Real-Time Motion Tracking of Robot Manipulators Using Adaptive Genetic Algorithms

The paper presents a genetic algorithm approach to real-time motion tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve real time tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position level rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic Research arm that demonstrate good tracking accuracy and reasonable joint velocities.     

Real-time Velocity Alteration Strategy for Collision-free Trajectory Planning of Two Articulated Robot Manipulators

Two articulated robots working in a shared workspace can be programmed by planning the tip trajectory of each robot independently. To account for collision avoidance between links, a real-time velocity alteration strategy based on fast and accurate collision detection is proposed in this paper to determine the step of next motion of slave (low priority) robot for collision-free trajectory planning of two robots with priorities. The effectiveness of the method depends largely on a newly developed method of accurate estimate of distance between links. By using the enclosing and enclosed ellipsoids representations of polyhedral models of links of robots, the minimum distance estimate and collision detection between the links can be performed more efficiently and accurately. The proposed strategy is implemented in an environment where the geometric paths of robots are pre-planned and the preprogrammed velocities are piecewise constant but adjustable. Under the control of the proposed strategy, the master robot always moves at a constant speed. The slave robot moves at the selected velocity, selected by a tradeoff between collision trend index and velocity reduction in one collision checking time, to keep moving as far as possible and as fast as possible while avoid possible collisions along the path. The collision trend index is a fusion of distance and relative velocity between links of two robots to reflect the possibility of collision at present and in the future. Graphic simulations of two PUMA560 robot arms working in common workspace but with independent goals are conducted. Simulations demonstrate the collision avoidance capability of the proposed approach as compared to the approach based on bounding volumes. It shows that advantage of our approach is less number of speed alterations required to react to potential collisions.     

Obstacle avoidance for redundant robots using configuration control

The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuration control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles. The simplicity and computational efficiency of the proposed scheme allows on-line implementation with a high sampling rate for real-time obstacle avoidance in a dynamically varying environment.     

On the connectivity of manipulator free workspace

This article presents a new topological characterization of the free workspace of manipulators moving among obstacles. The free workspace is the set of positions and orientations that the end-effector of the manipulator can reach, according to the joint limits of each of its links, and taking into account the obstacles of the environment. A classification of new connectivity properties of the free workspace is proposed, corresponding to different types of motions (point-to-point motions, following of continuous trajectories) that the manipulator can perform in the Cartesian space. For each property, a necessary and sufficient condition is given, which permits verification of the connectivity of the whole free workspace and leads to all the connected subspaces in it. These properties have been implemented in a Robotics C.A.D. system using octree representation of spaces. Some applications are presented, which show that this work is of primary interest for preparing off-line tasks, and is a new contribution to the problem of robotic cell layout design.     

Evaluation of head-collision safety of a 7-DOF manipulator according to posture variation

As the need for the improvement of the productivity in the manufacturing process grows, industrial robots are brought out of the safety fences and used in the direct collaborative operation with human workers. Consequently, the intended and/or unintended contact between the human and the robot in the collaborative operation is no longer an extraordinary event and is a mundane possibility. The level of the risk of the collision depends on various quantities associated with the collision, for example, inertia, velocity, stiffness, and so on. MSI (manipulator safety index) which is based on HIC (head injury criteria) conventionally used in the automotive industry is one of the practically available measures to estimate the risk of the collision between the human and the manipulator. In this paper MSI is applied to evaluate the collision safety of a 7-DOF articulated human-arm-like manipulator. The risk of the collision could be reduced by choosing different postures without deviating from the given end-effector trajectory using the redundant degree of freedom in the 7-DOF manipulator. The paper shows how the redundant degree of the freedom is utilized to design safer trajectories and/or safer manipulator configurations among many available. A parametric analysis and simulation results for a given trajectory illustrate the usefulness of the concept of the trajectory design for alleviating the risk of the manipulator operation in the human–robot coexisting workspace.     

A correlation between the state-space and the task-oriented path in the presence of obstacles for mechanical manipulators

This article proposes workspace analysis for redundant robot manipulators in the presence of obstacles. The analysis, based on a 3R planar robot and disk-shaped obstacles, is considered in detail and a computer program is developed for the calculation of the collision-free region of redundant robots. The research focuses on the state space of the robot with its end-effector forced to follow a linear path, with particular consideration of the effects of the link geometries and the location of the obstacles. © 1994 John Wiley & Sons, Inc.     

Motion Planning for Redundant Manipulators Using a Floating Point Genetic Algorithm

This paper deals with the trajectory planning problem for redundant manipulators. A genetic algorithm (GA) using a floating point representation is proposed to search for the optimal end-effector trajectory for a redundant manipulator. An evaluation function is defined based on multiple criteria, including the total displacement of the end-effector, the total angular displacement of all the joints, as well as the uniformity of Cartesian and joint space velocities. These criteria result in minimized, smooth end-effector motions. Simulations are carried out for path planning in free space and in a workspace with obstacles. Results demonstrate the effectiveness and capability of the proposed method in generating optimized collision-free trajectories.     

Determination of the orientation workspace of parallel manipulators

An important step during the design of a parallel manipulators is the determination of its workspace. For a 6-d.o.f. parallel manipulator workspace limitations are due to the bounded range of their linear actuators, mechanical limits on their passive joints and links interference. The computation of the workspace of a parallel manipulator is far more complex than for a serial link manipulator as its translation ability is dependent upon the orientation of the end-effector.We present in this paper an algorithm enabling to compute the possible rotation of the end-effector around a fixed point. This algorithm enables to take into account all the constraints limiting the workspace. Various examples are presented.     

Fuzzy-GA-based trajectory planner for robot manipulators sharing a common workspace

This paper presents a novel fuzzy genetic algorithm (GA) approach to tackling the problem of trajectory planning of two collaborative robot manipulators sharing a common workspace, where the manipulators have to consider each other as a moving obstacle whose trajectory or behaviour is unknown and unpredictable, as each manipulator has individual goals and where both have the same priority. The goals are not restricted to a given set of joint values, but are specified in the workspace as coordinates at which it is desired to place the end-effector of the manipulator. By not constraining the goal to the joint space, the number of possible solutions that satisfies the goal increases according to the number of degrees of freedom of the manipulators. A simple GA planner is used to produce an initial estimation of the movements of the robots' articulations and collision free motion is obtained by the corrective action of the collision-avoidance fuzzy units.     

Singularity-robust decoupled control of dual-elbow manipulators

The ability of a robot manipulator to move inside its workspace is inhibited by the presence of joint limits and obstacles and by the existence of singular positions in the configuration space of the manipulator. Several kinematic control strategies have been proposed to ameliorate these problems and to control the motion of the manipulator inside its workspace. The common base of these strategies is the manipulability measure which has been used to: (i) avoid singularities at the task-planning level; and (ii) to develop a singularity-robust inverse Jacobian matrix for continuous kinematic control. In this paper, a singularity-robust resolved-rate control strategy is presented for decoupled robot geometries and implemented for the dual-elbow manipulator. The proposed approach exploits the decoupled geometry of the dual-elbow manipulator to control independently the shoulder and the arm subsystems, for any desired end-effector motion, thus incurring a significantly lower computational cost compared to existing schemes.     

Obstacle avoidance control of redundant robots using variants of particle swarm optimization

Four variants of Particle Swarm Optimization (PSO) are proposed to solve the obstacle avoidance control problem of redundant robots. The study involved simulating the performance of a 5 degree-of-freedom (DOF) robot manipulator in an environment with static obstacle. The robot manipulator is required to move from one position to a desired goal position with minimum error while avoiding collision with obstacles in the workspace. The four variants of PSO are namely PSO-W, PSO-C, qPSO-W and qPSO-C where the latter two algorithms are hybrid version of the first two. The hybrid PSO is created by incorporating quadratic approximation operator (QA) alongside velocity update routine in updating particles' position. The computational results reveal that PSO-W yields better performance in terms of faster convergence and accuracy.     

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.     

一种基于相对坐标系下移动机器人动态实时避碰的新方法

本文提出了一种机器人在动态环境下的动态实时避碰的新方法．此方法是基于相 对坐标系，在加速度空间中，通过动态实时地调整机器人自身速度的大小和方向使其离开碰 撞区域，即碰撞危险区域，达到与动、静态障碍物之间的避碰．仿真实验验证了此方法的有 效性．     

Dimensional synthesis of kinematically redundant serial manipulators for cluttered environments

A systematic procedure for synthesizing kinematically redundant serial manipulators is proposed in this paper. For a given cluttered workcell, the task space locations (TSL’s) for the desired manipulator are prescribed. The synthesis is performed with the objective of reachability of the manipulator at specified TSL’s, while avoiding obstacles. The problem is formulated as a constrained optimization problem, minimizing the positional error and simultaneously avoiding any collision of the manipulator with either the obstacles or within its links. The technique used to solve the resulting constrained optimization problem is the classical Augmented Lagrangian Method. The paper presents a discussion on the past works in this field. It is observed that the presented literature is confined to special cases only while the proposed method involves full generality of the synthesis problem. The availability of such an algorithm working for full generality is important, particularly for highly constrained environments. The efficiency of the proposed approach to synthesize the desired redundant manipulators is exhibited through diverse cases. The resulting synthesized manipulators are further checked for the possibility of feasible paths between TSL’s. An outline of the development of a redundant manipulator, synthesized through the presented approach, is also included in this paper.     

Obstacle Avoidance for Redundant Manipulators Using Directional-Collidability/ Temporal-Collidability Measure

We present an efficient obstacle avoidance control algorithm for redundant manipulators using new measures called directional-collidability measure and temporal-collidability measure. Considering relative movements of manipulator links and obstacles, the directional-collidability/temporal-collidability measure is defined as the sum of inverse of predicted collision distances/times between manipulator links and obstacles. These measures are suitable for obstacle avoidance control since relative velocities between manipulator links and obstacles are as important as distances between them. Also, we present a velocity-bounded kinematic control law which allows reasonably large gain to improve the system performance. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.     

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.     

Fast and robust numerical method for inverse kinematics with prioritized multiple targets for redundant robots

In this paper, a new numerical method for inverse kinematics with prioritized multiple targets is proposed. The proposed method is constructed based on the virtual spring model and joint-based damping control. The targets are prioritized by adjusting the effect of the virtual springs. The proposed method has the following three features. First, it does not require complex calculations such as a Jacobian matrix projection into the null space. Second, it can solve prioritized inverse kinematics problems in the position level without integrating the joint velocity. Third, it is robust to parameter variations and singular configurations. The second feature is motivated by the background that most industrial robots in factories are used as position-controlled robots. Simulation experiments using a 9-DOF redundant robot show that the proposed method is faster and more robust than the conventional method. The proposed method is expected to be useful for helping to avoid collisions between links and obstacles using the redundancy.     

一种末端任务给定的移动机械手动态路径规划方法

移动机械手末端任务给定情况下的路径规划在喷绘、焊接等工作中有广泛的应用,但这方面的研究还比较少,尤其是在动态环境中.针对该情况提出一种动态规划方法,该方法包含预处理和动态规划两个阶段,使移动机械手在完成任务的前提下,能够有效地回避静态和动态障碍物.仿真结果证明了该方法的正确性.     

A force–impedance controlled industrial robot using an active robotic auxiliary device

A strategy to improve the performance of current commercial industrial robots is presented in this paper. This strategy involves cooperation of two robotic manipulators: the robotic controlled impedance device (RCID) and a commercial industrial robot. The RCID is a small six degrees-of-freedom (DOF) high bandwidth force–impedance controlled parallel manipulator, developed at the School of Engineering of the University of Porto (Portugal). The RCID works attached in series with a position controlled commercial industrial robot. Combination of the two manipulators behaves as a single manipulator having the impedance and force control dynamic performance of the RCID, as well as the workspace and trajectory tracking bandwidth of the industrial robot. Force–impedance control of the RCID, and experimental results on typical tasks that involve end-effector contact with uncertain environments of unknown stiffness are presented.     

Collision detection between the wrists of two robot arms in a common workspace

Detecting collisions for planning collision-free motion of the wrists of two robot arms in a common workspace is discussed in this paper. A collision-free motion can be obtained by detecting collisions along the preplanned trajectories using a sphere model for the wrist of each robot and then modifying the paths and/or trajectories of one or both robots to avoid the collision. In this paper, a collision detection algorithm is described and its role in collision avoidance is discussed. Collision detection is based on the premise that (1) the wrists of robots move monotonically on their preplanned straight line trajectories and (2) collisions never occur between the two wrists at the beginning points or end points.Research supported by the NASA-Langley Research Center under Grants #NAG-1-632 and #NAG-1-772 and the AT&T Foundation.