Charles A. Klein

Review of pseudoinverse control for use with kinematically redundant manipulators

Kinematically redundant manipulators have a number of potential advantages over current manipulator designs. For this type of arm, velocity control through pseudoinverses is suggested. Questions associated with pseudoinverse control are examined in detail and show that in some cases this control leads to undesired arm configurations. A method for distributing joint angles of a redundant arm in a good approximation to a true minimax criterion is described. In addition several numerical considerations are discussed.

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.

Dexterity measures for the design and control of kinematically redundant manipulators

In this paper, we have proposed a number of measures for the quantification of dexterity of manipulators. The use of such measures is especially important for kinematically redundant manipulators since they can satisfy secondary cri teria in addition to satisfying a specification of end-effector motion. We will compare several measures for the problems offinding an optimal configuration for a given end-effector position, finding an optimal workpoint, and designing the op timal link lengths of an arm.

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.

Optimal force distribution for the legs of a walking machine with friction cone constraints

The authors examine different methods of solving the force distribution problem for the limbs of a legged vehicle with friction cone constraints. A key concept in the proposed formulations is the use of pseudoinverses to provide a decomposition of the original problem in a form that is more amenable to optimization. The new formulations can be described as being either interior- or exterior-based methods. Geometrically, interior methods start a search in force space with a force that is inside the friction cone constraints but does not necessarily meet the required body forces and torques. Exterior methods start with forces that meet the required body forces and torques but may be outside the friction cone constraints. It is shown that exterior methods have the potential for providing better force command continuity when the solution from the previous control cycle is considered or, alternatively, these methods can be used to minimize the maximum friction cone angle over all the legs. >

Automatic body regulation for maintaining stability of a legged vehicle during rough-terrain locomotion

The evolution of legged vehicles has progressed significantly in recent years. These vehicles offer the potential of increased mobility for traversing rough terrain. The ability to maintain stability is an important consideration in the development of any control algorithm for a legged vehicle. Previous work on legged vehicle control generally assumes that the terrain is regular enough that only minimal operator interaction is necessary. However, for very irregular terrain the operator may require a guidance mode that gives maximum resolution and flexibility in controlling body, leg, position, and orientation. Several automatic body regulation schemes that aid the operator in this important task are described. A major development is the use of an improved stability measure which can be automatically optimized. This measure, together with a consideration of constraints on the kinematic limits of individual legs, leads to the development of schemes for automatic body regulation. The automatic body regulation schemes are incorporated into the vehicle control algorithm to provide a high degree of vehicle maneuverability while reducing the operators burden.

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.

Use of Force and Attitude Sensors for Locomotion of a Legged Vehicle over Irregular Terrain

A number of legged vehicles are being developed for their mobility characteristics over irregular terrain. One such vehicle is The Ohio State University Hexapod vehicle (OSU Hexapod). Recently, the vehicle has been modified so that it can successfully walk over uneven terrain. Each of the feet has been equipped with two semiconductor strain gauges to measure lateral forces and a piezoelectric load cell to measure vertical forces. A vertical gyroscope and pendulums for orientation sensing have also been added. The control of locomotion over rough terrain can be decomposed into two complementary control processes, attitude control and active compliance. Attitude control is used to maintain the body tilt in a desired orientation, and active compliance is used to provide a suspension system by distributing force loading among the legs. It has been found that optimal force setpoints for the active-compliance algorithm can be calculated in closed form. This paper discusses the sensing hardware and the control system needed for legged locomotion over irregular terrain. Experimental results are provided for both statically determinate and indeterminate hexapod gaits.

Use of Active Compliance in the Control of Legged Vehicles

Often it is desirable to specify both position and force at the end effector of a manipulator system; however, when the system forms a closed kinematic chain both cannot be realized independently. Active compliance is a trade-off method that can be easily incorporatd into the supervisory control philosophy which is often used to control complex man-machine systems. An example of such a system is the Ohio State University (OSU) Hexapod which is a legged walking vehicle. Active compliance is shown to be invaluable for allowing legged locomotion over irregular terrain.

Forward scattering from square cylinders in the resonance region with application to aperture blockage

The relationship between the induced field ratio (IFR) of a cylinder and aperture blocking of a constant-phase aperture by cylindrical struts is discussed. An analytical technique is presented whereby the IFR of rectangular cylinders can be calculated using the method-of-moments with internal constraint points. An experimental technique using a forward-scattering range is used to measure the IFRs of square and circular cylinders in an anechoic chamber. These experimental results are compared with the theory, and their implications on aperture blocking losses and boresight cross polarization are discussed.