Matrix Design for Optimal Sensing

We design optimal $2 \times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of $N$ observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary $N\geq3$, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of three columns. Surprisingly, a uniform distribution of the columns is \emph{not} the optimal design for odd $N\geq 7$.Comment: conferenc

Sub-optimal sensor scheduling with error bounds

Abstract: In this paper the problem of sub-optimal sensor scheduling with a guaranteed distance to optimality is considered. Optimal in the sense that the sequence that minimizes the estimation error covariance matrix for a given time horizon is found. The search is done using relaxed dynamic programming. The algorithm is then applied to one simple second order system and one sixth order model of a fixed mounted model lab helicopter. Copyright c○2005 IFA

Scheduling for Distributed Sensor Networks

We examine the problem of distributed estimation when only one sensor can take a measurement per time step. The measurements are then exchanged among the sensors. The problem is motivated by the use of sonar range-finders used by the vehicles on the Caltech Multi-Vehicle Wireless Testbed. We solve for the optimal recursive estimation algorithm when the sensor switching schedule is given. Then we investigate several approaches for determining an optimal sensor switching strategy. We see that this problem involves searching a tree in general and propose and analyze two strategies for pruning the tree to keep the computation limited. The first is a sliding window strategy motivated by the Viterbi algorithm, and the second one uses thresholding. We also study a technique that employs choosing the sensors randomly from a probability distribution which can then be optimized. The performance of the algorithms are illustrated with the help of numerical examples

Optimization and Control of Cyber-Physical Vehicle Systems

A cyber-physical system (CPS) is composed of tightly-integrated computation, communication and physical elements. Medical devices, buildings, mobile devices, robots, transportation and energy systems can benefit from CPS co-design and optimization techniques. Cyber-physical vehicle systems (CPVSs) are rapidly advancing due to progress in real-time computing, control and artificial intelligence. Multidisciplinary or multi-objective design optimization maximizes CPS efficiency, capability and safety, while online regulation enables the vehicle to be responsive to disturbances, modeling errors and uncertainties. CPVS optimization occurs at design-time and at run-time. This paper surveys the run-time cooperative optimization or co-optimization of cyber and physical systems, which have historically been considered separately. A run-time CPVS is also cooperatively regulated or co-regulated when cyber and physical resources are utilized in a manner that is responsive to both cyber and physical system requirements. This paper surveys research that considers both cyber and physical resources in co-optimization and co-regulation schemes with applications to mobile robotic and vehicle systems. Time-varying sampling patterns, sensor scheduling, anytime control, feedback scheduling, task and motion planning and resource sharing are examined

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions

Toward Co-Design of Autonomous Aerospace Cyber-Physical Systems.

Modern vehicles are equipped with a complex suite of computing (cyber) and electromechanical (physical) systems. Holistic design, modeling, and optimization of such Cyber-Physical Systems (CPS) requires new techniques capable of integrated analysis across the full CPS. This dissertations introduces two methods for balancing cyber and physical resources in a step toward holistic co-design of CPS. First, an ordinary differential equation model abstraction of controller sampling rate is developed and added to the equations of motion of a physical system to form a holistic discrete-time-varying linear system representing the CPS controller. Using feedback control, this cyber effector, sampling rate, is then co-regulated alongside physical effectors in response to physical system tracking error. This technique is applied to a spring-mass-damper, inverted pendulum, and finally to attitude control of a small satellite (CubeSat). Additionally, two new controllers for discrete-time-varying systems are introduced; a gain-scheduled discrete-time linear regulator (DLQR) in which DLQR gains are scheduled over time-varying sampling rates, and a forward-propagation Riccati-based (FPRB) controller. The FPRB CPS controller shows promise in balancing cyber and physical resources. Second, we propose a cost function of cyber and physical parameters to optimize an Unmanned Aircraft System (UAS) trajectory for a pipeline surveillance mission. Optimization parameters are UAV velocity and mission-critical surveillance task execution rate. Metrics for pipeline image information, energy, cyber utilization, and time comprise the cost function and Pareto fronts are analyzed to gain insight into cyber and physical tradeoffs for mission success. Finally, the cost function is optimized using numerical methods, and results from several cost weightings and Pareto front analyses are tabulated. We show that increased mission success can be achieved by considering both cyber and physical parameters together.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108823/1/justyn_1.pd

Performance optimization for unmanned vehicle systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 149-157).Technological advances in the area of unmanned vehicles are opening new possibilities for creating teams of vehicles performing complex missions with some degree of autonomy. Perhaps the most spectacular example of these advances concerns the increasing deployment of unmanned aerial vehicles (UAVs) in military operations. Unmanned Vehicle Systems (UVS) are mainly used in Information, Surveillance and Reconnaissance missions (ISR). In this context, the vehicles typically move about a low-threat environment which is sufficiently simple to be modeled successfully. This thesis develops tools for optimizing the performance of UVS performing ISR missions, assuming such a model.First, in a static environment, the UVS operator typically requires that a vehicle visit a set of waypoints once or repetitively, with no a priori specified order. Minimizing the length of the tour traveled by the vehicle through these waypoints requires solving a Traveling Salesman Problem (TSP). We study the TSP for the Dubins' vehicle, which models the limited turning radius of fixed wing UAVs. In contrast to previously proposed approaches, our algorithms determine an ordering of the waypoints that depends on the model of the vehicle dynamics. We evaluate the performance gains obtained by incorporating such a model in the mission planner.With a dynamic model of the environment the decision making level of the UVS also needs to solve a sensor scheduling problem. We consider M UAVs monitoring N > M sites with independent Markovian dynamics, and treat two important examples arising in this and other contexts, such as wireless channel or radar waveform selection. In the first example, the sensors must detect events arising at sites modeled as two-state Markov chains. In the second example, the sites are assumed to be Gaussian linear time invariant (LTI) systems and the sensors must keep the best possible estimate of the state of each site.(cont.) We first present a bound on the achievable performance which can be computed efficiently by a convex program, involving linear matrix inequalities in the LTI case. We give closed-form formulas for a feedback index policy proposed by Whittle. Comparing the performance of this policy to the bound, it is seen to perform very well in simulations. For the LTI example, we propose new open-loop periodic switching policies whose performance matches the bound.Ultimately, we need to solve the task scheduling and motion planning problems simultaneously. We first extend the approach developed for the sensor scheduling problems to the case where switching penalties model the path planning component. Finally, we propose a new modeling approach, based on fluid models for stochastic networks, to obtain insight into more complex spatiotemporal resource allocation problems. In particular, we give a necessary and sufficient stabilizability condition for the fluid approximation of the problem of harvesting data from a set of spatially distributed queues with spatially varying transmission rates using a mobile server.by Jerome Le Ny.Ph.D