Yogendra P. Kakad

Robust control of an adaptive optical system

Abstract Most adaptive optical systems are based on a least-squares fit algorithm to optimize performance, and generally do not adequately address stability or uncertainty in the system. This paper describes the implementation of an H-infinity controller for an adaptive optical system, in order to optimize the closed-loop stability of the system.

Transform domain technique for windowing the DCT and DST

In this paper, an algorithm is developed to apply Hann, Hamming, Blackman and related windows directly in the transform domain for the discrete cosine transform and discrete sine transform. These algorithms are useful in applications where windowing is required in order to minimize edge effects caused by implicit symmetries in the transform domain that are not replicated in the real-world data. Examples of such applications include data communication, adaptive system identification and filtering, real-time analysis of financial market data, etc. Software implementations in C language are also given.

Independently updating the DCT and DST for shifting windowed data

Abstract When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. In this paper we develop algorithms to “update” the DCT and DST to reflect the modified window contents using less computation than by directly evaluating the modified transform via standard Fast Transform algorithms. Our algorithms constitute an improvement over previous DCT/ DST update algorithms because our approach establishes independence between the DCT and the DST: the algorithm for DCT makes use only of DCT terms, and similarly for DST. Algorithms are derived for use without windowing and with split-triangular, Hanning, Hamming and Blackman windows.

Input and output transformations for a space robot modeled with quaternions

This paper describes a procedure for obtaining the dynamical model of a space robot in a form that is useful for simulation. The differential equations of motion of the space robot are derived using a constrained Lagrangian approach to mechanics. Quaternions are utilized to model rotation which gives rise to generalized forces that are in the direction of the quaternion elements. A transformation is presented which transforms realizable torques into these abstract forces. The form of a complete model with both realizable inputs and measurable outputs is described.

The Control Moment Gyroscope Inverted Pendulum

This paper presents the dynamics and control of a control moment gyroscope actuated inverted pendulum. The control technique utilizes partial feedback linearization, an appropriate global change of coordinates which transform the dynamics of the system into a lower nonlinear subsystem and a chain of double integrators. A control Lyapunov function is designed in order to stabilize the overall system using a backstepping procedure.

A Method of Gravity Offloading with a SCARA Manipulator

This paper presents a mechanism and control law which is currently under development that is intended to provide gravitational compensation so that lunar bound systems can be terrestrially tested in a simulated lunar gravitational field. The mechanism is a selective compliant articulated robotic arm (SCARA) manipulator. The object to be tested is rigidly attached to the end of the manipulator. The control scheme makes use of a copy of the test-objects dynamical model. This is integrated in real-time and includes the response due to any externally applied forces and torques. The result of this integration is a trajectory in the task-space. The inverse kinematic model of the manipulator is utilized to generate a trajectory in the joint-space and an exponentially stable tracking controller is implemented to drive the manipulator joints along this trajectory.

Contact force measurement noise in the partial feedback linearization control of humanoid robots

This paper examines the technique of partial feedback linearization for the positional control of the joints of a humanoid robot. The unique dynamical model of the humanoid robot is first presented. The dynamics have an Euler-Lagrange form but also contain mixed-continuous/ discrete forces that arise due to contact constraints. The mixed-continuous/discrete contact forces are modeled by using linear restoring and damping elements on the bottom of the feet of the humanoid upon contact with the ground. Also, the robot has six degrees-of-freedom that are not directly actuated. The collocated partial feedback linearization scheme is utilized to provide joint-level position control. Implementation of this control law relies upon contact force measurements. It is suggested that partial feedback linearization is a viable option for joint level control even in the presence of significant noise arising from the contact force measurements.

Simulating the Effects of a Non-Uniform Gravitational Field on a Space Robot

This paper investigates the influence that a nonuniform gravitational field has on the dynamics of a space robot. This is accomplished by obtaining the differential equations of motion of the space robot using three gravitational field potential approximations: a uniform field approximation, a zeroth-order Taylor series expansion of the field about the center of mass of each body, and a second-order binomial series expansion of the gravitational field. The three models are then simulated in a free-fall from identical initial conditions. The results indicate that a zeroth-order series expansion of the gravitational field about the center of mass of each body provides a sufficiently high degree of accuracy without resulting in a significant computational burden.

A target tracking algorithm that reduces designation time for laser guided weapons

We propose a new approach for laser guided weapon guidance that minimizes the total active laser target designation time. The weapon makes use of inertial or GPS guidance within a Kalman filtering framework, and maintains covariance information indicating the uncertainty of its knowledge of the weapon-to-target vector. At any time, the missile needs to be sure that it can navigate to any point within the area around the target that is described by this covariance. Therefore, at each moment during the flight, there exists a covariance threshold above which the weapon cannot guarantee its ability to navigate to the target. This threshold will decrease with time as the weapon-to-target distance decreases. In our proposed approach, when the threshold is exceeded, the weapon requests a brief laser designation of the target. The laser designation provides an accurate measurement of the bearing of the target with respect to the missile, and this is used to improve the estimate of the weapon-to-target vector. In turn, this can be fed back into the Kalman filter to improve the internal state estimate. By minimizing laser designation time, this approach reduces the chance of compromise of the designation agent, and of the fact that targeting is taking place. It also achieves the benefit of improving the accuracy of the underlying inertial or other navigational system, or alternatively the estimate of absolute target position.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Rapid update of discrete Fourier transform for real-time signal processing

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log 2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log 2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.