Journal of Intelligent and Robotic Systems 19: 1–3, 1997. 1

Guest Editorial:Recent Developments for Kinematically RedundantManipulators

It is with great pleasure that we welcome you to this special issue of the Journalof Intelligent and Robotic Systems devoted to Kinematically Redundant Robots.The allure of developing robots that possess the kinematic complexity of biologi-cal systems, along with the attendant advantages of dexterity, has been irresistiblefor many robotics researchers. Thus, research devoted to kinematically redundantrobots has enjoyed a long and exciting history. Many early efforts were gearedtowards anthropomorphic manipulator designs, motivated either by their appli-cations as prosthetic devices or for teleoperation. Indeed, the first appearanceof the now ubiquitous (weighted) pseudoinverse in the 1960’s was geared forthese applications. Seminal work in the 1970’s produced the scheme of using thegradient projection onto the nullspace of the Jacobian to utilize the manipulatorredundancy. The 1980’s provided additional techniques for resolving redundan-cy, most notably the use of extended and augmented Jacobians for optimizing amanipulator’s dexterity, avoiding obstacles, and a host of other intelligent behav-iors. During this same time period, fundamental work was performed to illustratethe inherent difficulties associated with both kinematic and algorithmic singular-ities, the damped least squares algorithm was introduced for ameliorating someof these difficulties, and the repeatability of inverse kinematic formulations wasbrought under scrutiny.

It is against this historical backdrop that we decided to organize this specialissue. Our goal was to provide a range of articles on topics that would providea snapshot of significant contributions to kinematic redundancy in the 1990s.These topics range from fundamental issues that are still unresolved to novelrobot designs and applications. A brief summary of accepted articles is providedbelow.

The first article by Chirikjian deals with the kinematics and trajectory plan-ning of robotic manipulators with Binary Actuators classified as actuators havingtwo discrete stable states such as in the case of pneumatic cylinders. The mainadvantage of binary actuators is that extensive feedback control is not required.Due to the fact that the number of configurations attainable by a binary manipula-tor grows exponentially with the number of actuated degrees of freedom (DOF),

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inverse kinematics calculation by direct enumeration of joint states and forwardkinematics calculation are not feasible in the highly actuated case. Employingthe methods of classical differential geometry to define a backbone curve andassociate set of frames, the author develops an efficient method for perform-ing the inverse kinematics and trajectory planning by making the manipulatorshape adhere closely to the frames. Analysis of the actuators show that with highenough damping and pressure for a given mass, the speed of each actuator canbe approximated as a constant.

Addressing the manipulator redundancy from a global perspective, Luck ex-plores the self motion topology to produce a topological description of the con-figuration and workspaces. The author develops a space discretization methodwhich enables an efficient exploration of global redundancy resolution and pathplanning, providing the means for avoiding local minima and deadlocks. Themethod is implemented on a redundant planar manipulator and the implementa-tion shows significant improvement in the search for globally optimal solutionsfor path planning as compared to traditional approaches.

Klein and Chu evaluate the performance of two redundancy resolution meth-ods, namely the extended Jacobian method (EJM) and the Lagrange multiplier-based method (LMM) for redundant manipulators. While the EJM constraints thegradient to be in the null space of the Jacobian matrix, the LMM represents thegradient as being in the row space. The article presents a numerically efficientform of the LMM and compares its performance analytically, computationallyand operationally with that of the EJM. The authors also propose a Jacobian-based tracing method to replace the conventional optimization-based method fortracking algorithmic singularities.

English and Maciejewski study the usefulness of a redundant manipulatorafter a free-swinging failure, defined as hardware or software failure preventingthe application of actuator torque on a manipulator joint. The article presents twomethods for the analysis of the postfailure workspace defined as the set of handposes reachable by the stationary manipulator with zero actuator torque on thefailed joint. Based on a positional inverse kinematic algorithm using polynomialroots, the first method is applicable to planar arms only and guarantees thatall solutions can be found. Having no such guarantee and being based on adifferential technique for tracing the postfailure workspace boundary, the secondmethod can be applied to both planar and spatial manipulators.

Mayorga and Wong introduce a fast procedure for the on-line concurrent pathplanning for multi manipulator systems by formulating an inverse kinematicsproblem for each manipulator under an inexact context. The problem comprisesa linear system of equations which take into account a vector in the null spacefor the motion planning and a novel scheme for the appropriate perturbation ofthe pseudo-inverse matrix. The proposed approach allows one to simultaneouslyaccomplish both motion coordination/planning and avoidance of singularities inreal-time and sensor-based environment. The efficiency of the proposed method

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is demonstrated by a computer simulation on a dual robot system consisting oftwo planar redundant manipulators.

Dubey, McGhee and Chan present a probability-based method to simulta-neously optimize multiple performance criteria for a kinematically redundantmanipulator. They utilize both variable and constant weighting using the stan-dard deviation or the probability density weighting to allow dissimilar perfor-mance criteria to be compared and properly prioritized. The proposed optimiza-tion scheme is experimentally evaluated on the seven DOF Robotics ResearchCorporation manipulator where multiple performance criteria are to be satisfiedsimultaneously.

In the final article of the issue, Zhou and Nguyen deal with off-line glo-bal trajectory planning formulated as an optimization problem whose solutionis derived using the Pontryagin’s maximum principle. The authors employ thestate augmentation method to obtain a set of optimal joint trajectories whichavoids manipulator joint limits and conserves joint configuration in cyclic motion.Computer simulation performed on a three DOF planar manipulator shows thatthe proposed planning scheme is able to maximize the utilization of allowed jointmotions and to conserve the joint configuration.

The successful completion of this special issue would be impossible withoutthe cooperation of the following individuals. First, we would like to express ourgratitude to Professor Spyros Tzafestas, Editor of the Journal of Intelligent andRobotic Systems, for inviting us to serve as the Guest Editors of this specialissue and for giving strong support to this project. We would like to thank thereviewers for their promptness and professionalism. Our thanks is extended toall authors for accepting to participate in this special issue and for giving theirvaluable contributions. Finally, we would like to express our appreciation to thestaff of the Kluwer Academic Publishers for their help and cooperation in theediting and production of the issue.

CHARLES C. NGUYEN, D.SC. ANTHONY A. MACIEJEWSKI, PH.D.Professor and Director Associate ProfessorRobotics and Control Laboratory School of Electrical EngineeringThe Catholic University of America Purdue UniversityWashington DC, 20064 West Lafayette, Indiana 47907Email: nguyen@pluto.ee.cua.edu Email: maciejew@ecn.purdue.edu

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