For control system analysis and design, and high-speed real-time computation, the transformations between the delta and forward shift operator transfer function models of dynamic physical systems are highlighted. In the fast sampling limit, the delta operator model tends to the analog dynamic system model. This intrinsic property of the delta operator model unifies continuous and discrete time control engineering and paves the way for the design of robust computational algorithms.>

For control system analysis and design, and high-speed real-time computation, the computational formulation, properties and applications of the delta operator model of dynamic physical systems are highlighted. Doubling algorithms for reliable computation are formulated, and the transfer function matrix of the delta operator model is illustrated. In the fast sampling limit, the delta operator model tends to the dynamic system model. This intrinsic property of the delta operator model unifies continuous and discrete time control engineering and paves the way for the design of robust computational algorithms.>

The authors apply two Cartesian-space manipulator control algorithms, resolved motion rate (kinematics-based) and resolved acceleration (dynamics-based) control, to wheeled mobile robot (WMR) servo control. They evaluate simulation studies of two exemplary WMRs-Uranus, a three-degree-of-freedom WMR, and Bicsun-Bicas, a two-degree-of-freedom WMR-under the control of these algorithms. Although resolved-motion-rate servo control is adequate for the control of Uranus, resolved-acceleration servo control is required for the control of the mechanically simpler Bicsun-Bicas because it exhibits more dynamic coupling and nonlinearities.>

The LU factorization of the Hessenberg matrix is explicitly presented. The matrix is recognized for reliable and robust numerical computation.>

A formulation is introduced for the dynamic modeling of multibody robotic mechanisms to incorporate closed chains, higher pair joints, friction (including stiction, Coulomb, rolling and viscous friction), and unactuated and unsensed joints. Although this formulation was developed for the dynamic modeling of Uranus, and omnidirectional wheeled mobile robot, the methodology is directly applicable to a spectrum of multibody robotic mechanisms. The methodology is based on Newtonian dynamics, kinematics, and the concepts of force/torque propagation and frictional coupling at a joint introduced in this work. The extensible matrix-vector dynamics formulation allows the application of classical methodologies for the solution of systems of linear algebraic equations. To illustrate the procedure, the dynamics formulation is applied to a planar double pendulum and a biped in the frontal plane.>

In 1983, the computer program called algebraic robot modeler (ARM) was implemented to generate symbolically complete closed-form and recursive dynamic robot models. To enhance computational efficiency for dynamic simulation and real-time control, the systematic organization of these symbolic models was introduced in 1985 to remove repetitive calculations within and across equations and thereby generate customized robot dynamics algorithms. The systematic organization procedure of ARM is detailed and its performance compared with documented organizations. It is pointed out that the systematic organization procedure, and the exploitation of kinematic and dynamic manipulator structures through symbolic modeling, make ARM-generated customized algorithms the most computationally efficient manipulator dynamics algorithms of those compared.>

We have introduced a methodology for the kinematic modeling of wheeled mobile robots. In this paper, we apply our methodology to Uranus, an omnidirectional wheeled mobile robot which is being developed in the Robotics Institute of Carnegie Mellon University. We assign coordinate systems to specify the transformation matrices and write the kinematic equations-of-motion. We illustrate the actuated inverse and sensed forward solutions; i.e., the calculation of actuator velocities from robot velocities and robot velocities from sensed wheel velocities. We apply the actuated inverse and sensed forward solutions to the kinematic control of Uranus by: calculating in real-time the robot position from shaft encoder readings (i.e., dead reckoning); formulating an algorithm to detect wheel slippage; and developing an algorithm for feedback control.

Sensor-based robot control may be viewed as a hierarchical structure with multiple observers. Actuator, feature-based, and recognition observers provide the basis for multilevel feedback control at the actuator, sensor, and world coordinate frame levels, respectively. The analysis and design of feature-based control strategies to achieve consistent dynamic performance is addressed. For vision sensors, such an image-based visual servo control is shown to provide stable and consistent dynamic control within local regimes of the recognition observer. Simulation studies of two- and three-degree-of-freedom systems show the application of an adaptive control algorithm to overcome unknown and nonlinear relations in the feature to world space mapping.

In 1983, the computer program Algebraic Robot Modeler (ARM) was implemented to generate symbolically complete closed-form and recursive dynamic robot models. Then, in 1985, heuristic rules for the systematic organization of dynamic robot models were incorporated in ARM to reduce the computational requirements of forward and inverse dynamics calculations. For the robotics and control engineering communities, the dynamic coefficients and the complete closed-form ARM-generated symbolic dynamic model of the six degree-of-freedom (DOF) Puma robot (which has not heretofore appeared in the literature) are displayed. The performance of ARM is compared with recently introduced computational robot dynamics software. In spite of the analytic and numeric complexities of the complete closed-form dynamic model of the Puma robot, our findings indicate that 1) ARM-generated customized closedform algorithms can compute the inverse dynamics (i.e., the joint torques from the joint positions, velocities, and accelerations) twice as fast as the general-purpose recursive Newton-Euler algorithm, and 2) the ARM-generated customized recursive inverse dynamics algorithm can be evaluated twice as fast as the customized closed-form inverse dynamics algorithm.

The positioning accuracy of commercially-available industrial robotic manipulators depends upon a kinematic model which describes the robot geometry in a parametric form. Manufacturing errors in machining and assembly of manipulators lead to discrepancies between the design parameters and the physical structure. Improving the kinematic performance thus requires identification of the actual kinematic parameters of each individual robot. This identification of the individual kinematic parameters is called the arm signature which is then incorporated into the manipulator's controller to improve positional accuracy. In this paper, an approach, based on a new parametric model of the kinematics, is introduced for arm signature identification. The S-Model utilizes 6.n parameters to describe the robot geometry and offers advantages for identification by decomposing the parameters into individually identified subsets. The S-Model parameters are then mapped into the equivalent Denavit-Hartenberg parameters for implementation into the controller. The S-Model arm signature identification algorithm can be implemented with relatively simple sensors and improves accuracy through statistical averaging. This algorithm has been implemented with an external ultrasonic range sensor to measure robot end-effector positions. Experimental results of arm signature identification of seven Unimation/Westinghouse Puma 560 robots demonstrated an average reduction in positioning error by a factor of 5-10 for a spectrum of representative test tasks.

Sensory systems, such as computer vision, can be used to measure relative robot end-effector positions to derive feedback signals for control of end-effector positioning. The role of vision as the feedback transducer affects closed-loop dynamics, and a visual feedback control strategy is required. Vision-based robot control research has focused on vision processing issues, while control system design has been limited to ad-hoc strategies. We formalize an analytical approach to dynamic robot visual servo control systems by first casting position-based and image-based strategies into classical feedback control structures. The image-based structure represents a new approach to visual servo control, which uses image features (e.g., image areas, and centroids) as feedback control signals, thus eliminating a complex interpretation step (i.e., interpretation of image features to derive world-space coordinates). Image-based control presents formidable engineering problems for controller design, including coupled and nonlinear dynamics, kinematics, and feedback gains, unknown parameters, and measurement noise and delays. A model reference adaptive controller (MRAC) is designed to satisfy these requirements.

An inherently discrete-time dynamic model is introduced for robotic manipulators. Although robot dynamics are highly coupled and nonlinear, the model is compact and suitable for control engineering applications. The model is designed to guarantee conservation of energy (and momentum, if appropriate) at each sampling instant. Initial numerical experiments with cylindrical robots confirm the feasibility and applicability of the discrete dynamic robot model.

The authors highlight inverse dynamics applications of their recently introduced discrete-time dynamic robot model. The model is designed to guarantee conservation of energy (and momentum, if appropriate) over each sampling period, is accelerometer-free, and can reduce the computational time requirements of the real-time controller. Simulation experiments with three-degree-of-freedom cylindrical and articulated robots confirm the efficacy of the approach for inverse dynamics and trajectory planning applications.

The computer program ARM (Algebraic Robot Modeler) has been implemented to generate symbolically the forward solution and complete Lagrangian dynamic robot model for control engineering applications. Development and application of this versatile dynamic modeling and control engineering tool are highlighted in this paper. The Q matrix formulation is employed to develop nested iterative algorithms for the symbolic computation of the inertial, centrifugal and Coriolis, and gravitational components of the Lagrangian dynamic robot model. The computational requirements are enumerated as functions of the number of degrees-of-freedom of the manipulator. Automatic generation of the centrifugal and Coriolis force vector dominates the computational load for both state-of-the-art and futuristic robots. The forward solution and complete dynamic model for the three degree-of-freedom positioning system of the Puma robot are exhibited to illustrate the capabilities of Arm. On-going enhancements to ARM are then summarized.

The authors have implemented the computer program Algebraic Robot Modeler (ARM) to generate symbolically the forward solution and complete dynamic robot model for control engineering applications. ARM incorporates theQ-matrix formulation of the Lagrangian (Lagrange-Euler) dynamic robot model. The symbolic formulation of dynamic robot models is extended in two directions:Q-matrices and the Bejczy theorem are applied to linearize symbolically the Lagrangian dynamic robot model about a nominal trajectory; and a methodology is developed to generate symbolically the trajectory sensitivity models of a manipulator with respect to the kinematic and dynamic link parameters. The classical sensitivity point method is thereby extended to include dynamic robot models. Control engineering applications of the linearized and sensitivity models are described. The properties and structural characteristics of these models are identified, and the computational requirements for their implementation in ARM are estimated. The results are illustrated through the double pendulum.

Transfer function models that can provide physical insight into the dynamic behavior of manipulators and establish a foundation for control system analysis and design are identified. Emphasis is directed toward increasing the computational efficiency of the manipulator dynamic equations of motion. A conceptual three-degrees-of-freedom manipulator, which represents state-of-the-art configurations, is designed and simulated on a digital computer. The Lagrangian formulation is applied to develop the complete dynamic equations of motion of the manipulator. The simulation model includes the dynamic interactions of the centrifugal, Coriolis, inertial, and gravitational generalized forces along with the kinematic coupling, and it can accommodate load variations. The simulation model is interfaced to the Steiglitz-McBride identification algorithm to extract, from the complete nonlinear model, simplified linear models that characterize the arm in various regions of the work space. The simplified linear models are second-order discrete-time (input-output) transfer functions.

An engineering approach to the solution of multicomponeint inspection and repair problems is introduced. This approach utilizes the practical fact that in realistic situations failure and wear processes in individual components are mutually independent. A stochastic model comprising a number of independent Markov chains is developed and operating and maintenance costs are expressed in terms of the failure and maintenance actions for the individual components. While this approach has the advantage that the problem size grows linearly rather than exponentially with the number of system components, it does increase the complexity of the objective function. For systems with a series structure, the objective function is concave, and concave programming techniques are employed to generate maintenance schedules. The computational experience gained from a number of practical examples, which is summarized in this paper, confirms the expectation that the feasibility of the solution is dependent primarily on the structure of the cost function rather than on the problem size (number of variables). These numerical examples illustrate the feasibility of the proposed approach.