Internal singularity analysis of a class of lower mobility parallel manipulators with articulated traveling plate

This paper deals with a particular family of lower mobility parallel kinematic manipulators. The four degrees of freedom of the end-effector consist of three translations plus one rotation with a high tilting angle. Robots belonging to this family are first introduced, and a common parameterization is established. Then an extended kinematic model is proposed for this family of robots using a new Jacobian matrix. Relevant information about robot kinematic singularities, internal singularities, and possible end-effector motions can be obtained by resorting to this matrix. The efficiency of this method is proven by applying it to several traveling-plate architectures corresponding to already built robot prototypes. The results of the expected behavior are compared with the prototype's real behavior. The goal of this paper is to show that internal (or constraint) singularities can occur in lower mobility parallel kinematic manipulators, and to underline the influence they have during the design stage.     

Obstacle avoidance of snake robot by switching control constraint

In this paper, we propose an obstacle avoidance method for autonomous locomotion control of a snake robot. The snake robot consists of rigid links, active joints and passive wheels, and can move only by varying its shape. The pass planning for the obstacle avoidance is a complicated problem because the snake robot has many states, control inputs and the under-actuated property. In our proposed method, the snake motion is restricted to a periodic undulate curve (called a serpenoid curve) by an additional control constraint and the undulate curve is tuned by switching the control constraint in order that the snake robot avoids the obstacle. Therefore, the path planning is simplified and the snake robot will achieve the obstacle avoidance with an efficient path. In this paper, we denote the details of our method and investigate the effectiveness of our strategy by numerical simulations.     

Modeling and Control of Head Raising Snake Robots by Using Kinematic Redundancy

In this paper, we consider trajectory tracking control of a head raising snake robot on a flat plane by using kinematic redundancy. We discuss the motion control requirements to accomplish trajectory tracking and other tasks, such as singular configuration avoidance and obstacle avoidance, for the snake robot. The features of the internal motion caused by kinematic redundancy are considered, and a kinematic model and a dynamic model of the snake robot are derived by introducing two types of shape controllable point. The first is the head shape controllable point, and the other is the base shape controllable point. We analyzed the features of the two kinds of shape controllable point and proposed a controller to accomplish the trajectory tracking of the robot’s head as its main task along with several sub-tasks by using redundancy. The proposed method to accomplish several sub-tasks is useful for both the kinematic model and the dynamic model. Experimental results using a head raising snake robot which can control the angular velocity of its joints show the effectiveness of the proposed controller.     

基于高阶多项式的爬游机器人足端轨迹规划

针对深海爬游机器人足端轨迹规划问题,采用高阶多项式拟合的方法对其进行研究;首先,介绍了爬游机器人整体结构并对其进行运动学建模,结合爬游机器人运动学模型提出了一种直线与曲线相结合的机器人足端轨迹;其次,利用四阶多项式和六阶多项式分别对机器人足端轨迹进行拟合,比较两种拟合结果可知,六阶多项式拟合方法对机器人足端速度、加速度的规划效果更佳;利用六阶多项式轨迹拟合方法对多段轨迹连接点处的速度问题进行了分析,解决了机器人在运动过程中腿部抖动问题,使机械腿具有良好的控制柔顺性;最后,根据D-H法则建立机器人单腿仿真模型,通过仿真验证了算法的可行性,进一步在水池中利用机器人实物样机验证了算法的有效性.     

Classification of kinematic singularities in planar robot manipulators

In [13, 14] we have proclaimed a singularity theory based programme of investigations of kinematic singularities in robot manipulators. The main achievement of the programme consists in providing local candidate models of kinematic singularities. However, due to the specific form of the manipulator kinematics, fitting the candidate models into the prescribed robot kinematics is a fairly open problem. The problem is easily solvable only around non-singular configurations of manipulators, where locally the kinematics can be modelled by linear injections or projections. In this paper we are concerned with planar manipulator kinematics, and prove that, under a mild geometric condition, such kinematics can be transformed around singular configurations to simple quadratic models of the Morse type. The models provide a complete local classification of generic planar kinematics of robot manipulators.     

Formation control of underactuated bio-inspired snake robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.     

Redundant Control of a Planar Snake Robot with Prismatic Joints

This paper presents a control method of a planar snake robot with prismatic joints. The kinematic model is derived considering velocity constraints caused by passive wheels. The proposed control method based on the model allows the robot to track a target trajectory by appropriately changing its link length using prismatic joints. The degrees of freedom of prismatic joints are represented as kinematic redundancy in the model and are used in realizing subtasks such as singularity avoidance and obstacle avoidance. In addition, the link length is below its limit when introducing a sigmoid function into the kinematic model. Simulations are carried out to demonstrate the effectiveness of the proposed method and show a novel motion that avoids singular configurations through changes in link lengths.

     

考虑动力学模型的非完整移动机器人运动规划

针对非完整移动机器人,在运动学和动力学约束条件下提出了一种运动规划方法.在工作环境已知情况下,根据移动机器人的动力学模型和无打滑非完整运动约束条件,采用立方螺线对规划的路径光滑化,从而使得移动机器人易于跟踪所规划的路径,同时考虑了移动机器人速度的限制.最后采用Matlab对该算法进行了数值仿真,结果表明该方法是有效的.     

Dynamics and Motion Planning of Trident Snake Robot

The trident snake robot is a mechanical device that serves as a demanding testbed for motion planning and control algorithms of constrained non-holonomic systems. This paper provides the equations of motion and addresses the motion planning problem of the trident snake with dynamics, equipped with either active joints (undulatory locomotion) or active wheels (wheeled locomotion). Thanks to a partial feedback linearization of the dynamics model, the motion planning problem basically reduces to a constrained kinematic motion planning. Two kinds of constraints have been taken into account, ensuring the regularity of the feedback and the collision avoidance between the robot’s arms and body. Following the guidelines of the endogenous configuration space approach, two Jacobian motion planning algorithms have been designed: the singularity robust Jacobian algorithm and the imbalanced Jacobian algorithm. Performance of these algorithms have been illustrated by computer simulations.     

机器蛇三维运动仿真的研究与实现

该文将机器蛇的蠕动、游动等运动方式简化为正弦曲线,采用单侧对分法的迭代方法,将关节的长度和正弦曲线的数据进行拟合,得到在不同时刻下每一关节在统一坐标系内的具体位置和方向参数.利用关节坐标架的方法,将坐标系附着在关节坐标点上,建立一系列具有可继承性的关节链结构,调节不同时间的曲线变换规律,实现机器蛇的运动姿态的调整,进而在屏幕上实现三维的可视运动.针对OpenGL系统的开发特点,对机器蛇建模过程中的注意问题、关节动画中的坐标架复合变换等关键问题,进行了具体的分析提出了有效的解决方案.     

Control of snake robots with switching constraints: trajectory tracking with moving obstacle

We propose control of a snake robot that can switch lifting parts dynamically according to kinematics. Snakes lift parts of their body and dynamically switch lifting parts during locomotion: e.g. sinus-lifting and sidewinding motions. These characteristic types of snake locomotion are used for rapid and efficient movement across a sandy surface. However, optimal motion of a robot would not necessarily be the same as that of a real snake as the features of a robot’s body are different from those of a real snake. We derived a mathematical model and designed a controller for the three-dimensional motion of a snake robot on a two-dimensional plane. Our aim was to accomplish effective locomotion by selecting parts of the body to be lifted and parts to remain in contact with the ground. We derived the kinematic model with switching constraints by introducing a discrete mode number. Next, we proposed a control strategy for trajectory tracking with switching constraints to decrease cost function, and to satisfy the conditions of static stability. In this paper, we introduced a cost function related to avoidance of the singularity and the moving obstacle. Simulations and experiments demonstrated the effectiveness of the proposed controller and switching constraints.     

Autonomous robot calibration using a trigger probe

This paper presents a new robot autonomous calibration method using a trigger probe. The robot grips a simple probe (which was manufactured as a standard end-effector tool) automatically to touch constraint planes in a workspace (the locations of the constraint planes are not necessarily known exactly). The robot internal sensor measurements are recorded for kinematic calibration while the tip-point of the probe is in contact with the constraint plane. The kinematic constraint conditions are obtained from the known shape of the constraint surface, rather than from the measured reference locations in a workspace. The new method eliminates any use of external measuring devices for robot end-effector location measurements for robot calibration; thus it is suitable for a periodic robot re-calibration in a shop-floor environment. Both simulation and experimental results for a six degree-of-freedom (DOF) PUMA robot are given in this paper. The evaluation results using an external precision measuring device — Coordinate Measuring Machine(CMM) — are also presented.     

On the Stability of the Quadruple Solutions of the Forward Kinematic Problem in Analytic Parallel Robots

Many parallel robots can change between different assembly modes (solutions of the forward kinematic problem) without crossing singularities, either by enclosing cusps or alpha-curves of the planar sections of their singularity loci. Both the cusps and the alpha-curves are stable singularities, which do not disappear under small perturbations of the geometry of the robot. Recently, it has been shown that some analytic parallel robots can also perform these nonsingular changes of assembly mode by encircling isolated points of their singularity loci at which the forward kinematic problem admits solutions with multiplicity four. In this paper, we study the stability of these quadruple solutions when the design of the robot deviates from the analytic geometry, and we show that such quadruple solutions are not stable since the isolated singular points at which they occur degenerate into closed deltoid curves. However, we also demonstrate that, although the quadruple solutions are unstable, the behavior of the robot when moving around them is practically unaffected by the perturbations from the analytic geometry. This means that the robot preserves its ability to perform nonsingular transitions by enclosing the quadruple solutions, even when its geometry is not exactly analytic due to small manufacturing tolerances.     

软体机器人手眼视觉/形状混合控制

当末端带有相机的连续型软体机器人进行作业时,由于避障、安全性等多方面因素,既需要末端相机－机器人系统的视觉伺服,也需要机器人的整体形状控制．针对这个问题,本文提出了一种软体机器人手眼视觉/形状混合控制方法．该方法无需知道空间特征点的3维坐标,只需给定特征点在末端相机像平面的期望像素坐标和软体机器人的期望形状就可达到控制目的．建立了软体机器人的运动学模型,利用该模型,结合深度无关交互矩阵自适应手眼视觉控制和软体机器人形状控制,提出了一种混合控制律,并用李亚普诺夫稳定性理论对该控制律进行证明．仿真和实验的结果均表明,末端相机特征点像素坐标和形状可以收敛到期望值．     

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model.     

On inverting singular kinematics and geodesic trajectory generation for robot manipulators

In this paper, a new method is proposed of solving the inverse kinematic problem for robot manipulators whose kinematics are allowed to possess singularities. The method is based upon the so-called generalized Newton algorithm, introduced by S. Smale, and can be adopted to both nonredundant and redundant kinematics. Moreover, given a pair of points in the external space of a manipulator, the method is capable of generating a minimum-length trajectory joining the points (a geodesic), in particular a straight-line trajectory. Results of representative computer experiments, including those with the PUMA 560 kinematics, are reported in order to illustrate the performance of the method.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

Robot calibration using the CPC error model

The complete and parametrically continuous (CPC) robot kinematic modeling convention has no model singularities and allows the modeling of the robot base and tool in the same manner by which the internal links are modeled. These two properties can be utilized to construct robot kinematic error models employing the minimum number of kinematic error parameters. These error parameters are independent and span the entire geometric error space. The BASE and TOOL error models are derived as special cases of the regular CPC error model. The CPC error model is useful for both kinematic identification and kinematic compensation. This paper focuses on the derivation of the CPC error models and their use in the experimental implementation of robot calibration.     

Real-Time Kinematics of Continuum Robots: Modelling and Validation

Kinematics of flexible backbone continuum robots is highly non linear and its complexity quickly escalates with the number of sections of the robot, which is usually more than three. This paper introduces a kinematic modelling of actuation and configuration spaces that greatly simplifies the computational requirements compared to the commonly used Piecewise Constant Curvature Kinematics which results in a faster algorithm at a rate proportional to the number of sections. This new algorithm is firstly developed for Twin Pivot Compliant Joint continuum robots but then extended to a general single neutral axis backbone configuration, both achieving a very low error of approximation (0.7% for the prototype developed), which results in several advantages such as the avoidance of highly non-linear functions and singularities, great reduction of computational complexity and an user-friendly graphical representation to help operation and status monitoring of this kind of robots. Moreover, a slender, small diameter and hyper-redundant (175 mm length, 6 mm diameter, 10 Degrees of Freedom) continuum robot prototype is developed and tested in a real-case industrial application for inspection and repair of aero engines in order to validate the proposed model.