The extended Jacobian method resolves the redundancy of a kinematically redundant manipulator such that a secondary criterion is kept at an optimal value. This paper describes a new formulation of this algorithm that is well suited numerically for systems with multiple degrees of redundancy and for more general choices of the secondary criterion. This formulation is used here for tracing algorithmic singularities, which mark a boundary of operation for any algorithm using the same secondary criterion to resolve the redundancy. Examples of tracing algorithmic singularities are presented for both planar and spatial systems.>

The necessary and sufficient conditions for repeatable pseudoinverse control are now well known. A very simple example of a configuration for planar manipulators that is conservative is also known. It is also known there is no conservative configuration for the most common definition of joint angles. The question remains whether there exists any other conservative case using other definitions of joint angles, or equivalently, for pseudoinverse control using different, but constant, joint norms. This paper addresses this question using a combination of analytical and numerical methods. Such cases have been found, however, the resulting configurations are the same as previously known.

C. Klein and K. Kee (1989) showed numerically that pseudoinverse control, while generally being nonconservative, in some cases appears to give conservative results and described a numerical procedure for finding stable, drift-free trajectories. T. Shamir and Y. Yomdin (1988) discuss using the Lie bracket condition (LBC) as a test of the repeatability of redundant manipulator control. The present author examines the hypothesis that the above-mentioned stable trajectories, which are done numerically on a three-link, planar manipulator with relative joints, might be predicted by the LBC. He concludes that the stable trajectories are not contained in the LBC surfaces, but that their closeness suggests that the LBC is a useful analytical test for locating them.>

An adaptive gait algorithm for multilegged walking machines over rough terrain has been developed. The heuristic and hierarchical approach for the three levels of: 1) body motion adaptation; 2) leg sequence adaptation; and 3) leg position adaptation is effective, straightforward, and relatively independent of the number of legs. On rough terrains with depressions the algorithm behaves like a "free gait"; on level ground terrain it behaves more like a periodic gait. The effectiveness of the proposed gait over rough terrains with depressions is demonstrated with several computer simulations.>

The authors discuss a number of principles associated with the rate of convergence of iterative robotic calculations that have been found to be helpful in testing the correctness of such programs. One example of an iterative robotic calculation is performing inverse kinematics by an indirect method such as Jacobian control. Because such a method is based on a local approximation, the numerical results are not supposed to be perfect after changing joint angles a finite amount. It is not obvious how much error is inherent in the method. It is known that if the interval size is reduced to zero, the results will reach the ideal value. It has been the authors' experience, however, that even when the errors numerically reduce to zero in the limit, there can still be serious errors in the formulation or the computer program. Based on the authors' experience in developing and debugging new algorithms, several principles that will greatly aid in detecting errors are presented.>

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.>

The control of kinematically redundant manipulators using only pseudoinverse control is known to produce drift in joint space when a cyclic task is performed in rectilinear space. The properties of this drift are examined by performing numerical experiments. This drift has predictable properties including a numerically stable limit in some situations. At this limit the arc length of the path in joint space appears to be near a minimum.>

Force is often used in the control of the legs of a walking machine to allow a vehicle to adapt to terrain irregularity. However, interactions in force among the legs have the capability of causing control system instabilities if not properly treated. Different criteria for allocating forces to the legs of a walking machine are considered, properties of force-induced instability modes are studied, and the plan of hybrid control allocated by legs as a means of avoiding these force interaction modes without requiring an excessively high control frequency is introduced.

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 operator's burden.

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.

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.