Anthony A. Maciejewski

Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments

The vast majority of work to date concerned with obstacle avoidance for manipulators has dealt with task descriptions in the form ofpick-and-place movements. The added flexibil ity in motion control for manipulators possessing redundant degrees offreedom permits the consideration of obstacle avoidance in the context of a specified end-effector trajectory as the task description. Such a task definition is a more accurate model for such tasks as spray painting or arc weld ing. The approach presented here is to determine the re quired joint angle rates for the manipulator under the con straints of multiple goals, the primary goal described by the specified end-effector trajectory and secondary goals describ ing the obstacle avoidance criteria. The decomposition of the solution into a particular and a homogeneous component effectively illustrates the priority of the multiple goals that is exact end-effector control with redundant degrees of freedom maximizing the distance to obstacles. An efficient numerical implementation of the technique permits sufficiently fast cycle times to deal with dynamic environments.

Task Matching and Scheduling in Heterogeneous Computing Environments Using a Genetic-Algorithm-Based Approach

To exploit a heterogeneous computing (HC) environment, an application task may be decomposed into subtasks that have data dependencies. Subtask matching and scheduling consists of assigning subtasks to machines, ordering subtask execution for each machine, and ordering intermachine data transfers. The goal is to achieve the minimal completion time for the task. A heuristic approach based on a genetic algorithm is developed to do matching and scheduling in HC environments. It is assumed that the matcher/scheduler is in control of a dedicated HC suite of machines. The characteristics of this genetic-algorithm-based approach include: separation of the matching and the scheduling representations, independence of the chromosome structure from the details of the communication subsystem, and consideration of overlap among all computations and communications that obey subtask precedence constraints. It is applicable to the static scheduling of production jobs and can be readily used to collectively schedule a set of tasks that are decomposed into subtasks. Some parameters and the selection scheme of the genetic algorithm were chosen experimentally to achieve the best performance. Extensive simulation tests were conducted. For small-sized problems (e.g., a small number of subtasks and a small number of machines), exhaustive searches were used to verify that this genetic-algorithm-based approach found the optimal solutions. Simulation results for larger-sized problems showed that this genetic-algorithm-based approach outperformed two nonevolutionary heuristics and a random search.

Numerical filtering for the operation of robotic manipulators through kinematically singular configurations

The loss of independent degrees of freedom at singular configurations is an inherent characteristic of robotic manipulators. Due to the unavoidable singularity of mechanical wrists, singular configurations cannot be avoided by simply restricting the bounds of the workspace. Techniques for operating at singular configurations without inducing unacceptably high joint velocities or end effector tracking errors are presented. Extensions to the damped least-squares formulation which incorporate estimates of the proximity to singularities and selective filtering of singular components are illustrated. The generality of the technique presented is illustrated in a computer simulation of a commercially available manipulator operating through singular configurations.

The singular value decomposition: computation and applications to robotics

The singular value decomposition has been extensively used for the analysis of the kinematic and dynamic characteristics of robotic manipulators. Due to a reputation for being nu merically expensive to compute, however, it has not been used for real-time applications. This work illustrates a for mulation for the singular value decomposition that takes advantage of the nature of robotics matrix calculations to ob tain a computationally feasible algorithm. Several applica tions, including the control of redundant manipulators and the optimization of dexterity, are discussed. A detailed illus tration of the use of the singular value decomposition to deal with the general problem of singularities is also presented.

A local measure of fault tolerance for kinematically redundant manipulators

When a manipulator suffers a joint failure, its performance can be significantly affected. If the failed joint is locked, the resulting manipulator Jacobian is given by the original Jacobian, except that the column associated with the failed joint is removed. The rank of the resulting Jacobian then determines if the manipulator still has the ability to perform arbitrary end-effector motions. Unfortunately, even at an operating configuration that has a relatively high manipulability index, a joint failure may still result in a singular Jacobian. This work examines the problem of determining the reduced manipulability of a manipulator after one or more joint failures. Configurations that result in a minimal reduction of the manipulability index for any set of joint failures are determined.

Fault tolerance for kinematically redundant manipulators: anticipating free-swinging joint failures

Fault tolerance is an important design criterion for robotic systems operating in hazardous or remote environments. This article addresses the issue of tolerating a free-swinging joint failure by focusing on how to best configure a slow-moving manipulator before a failure. Three scalar measures of fault susceptibility are defined using joint torques/forces, accelerations, and swing angles. Minimizing these measures is an approach to achieving fault tolerance, and for this, algorithms to calculate their gradients are also given. The formulas are valid for general n-link manipulators.

Fault tolerant properties of kinematically redundant manipulators

A measure of fault tolerances for redundant manipulators is derived based on the remaining dexterity following the loss of degree of freedom. Using this measure as a criterion, a technique for calculating optimal fault tolerant configurations for redundant manipulators is presented. The properties of these configurations are analyzed in order to assist designers in determining the number of degrees of freedom required to maintain a minimum level of dexterity under a worst-case scenario.<<ETX>>

Fault tolerant operation of kinematically redundant manipulators for locked joint failures

This paper studies the degree to which the kinematic redundancy of a manipulator may be utilized for failure tolerance. A redundant manipulator is considered to be fault tolerant with respect to a given task if it is guaranteed to be capable of performing the task after any one of its joints has failed and is locked in place. A method is developed for determining the necessary constraints which insure the failure tolerance of a kinematically redundant manipulator with respect to a given critical task. This method is based on estimating the bounding boxes enclosing the self-motion manifolds for a given set of critical task points. The intersection of these bounding boxes provides a set of artificial joint limits that may guarantee the reachability of the task points after a joint failure. An algorithm for dealing with the special case of 2-D self-motion surfaces is presented, These techniques are illustrated on a PUMA 560 that is used for a 3-D Cartesian positioning task.

Dynamically mapping tasks with priorities and multiple deadlines in a heterogeneous environment

In a distributed heterogeneous computing system, the resources have different capabilities and tasks have different requirements. To maximize the performance of the system, it is essential to assign the resources to tasks (match) and order the execution of tasks on each resource (schedule) to exploit the heterogeneity of the resources and tasks. Dynamic mapping (defined as matching and scheduling) is performed when the arrival of tasks is not known a priori. In the heterogeneous environment considered in this study, tasks arrive randomly, tasks are independent (i.e., no inter-task communication), and tasks have priorities and multiple soft deadlines. The value of a task is calculated based on the priority of the task and the completion time of the task with respect to its deadlines. The goal of a dynamic mapping heuristic in this research is to maximize the value accrued of completed tasks in a given interval of time. This research proposes, evaluates, and compares eight dynamic mapping heuristics. Two static mapping schemes (all arrival information of tasks are known) are designed also for comparison. The performance of the best heuristics is 84% of a calculated upper bound for the scenarios considered.

Dexterity optimization of kinematically redundant manipulators in the presence of joint failures

Abstract Robotic manipulators working in remote or hazardous environments require additional measures to ensure their usability upon the failure of an actuator. This work considers failure modes that result in an immobilized joint and uses the concept of worst-case dexterity to define kinematic and dynamic fault tolerance measures for redundant manipulators. These measures are then used to specify the operating configuration which is optimal in the sense that the manipulators dexterity remains high even if one of its joints fails in a locked position. The close relationship between fault tolerance and dexterity is examined using a simple planar manipulator as an example. It is demonstrated that an inverse kinematic function which maintains a high level of fault tolerance also keeps the manipulator in well-conditioned configurations known to have desirable properties.