Showing papers by "Brian C. Williams published in 2005"

Hybrid Estimation of Complex Systems

Abstract: Modern automated systems evolve both continuously and discretely, and hence require estimation techniques that go well beyond the capability of a typical Kalman filter. Multiple model (MM) estimation schemes track these system evolutions by applying a bank of filters, one for each discrete system mode. Modern systems, however, are often composed of many interconnected components that exhibit rich behaviors, due to complex, system-wide interactions. Modeling these systems leads to complex stochastic hybrid models that capture the large number of operational and failure modes. This large number of modes makes a typical MM estimation approach infeasible for online estimation. This paper analyzes the shortcomings of MM estimation, and then introduces an alternative hybrid estimation scheme that can efficiently estimate complex systems with large number of modes. It utilizes search techniques from the toolkit of model-based reasoning in order to focus the estimation on the set of most likely modes, without missing symptoms that might be hidden amongst the system noise. In addition, we present a novel approach to hybrid estimation in the presence of unknown behavioral modes. This leads to an overall hybrid estimation scheme for complex systems that robustly copes with unforeseen situations in a degraded, but fail-safe manner.

Coordinating agile systems through the model-based execution of temporal plans

Abstract: Agile autonomous systems are emerging, such as unmanned aerial vehicles (UAVs), that must robustly perform tightly coordinated time-critical missions; for example, military surveillance or search-and-rescue scenarios. In the space domain, execution of temporally flexible plans has provided an enabler for achieving the desired coordination and robustness. We address the challenge of extending plan execution to underactuated systems that are controlled indirectly through the setting of continuous state variables. Our solution is a novel model-based executive that takes as input a temporally flexible state plan, specifying intended state evolutions, and dynamically generates a near-optimal control sequence. To achieve optimality and safety, the executive plans into the future, framing planning as a disjunctive programming problem. To achieve robustness to disturbances and tractability, planning is folded within a receding horizon, continuous planning framework. Key to performance is a problem reduction method based on constraint pruning. We benchmark performance through a suite of UAV scenarios using a hardware-in-the-loop testbed.

Model-based monitoring and diagnosis of systems with software-extended behavior

Abstract: Model-based diagnosis has largely operated on hard-ware systems. However, in most complex systems today, hardware is augmented with software functions that influence the system's behavior. In this paper, hard-ware models are extended to include the behavior of associated embedded software, resulting in more comprehensive diagnoses. Prior work introduced probabilistic, hierarchical, constraint-based automata (PHCA) to allow the uniform and compact encoding of both hard-ware and software behavior. This paper focuses on PHCA-based monitoring and diagnosis to ensure the robustness of complex systems. We introduce a novel approach that frames diagnosis over a finite time horizon as a soft constraint optimization problem (COP), allowing us to leverage an extensive body of efficient solution methods for COPs. The solutions to the COP correspond to the most likely evolutions of the complex system. We demonstrate our approach on a vision-based rover navigation system, and models of the SPHERES and Earth Observing One spacecraft.

Finite Horizon Control Design for Optimal Model Discrimination

Abstract: In many fault detection and system identification problems, it is essential to be able to discriminate between a number of competing models of a system based on observed system outputs. For example, in a fault detection scenario we may wish to determine whether a system is best modeled by a known nominal model, or a known failure model. The probability of detecting the true system model can be enhanced by design of the control inputs applied to the system. In this paper we present a method by which a finite sequence of control inputs is designed automatically in order to minimize an upper bound on the probability of model selection error between any two linear, discrete-time systems. We are able to solve this problem efficiently by showing that it is an instance of a Quadratic Program. In addition, linear equality and inequality constraints can be applied to the control inputs and expected system state. These constraints can be used to ensure that a certain task is fulfilled, make sure the system stays within a valid linearization region, or to guarantee safe operation. Experimental results for the case of an aircraft actuator failure scenario show that the method significantly reduces the upper bound on the probability of model selection error when compared to a manually generated sequence and a fuel-optimal sequence.

Diagnosis as approximate belief state enumeration for probabilistic concurrent constraint automata

Abstract: As autonomous spacecraft and other robotic systems grow increasingly complex, there is a pressing need for capabilities that more accurately monitor and diagnose system state while maintaining reactivity. Mode estimation addresses this problem by reasoning over declarative models of the physical plant, represented as a factored variant of Hidden Markov Models (HMMs), called Probabilistic Concurrent Constraint Automata (PCCA). Previous mode estimation approaches track a set of most likely PCCA state trajectories, enumerating them in order of trajectory probability. Although Best-First Trajectory Enumeration (BFTE) is efficient, ignoring the additional trajectories that lead to the same state can significantly underestimate the true state probability and result in misdiagnosis. This paper introduces an innovative belief approximation technique, called Best-First Belief State Enumeration (BFBSE), that addresses this limitation by computing estimate probabilities directly from the HMM belief state update equations. Theoretical and empirical results show that BFBSE significantly increases estimator accuracy, uses less memory, and requires less computation time when enumerating a moderate number of estimates for the approximate belief state of subsystem sized models.

Enabling fast flexible planning through incremental temporal reasoning with conflict extraction

Abstract: In order for an autonomous agent to successfully complete its mission, the agent must be able to quickly re-plan on the fly, as unforeseen events arise in the environment. This is enabled through the use of temporally flexible plans, which allow the agent to adapt to execution uncertainties, by not over committing to timing constraints, and through continuous planners, which are able to replan at any point when the current plan fails. To achieve both of these requirements, planners must have the ability to reason quickly about timing constraints. We enable continuous, temporally flexible planning through a temporal consistency algorithm (ITC), which supports incremental consistency testing on a new type of disjunctive temporal constraint network, the Temporal Plan Network (TPN), and supports focused search through incremental conflict extraction. The ITC algorithm combines the speed of shortest-path algorithms known to network optimization with the spirit of incremental algorithms such as Incremental A* and those used within truth maintenance systems (TMS). Empirical studies of ITC applied to the Kirk temporal planner demonstrate an order of magnitude speed increase on cooperative air vehicle scenarios and on randomly generated plans.

Generalized conflict learning for hybrid discrete/linear optimization

Abstract: Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. At the core of many of these applications is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal feasible solution. In the arena of model-based autonomy, deep space probes have given way to more agile vehicles, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, carried from the conflict-directed search algorithm in model-based reasoning. We introduce a novel algorithm called Generalized Conflict-Directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or sub-optimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. Evaluated empirically on a range of test problems of coordinated air vehicle control, GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm applied to either disjunctive linear programs or an equivalent binary integer programming encoding. This research is funded by The Boeing Company grant MIT-BA-GTA-1 and by NASA grant NNA04CK91A.

Combining stochastic and greedy search in hybrid estimation

Abstract: Techniques for robot monitoring and diagnosis have been developed that perform state estimation using probabilistic hybrid discrete/continuous models. Exact inference in hybrid dynamic systems is, in general, intractable. Approximate algorithms are based on either 1) greedy search, as in the case of k-best enumeration or 2) stochastic search, as in the case of Rao-Blackwellised Particle Filtering (RBPF). In this paper we propose a new method for hybrid state estimation. The key insight is that stochastic and greedy search methods, taken together, are often particularly effective in practice. The new method combines the stochastic methods of RBPF with the greedy search of k-best in order to create a method that is effective for a wider range of estimation problems than the individual methods alone. We demonstrate this robustness on a simulated acrobatic robot, and show that this benefit comes at only a small performance penalty.

Diagnosing Complex Systems with Software-Extended Behavior using Constraint Optimization

Abstract: Model-based diagnosis has traditionally operated on hardware systems. However, in most complex systems today, hardware is augmented with software functions that inuence the system’s behavior. In this paper hardware models are extended to include the behavior of associated embedded software, resulting in more comprehensive diagnoses. Capturing the behavior of software is much more complex than that of hardware due to the potentially enormous state space of a program. This complexity is addressed by using probabilistic, hierarchical, constraint-based automata (PHCA) that allow the uniform and compact encoding of both hardware and software behavior. We introduce a novel approach that frames PHCA-based diagnosis as a soft constraint optimization problem over a nite time horizon. The problem is solved using efcient, decomposition-based optimization techniques. The solutions correspond to the most likely evolutions of the software-extended system.

A Tractable Approach to Probabilistically Accurate Mode Estimation

Abstract: As space exploration missions grow increasingly complex and are required to operate over extended durations of time, there is an amplified demand for accurate autonomous health management systems. In response, model-based programming approaches have been developed as scalable solutions to autonomous health management. Previous model-based monitoring and diagnosis techniques, such as Livingstone, were demonstrated to successfully and efficiently track nominal and failure modes in an abundance of scenarios, but at the cost of making simplifying assumptions about the observation probability that can lead to erroneous diagnoses after extended operation. Extending on Best-First-Belief-StateEnumeration (BFSE), this paper presents a new mode estimation technique called Best-First Belief State Update (BFBSU) that eliminates the observation probability assumption. BFBSU uses the full two-stage HMM belief state update equations as its utility function, thus further increasing estimator accuracy, while maintaining the efficiency required for real-time monitoring and fault detection.

Bounded search and symbolic inference for constraint optimization

Abstract: Constraint optimization underlies many problems in AI. We present a novel algorithm for finite domain constraint optimization that generalizes branch-and-bound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can be represented implicitly and compactly using symbolic techniques such as decision diagrams, the set-based algorithm can compute bounds faster than explicitly searching over individual assignments, while memory explosion can be avoided by limiting the size of the sets. Varying the size of the sets yields a family of algorithms that includes known search and inference algorithms as special cases. Furthermore, experiments on random problems indicate that the approach can lead to significant performance improvements.

Robust distributed coordination of heterogeneous robots through temporal plan networks

Abstract: Real-world applications of autonomous agents require coordinated groups to work in collaboration. Dependable systems must plan and carry out activities in a way that is robust to failure to and uncertainty. Previous work has produced algorithms that provide robustness at the planning phase, by choosing between functionally redundant methods, and at the execution phase, by dispatching temporally flexible plans. However, these algorithms use a centralized architecture in which all computation is performed by a single processor. As a result, these implementations suffer from communication bottlenecks at the master processor, require significant computational capabilities, and do not scale well. This paper introduces the plan extraction component of a robust, distributed executive for contingent plans. Contingent plans are encoded as Temporal Plan Networks (TPNs), which compose temporally flexible plans hierarchically and provide a choose operator. First, the TPN is distributed over multiple agents, by creating a hierarchical ad-hoc network and mapping the TPN onto this hierarchy. Second, candidate plans are extracted from the TPN with a distributed, parallel algorithm that exploits the structure of the TPN. Third, temporal consistency of the candidate plans is tested using a distributed BellmanFord algorithm. This algorithm is empirically validated on randomized contingent plans.

Autonomous Diagnosis based on Software-Extended Behaviour Models

Abstract: Model-based diagnosis has traditionally operated on hardware systems. However, in most complex systems today, hardware is augmented with software functions that inuence the system’s behavior. In this paper hardware models are extended to include the behavior of associated embedded software, resulting in more comprehensive diagnoses. Capturing the behavior of software is much more complex than that of hardware due to the potentially enormous state space of a program. This complexity is addressed by using probabilistic, hierarchical, constraint-based automata (PHCA) that allow the uniform and compact encoding of both hardware and software behavior. We introduce a novel approach that frames PHCA-based diagnosis as a soft constraint optimization problem over a nite time horizon. The problem is solved using efcient, decomposition-based optimization techniques. The solutions correspond to the most likely evolutions of the software-extended system.

Progress towards task-level collaboration between astronauts and their robotic assistants

Abstract: In the future, NASA envisions robotic assistants seamlessly interacting with astronauts. These robots must be capable of understanding abstract tasks, and must also reliably execute the tasks. We make progress towards these goals by firstly developing a task-level programming language, called RMPL, that robots can directly interpret and understand. Secondly, we develop a hybrid executive that can execute the tasks reliably, even while adapting to disturbances and execution uncertainties.

Diagnosis using Bounded Search and Symbolic Inference

Abstract: Model-based diagnosis can be framed as optimization for constraints with preferences (soft constraints). We present a novel algorithm for solving soft constraints that generalizes branch-andbound search by reasoning about sets of assignments rather than individual assignments. Because in many practical cases, sets of assignments can be represented implicitly and compactly using symbolic techniques such as decision diagrams, the setbased algorithm can compute bounds faster than explicitly searching over individual assignments, while memory explosion can be avoided by limiting the size of the sets. Varying the size of the sets yields a family of algorithms that includes known search and inference algorithms as special cases. Experiments indicate that the approach can lead to significant performance improvements.

A* Search for Soft Constraints Bounded by Tree Decompositions

Abstract: Some of the most e-cient methods for solving soft con- straints are based on heuristic search using an evaluation function that is mechanically generated from the problem. However, if only a few best so- lutions are needed, signiflcant efiort can be wasted pre-computing heuris- tics that are not used during search. Recently, a scheme for depth-flrst branch-and-bound search has been proposed that avoids the problems of pre-computation by interleaving search with the generation of heuristics using tree decomposition and dynamic programming. In this paper, we extend this idea to A* search, which has the advantage of expanding a minimal number of search nodes to flnd optimal solutions, and allows to generate solutions in best-flrst order. The approach uses tree decomposi- tion and dynamic programming to generate only those heuristics that are speciflcally required to generate a next best solution. The time complex- ity of the approach is thus optimal among all search algorithms having access to the same heuristics, while its space complexity is bounded by structural parameters of the constraint graph (induced width) in the worst case, and is even lower in the average case.