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Harvard University - HRL
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  • Offer Profile
  • The Harvard Robotics Laboratory was founded in 1983 by Prof. Roger Brockett. Our current research projects include the following.
    • Analog Computation
    • Choreography of Dynamical Systems
    • Control of Quantum Systems
    • Pattern Generation
    • Robotic Manipulation
    • System Identification
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  •  Research Overview

    • Analog Computation

    • Many powerful biological and man-made systems contain inherently analog processing elements. Until recently there has been very little theoretical work on models of this type and many basic questions remain unresolved. We are interested in describing input-output systems governed by ordinary differential equations whose behavior robustly executes arithmetic or logical operations. We have had success in designing continuous-time dynamical systems which perform discrete operations, such as sorting numbers and data clustering, and are interested in exploring the use of flows for performing a wide range of computation
    • Choreography of Dynamical Systems

    • Motivation
      We have developed an experimental test bed consisting of a double circular pendulum with a radio link to transmit position data from the two of the three shaft encoders. This eliminates wires and the friction effects that go along with them. We refer to this work as "choreography" but acrobatics would have been just as appropriate. The idea is to be able to give a linguistic input to the machine and have it execute the kind of swing up, rotate, balance, etc. sequences that one might expect from an Olympian on the parallel bars. Along the way we have learned something about problems involved in enlarging the domain of stability of nonlinear systems.

      Apparatus
      The pendulum consists of a horizontal arm and a vertical arm which are always orthogonal to one another. There is a servo motor driving the horizontal arm. The joint between the horizontal and vertical arm is a free joint. A rotary electric encoder is mounted on each of the joints. The encoder measures the absolute angular position (instead of incremental) and outputs analog signals. Then each analog signal is converted into 12bits binary number then sent to the host computer through a RS232 radio link, as shown in figure below. The radio link can send 50 readings of both the encoders per second which limits the sample frequency of the whole system to 50Hz. Each encoder has accuracy of .04 deg. The base of the pendulum is leveled with an error of .06 deg.

    • Control of Quantum Systems

    • The control of quantum systems has many applications, ranging from coherent spectroscopy to quantum information processing. In most applications, the system of interest is not isolated but interacts with its environment. This leads to the phenomenon of relaxation, which in practice results in signal loss and ultimately limits the range of applications. The goal of our research is the manipulation of quantum systems in a manner that minimizes relaxation losses. Specifically, for each system we want to calculate the theoretical upper limit for the coherence transfer efficiency in the presence of relaxation and to develop optimal controls (pulse sequences) that achieve this limit experimentally.

      From a control theory point of view, the above problems give as the physical motivation to study a new class of control systems that are linear in state and are characterized by the fact that the original controls can be expressed as polynomial functions of some new control parameters. Up to now, our research has been focused in the control of coupled spin dynamics in nuclear magnetic resonance (NMR) spectroscopy in liquids. We have developed relaxation optimized pulse elements that in many cases of practical interest give much better efficiency than the conventionally used pulse sequences, for example INEPT. The methods developed are by no means restricted to NMR applications but are broadly applicable to coherent control of quantum-mechanical phenomena in presence of dissipation.
    • Pattern Generation

    • Many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control. Examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy. Likewise, cyclic processes are widely found in nature and the idea of a pattern generation is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration. Here we develop a linkage between the use of cyclic processes and the control of nonholonomic systems, emphasizing the stable regulation of such processes. One goal is to bring out the characteristic phenomena that distinguish the regulation of such strongly nonlinear systems from more commonly studied types of feedback regulators.
    • Robotic Manipulation

    • Apparatus
      The HRL Manipulator consists of two two-link "fingers," each with three degrees of freedom. Each of the finger's links rotates in the plane parallel to the worksurface and the entire finger can be moved perpendicular to the worksurface. The actuation is provided by six servomotors that communicate with a computer via the RS-232 serial protocol. In addition, there is a camera mounted above the worksurface used to track the movements of the manipulator and the objects which are being manipulated.

      Each finger has a tactile sensor attached to its end which consist of a compliant fingertip made from a latex membrane filled with silicone. When the fingertip deforms, a set of dots drawn on the inside of the membrane moves. The new location of the dots is captured by a small camera mounted inside the fingertip. The image taken by the camera is processed to determine the location of the dots on the image plane. We use these 2-dimensional coordinates along with a physical model of the fingertip to determine the dots' locations in 3-dimensional space. This provides information about the shape of the fingertips which can be used as feedback in our manipulation algorithms.

      Block Stacking
      One task which is currently being investigated on this system is block stacking. We would like to be able to place two blocks of unknown height anywhere in the manipulator's workspace and have it stack one on top of another. This requires the manipulator to identify the locations of both blocks, send the fingers to one of the blocks, grasp the block securely, lift it over the other block and place it on top of that block --- all without causing any collisions or dropping any blocks. This task makes use of the overhead camera to locate the blocks and the tactile sensors to ensure a secure grasp and detect block placement. It also requires accurate path planning and execution to avoid any collisions.

      Motion Description
      A fundamental question that is addressed in this research is how best to describe motions. The task of programming a robot can often be time-consuming and specific to the hardware that is being used. In this case, motions are described in terms of specific commands that control the robot's hardware and are not portable to other robots. It would be convenient to have a machine-independent language for describing motions that a robot performs.

      Programming convenience is not our only goal, however. We desire to establish a mathematical framework for describing motion in general. Our strategy involves combining motion segments or "atoms" composed of open-loop and closed-loop control laws into motion programs which are executed by the robot. Such a framework would be useful in the formulation of problems involving the amount of information necessary to describe a motion. These problems include the minimization of data required to control a robot (e.g. in space robotics) and the design of robots for tasks whose motions are required to be described with a minimum of instructions.
    • System Identification

    • Consider a simple linear stochastic system of the form dx = Ax dt + B dw with the state and observation noise terms dw and du being independent Wiener processes. We consider the (A,B,C) triple as unknown, and the goal of this research program is to identify (A,B,C) given the observations dy(t). This may be framed as a nonlinear filtering problem, and generally such filtering problems require an infinite number of sufficient statistics. However, the assumption that the unknown variables come from a finite set leads to a finite set of sufficient statistics.
    • Systems with Limited Communication

    • Information theoretical issues are traditionally decoupled from consideration of decision and control problems. The decoupling is achieved by ignoring the capacity constraints on communication channels connecting different components of a system. Decoupling information theoretical issues from the decision and control problems in a system greatly simplifies the analysis and generally works well for classical applications. Advances in communication, computation and networks greatly expanded the range and complexity of a control system. Many newly emerged control systems are distributed, asynchronous and networked. These systems pose challenges to the traditional assumption which ignores the communication constraints on channels among different components of a system. Integrating communication constraints into estimation and control of a system becomes an inevitable task on our way to achieve deeper understanding of distributed, asynchronous and networked control systems.