R. Scott Erwin

Sliding mode control of underactuated multibody systems and its application to shape change control

In this article, we introduce an approach based on sliding mode control to design full state feedback controllers for stabilisation of underactuated non-linear multibody systems. We define first order sliding surfaces as a linear combination of actuated and unactuated coordinate tracking errors. Lyapunov stability analysis guarantees that all system trajectories reach and remain on the sliding surfaces. However, stability of the sliding surfaces depends on the equilibrium manifold. If the system has isolated equilibrium points, it is linearly controllable and asymptotic stability can be guaranteed under certain conditions. Otherwise, the control system fails Brocketts necessary condition for existence of a smooth stabilising feedback. In the latter case, if the total momentum is conserved, the closed-loop control system will be marginally stable. Consequently, a procedure is proposed to achieve an asymptotically stable discontinuous control law through sliding surface redefinition and shape changes. It is proposed that repetitive application of shape changes will lead to asymptotic convergence of the system to the desired configuration. Simulation results are presented for an inverted pendulum as an example of a system with isolated equilibrium points and an existing communication satellite as an example of shape change control. In both cases, the control is shown to be effective and robust with respect to uncertainties and disturbances.

Model Predictive Control of three dimensional spacecraft relative motion

This paper further develops an approach for spacecraft relative motion control based on the application of linear quadratic Model Predictive Control (MPC) with dynamically reconfigurable constraints. Previous results for maneuvers confined to the orbital plane are extended to three dimensional maneuvers with three dimensional Line-of-Sight (LoS) constraint handling. The MPC controller is designed to prescribe Δv impulsive velocity changes rather than piecewise constant thrust profiles. The ability to transition between MPC guidance in the spacecraft rendezvous phase and MPC guidance in the spacecraft docking phase, with requirements, constraints, and sampling rates specific to each phase, is demonstrated. Bandwidth constraints of the spacecraft attitude control system and exhaust plume direction constraints are also addressed. The MPC controller is validated on the full nonlinear model of spacecraft orbital motion and augmented with an Extended Kalman Filter (EKF) to estimate spacecraft states based on relative angles and relative range measurements.

Decentralized Real Structured Singular Value Synthesis

Abstract This paper describes and illustrates a practical methodology for robust, fixed-structure controller synthesis using a decentralized static output feedback problem formulation. To account for real-parameter structured uncertainty, scaled Popov bounds for the real structured singular value are employed. A worst-case H 2 cost bound with respect to the controller parameters is formed, and quasi-Newton optimization algorithms are used to solve the numerical optimization problem. Numerical results are provided for a MIMO 16th-order acoustic duct model with uncertain dynamics for both centralized and decentralized controller structures.

Advanced smart structures flight experiments for precision spacecraft

Abstract This paper presents an overview as well as data from four smart structures flight experiments directed by the U.S. Air Force Research Laboratorys Space Vehicles Directorate in Albuquerque, New Mexico. The Middeck Active Control Experiment

Dynamic sensor tasking for Space Situational Awareness

Flight II (MACE II) is a space shuttle flight experiment designed to investigate modeling and control issues for achieving high precision pointing and vibration control of future spacecraft. The Advanced Controls Technology Experiment (ACTEX-I) is an experiment that has demonstrated active vibration suppression using smart composite structures with embedded piezoelectric sensors and actuators. The Satellite Ultraquiet Isolation Technology Experiment (SUITE) is an isolation platform that uses active piezoelectric actuators as well as damped mechanical flexures to achieve hybrid passive/active isolation. The Vibration Isolation, Suppression, and Steering Experiment (VISS) is another isolation platform that uses viscous dampers in conjunction with electromagnetic voice coil actuators to achieve isolation as well as a steering capability for an infra-red telescope.

Safe Positively Invariant Sets for Spacecraft Obstacle Avoidance

This paper examines the problem of tracking multiple spacecraft using a combination of ground- and space-based sensors. The problem is formulated in a simplified two-dimensional setting to reduce computational complexity while retaining elements of the problem that pose theoretical or practical difficulties (such as inverse square-law dynamics). As a baseline approach for comparison purposes, a centralized Extended Kalman Filter (EKF) estimator is used to provide position/velocity estimates of all tracked objects. These estimates and their associated covariances are used to execute a closed-loop sensor tasking approach to determine which sensors will track which objects. A tasking approach from the literature is utilized as a baseline methodology and compared to an ad-hoc modification which may offer improved performance in certain situations. The paper concludes with a numerical example demonstrating the approaches as well as a summary of avenues for future research.

Identification of Wiener Systems With Known Noninvertible Nonlinearities

This paper presents an obstacle avoidance method for spacecraft relative motion control. In this approach, a connectivity graph is constructed for a set of relative frame points, which form a virtual net centered around a nominal orbital position. The connectivity between points in the virtual net is determined based on the use of safe positively invariant sets for guaranteed collision free maneuvering. A graph search algorithm is then applied to find a maneuver that avoids specified obstacles and adheres to specified thrust limits. As compared to conventional open-loop trajectory optimization, this approach enables the handling of bounded disturbances, which can represent the effects of perturbing forces and model uncertainty, while rigorously guaranteeing that nonconvex and possibly time-varying obstacle avoidance constraints are satisfied. Details for handling a single stationary obstacle, multiple stationary obstacles, moving obstacles, and bounded disturbances are reported and illustrated with simula...

Information space receding horizon control

In this paper we develop a method for identifying SISO Wiener-type nonlinear systems, that is, systems consisting of a linear dynamic system followed by a static nonlinearity. Unlike previous techniques developed for Wiener system identification, our approach allows the identification of systems with nonlinearities that are known but not necessarily invertible, continuous, differentiable, or analytic.

On the tractability of satellite range scheduling

In this paper, we present a receding horizon solution to the problem of optimal sensor scheduling problem. The optimal sensor scheduling problem can be posed as a Partially Observed Markov Decision Process (POMDP) whose solution is given by an Information Space (I-space) Dynamic Programming (DP) problem. We present a simulation based stochastic optimization technique that, combined with a receding horizon approach, obviates the need to solve the computationally intractable I-space DP problem. The technique is tested on a simple sensor scheduling problem where a sensor has to choose among the measurements of N dynamical systems such that the information regarding the aggregate system is maximized over an infinite horizon.

Modular FPGA-based software defined radio for CubeSats

Scheduling of contacts between several satellites and ground stations has been historically sub-optimally approached. This fact raises the question: can this problem be solved in polynomial time? Although existing literature provided optimal solutions for some simplified versions of this problem and studied some connections with general scheduling, few has been said on the complexity of more general cases. We formally characterize the complexity of the satellite scheduling problem, and provide the sufficient conditions for polynomial time solvability. We back up these results with a survey on several problem instances covering existing and new connections between these problems and those from general scheduling, which allow us to formally define how satellite scheduling relates to general scheduling. To the best of our knowledge, this is the most extensive characterization of satellite range scheduling, covering its definition, complexity and connections to general scheduling.