Andrew A. Goldenberg

Robust control of a general servomechanism problem: The servo compensator

The robust control of a general servomechanism problem, which is an extension to the results of [1], is considered in this paper. Necessary and sufficient conditions, together with a characterization of all robust controllers which enables asymptotic tracking to occur, independent of disturbances in the plant and perturbations in the plant parameters and gains of the system, are obtained. A new type of compensator, introduced in [1], called a servo-compensator which is quite distinct from an observer is shown to play an essential role in the robust servomechanism problem. It is shown that this compensator, which corresponds to an integral controller in classical control theory, must be used in any servomechanism problem to assure that the controlled system is stabilizable and achieves robust control; in particular, it is shown that a robust controller of a general servomechanism problem must consist of two devices (i) a servo-compensator and (ii) a stabilizing compensator. A study of the stabilizing compensator is made; in particular, it is shown that a new type of stabilizing compensator called a complementary controller, may be used together with the servo-compensator to form a robust controller for the servo-mechanism problem. A study of the case when perturbations in the robust controller are also allowed is then made; this leads to the Strong robust servo limitation theorem which imposes a fundamental limitation on the ability of practical servomechanisms to regulate a system.

A complete generalized solution to the inverse kinematics of robots

The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. A solution to the inverse kinematics is a vector of joint configuration coordinates that corresponds to a set of task space coordinates. For a class of robots closed form solutions always exist, but constraints on joint displacements cannot be systematically incorporated in the process of obtaining a solution. An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots. The solution can be obtained subject to specified constraints and based on certain performance criteria. The solution is based on a new rapidly convergent constrained nonlinear optimization algorithm which uses a modified Newton-Raphson technique for solving a system nonlinear equations. The algorithm is illustrated using as an example a kinematically redundant robot.

Neural-network control of mobile manipulators

In this paper, a neural network (NN)-based methodology is developed for the motion control of mobile manipulators subject to kinematic constraints. The dynamics of the mobile manipulator is assumed to be completely unknown, and is identified online by the NN estimators. No preliminary learning stage of NN weights is required. The controller is capable of disturbance-rejection in the presence of unmodeled bounded disturbances. The tracking stability of the closed-loop system, the convergence of the NN weight-updating process and boundedness of NN weight estimation errors are all guaranteed. Experimental tests on a 4-DOF manipulator arm illustrate that the proposed controller significantly improves the performance in comparison with conventional robust control.

Computer- and Robot-assisted Resection of Thalamic Astrocytomas in Children

Six children ranging in age from 2 to 10 years who harbored deep benign astrocytomas were operated upon using a computer- and robot-assisted system. A radical excision was achieved in all cases with no significant morbidity nor any mortality. The system consists of an interactive, three-dimensional display of computed tomographic image contours and digitized cerebral angiograms taken using the Brown-Roberts-Wells stereotactic frame. The surgical retractor is held and manipulated using a PUMA 200 robot. The position and orientation of the surgical retractor is displayed on the three-dimensional display. Preoperative planning and simulation are important features of this system. Movement of the brain after removal of the tumor and cerebrospinal fluid is substantial, so the tumor removal is based on visually defined margins. Enhanced computer graphics and robotic devices are important adjuncts to neurosurgical procedures and will find increasing use in the future.

Design of a new high-performance electrohydraulic actuator

This paper describes the design and prototyping of a new high-performance actuation system that combines the benefits of conventional hydraulic systems and direct-drive electrical actuators, namely high torque/mass ratio and modularity. It is referred to as the electrohydraulic actuator (EHA) and results from the fusion of the above-mentioned technologies. The EHA is a unique device with its own characteristics and requires hydraulic components that are specifically tailored to its needs and requirements. Based on a mathematical model of the EHA, the requirements for its components are determined. These requirements are used as a basis for component selection, component modification, and design of a customized new symmetrical linear actuator. The analysis of the EHA presented is supported by experimental data and explains the extremely high level of performance attained by a prototype of the EHA.

An experimental study of nonlinear stiffness, hysteresis, and friction effects in robot joints with harmonic drives and torque sensors

Despite widespread industrial applicatzon of harmonic drives, the source of some elastokinetic phenomena and their impact on overall system behavior has not been fully addressed thus far. Some of these phenomena severely influence the behavior of robot arms, both in free and constrained motions, when the end effector is in contact with an environment. The primary goal of this study is to derive an effective, control-oriented model of a harmonic-drive-based robot joint. Systematic observations of an experimental robot with harmonic drives has revealed that the harmonic drive could not entirely transmit the input torque to the output shaft, due to a nonlinear meshing process between the flexible and circular spline teeth. The torque transmitted to the output shaft might saturate at a much lower value than expected (e.g., motor torque multiplied by the gear ratio). This phenomenon may severely influence the system behavior, par ticularly in force/impedance control tasks when full joint-torque capacity and wide bandwidth are needed. To understand the harmonic-drive behavior, as well as to derive a convenient form of its model, we have shown restrained motion experi ments to be much more useful than free-motion experiments. In this article, we also introduce mathematical models and describe experiments related to other physical phenomena, such as nonlinear stiffness, hysteresis, and soft windup. The goal of our modeling strategy was not to develop a precise and possi bly complicated model, but to generate an appropriate model that could be easily used by control engineers to improve joint behavior To visualize the developed model, equivalent mechan ical and electrical schemes of the joint are introduced. Finally, a simple and reliable estimation procedure has been established for obtaining joint parameters, to ascertain the integrity of the proposed model.

MEMS optical switches

Leveraging MEMSs inherent advantages such as the batch fabrication technique, small size, integrability, and scalability, MEMS is positioned to become the dominant technology in optical crossconnect switches. MEMS optical switches with complex movable 3D mechanical structures, micro-actuators, and micro-optics can be monolithically integrated on the same substrate by using the matured fabrication process of the integrated circuit industry. In this article we report various popular actuating mechanisms and switch architectures of MEMS optical switches. The basics of surface and bulk micromachining techniques used to fabricate MEMS devices are reviewed. Examples of 2D and 3D approaches to MEMS optical switches are described. The pros and cons of the two approaches are analyzed. In the short term, MEMS-based optical switches seem to have captivated the attention of both the industry and academia. However, there are challenges that threaten the long-term survival of this technology. The problems that remain to be fully addressed are discussed.

An adaptive approach to motion and force control of multiple coordinated robot arms

An approach to motion and force control of multiple coordinated robot arms based on an adaptive scheme is developed. The adaptation law uses Popov hyperstability theory to estimate online the uncertain parameters of multiple robot arms and payload. The approach can be used to control the motion of an object held by the arms, the contact forces between the object and the environment, and the internal forces that do not contribute to the motion and the contact forces. Three subsystem error equations are generated, i.e. a position error subsystem, a contact force error subsystem, and an internal force error subsystem. The unknown parameters of the multiple coordinated robot arms and the object are estimated in terms of the three error subsystem equations. It is shown that the proposed adaptive control scheme improves the position and internal and contact force tracking accuracy of a class of systems with an uncertain knowledge of the dynamic model.<<ETX>>

Soft robotic fingertips. Part I: a comparison of construction materials

Three potential problems exist in multifingered robotic hands. First, the impact forces that result during each instant of grasping a rigid object can affect the functioning of the fingertip sensors. Second, a hand with hard fingers cannot securely grasp objects that have uneven surfaces due to the poor conformability of the fingers. Third, repetitive strains are induced into the fingers throughout a manipulation task. If they are not dissipated, the manipulation becomes jerky, the func tioning of the fingertip sensors is affected, and the life of the fingers skeletal structure may become short. In this work, six fingertips constructed from plastic, rub ber, sponge, fine powder, paste, and gel are experimentally compared for their ability to overcome the above problems. Results show that the sponge fingertip is the most suitable and the plastic fingertip the least suitable for our application. For practical reasons, however, gel is preferred over sponge. In view of these results, it is recommended that future robotic hands employ soft fingers, or at least fingers with soft tips, constructed out of carefully chosen materials.

Robust hybrid impedance control of robot manipulators

The objective of hybrid impedance control is defined, and a robust hybrid impedance control method is proposed. The task space is split into force-controlled and position-controlled subspaces based on the concept of hybrid control. Desired inertia and damping are introduced in the force control subspace to improve the dynamic behavior, and impedance control is used in the position-controlled subspace. In the proposed control scheme, the hybrid impedance control is equivalent to tracking a desired acceleration trajectory, which is generated in real-time. The computed torque technique and a PI control law are used to reduce the influence of model uncertainties. Experimental results obtained with a two-degree-of-freedom direct drive robot have shown the effectiveness of the proposed hybrid impedance control method.<<ETX>>