Robert B. McGhee

Aircraft Identification by Moment Invariants

Although many systems for optical reading of printed matter have been developed and are now in wide use, comparatively little success has been achieved in the automatic interpretation of optical images of three-dimensional scenes. This paper is addressed to the latter problem and is specifically concerned with automatic recognition of aircraft types from optical images. An experimental system is described in which certain features called moment invariants are extracted from binary television images and are then used for automatic classification. This experimental system has exhibited a significantly lower error rate than human observers in a limited laboratory test involving 132 images of six aircraft types. Preliminary indications are that this performance can be extended to a wider class of objects and that identification can be accomplished in one second or less with a small computer.

On the stability properties of quadruped creeping gaits

Abstract While the total number of theoretically possible quadruped gaits is quite large, only six gaits have the property that they can be executed while keeping at least three feet on the ground at all times. These gaits, called creeping gaits, seem to be well suited for low-speed locomotion since they permit a quadruped to remain statically stable during most of a locomotion cycle. A mathematical analysis shows, however, that for only three of the six creeping gaits it is possible to place the feet of an animal or machine so that it is statically stable at all times. Furthermore, among these three, there exists a unique optimum gait that maximizes static stability. This gait corresponds to the normal quadruped crawl favored by most animals for very low-speed locomotion.

An extended Kalman filter for quaternion-based orientation estimation using MARG sensors

Presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this approach, the measurement equations of the Kalman filter become linear, and the computational requirements are significantly reduced, making it possible to estimate orientation in real time. Extensive testing of the filter with synthetic data and actual sensor data proved it to be satisfactory. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track rotational motions.

Adaptive Locomotion of a Multilegged Robot over Rough Terrain

Although the off-road mobility characteristics of wheeled or tracked vehicles are generally recognized as being inferior to those of man and cursorial animals, the complexity of the joint-coordination control problem has thus far frustrated attempts to achieve improved vehicular terrain adaptability through the application of legged locomotion concepts. Nevertheless, the evident superiority of biological systems in this regard has motivated a number of theoretical studies over the past decade which have now reached a state of maturity sufficient to permit the construction of experimental computer-controlled adaptive walking machines. At least two such vehicles are known to have recently demonstrated legged locomotion over smooth hard-surfaced terrain. This paper is concerned with an extension of the present theory of limb coordination for such machines to the case in which the terrain includes regions not suitable for weight-bearing and which must consequently be avoided by the control computer in deciding when and where to successively place the feet of the vehicle. The paper includes a complete problem formalization, a heuristic algorithm for solution of the problem thus posed, and a preliminary evaluation of the proposed algorithm in terms of a computer simulation study.

A Simplified Quaternion-Based Algorithm for Orientation Estimation From Earth Gravity and Magnetic Field Measurements

Orientation of a static or slow-moving rigid body can be determined from the measured gravity and local magnetic field vectors. Some formulation of the QUaternion ESTimator (QUEST) algorithm is commonly used to solve this problem. Triads of accelerometers and magnetometers are used to measure gravity and local magnetic field vectors in sensor coordinates. In the QUEST algorithm, local magnetic field measurements affect not only the estimation of yaw but also that of roll and pitch. Due to the deviations in the direction of the magnetic field vector between locations, it is not desirable to use magnetic data in calculations that are related to the determination of roll and pitch. This paper presents a geometrically intuitive 3-degree-of-freedom (3-DOF) orientation estimation algorithm with physical meaning [which is called the factored quaternion algorithm (FQA)], which restricts the use of magnetic data to the determination of the rotation about the vertical axis. The algorithm produces a quaternion output to represent the orientation. Through a derivation based on half-angle formulas and due to the use of quaternions, the computational cost of evaluating trigonometric functions is avoided. Experimental results demonstrate that the proposed algorithm has an overall accuracy that is essentially identical to that of the QUEST algorithm and is computationally more efficient. Additionally, magnetic variations cause only azimuth errors in FQA attitude estimation. A singularity avoidance method is introduced, which allows the algorithm to track through all orientations.

Kinematic and kinetic analysis of open-chain linkages utilizing Newton-Euler methods

Abstract This paper presents some improvements in a Newton-Euler approach to spatial open-chain mechanism analysis introduced by one of the authors in an earlier publication. The improvements have to do both with the introduction of simplified notation and with more efficient computational procedures. The validity and utility of the method is illustrated by an application to the problem of calculating joint torques for the legs of a hexapod locomotion system. The results obtained agree well with experimental measurements and are also shown to satisfy a number of necessary conditions, thereby validating to some extent both the methodology and the corresponding computer program.

On the Dynamic Stability of Biped Locomotion

While biped locomotion involves very complicated dynamical processes, a good deal can be learned about stability and feedback control from an analysis of simplified mathematical models. This paper treats locomotion dynamics relative to planar motion under an assumption that leg mass can be ignored in comparison to body mass. Thus the hypothetical biped possesses one rotational degree of freedom and two translational degrees, leading to a sixth-order system of nonlinear differential equations. These equations are linearized and feedback control laws are then derived to produce the desired stable forward motion. The feedback laws proposed involve a combination of continuous and discrete concepts to produce both step length and step period control as well as control of body attitude and altitude. The applicability of the control laws to the nonlinear system in the presence of large disturbances is verified by computer simulation. Hopefully, the results presented are significant relative to control processes arising in lower extremity prostheses and orthoses as well as to the design of biped robots.

Some finite state aspects of legged locomotion

Abstract Animal locomotion systems making use of legs as the basic component for support and propulsion can be studied from the point of view of finite state machine theory by regarding each leg as an elementary two-state sequential machine. The two states are simply the state of being in contact with the supporting surface and the state of being raised above it. This idealization permits the construction of a general theory of locomotion equally applicable to animals and legged locomotion machines. Such a theory can be made sufficiently complete to permit the synthesis of finite control algorithms capable of coordinating limb movements in either animals or machines. The validity of the finite state approach has been established by the construction and testing of an artificial quadruped based entirely upon finite state principles.

Inertial and magnetic posture tracking for inserting humans into networked virtual environments

Rigid body orientation can be determined without the aid of a generated source using nine-axis MARG (Magnetic field, Angular Rate, and Gravity) sensor unit containing three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers. This paper describes a quaternion-based complementary filter algorithm for processing the output data from such a sensor. The filter forms the basis for a system designed to determine the posture of an articulated body in real-time. In the system the orientation relative to an Earth-fixed reference frame of each limb segment is individually determined through the use of an attached MARG sensor. The orientations are used to set the posture of an articulated body model. Details of the fabrication of a prototype MARG sensor are presented. Calibration algorithms for the sensors and the human body model are also presented. Experimental results demonstrate the effectiveness of the tracking system and verify the correctness of the underlying theory.

A Finite State Approach to the Synthesis of Bioengineering Control Systems

The design of devices capable of duplicating the function of human extremities has become increasingly important in science, industry, and medicine. This paper presents an approach to the synthesis of control systems for such machines which results in extremely simple finite state controllers. The technique proposed rests on the definition of a new type of actuator, called a cybernetic actuator, which possesses the property of producing continuous controlled motion from an input which may assume only four distinct states. The application of such actuators to bioengineering systems is illustrated by the design of a control system for an artificial leg.