Avoiding collision between two robot arms in a common workspace is non-trivial, since each arm acts as a dynamic obstacle for the other one. In this context, Motion Path Planning (MPP) is the process of finding an optimal and collision-free track that a robot/robot arm can follow to get to the target position starting from any point in its workspace. We propose a reinforcement learning approach to MPP for two manipulators, the first one of which tries to avoid collision with the second one. Initially, the first manipulator has no knowledge about the environment, but it successfully learns optimal collision-free paths through a Team Q-learning algorithm. We present experiments using two different methods for state discretization, namely General State (GS) Discretization and Tile Coding (TC) Discretization, as well as two different Q-learning methods, namely single-agent (SA) and multi-agent (MA) approaches.

In this article an Artificial Neural Network (ANN) approach for the obstacle avoidance of redundant robot manipulators is presented. The approach is based on formulating an inverse kinematics problem under an inexact context. This procedure permits to deal 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 pseudo inverse perturbation. Here the computation of the inverse kinematics problem is performed by a properly trained ANN and including a null space vector for obstacle avoidance which is also realized by another properly trained ANN. The approach is tested on the simulation of a planar redundant manipulator performing some obstacle avoidance tasks. From the results obtained, the approach compares favorably with the numerical approach.

In this article an Artificial Neural Network (ANN) approach for the motion coordination of hyper- redundant systems is presented. In particular, the approach is exemplified for the posture optimization of articulated systems under a framework conducing to the fast/efficient computation of an under-laying inverse continuous time-variant function. The ANN approach consists on the fast computation of the inverse function and an associated null space vector derived from also some novel geometrical concepts.

In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.

This Paper presents an efficient approach for the fast computation of inverse continuous time variant functions with the proper use of Radial Basis Function Networks (RBFNs). The approach is based on implementing RBFNs for computing inverse continuous time variant functions via an overall damped least squares solution that includes a novel null space vector for singularities prevention. The singularities avoidance null space vector is derived from developing a sufficiency condition for singularities prevention that conduces to establish some characterizing matrices and an associated performance index.

The paper presents a new hybridization methodology involving neural, fuzzy and rough computing. A rough sets based approximation technique has been proposed based on a certain neuro-fuzzy architecture. A new rough neuron composition consisting of a combination of a lower bound neuron and a boundary neuron has also been described. The conventional convergence of error in back propagation has been given away for a new framework based on 'output excitation factor' and an inverse input transfer function. The paper also presents a brief comparison of performances, of the existing rough neural networks and ANFIS architecture against the proposed methodology. It can be observed that the rough approximation based neuro-fuzzy architecture is superior to its counterparts.

In this article a simple index for robot manipulator kinematics design and motion performance is presented. This index is derived by establishing a simple upper bound on the norm of the Jacobian rate of change matrix. Here, the proposed index behaviour is analyzed/tested on a redundant manipulator executing tasks under various scenarios. The results obtained demonstrate that this index compares favorably with other criteria that have been proposed in the literature

This paper proposes a novel method of combining rough concepts with neural computation. The proposed new rough neuron consists of, one lower bound neuron and another boundary neuron. The combination is designed in such a way that the boundary neuron deals only with the random and unpredictable part of the applied signal. Such architecture effectively prunes the search space for the respective constituent neurons based on the certain and uncertain behaviors. This division results in an improved rate of error convergence in the back propagation of the neural network along with an improved parameter approximation during the network learning process. Preliminary structures of the rough neural network along with some testing results have been presented. Further, performance comparisons with some of the prevalent designs have been done.

Recently, the author presented a paradigm that can serve as a general framework for the development of sapient (wise) systems. It is demonstrated here that, under the proposed paradigm, it is possible to establish some performance criteria for the proper design and operation of sapient (wise) systems. These criteria are based on establishing proper bounds on some characterizing matrices having a prominent role on the performance of intelligent and sapient (wise) systems.

This paper outlines a neuro-fuzzy inference systems approach to efficient path planning in the work envelope of a redundant robot manipulator. The proposed methodology is two tier; i.e. it deals with continuous obstacle avoidance along with singularities avoidance in the task space. Obstacle avoidance is achieved based on the calculation of an appropriate null space vector and a proper pseudo inverse perturbation helps avoid singularities effectively. The computation of the inverse kinematics is accomplished with the help of dully trained Adaptive Neuro-Fuzzy Inference Systems, thus enabling the methodology to be applicable to all redundant robots operating in a sensor based real time environment. The methodology has been successfully tested on the simulation of a planar redundant manipulator performing some benchmark tasks.

The paper presents a new hybridization methodology involving neural, fuzzy and rough computing. A rough sets based approximation technique has been proposed based on a certain neuro-fuzzy architecture. A new rough neuron composition consisting of a combination of a lower bound neuron and a boundary neuron has been presented. The conventional convergence of error in back propagation has been given away for a new framework based on 'output excitation factor' and an inverse input transfer function. The paper also presents a brief comparison of performances based on which it can be observed that the proposed architecture is superior to its counterparts.

In this article an inverse functional approach for the motion coordination of hyper-redundant systems is presented. In particular, the approach is exemplified for the posture optimization of articulated systems under a framework conducing to the fast and efficient computation of inverse continuous time-variant functions. A novel approach for balance/posture optimization of articulated models is also presented. The approach consists on establishing some characterizing matrices, representing some geometrical concepts in order to obtain a simple performance index and a null space vector for balance/posture optimization.

In this article a radial basis function network (RBFN) approach for fast inverse kinematics computation and effective geometrically bounded singularities prevention of redundant manipulators is presented. The approach is based on establishing some characterizing matrices, representing some bounded 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 RBFN and included in the computation of the inverse kinematics being performed also by another properly trained RBFN.

A radial basis function network (RBFN) approach for fast inverse kinematics computation and effective singularities prevention of redundant manipulators is presented. The approach is based on using a RBFN approach for computing the inverse kinematics and also on a nonconventional implementation of an original geometric framework for the singularities prevention of redundant manipulators. The proposed implementation consists on establishing some characterizing matrices, representing some geometrical concepts, in order to obtain a performance index and a null space vector for singularities avoidance/prevention and safe path generation, and then properly including it in the overall RBFN approach.

The objective of the paper is to establish a mathematical framework for the variational approach for collision free trajectory planning of a robot manipulator, examine it from an engineering perspective and demonstrate the importance of the dynamic characteristics. The framework is based on the energetic concept of an instantaneous energy balance of a dynamic system. Within the framework, different energy forms are defined for obstacle, environmental constraints and task requirements according to their functional characteristics. By applying Hamilton's principle, the general differential control equations of the system are derived. The simulated results demonstrate the elegance and robustness of the current variational approach.

In this article a simple performance index for proper manipulator motion planning is presented. This index is derived by establishing a simple upper bound for a standard condition number of the Jacobian matrix. Here the proposed index behaviour is analyzed/tested on a planar redundant manipulator executing tasks under various scenarios.

In this article a fast, geometrically bounded, method for the online obstacle avoidance of redundant manipulators is presented. The approach is based on formulating an inverse kinematics problem under an inexact context. This approach allows to deal with the avoidance of obstacles utilizing an appropriate and easy to calculate null space, geometrically bounded based, vector; whereas the avoidance of singularities is attained by the proper pseudoinverse robustness. Here the computation of the inverse kinematics problem is accomplished by solving numerically a linear system, which includes the vector for obstacle avoidance and a proper scheme for the proper pseudoinverse robustness. The developed algorithm is successfully tested on the simulation of a 7 DOF redundant manipulator.

A simple index for the manipulator kinematic design optimization and/or best posture determination is presented. This index is derived by establishing a simple upper bound for a standard condition number of the Jacobian matrix. Here it is shown that it is relatively easy to determine a joint configuration neighborhood where the rank is preserved and characterized with a small standard condition number. Here the proposed index is applied to the kinematic design optimization of a planar redundant manipulator.

A simple and fast procedure for on-line concurrent motion planning of multi-manipulators systems is presented. The method is based on solving for each manipulator a linear system of equations taking into account a geometrical bounded null space vector for motion planning, and a scheme for the appropriate robustness of the pseudoinverse matrix. This method can achieve simultaneously both motion, collision-free, interaction and singularities prevention in real time in a sensor based environment.

In this article a bounded geometry paradigm for the singularities avoidance of redundant manipulators is presented. Such a paradigm enables the development of fast and robust algorithms. The approach is based on establishing appropriate bounds for the norm of some characterizing matrices, representing some geometrical concepts, in order to obtain some performance indices for singularities avoidance and robust path generation.

This article presents a vision based online system for the robust trajectory planning of robot manipulators. It uses a 3D vision system to determine the relative position of the objects to be engaged and the obstacle to avoid, and a novel obstacle avoidance procedure for manipulator motion planning. From intensity images acquired by a CCD camera mounted on the robot arm, the salient features are first accurately and robustly detected and then grouped. Through the correspondences between the feature groupings and the model features, the 3D poses of the objects and the obstacles are determined and confirmed by back-projection. Once these poses are determined, an online procedure, based on redundancy resolution, is used to achieve obstacle avoidance. The approach utilizes a null space vector to set properly the robot configuration, and a potential field method to guide the end-effector. By pseudoinverse perturbation it also prevents singular configurations and local minima. The feasibility and effectiveness of the system is demonstrated by an experiment with online engagement and transportation of objects posed inside an aluminium frame.

In this article a fast and simple method for the motion planning of telerobotic manipulators is presented. It is based on solving numerically a linear system of equations that includes a simple null space vector for obstacle avoidance, and an efficient procedure for the appropriate damping of the pseudoinverse matrix. This approach enables the pursuance simultaneously, of both collision avoidance and singularities prevention on-line in a sensor based environment. These properties also make it suitable for entirely autonomous operations.>

The authors present a kinematic measure of global performance for the design evaluation and optimization of robot (redundant) manipulators. The proposed criterion has been applied to optimize each of several different designs of a HERA arm as a redundant manipulator. The results obtained have shown the ability of the proposed approach to establish quantitative kinematic distinctions among a set of designs.>

In this article a fast approach for the ob- stacle avoidance of robot manipulators is presented. The approach is based on formulating an inverse kinematics problem under an inexact context. This procedure per- mits to deal with the avoidance of obstacles with an ap propriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Here the computation of the inverse kinematics problem is accomplished by solving nu- merically a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoin- verse perturbation. These properties make the proposed approach suitable for robots operating 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 proposed.

In this article the inverse kinematics problem for robot manipulators is considered under an inexact context; and a fast procedure for its solution and pseudoinverse robustness is presented. The approach is based on solving the linear system based on the symmetric matrix JJT+pl (where, J and I are the Jacobian and the identity matrix respectively, and p is a damping factor) by a Gaussian elimination process that takes into account the matrix symmetry, and automatically evaluating some simple parameters. These parameters are used in either one of two original schemes, which are theoretically justifiable, that are also proposed for the appropiate evaluation of the damping factor. In the first scheme an upper bound for the condition number of the matrix JJT+pl, in terms of some of the calculated parameters is used. Alternatively, in the second scheme the sufficiency condition for the rank preservation of the Jacobian developed in [5] is considered. First, an upper bound for the pseudoinverse matrix p, in terms of some of the evaluated parameters is found. Then, it is easily shown that the sufficiency condition for rank preservation can be established in terms of this bound and on the 00 norm of the Jacobian rate of change matrix. Furthermore, and as important, here it is also shown how to properly implement these schemes, in particular the one based on an upper bound for the pseudoinverse, in conjuction with a recently developed approach [4] for the singularities prevention of redundant manipulators. The developed algorithms are tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach (in terms of efficiency, robustness and ability to prevent large joint speeds) compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure. 2. The inverse Linematics problem.

A fast procedure for the computation of manipulator inverse kinematics and pseudoinverse robustness is presented. The approach is based on solving a linear algebraic system and evaluating the norm of the Jacobian matrix. This value is properly used in an original scheme that is also proposed for the appropriate robustness of the pseudoinverse matrix. The developed algorithm is tested on the simulation of a planar redundant manipulator and of an industrial robot arm. From the results obtained it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.>

A dexterity measure is presented which can be used for the design evaluation of robot (redundant) manipulators. The proposed criterion is applied (in an absolute fashion) to the evaluation of the kinematic dexterity of five different designs of a HERA redundant manipulator to be used in space operations. The selection of these designs is based on augmenting the original HERA six-degree-of-freedom design with an extra joint and considering only the resultant manipulators to be capable of avoiding all possible kinds of internal singularity. The results are in agreement with the conclusions from previous subjective studies conducted for the design analysis of an industrial arm as a redundant manipulator.>

A singularity-prevention approach is presented for redundant robot manipulators. The approach is based on establishing a local sufficiency condition that guarantees the rank preservation of the Jacobian matrix. This condition has been used directly as the constraint in the optimization problem which is formulated to obtain the optimal path of the robot manipulator. From the formulation a closed-form solution is derived and tested in the simulation of a planar redundant manipulator. The results obtained show that the approach compares favorably with methods formulated at the resolved-motion level.>

A singularities avoidance approach suitable for the optimal path planning of redundant robot manipulators is presented. The approach is based on establishing proper bounds for the rate of change of the Jacobian matrix of the transformation between the joint speeds and the end effector Cartesian speed. These bounds become an additional constraint for an optimization problem that is formulated to obtain the optimal path of the robot manipulator. Here, the optimization problem is formulated globally as a state-constrained continuous optimal control problem which can consider joint (speeds) constraints and/or manipulator dynamics, and be solved by an efficient iterative numerical technique. This approach is particularly exemplified for the optimal path generation of a simulated planar redundant manipulator, and its results are compared with the results yielded by a local approach. The results obtained (although not adequate for present real-time implementation) confirm the superiority of the global approach.>

A singularities-avoidance approach suitable for the optimal local path generation of redundant robot manipulators is presented. It is based on establishing proper bounds for the rate of change of the Jacobian matrix representing the transformation between the joints speeds and the end-effector Cartesian speed. These bounds become an additional constraint for an optimization problem which is formulated locally to obtain the optimal path of the considered robot manipulator. The problem is considered as a minimization of energy with given robot kinematics (and dynamics) and subject to the robot requirements and singularities-avoidance constraint. From this formulation, a closed-form solution is derived which allows online interaction with sensors.>

In this paper, a singularities avoidance method suitable for the trajectory planning of redundant and nonredundant robot manipulators is presented. This method is based on establishing proper bounds for the rate of change of the Jacobian matrix of the transformation between the joints speed and end effector Cartesian speed These bounds are computationally inexpensive and easy to deal with by their conversion into additional constraints for any optimization problem which may be formulated to obtain the local or global optimal control of the robot manipulator. Here, this approach is exemplified for the trajectory planning problem of a particular type of redundant and nonredundant robot manipulators studied under an optimal control problem formulation. For each case, this problem is treated as a minimum energy problem with given kinematics and dynamics and subject to the robot requirements, tasks, and the additional singularities avoidance constraints; resulting in a state constrained continuous optimal control which is solved numerically.