Nazareth Bedrossian

Guided Expansive Spaces Trees: a search strategy for motion- and cost-constrained state spaces

Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space with motion constraints. Path Gradient Descent, which builds on the idea of Elastic Strips, finds the locally optimal path for an existing path. These techniques are tested on simulations of rendezvous and docking of the space shuttle to the International Space Station and of a 4-foot fan-controlled blimp in a factory setting.

Classification of singular configurations for redundant manipulators

A general methodology is presented for the singularity analysis of kinematically redundant manipulators. The singular configurations are classified based on the possibility of reconfiguration into a nonsingular posture using self-motion. A procedure is presented to test for the possibility of self-motion at a singular configuration. Necessary and sufficient conditions for admissible tangent vectors at the singular configuration are presented, as well as a method to construct such vectors. Sufficient conditions are derived for instances when the singular system can be reconfigured into a nonsingular state by displacements along the admissible null vectors.<<ETX>>

Zero-propellant maneuver guidance

This article deals with a zero-propellant maneuver guidance (ZPM) architecture to provide large-angle ISS (International Space Station) rotations. ZPM guidance commands are designed to avoid CMG (control moment gyroscope) momentum saturation. CMG desaturation is required to maintain spacecraft control capability and the manipulators direction. The ZPM momentum-optimal trajectories were developed using computational dynamic optimization, these optimal trajectories are used to shape the command to a standard feedback controller. Using ZPM, the need for thrusters as backup to momentum-storage actuators for rotational control is minimized.

First Flight Results on Time-Optimal Spacecraft Slews

This paper describes the design and flight implementation of time-optimal attitude maneuvers performed onboard NASA’s Transition Region and Coronal Explorer spacecraft. Minimum-time reorientation maneuvers have obvious applications for improving the agility of spacecraft systems, yet this type of capability has never before been demonstrated in flight due to the lack of reliable algorithms for generating practical optimal control solutions suitable for flight implementation. Constrained time-optimal maneuvering of a rigid body is studied first, in order to demonstrate the potential for enhancing the performance of the Transition Region and Coronal Explorer spacecraft. Issues related to the experimental flight implementation of time-optimal maneuvers onboard Transition Region and Coronal Explorer are discussed. A description of an optimal control problem that includes practical constraints such as the nonlinear reaction wheel torque-momentum envelope and rate gyro saturation limits is given. The problem is solved using the pseudospectral optimal control theory implemented in the MATLAB® software DIDO. Flight results, presented for a typical large-angle time-optimal reorientation maneuver, show that the maneuvers can be implemented without any modification of the existing spacecraft attitude control system. A clear improvement in spacecraft maneuver performance as compared with conventional eigenaxis maneuvering is demonstrated.

Characterizing spatial redundant manipulator singularities

A general methodology for the classification of kinematically redundant spatial manipulator singular configurations is presented. The singular configurations are classified based on the possibility of reconfiguration into a nonsingular posture using self-motion. For one degree-of-freedom redundancy manipulators, an alignment condition is introduced, and methods from dynamical systems analysis and the center manifold theorem are used to characterize singularities.<<ETX>>

Feedback linearization of robot manipulators and riemannian curvature

In this paper we discuss the problem of feedback linearization of rigid robot manipulators. We have shown previously that a necessary and sufficient condition for exact linearization of such systems under a nonlinear coordinate transformation in the state and input space is that the Riemannian curvature tensor associated with the robot inertia matrix vanish identically [17]. Moreover the coordinate transformation is given as the solution of an easily characterized system of partial differential equations. We first review the result from [17] and then discuss the idea of approximate feedback linearization, i.e. feedback linearization of a simplified model. Approximate feedback linearization is useful in this context since the class of robots that satisfy the conditions for exact linearizability is limited. We will show a connection between approximate feedback linearization based on Riemannian curvature and both the imaginary robot concept of Gu and Loh [12] and thepassive computed torque of Anderson [3].

Approximate feedback linearization: the cart-pole example

An existing nonlinear design methodology developed by Krener (1984, 1987), approximate feedback linearization, is applied to the control of underactuated single-input-single-output nonlinear systems. A computational approach to test for the order of linearization as well as a method to compute the approximate output function is derived. A method to simplify the dynamics using partial precompensation which uses the constraint equations of motion is presented. This approach is applied to a simple example. Simulation results showed a substantial improvement in the operating range of the linear controller by using this approach.<<ETX>>

Overclock My Satellite

The Draper group teamed up with engineers at the Naval Postgraduate School, in Monterey, Calif. And in 2010, we carried out our promise to make the NASA observation satellite scan the sky faster than even its mission controllers thought possible. By operating spacecraft beyond their purported limits, we can extend their life and usefulness without installing new hardware and driving up costs. So how do we achieve this clever hack? Ultimately, we overclock a satellite by uploading a set of precise steering instructions from the ground to its onboard flight computer, essentially overriding its automated route. But thats the easy part. The real challenge is figuring out what those instructions should be, which requires solving mathematical puzzles known as optimal control problems.

Linearizing coordinate transformations and Riemann curvature

Using the Lagrangian framework and point transformations, an alternative derivation of an existing result on the special decomposition of the inertia matrix is presented. The Riemann curvature tensor is introduced as a computational tool to test for this special decomposition. An example with configuration-dependent inertia which admits such a factorization is presented. For the cart-pole problem, it is shown that such a decomposition is possible and the linearizing transformation is computed. It is shown that a planar two-link manipulator cannot be linearized by point transformations only.<<ETX>>

Design of robust Nash game theoretic controllers with time domain constraints

The Nash differential game theory does not directly handle the specifications on either closed-loop time-domain constraints or model uncertainties. An inverse solution procedure, which converts the Nash game theoretic controller design task to a constrained optimization problem, can take account of these control design requirements directly. In this paper, the authors propose a constrained robust Nash game controller design procedure for uncertainty systems with time-domain constraints.