an optimal mapping of joint failures into healthy joints velocity space can be regarded as the main contribution of this reconfiguration approach. This algorithm has been simulated and implemented on a four-link serial manipulator named as TaArm. It should be mentioned that for simulation and practical tests, C++ programming language in QtCreator environment has been used which provided high computational speed. Two scenarios has been selected for simulation and implementation studies and results shows that the algorithm considerably removes the velocity jump of the end-effector in both simulation and experimetal studies.

An introduction to utilising the redundancy of a kinematically redundant parallel manipulator to operate a gripper

Although parallel manipulators provide several benefits compared to similar-sized serial manipulators, they typically exhibit a limited rotational workspace. One approach to designing a parallel manipulator with infinite range of tool rotation around one axis is to introduce kinematic redundancy. This is typically achieved by extending a non-redundant mechanism with an additional actuator and a supplemental degree of freedom, while the degrees of freedom of the tool platform remain the same. The main drawback of this approach is the cost of the additional actuator. In this paper, we discuss the possibility of harvesting the motion in the additional degree of freedom to operate a gripper. The benefits of the proposed idea include saving the cost of a gripper actuator and reducing the mass of the manipulated platform. Additionally, the requirement to provide the manipulated platform with compressed air or electric power is removed. Several variants of a kinematically redundant manipulated platform with five degrees of freedom are introduced along with conceptual mechanical designs for transforming the redundant platform motion into the opening and closing of a gripper.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.