P. R. McAree

Fundamental limits of performance for force reflecting teleoperation

The quality of telepresence provided by a force-reflecting teleopera tor is determined, for the most part, by the fidelity of the contact-force information fed back to the operator. These fed-back forces, how ever, also directly influence system stability, and in this paper we investigate the relationship between fidelity and stability with a view toward understanding how stability considerations impose funda mental limits on system performance. The key idea of our work is to draw an explicit distinction between the information conveyed by the force signal and the energy inherent in that signal. Using known physiological properties of the operator, we argue that there exists a natural partitioning between information and energy wherein in formation is conveyed at frequencies above roughly 30 Hz, while the energetic interaction between the slave and the environment takes place at frequencies below this. We embody this distinction in a two-channel framework that we claim provides insight into the de sign of force-reflecting systems. Using a 1-DOF model, we study the effect of various system characteristics, notably mass, stiffness, and damping properties, on performance and stability. This model is used to derive expressions for the maximum force-reflection ratio that guarantees stability against pure-stiffness environments and to investigate the role of various compensation elements, including lo cal force control around the slave. Finally, a framework is developed for force-reflecting teleoperation that maximizes the force informa tion conveyed to the operator, subject to the constraints imposed by stability considerations.

An Explanation of Never-Special Assembly Changing Motions for 3–3 Parallel Manipulators

When the leg rods of a fully in-parallel manipulator are fixed in their lengths, it is usual that the device can be assembled in several distinct ways. Sometimes it happens that motion between such assemblies can take place such that the linkage is never at a special configuration; that is, a configuration where the moving-platform body acquires uncontrollable freedom relative to the base. The possibility of such motion has implications for control. Focusing on 3–3 devices, we present a geometric explanation of how these motions arise, and give a sufficient condition for their existence. For the 3–3 planar-motion device, we show that never-special assembly changing motions can be excluded by making platform and base triangles similar, and we conjecture that appropriate, perhaps identical, specialization for the octahedral manipulator has the same effect.

The Octahedral Manipulator: Geometry and Mobility:

In most of the practical six-actuator, in-parallel manipulators, the octahedral form is either taken as it stands or is approximated. Yet considerable theoretical attention is paid in the literature to more general forms. Here we touch on the general form, and describe some aspects of its behavior that vitiate strongly against its adoption as a pattern for a realistic manipulator. We reach the conclusion that the structure for in-parallel manipulators must be triangulated as fully as possible, so leading to the octahedral form. In describing some of the geometrical properties of the general octahedron, we show how they apply to manipulators. We examine in detail the special configurations at which the 6 x 6 matrix of leg lines is singular, presenting results from the point of view of geometry in preference to analysis. In extending and enlarging on some known properties, a few behavioral surprises materialize. In studying special configurations, we start with the most general situation, and every other case derives from this. Our coverage is more comprehensive than any that we have found. We bring to light material that is, we think, of significant use to a designer.

Special configurations of multi-finger multi-freedom grippers—a kinematic study

Screw theory is used to establish the general kinematic prin ciples offully-in-series and fully-in-parallel devices. Through screw theory, we show that a workpiece grasped by a fully-in- series manipulator can only lose freedom while a workpiece grasped by a fully-in-parallel manipulator can only gain freedom. Multi-finger multi-freedom grippers or robot hands use a mixture of in-parallel and serial actuation, and so a workpiece grasped by such a device can both gain and lose freedom. These linkages belong to a class called composite serial/in-parallel manipulators. Using the well-established concepts of screw systems and reciprocity, we identify the general criteria that govern the gain and loss of workpiece freedoms. We illustrate how these gains and losses of work piece freedom arise, by considering the Stanford/JPL hand.

Unifying screw geometry and matrix transformations

Transformation matrices are widely used in robotics for kinematic analysis and trajectory planning. Screw geome try offers better geometric insight into such analyses. In this article we unify the two approaches through the use of invariant properties of orthogonal matrices under simi larity transformations. We give a complete expression for the finite screw motion in terms of the entires of a 3 x 3 dual-number transformation matrix. Our analysis suggests that the finite screw is suitable for trajectory planning, and we develop a concise expression that gives the trans formation matrix describing the displacement at each point along the path of the finite screw motion.

A fast, robust solution to the Stewart platform forward kinematics

The Stewart platform is a six degree-of-freedom fully-in-parallel linkage well-suited to robotic tasks where structural rigidity and high small motion bandwidth are required. In this article we describe an approach for computing the forward kinematics of this device that is both fast and robust. Our solution is based on the simultaneous solution of three constraint equations using a Newton-Raphson scheme. A well-known property of Newton-Raphson is its tendency to fail when the constraint equations become poorly conditioned, and the main contribution of this article is the development of two algorithms for overcoming this limitation and hence for providing robustness. Certain other matters, such as the singular configurations of the Stewart platform and its assembly modes, are touched upon.

A dexterity measure for the kinematic control of a multifinger, multifreedom robot hand

This work examines the properties of the manifold gener ated as the configuration space of the linkage used for each finger of the Salisbury hand. We begin with an exhaustive catalog of design types for the finger based on an analysis of its branch loci. We then study the condi tions under which the forward kinematic map becomes singular. These singularities define a submanifold that partitions the linkages configuration space into a number of open sheets, each of which maps diffeomorphically onto a corresponding open region in the fingers reach able work space. Next we consider the determinant func tion of the fingers Jacobian matrix. The stationary points of this function reveal those configurations where the Jacobian determinant is a maximum. The Jacobian deter minant can be thought of as an oriented volume in the tangent space to the fingers work space, and the orienta tion of this volume reveals the most favorable direction(s) for effecting tip motion or, reciprocally, for applying tip forces. From this we establish a simple criterion that can be used to find the optimal grasp configuration(s) for a given finite displacement of the workpiece.

A simple approach to invariant hybrid control

We give a geometrical description of Raibert and Craigs hybrid force/position control method (1981). Our description is coordinate free, hence answering the criticism of the original work that it was not transformation invariant. However, our approach avoids the complications introduced in the work of Lipkin and Duffy (1988). This simplification is achieved by recognising that velocity screws and wrenches are different geometrical objects and then keeping them separate throughout the discussion. So we do not use any metric properties of the screw space of infinitesimal rigid body motions. Rather, we employ the duality between the vector space of screws and the linear functionals on them. We give several examples and show how changes of coordinates should be handled.

Stability analysis of force reflecting telerobotic systems

In the paper we aim to enhance the understanding of the effects of system properties, most notably the role of slave damping, on the performance of force reflecting teleoperators. Building on work by Daniel and McAree we argue that if a slave manipulator is critically damped then system performance, as measured by the maximum achievable force reflection ratio, becomes independent of the mass and stiffness of the operator. We give some experimental results in support of this.

Tyre-force estimation by Kalman inverse filtering : applications to off-highway mining trucks

Kalman inverse filtering is used to develop a methodology for real-time estimation of forces acting at the interface between tyre and road on large off-highway mining trucks. The system model formulated is capable of estimating the three components of tyre-force at each wheel of the truck using a practical set of measurements and inputs. Good tracking is obtained by the estimated tyre-forces when compared with those simulated by an ADAMS virtual-truck model. A sensitivity analysis determines the susceptibility of the tyre-force estimates to uncertainties in the truck’s parameters.