Path planning in the presence of obstacles based on task requirements

We propose a novel and efficient scheme for planning a kinematically feasible path in the presence of obstacles according to task requirements. By employing geometrical analysis, we derive expressions to describe the relationship between the planned path, kinematic constraints, and obstacles in the robot workspace. The freedom available according to task requirements is then utilized to modify the infeasible portions of the planned path. We use a 6R (revolute) wrist-partitioned type of robot manipulator and a spherical obstacle as a case study to demonstrate the proposed scheme. We then extend our results to general wrist-partitioned types of robot manipulators and arbitrarily-shaped or multiple obstacles. © 1994 John Wiley & Sons, Inc.     

一种新型机器人自标定装置及其算法

针对传统基于几何约束的机器人自标定装置仅能对局部工作空间内的机器人位型进行标定测量的问题,提出了一种由安装于机器人末端的球心位置测量装置和可移动球杆组成的新型便携式机器人自标定装置,通过利用球面约束和距离约束,可在较大工作空间内对机器人进行标定测量,从而提高标定结果的可靠性．根据可移动球杆的单、双球布置方式,分别建立了基于向量差和距离差的2种机器人自标定模型及其算法．通过采用局部指数积公式并引入位置伴随变换矩阵,简化了2种自标定模型,从而降低了对运动学方程线性化的计算量．最后,对一种6自由度串联机器人进行了仿真实验,实验结果表明2种自标定算法均能够快速收敛,验证了2种算法的有效性和鲁棒性．     

Posture optimization methodology of 6R industrial robots for machining using performance evaluation indexes

For industrial robots, the relatively low posture-dependent stiffness deteriorates the absolute accuracy in the robotic machining process. Thus, it is reasonable to consider performing machining in the regions of the robot workspace where the kinematic, static and even dynamic performances are highest, thereby reducing machining errors and exhausting the advantages of the robot. Simultaneously, an optimum initial placement of the workpiece with respect to the robot can be obtained by optimizing the above performances of the robot. In this paper, a robot posture optimization methodology based on robotic performance indexes is presented. First, a deformation evaluation index is proposed to directly illustrate the deformation of the six-revolute (6R) industrial robot (IR) end-effector (EE) when a force is applied on it. Then, the kinematic performance map drawn according to the kinematic performance index is utilized to refine the regions of the robot workspace. Furthermore, main body stiffness index is proposed here to simplify the performance index of the robot stiffness, and its map is used to determine the position of the EE. Finally, the deformation map obtained according to the proposed deformation evaluation index is used to determine the orientation of the EE. Following these steps, the posture of the 6R robot with the best performance can be obtained, and the initial workpiece placement can be consequently determined. Experiments on a Comau Smart5 NJ 220-2.7 robot are conducted. The results demonstrate the feasibility and effectiveness of the present posture optimization methodology.     

Optimal design and workspace analysis of a mobile welding robot with a 3P3R serial manipulator

This paper presents the design optimization of a mobile welding robot based on the analysis of its workspace. A welding robot has been developed to be used inside the double-hull structure of ships, and it shows good welding functionality. But there is a need to optimize the kinematic variables ensuring that the required welding functions inside the ships are satisfied. The task-oriented workspace, which is the workspace enabling specific rotations, has been defined in order to validate the welding ability of the robot, and incorporating the required rotational capabilities. To calculate the workspace, a geometric approach is adopted which considers the pitching and yawing angles simultaneously. Based on the workspace analysis, a scenario is compiled for considering a mass reduction, and a ratio between the design parameters and the workspace, with constraints on the workspace margins. The proposed optimization procedure is composed of two steps of coarse and fine searching. In the coarse searching step, a feasible parameter region (FPR) is defined, which satisfies the geometrical design constraints, and can be obtained without any considerations of the objective functions. In the fine searching step, the design parameters are determined by using the optimization technique of the conjugate gradient method in the overall FPRs. The suggested approach to calculating the task-oriented workspace, and the procedure of optimal design, are expected to be applied to general industrial robots.     

Joint workspace of parallel kinematic machines

Robot workspace is the set of positions a robot can reach. Workspace is one of the most useful measures for the evaluation of a robot. Workspace is usually defined as the reachable space of the end-effector in Cartesian coordinate system. However, it can be defined in joint coordinate system in terms of joint motions. In this paper, workspace of the end-effector is called task workspace, and workspace of the joint motions is called joint workspace. Joint workspace of a parallel kinematic machine (PKM) is focused, and a tripod machine tool with three degrees of freedom (DOF) is taken as an example. To study the joint workspace of this tripod machine tool, the forward kinematic model is established, and an interpolating approach is proposed to solve this model. The forward kinematic model is used to determine the joint workspace, which occupies a portion of the domain of joint motions. The following contributions have been made in this paper include: (i) a new concept so-called joint workspace has been proposed for design optimization and control of a PKM; (ii) an approach is developed to determine joint workspace based on the structural constraints of a PKM; (iii) it is observed that the trajectory planning in the joint coordinate system is not reliable without taking into considerations of cavities or holes in the joint workspace.     

Body Workspace of Quadruped Walking Robot and its Applicability in Legged Locomotion

This paper discusses on determination of the workspace of the body of a quadruped walking robot, called “body workspace”, and its applicability in legged locomotion. The body workspace represents the set of all valid body configurations for a next step by considering three constraints of a body position: existence of the inverse kinematic solutions, reach-ability of the next swing leg to the next desired foothold, and static equilibrium of the robot when the next swing leg is lifted. The space contains all the body positions that ensure the existence of inverse kinematic solutions, is calculated in the first. Then, a subspace inside the determined space that allows the robot to reach the next desired foothold is analyzed. Finally, the workspace is obtained by excluding all the positions inside the subspace that do not ensure the equilibrium of the robot when the next swing leg is lifted. Therefore, the workspace shows all possible solutions for choosing the next body configuration of a given static walking problem. It is significant in improving the robot’s performances since moving body takes an intrinsic role in static walking, besides swinging a leg. The algorithm runs fast in real-time because it is a pure geometric method. The body workspace of a quadruped walking robot is visualized to help the understanding of the algorithm. In addition, applications of using the body workspace in improving the robot’s ability are presented to show potential applicability of the workspace.     

Software Tool to Compute,Analyze and Visualize Workspaces of Parallel Kinematics Robots

The aim of this paper is to present a new software tool designed to compute and allow visualization of the different types of workspaces of parallel manipulators in the most user-friendly and efficient way. The graphical interface of this program makes it possible to define the geometrical scheme of the robot. All required parameters of the kinematic model can be set easily and quickly. Given that the workspace of a parallel manipulator is a complex entity, this CAD tool has implemented all the controls needed to visually define all the complicated parameters required to launch a workspace computation. Once the calculations are performed, the challenging task of visualizing the results has been optimized. Due to the circumstance that a workspace can be a higher than three-dimensional (3-D) mathematical entity, which cannot be graphically represented, the user can choose the specific variables (two or three) onto which to project the workspace obtained (2-D or 3-D representations). Within these surfaces and volumes, several color maps, associated with kinematic indicators, can be traced to enable the most efficient path planning of the manipulator analyzed.     

Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

Kinematic control of redundant robots with guaranteed joint limit avoidance

A novel approach for addressing the inverse differential kinematics of redundant manipulators in the presence of hard joint position constraints is presented. A prescribed performance signal for joint limit avoidance guarantees is proposed that can be utilized with both planned and on-line generated trajectories. In the first case, it is a null space velocity for the primary task velocity mapping while in the second case, it modifies the generated reference by acting on the whole velocity space producing a feasible path to the target. Experimental results utilizing a 7DOF KUKA LWR4+ arm demonstrate the performance of the proposed kinematic controller.     

Constrained multi-objective trajectory planning of parallel kinematic machines

This paper presents a new approach to multi-objective dynamic trajectory planning of parallel kinematic machines (PKM) under task, workspace and manipulator constraints. The robot kinematic and dynamic model, (including actuators) is first developed. Then the proposed trajectory planning system is introduced. It minimizes electrical and kinetic energy, robot traveling time separating two sampling periods, and maximizes a measure of manipulability allowing singularity avoidance. Several technological constraints such as actuator, link length and workspace limitations, and some task requirements, such as passing through imposed poses are simultaneously satisfied. The discrete augmented Lagrangean technique is used to solve the resulting strong nonlinear constrained optimal control problem. A decoupled formulation is proposed in order to cope with some difficulties arising from dynamic parameters computation. A systematic implementation procedure is provided along with some numerical issues. Simulation results proving the effectiveness of the proposed approach are given and discussed.     

Modelling and analysis of a novel CT-guided puncture robot for lung brachytherapy

In this paper, we present a novel CT-guided needle puncture robot system with seven degree of freedoms. All basic requirements of interventional radiology can be met. To solve the space constraints and compatibility requirement, tendon-sheath transmission is used as the drive mode of the end-effector. According to the kinematics analysis of the robot configuration, the reachable workspace is obtained, which can completely cover the chest of patient. Based on the Jacobian matrix, dimension parameters are optimised for better flexibility and kinematic performance in the workspace. Since respiratory movement will cause real-time motion of the tumour, a method is proposed to decrease the puncture error caused by respiratory movement. And the feasibility of this method is verified by puncture experiment based on independent design of respiratory motion simulation device. It is proved that this method will lead to an increase in the puncture accuracy by 2.4 times. In addition, the CT compatibility of the robot is verified, and the positioning accuracy is also measured through the experiments.     

外骨骼式遥操作主手设计及主从异构映射算法研究

为了更好地促进机器人适应复杂的遥操作任务,开发了能够精确获取人体上肢运动信息的外骨骼式遥操作主手,并通过异构映射算法,实现对6自由度协作机械臂的遥操作．首先,基于人体仿生结构,设计了可穿戴式8自由度外骨骼主手（臂部7自由度和手部1自由度）;其次,通过改进的D-H（Denavit-Hartenberg）方法建立遥操作系统的运动学模型,基于Matlab的机器人工具箱进行了工作空间仿真,并设计主从异构映射算法;最后,实验验证外骨骼主手在遥操作系统中的可操作性,以及工作空间异构映射算法的可行性．实验表明,外骨骼主手能够控制从端机械手臂,且保证末端位置和姿态一致,可在大范围工作空间内复现人体上肢精细运动,主从跟随误差达2 mm,工作空间类似于直径1.08 m的半球形．因此,可穿戴式的外骨骼主手使操作者能更加直观地参与到遥操作系统当中,辅助操作者更加高效地完成精细复杂任务．     

Workspace Generation for Multifingered Manipulation

In this paper, we propose a novel numerical approach and algorithm to compute and visualize the workspace of a multifingered hand manipulating an object. Based on feasibility analysis of grasps, the proposed approach uses an optimization technique to first compute discretely the position boundary of the grasped object and then calculate the rotation ranges of the object at specified positions within the boundary. In other words, workspace generation with the approach is fulfilled by obtaining reachable boundaries of the grasped object in the sense of both position and orientation, and the discrete boundary points are computed by a series of optimization models. Unlike in workspace generation of other robotic systems where only geometric and kinematic parameters of the robots are considered, all factors including geometric, kinematic and force-related factors that affect the workspace of a hand–object system can be taken into account in our approach to generate the workspace of multifingered manipulation. Since various constraints can be integrated into the optimization models, our method is general and complete, with adaptability to various grasps and manipulations. Workspace generation with the approach in both planar and spatial cases are illustrated with examples. The approach provides an effective and general solution to the long-term open and challenging problem of workspace generation of multifingered manipulation. Part of the work has been published in the Proceedings of IEEE/RSJ IROS2008 and IEEE/ASME AIM2008.     

基于非均匀环境建模与三阶Bezier曲线的平滑路径规划

针对工作于复杂环境下的大型工装,本文提出了一种基于非均匀环境建模与三阶Bezier曲线的平滑路径规划算法,以指导工装的运动.在环境建模方面,利用四叉树建立环境的非均匀模型,能够有效压缩环境信息,提高搜索效率;在路径搜索方面,以非均匀环境模型为基础,提出一种距离启发搜索和信息素混合更新的蚁群算法,能够得到工装的安全可行路径点;在路径平滑方面,基于三阶Bezier曲线,提出能够连接任意位置和任意方向两点的转弯单元的设计方法,利用转弯单元连接路径搜索算法得到的路径点,能够获得满足工装非完整性约束的平滑路径.最后,以大型激光驱动器的靶场环境为对象,对本文算法的有效性和可靠性进行验证,并利用DELMIA平台进一步验证了规划路径的运动平滑性和安全性.     

Time optimal path planning for a wheeled mobile robot

This paper investigates time optimal path planning under kinematic and dynamic constraints for a 2‐DOF wheeled mobile robot (WMR). The dynamic model of a WMR is derived using the Newton–Euler method and the constraints are analyzed. Kinematic constraints are imposed by WMR's nonholonomy and structural limits, while dynamic constraints are due to motor saturation. The path planning is formulated as a two‐stage planning. First, path planning under kinematic constraints is transformed into a pure geometric problem. The shortest path composed of circular arcs and straight lines is obtained. Then, a time optimal velocity profile is generated under dynamic constraints. Since constraints of a WMR are fully exploited, the proposed method is simple and effective. Simulation results are demonstrated. © 2000 John Wiley & Sons, Inc.     

Minimum-time control of robotic manipulators with geometric path constraints

Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing robot's capabilities. To remove at least partially this inefficiency, this paper considers a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints. We first describe the manipulator dynamics using parametric functions which represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/ forces are converted to those on the parameters. Third, the minimum-time solution is deduced in an algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate utility of the trajectory planning method developed.     

Safe and intuitive manual guidance of a robot manipulator using adaptive admittance control towards robot agility

Key areas of robot agility include methods that increase capability and flexibility of industrial robots and facilitate robot re-tasking. Manual guidance can achieve robot agility effectively, provided that a safe and smooth interaction is guaranteed when the user exerts an external force on the end effector. We approach this by designing an adaptive admittance law that can adjust its parameters to modify the robot compliance in critical areas of the workspace, such as near and on configuration singularities, joint limits, and workspace limits, for a smooth and safe operation. Experimental validation was done with two tests: a constraint activation test and a 3D shape tracing task. In the first one, we validate the proper response to constraints and in the second one, we compare the proposed approach with different admittance parameter tuning strategies using a drawing task where the user is asked to guide the robot to trace a 3D profile with an accuracy or speed directive and evaluate performance considering path length error and execution time as metrics, and a questionnaire for user perception. Results show that appropriate response to individual and simultaneous activation of the aforementioned constraints for a safe and intuitive manual guidance interaction is achieved and that the proposed parameter tuning strategy has better performance in terms of accuracy, execution time, and subjective evaluation of users.     

Kinematic and dynamic models of hybrid robot manipulator for propeller grinding

In this article, we develop a hybrid robot manipulator for propeller grinding and derive its kinematic and dynamic models. The manipulator is constructed by combining a parallel mechanism and a serial one to increase high stiffness as well as workspace. Based on geometric constraints, inverse–direct kinematics and Jacobian are derived to be implemented in real time control. The velocity control is used to measure the surface of a propeller blade and the position control is conducted to grind the removal depth. The dynamic model, which is developed by a motor algebra, can compute the forces and moments acting at a passive joint and an active one. ©1999 John Wiley & Sons, Inc.     

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.     

A case study of two-robot-arm workcell material handling

More problems are involved in collaborating multi-robot-arm systems than in single robot arms. These problems stem from mutual dynamic and kinematic effects between the arms. This work is confined to only the kinematics of two robot arms; other problems like control, force distribution, and so on are not addressed here. A particular case of a material handling problem with two collaborating robot arms loading/unloading long objects from a conveyor is studied. The feasibility of the task from a kinematics point of view, and the necessary conditions and constraints for the relative set-up of the two manipulators are discussed. These conditions originate from the working envelope of the two arms which depends on three factors: the working envelope of each individual arm, the spacing between them, and the dimensions of the workpiece. To assist this study, an efficient algorithm for determining the two-dimensional contours of the workspace of a single arm is included.