A framework for large‐force task planning of mobile and redundant manipulators

A framework tackling the problem of large wrench application using robotic systems with limited force or torque actuators is presented. It is shown that such systems can apply a wrench to a limited set of Cartesian locations called force workspace (FW), and its force capabilities are improved by employing base mobility and redundancy. An efficient numerical algorithm based on 2ⁿ‐tree decomposition of Cartesian space is designed to generate FW. Based on the FW generation algorithm, a planning method is presented resulting in proper base positioning relative to large‐force quasistatic tasks. Additionally, the case of tasks requiring application of a wrench along a given path is considered. Task workspace, the set of Cartesian space locations that are feasible starting positions for such tasks, is shown to be a subset of FW. This workspace is used for identifying proper base or task positions guaranteeing task execution along desired paths. Finally, to plan redundant manipulator postures during large‐force‐tasks, a new method based on a min–max optimization scheme is developed. Unlike norm‐based methods, this method guarantees no actuator capabilities are exceeded, and force or torque of the most loaded joint is minimized. Illustrative examples are given demonstrating validity and usefulness of the proposed framework. ©1999 John Wiley & Sons, Inc.     

A genetic approach to motion planning of redundant mobile manipulator systems considering safety and configuration

This article presents a genetic algorithm approach to multi-criteria motion planning of mobile manipulator systems. For mobile robot path planning, traveling distance and path safety are considered. The workspace of a mobile robot is represented as a grid by cell decomposition, and a wave front expansion algorithm is used to build the numerical potential fields for both the goal and the obstacles. For multi-criteria position and configuration optimization of a mobile manipulator, least torque norm, manipulability, torque distribution and obstacle avoidance are considered. The emphasis of the study is placed on using genetic algorithms to search for global optimal solutions and solve the minimax problem for manipulator torque distribution. Various simulation results from two examples show that the proposed genetic algorithm approach performs better than the conventional methods.     

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.

     

A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

Mobile robot with a self-positioning system

This paper describes a general method using configuration space for planning a collision-free path of a manipulator with 6 degrees of freedom (DOF). The basic approach taken in this method is to restrict the free space concerning path planning and to avoid executing unnecessary collision detections, based on the idea that a collision-free path can be planned using only partial information of the configuration space. The configuration space is equally quantized into cells, and the cells concerning path planning are efficiently enumerated based on a heuristic graph search algorithm. A heuristic function which characterizes the search strategy can be defined to give priority to the gross motion using the first few joints. A bi-directional search strategy is also introduced to improve efficiency. The memory is allocated only to the portion of the configuration space concerning path planning, and the data of the free space defined in the 6-dimensional configuration space can be efficiently stored. This algorithm of free space enumeration is independent of the kinematic characteristics of the manipulator. Therefore, this method is generally applicable to any type of manipulator. It has actually been implemented and has been applied to a 6-DOF articulated manipulator.     

一种基于几何力学的机械臂末端规划算法

在几何力学框架下提出了开链机械臂末端实时追踪避障算法.首先,将回转力引入机械臂末端的自然运动方程,可以在工作空间获得光滑的避障轨迹;其次,利用阻尼最小二乘法求解相应的逆运动学问题,得到关节空间的平滑运动轨迹;最后,通过6自由度机械臂的仿真,并与经典的RRT算法作对比,验证了所提算法的有效性.     

Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

基于遗传算法的机械臂实时避障路径规划研究

针对模块化机械臂在运行时可能与工作空间中的障碍物发生碰撞的问题, 提出一种基于遗传算法的避障路径规划算法。首先采用D-H(Denavit-Hartenberg)表示法对机械臂进行建模, 并进行运动学和动力学分析, 建立机械臂运动学和动力学方程。在此基础上, 利用遗传算法分别在单/多个障碍物工作环境中, 以运动的时间、移动的空间距离和轨迹长度作为优化指标, 实现机械臂避障路径规划的优化。通过仿真验证了基于遗传算法的机械臂避障路径规划算法的有效性与可行性, 该算法提高了运行中的机械臂有效避开工作空间中障碍物的效率。     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.     

基于引力自适应步长RRT的双臂机器人协同路径规划

快速扩展随机树（RRT）方法的步长确定过分依赖于程序调试,而且固定的步长会导致碰撞检测失效问题．针对此问题,本文提出一种适用于双臂机器人协同路径规划的引力自适应步长RRT．首先,通过建立构型空间与工作空间的步长范数不等式,对双臂机器人在工作空间中所产生的步长进行约束,进而确保实现有效的碰撞检测;然后,提出随机树被动生长方法,在保证双臂机器人协同运动的基础上,降低规划空间的维度．最后,在随机树的节点处引入引力函数,加快算法的融合速度．仿真结果表明,引力自适应步长RRT方法可对工作空间中的步长进行有效约束,确保算法碰撞检测的有效性．在无碰撞的前提下,引力自适应步长RRT方法相比于其他算法减少了迭代次数,降低了运行时间并缩短了路径长度．将所提算法应用于双臂机器人的样机实验,结果表明双臂机器人可在保持位置协同的前提下,完成避障运动,验证了算法的可行性．     

基于运动学模型重构的单关节故障机械臂容错路径规划

针对单关节故障机械臂的路径规划问题,提出一种基于运动学模型重构的容错路径规划方法.首先基于旋量理论进行单关节故障机械臂的通用运动学模型重构;然后分析机械臂的退化工作空间,并以运动性能平稳为约束对其进行栅格化处理;最后通过改进传统的A$^\ast$算法,在退化工作空间中搜索出能够满足任务要求的轨迹.以七自由度机械臂为对象进行仿真实验,验证了所提出方法的正确性和有效性.     

Maximum DLCC of Spatial Cable Robot for a Predefined Trajectory Within the Workspace Using Closed Loop Optimal Control Approach

One of the most important applications of cable robots is load carrying along a specific path. Control procedure of cable robots is more challenging compared to linkage robots since cables can’t afford pressure. Meanwhile carrying the heaviest possible payload for this kind of robots is desired. In this paper a nonlinear optimal control is proposed in order to control the end-effector within a predefined trajectory while the highest Dynamic Load Carrying Capacity (DLCC) can be carried. This purpose is met by applying optimum torque distribution among the motors with acceptable tracking accuracy. Besides, other algorithms are applied to make sure that the allowable workspace constraint is also satisfied. Since the dynamics of the robot is nonlinear, feedback linearization approach is employed in order to control the end-effector on its desirable path in a closed loop way while Linear Quadratic Regulator (LOR) method is used in order to optimize its controlling gains since the state space is linearized by the feedback linearization. The proposed algorithm is supported by doing some simulation studies on a two Degrees of Freedom (DOF) constrained planar cable robot as well as a six DOFs under constrained cable suspended robot and their DLCCs are calculated by satisfying the motor torque, tracking error and allowable workspace constraints. The results including the angular velocity, motors’ torque, actual tracking of the end-effector and the DLCC of the robot are calculated and verified using experimental tests done on the cable robot. Comparison of the results of open loop simulation results, closed loop simulation results and experimental tests, shows that the results are improved by applying the proposed algorithm. This is the result of tuning the motors’ torque and accuracy in a way that the highest DLCC can be achieved.     

基于速度修正项的机械臂避障路径规划

针对机械臂运行过程中存在的碰撞问题, 提出一种基于速度修正项的机械臂避障路径规划方法. 利用B 样条曲线进行机械臂关节空间规划, 使机械臂能够在特定时刻运行到指定构型. 在运行过程中, 利用碰撞检测算法实时计算机械臂与障碍物的最小距离, 在碰撞即将发生时引入积分为零的避障速度修正项改变机械臂运行轨迹, 使得机械臂能够在实现障碍回避的同时, 保证其在特定时刻通过指定构型的要求. 仿真实验表明了所提出方法的正确性和有效性.     

基于采样点优化RRT算法的机械臂路径规划

针对基于随机采样的RRT机械臂路径规划算法在全局工作空间下采样效率低、随机性强等问题,提出一种基于采样点优化RRT算法的机械臂路径规划算法.相对于全局工作空间采样,优化算法首先基于非障碍物空间生成随机采样点,以降低算法碰撞检测概率与冗余节点的生成,再结合一定概率的人工势场法产生启发式采样点,使得机械臂臂体于路径规划采样过程中既能保证随机采样的概率完备,又能使采样点更具目标导向性.其次,为使得路径更加简洁平滑,使用冗余节点删除策略剔除路径中的冗余节点来优化最终路径.最后在二维、三维的仿真环境中对优化算法进行对比实验分析,以验证算法在随机采样路径规划算法中的良好性能,并在IRB 1200-7/0.7机械臂上进行避障规划算法实验.仿真和实验结果都表明,所提出的算法在机械臂路径规划中可以获得更高的规划效率和更优的路径.     

Gravity compensation of spatial two‐DOF serial manipulators

This article presents the analysis of gravity compensation of a two‐DOF serial manipulator operating in three‐dimensional space by means of linear spring suspension. The physical configuration of the serial manipulator is assumed general. The analysis begins with gravity compensation of a one‐DOF manipulator in order to form the basis which is then extended to a two‐DOF manipulator. The approach taken in the analysis is that of conservation of potential energy. The goal is to seek the location and the stiffness of springs that provide complete compensation of gravity in the manipulator system. It has been found that complete compensation of gravity in a two‐DOF serial manipulator system is possible. Unlike many previous works on spring suspension of a rigid body, which assume that one end of the suspending spring is attached to ground, it is proven in this study that, for complete compensation in a two‐DOF manipulator, the spring that suspends the distal link cannot be connected to ground. Instead, it must be in certain motion relative to the proximal link. The discussion on how to provide such a motion for the spring is given. It is also explained how the problem of gravity compensation of a robot manipulator can be shifted to that of changing gravity environment within a manipulator system. The concept can be applied to simulation and testing of robot manipulators that will be sent to operate in a different gravity environment, such as space. © 2002 Wiley Periodicals, Inc.     

Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

An analytically tractable potential field model of free space andits application in obstacle avoidance

An analytically tractable potential field model of free space is presented. The model assumes that the border of every two dimensional (2D) region is uniformly charged. It is shown that the potential and the resulting repulsion (force and torque) between polygonal regions can he calculated in closed form. By using the Newtonian potential function, collision avoidance between object and obstacle thus modeled is guaranteed in a path planning problem. A local planner is developed for finding object paths going through narrow areas of free space where the obstacle avoidance is most important. Simulation results show that not only does individual object configuration of a path obtained with the proposed approach avoid obstacles effectively, the configurations also connect smoothly into a path.     

空间冗余机械臂路径规划方法研究

针对空间站遥操作7DOF冗余机械臂路径规划的安全性、可靠性问题,提出了基于臂型角逆运动学的优化A*路径规划算法.本文根据臂型角参数化完善了逆运动学方法,得到了32组完备逆解集,增加了路径规划时逆解选择的灵活性;通过臂型角搜索和最小奇异值优化A*路径规划算法,提高机械臂避障、避奇异能力,机械臂操作的灵活性和路径的安全可靠性;同时根据路径优化策略,有效平滑了路径,减少了机械臂的磨损.仿真结果说明了该方法的有效性.     

空间机器人随机故障容错规划的蜜蜂算法

本文为解决复杂的随机规划问题设计了一种基于随机模拟的混沌量子蜜蜂算法,证明了该算法的收敛 性,并分析了算法的收敛速度．分析6 自由度空间机器人系统的不确定性,采用基于微分变换法进行误差分析,建 立了随机数学规划模型．为涉及故障前后运动学与动力学约束限制的容错轨迹规划,以加权最小驱动力矩为优化性 能指标,采用混沌量子蜜蜂算法求解全部工作时间中机械臂故障前后的最优轨迹．通过降低异常关节的运动速度来 降低故障关节力矩,保证机械臂在发生故障后具有较高的操作能力．案例研究验证了该算法的有效性、稳定性及准 确性．     

基于PS-RRT算法的机械臂避障路径规划

针对应用快速搜索随机树（RRT）算法进行机械臂路径规划时,存在采样区域大、有效区域小、路径冗余节点多、剪枝时间长等问题,提出一种基于分区动态采样策略和重复区域节点拒绝机制的高效RRT路径规划算法PS-RRT（partitioned sampling RRT）。首先,通过PS-RRT快速规划机械臂末端初始路径;其次,分段检测机械臂跟随该路径时的连杆碰撞情况,对碰撞路段进行带臂形约束的第二次规划;最后,将初始路径和第二次规划的路径拼接后进行路径裁剪。将所提方法在多种场景中进行仿真验证,结果表明：基于PS-RRT算法的机械臂避障路径规划策略使得无效节点数大幅减少,可高效规划出机械臂的无碰路径,验证了算法的可行性。