A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

A fast approach for the robust trajectory planning of redunant robot manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end-effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor-based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.     

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.     

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.     

On-line collision avoidance system for two PTP command-based manipulators with distributed controller

This research aims to solve online collision avoidance problem of two manipulators with independent controller. Since industrial robot controller is a closed commercial system, trajectory generation part of robot controlling is always proprietary or unknown. Thus, this paper proposes a collision avoidance system of two manipulators which are controlled by point-to-point (PTP) commands, in condition that the internal of robot controller is unknown and unchangeable. Based on this condition, collision avoidance is supposed to be realized by online scheduling of these PTP controlling commands. This paper proposes the collision avoidance method that assumes the three-dimensional common workspace between two manipulators can be partitioned into many subregion elements. And with managing these subregion elements, which are occupied by robot motion, PTP commands are scheduled to adjust execution timing for collision avoidance. A deadlock problem caused by the partition of the workspace is also taken into consideration in the method. And the effectiveness and efficiency of the method have been verified by simulations and experiments.     

A Fast Approach for Robot Motion Planning

This paper describes a new approach to robot motion planning that combines the end-point motion planning with joint trajectory planning for collision avoidance of the links. Local and global methods are proposed for end-point motion planning. The joint trajectory planning is achieved through a pseudoinverse kinematic formulation of the problem. This approach enables collision avoidance of the links by a fast null-space vector computation. The power of the proposed planner derives from: its speed; the good properties of the potential function for end-point motion planning; and from the simultaneous avoidance of the links collision, kinematic singularities, and local minima of the potential function. The planner is not defined over computationally expensive configuration space and can be applied for real-time applications. The planner shows to be faster than many previous planners and can be applied to robots with many degrees of freedom. The effectiveness of the proposed local and global planning methods as well as the general robot motion planning approach have been experimented using the computer-simulated robots. Some of the simulation results are included in this paper.     

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.     

基于简单模糊逻辑的冗余度机器人动力学路径规划新方法

论文提出了基于模糊逻辑的冗余度机器人避障算法,算法中利用模糊规则自动调整避障控制参数,使机器人在最短的时间内做出快速回避反应,提高了系统的智能性;另一方面,算法中利用动力学控制代替了位置控制,减少了避障过程中,由于速度突变引起的关节冲击力,提高了系统使用寿命。最后通过一平面三连杆三自由度机器人进行仿真研究,结果证实了该算法的有效性。     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

Redundancy modelling and resolution for robotic mobile manipulators: a general approach

In this work the topic of kinematic redundancy modelling and resolution for robotic mobile manipulators is considered. A set of redundancy parameters is introduced to define a general inverse kinematic procedure for mobile manipulators. Then, redundancy is treated as a non-linear optimization problem with the purpose of finding robot configurations that maximize the designed metric measures. Some strategies to design the optimization objective function are introduced in order to achieve desirable redundant behaviours, such as obstacles avoidance, mobile base motions reductions and dexterity optimization. Moreover, the robot controller has been developed following an object-oriented software architecture principle that allows to keep it general and robot independent. As a prove of reliability and generality of our approach, the same controller has been used to control several different mobile manipulators in a simulation environment, as well as a real KUKA youBot robot.     

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.     

Motion planning of redundant robots

Motion planning of robot manipulators is one of the most challenging problems encountered in the field of robotics. This article concentrates on those problems that require geometrical singularity and task priority. An alternative to the conventional approach is proposed, using a forward kinematics and optimization technique. The solution can be obtained corresponding to the design objective using an optimization procedure. The robustness of the proposed method to geometrical singularity is demonstrated. The concept of the permissible region is proposed for the motion planning problem with obstacle avoidance. Illustrated examples are also given.© 1997 John Wiley & Sons, Inc.     

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.     

Complete and Rapid Regrasp Planning with Look-up Table

A pick-and-place operation in a 3-dimensional environment is a basic operation for humans and multi-purpose manipulators. However, there may be a difficult problem for such manipulators. Especially, if the object cannot be moved with a single grasp, regrasping, which can be a time-consuming process, should be carried out. Regrasping, given initial and final poses of the target object, is a construction of sequential transition of object poses that are compatible with two poses in the point of grasp configuration. This paper presents a novel approach for solving the regrasp problem. The approach consists of a preprocessing and a planning stage. Preprocessing, which is done only once for a given robot, generates a look-up table which has information on kinematically feasible task space of the end-effector throughout the entire workspace. Then, using this table, the planning automatically determines a possible intermediate location, pose and regrasp sequence leading from the pick-up to put-down grasp. With a redundant robot, it is shown experimentally that the presented method is complete in the entire workspace and can be implemented in real-time applications due to rapid regrasp planning time. The regrasp planner was combined with an existing path.     

Robot path planning in a constrained workspace by using optimal control techniques

Robot manipulators are programmable mechanical systems designed to execute a great variety of tasks in a repetitive way. In industrial environment, while productivity increases, cost reduction associated with robotic operation and maintenance can be obtained as a result of decreasing the values of dynamic quantities such as torque and jerk, with respect to a specific task. Furthermore, this procedure allows the execution of various tasks that require maximum system performance. By including obstacle avoidance ability to the robot skills, it is possible to improve the robot versatility, i.e., the robot can be used in a variety of operating conditions. In the present contribution, a study concerning the dynamic characteristics of serial robot manipulators is presented. An optimization strategy that considers the obstacle avoidance ability together with the dynamic performance associated with the movement of the robot is proposed. It results an optimal path planning strategy for a serial manipulator over time varying constraints in the robot workspace. This is achieved by using multicriteria optimization methods and optimal control techniques. Numerical simulation results illustrate the interest of the proposed methodology and the present techniques can be useful for the design of robot controllers. Commemorative contribution.     

Study and resolution of singularities for a 6-DOF PUMA manipulator

Upon solving the inverse kinematics problem of robot manipulators, the inherent singularity problem should always be considered. When a manipulator is approaching a singular configuration, a certain degree of freedom will be lost such that there are no feasible solutions of the manipulator to move into this singular direction. In this paper, the singularities of a 6-DOF PUMA manipulator are analyzed in detail and all the corresponding singular directions in task space are clearly identified. In order to resolve this singularity problem, an approach denoted Singularity Isolation Plus Compact QP (SICQP) method is proposed. The SICQP method decomposes the work space into achievable and unachievable (i.e., singular) directions. Then, the exactness in the singular directions are released such that extra redundancy is provided to the achievable directions. Finally, the Compact QP method is applied to maintain the exactness in the achievable directions, and to minimize the tracking errors in the singular directions under the condition that feasible joint solutions must be obtained. In the end, some simulation results for PUMA manipulator are given to demonstrate the effectiveness of the SICQP method.     

Singularity-consistent path planning and motion control through instantaneous self-motion singularities of parallel-link manipulators

The newly proposed singularity-consistent path tracking approach is applied to nonredundant parallel-link manipulators. We analyze the singularities of such manipulators under the assumption that the output-link moves on a pre-defined and parameterized path. Special attention is paid to the so-called instantaneous self-motion type singularity. We propose a velocity-command generator type closed-loop controller that guarantees asymptotic stability when tracking paths through such singularities. As a comprehensive analytical example we use a planar five bar mechanism. Results from computer simulations with the five bar mechanism and the HEXA parallel robot are also presented. © 1997 John Wiley & Sons, Inc.     

Obstacle avoidance for kinematically redundant manipulators using a dual neural network.

One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.     

Robot arm reaching through neural inversions and reinforcement learning

We present a neural method that computes the inverse kinematics of any kind of robot manipulators, both redundant and non-redundant. Inverse kinematics solutions are obtained through the inversion of a neural network that has been previously trained to approximate the manipulator forward kinematics. The inversion provides difference vectors in the joint space from difference vectors in the workspace. Our differential inverse kinematics (DIV) approach can be viewed as a neural network implementation of the Jacobian transpose method for arm kinematic control that does not require previous knowledge of the arm forward kinematics. Redundancy can be exploited to obtain a special inverse kinematic solution that meets a particular constraint (e.g. joint limit avoidance) by inverting an additional neural network The usefulness of our DIV approach is further illustrated with sensor-based multilink manipulators that learn collision-free reaching motions in unknown environments. For this task, the neural controller has two modules: a reinforcement-based action generator (AG) and a DIV module that computes goal vectors in the joint space. The actions given by the AG are interpreted with regard to those goal vectors.     

7自由度机器人的图谱问题

本文在分析、归纳、综合的基础上作出了7自由度机械臂的图谱.包括位置空间、奇异空间、回避障碍和回避奇异等问题.给出了一种普遍适用的方法.并介绍了该方法的使用,对7自由度机器人的结构设计和选型有一定的参考价值.