Richard Scott Erwin

Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies

This paper presents a strategy and case studies of spacecraft relative motion guidance and control based on the application of linear quadratic model predictive control (MPC) with dynamically reconfigurable constraints. The controller is designed to transition between the MPC guidance during a spacecraft rendezvous phase and MPC guidance during a spacecraft docking phase, with each phase having distinct requirements, constraints, and sampling rates. Obstacle avoidance is considered in the rendezvous phase, while a line-of-sight cone constraint, bandwidth constraints on the spacecraft attitude control system, and exhaust plume direction constraints are addressed during the docking phase. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. The implementation uses estimates of spacecraft states derived from relative angle and range measurements, and is robust to estimator dynamics and measurement noise.

Direct adaptive disturbance rejection and control for a deployable space telescope, theory and application

Discrete time direct adaptive control with disturbance rejection is derived using the command tracker generator (CGT) design. A proof of stability for this controller is provided and the special case of adaptive disturbance rejection using a fixed gain controller is considered Preliminary results of the simplified adaptive controller performance on the Deployable Optical Telescope (DOT) prove promising, but overall reduction of observed motion in the multi-input, multi-output system is not easily achieved.

Satellite Rendezvous and Conjunction Avoidance: Case Studies in Verification of Nonlinear Hybrid Systems

Satellite systems are beginning to incorporate complex autonomous operations, which calls for rigorous reliability assurances. Human operators usually plan satellite maneuvers in detail, but autonomous operation will require software to make decisions using noisy sensor data and problem solutions with numerical inaccuracies. For such systems, formal verification guarantees are particularly attractive. This paper presents automatic verification techniques for providing assurances in satellite maneuvers. The specific reliability criteria studied are rendezvous and conjunction avoidance for two satellites performing orbital transfers. Three factors pose challenges for verifying satellite systems: (a) incommensurate orbits, (b) uncertainty of orbital parameters after thrusting, and (c) nonlinear dynamics. Three abstractions are proposed for contending with these challenges: (a) quotienting of the state-space based on periodicity of the orbital dynamics, (b) aggregation of similar transfer orbits, and (c) overapproximation of nonlinear dynamics using hybridization. The method’s feasibility is established via experiments with a prototype tool that computes the abstractions and uses existing hybrid systems model checkers.

An AEGIS-FISST Algorithm for Multiple Object Tracking in Space Situational Awareness

In this paper we use Finite Set Statistics (FISST) to track an arbitrary but known number of objects in the presence of clutter for Space SituationalAwareness (SSA). The sensors are assumed faulty with possible misdetections, false alarms and/or noisy data. The measurements are unassociated and, hence, we also solve the data association problem, which is integral to the FISST algorithm. The main contribution of the paper is that, in order to reduce the computational burden entailed in FISST, we employ a Gaussian mixture approximation,not to the first-moment of the full FISST updateequations(knownasGM-PHD),butapplytheapproximationdirectlytothefullFISSTequations. The specific GM technique we employ is the Adaptive Entropy-based Gaussian-mixture Information Synthesis (AEGIS). The approachis demonstratedin two a multiple object SSA applicationexamples.

Development of a sparse-aperture testbed for optomechanical control of space-deployable structures

This paper presents an overview of the development and capabilities of a space-traceable testbed developed for investigation of research issues related to deployable space telescopes. The Air Force Research Laboratory (AFRL) is developing the Deployable Optical Telescope (DOT), which upon completion will be a fully-deployable, sub-scale, space-traceable ground testbed for development and demonstration of critical technologies for the next-generation of space-optics systems. The paper begins with an overview of the DOT project’s technology goals, including the specific performance objectives of the various technologies that are being incorporated into the DOT testbed. The paper presents an overview of the DOT design, including the central integrating structure, deployable primary mirror petals, deployable secondary tower, deployment mechanisms, lightweight mirror segments, metrology, and control systems. The paper concludes with a report on the current status of DOT activities as well as a view of the future research that is planned for the project.

Multiple-Object Space Surveillance Tracking Using Finite-Set Statistics

The dynamic tracking of objects is, in general, concerned with state estimation using imperfect data. Multiple object tracking adds the difficulty of encountering unknown associations between the collected data and the objects. State estimation of objects necessitates the prediction of uncertainty through nonlinear (in the general case) dynamical systems and the processing of nonlinear (in the general case) measurement data in order to provide corrections that refine the system uncertainty, where the uncertainty may be non-Gaussian in nature. The sensors, which provide the measurement data, are imperfect with possible misdetections, false alarms, and noise-affected data. The resulting measurements are inherently unassociated upon reception. In this paper, a Bayesian method for tracking an arbitrary, but known, number of objects is developed. The method is based on finite-set statistics coupled with finite mixture model representations of the multiobject probability density function. Instead of relying on ...

Interference mitigation using spectrum sensing and dynamic frequency hopping

Wireless communications are prone to both unintentional and intentional RF interference. Such interference has significant impact on the reliability of packet transmissions. In this paper, we consider interference mitigation in frequency hopping (FH) systems. We employ cognitive radios (CRs) for proactive interference sensing in such systems. Through this proactive approach, we propose a scheme for dynamic adjustment of the FH sequence. Our protocol, called SSDFH, relies on exploiting the spectrum sensing capabilities of CRs for proactive detection of channel quality. We analyze the characteristics of the proposed SSDFH using a continuous-time Markov chain framework. Level crossing rate (LCR) analysis is used to determine the transition rates for the Markov chain, which are then used to measure the “channel stability,” a metric that reflects the freshness of sensed channel interference. The selection of different protocol parameters is studied by means of analysis. In particular, we provide a numerical procedure for determining the “optimal” total sensing time that minimizes the probability of “black holes.” We run simulations to study the performance of our proposed protocol.

Cost-aware sequential Bayesian tasking and decision-making for search and classification

This paper focuses on the development of a cost-aware sequential Bayesian decision-making strategy for the search and classification of multiple unknown objects within a task domain. Search and classification of multiple objects of unknown numbers are competing tasks under limited vehicle and sensory resources. This is because sensor-equipped vehicles in the system can perform either the search or classification task but not both at the same time. The decision of one task over the other may result in missing other, more important objects not yet found or missing the opportunity to classify a found critical object. In this paper we develop a cost-aware sequential Bayesian decision-making strategy for search and classification, which results in the detection and satisfactory classification of all the unknown objects in the task domain.

Exploiting cognitive radios for reliable satellite communications

Summary Satellite transmissions are prone to both unintentional and intentional RF interference. Such interference has significant impact on the reliability of packet transmissions. In this paper, we make preliminary steps at exploiting the sensing capabilities of cognitive radios for reliable satellite communications. We propose the use of dynamically adjusted frequency hopping (FH) sequences for satellite transmissions. Such sequences are more robust against targeted interference than fixed FH sequences. In our design, the FH sequence is adjusted according to the outcome of out-of-band proactive sensing, carried out by a cognitive radio module that resides in the receiver of the satellite link. Our design, called out-of-band sensing-based dynamic FH, is first analyzed using a discrete-time Markov chain (DTMC) framework. The transition probabilities of the DTMC are then used to measure the ‘channel stability’, a metric that reflects the freshness of sensed channel interference. Next, out-of-band sensing-based dynamic FH is analyzed following a continuous-time Markov chain model, and a numerical procedure for determining the ‘optimal’ total sensing time that minimizes the probability of ‘black holes’ is provided. DTMC is appropriate for systems with continuously adjustable power levels; otherwise, continuous-time Markov chain is the suitable model. We use simulations to study the effects of different system parameters on the performance of our proposed design. Copyright

Finite-horizon controllability and reachability for deterministic and stochastic linear control systems with convex constraints

This paper presents a method for rapidly generating controllability and reachability sets for constrained finite horizon Linear Time Varying (LTV) control systems by using convex optimization techniques. Set generation is accomplished by first solving a Semi-Definite Programming (SDP) problem and then solving a series of Second Order Cone Programming (SOCP) problems. Recent advances in convex optimization solvers have made it possible to find the solutions to these problems very quickly. From a geometric stand-point, we first find the largest volume symmetric simplex that fits within the constrained control problem, then grow new simplices out of the faces of the original simplex. This process is repeated until the growing polytope converges to the constraint boundaries of the actual set. Additionally, a method for incorporating stochastic constraints and uncertainties into the deterministic framework is developed by posing the stochastic constraints as chance-constrained constraints. Finally, the controllability set for a two-vehicle Low Earth Orbit (LEO) rendezvous problem with stochastic uncertainties is generated using the new algorithm.