Kurt Krebsbach | Lawrence University (original) (raw)

Papers by Kurt Krebsbach

Research paper thumbnail of Iterative-Expansion A

The Florida AI Research Society, 2012

In this paper we describe an improvement to the popular IDA* search algorithm that emphasizes a d... more In this paper we describe an improvement to the popular IDA* search algorithm that emphasizes a different spacefor-time trade-off than previously suggested. In particular, our algorithm, called Iterative-Expansion A* (IEA*), focuses on reducing redundant node expansions within individual depth-first search (DFS) iterations of IDA* by employing a relatively small amount of available memorybounded by the error in the heuristic-to store selected nodes. The additional memory required is exponential not in the solution depth, but only in the difference between the solution depth and the estimated solution depth. A constanttime hash set lookup can then be used to prune entire subtrees as DFS proceeds. Overall, we show 2-to 26-fold time speedups vs. an optimized version of IDA* across several domains, and compare IEA* with several other competing approaches. We also sketch proofs of optimality and completeness for IEA*, and note that IEA* is particularly efficient for solving implicitly-defined general graph search problems.

Research paper thumbnail of Improving Trust Estimates in Planning Domains with Rare Failure Events

National Conference on Artificial Intelligence, Mar 15, 2013

In many planning domains, it is impossible to construct plans that are guaranteed to keep the sys... more In many planning domains, it is impossible to construct plans that are guaranteed to keep the system completely safe. A common approach is to build probabilistic plans that are guaranteed to maintain system with a sufficiently high probability. For many such domains, bounds on system safety cannot be computed analytically, but instead rely on execution sampling coupled with a plan verification techniques. While probabilistic planning with verification can work well, it is not adequate in situations in which some modes of failure are very rare, simply because too many execution traces must be sampled (e.g., 10 12) to ensure that the rare events of interest will occur even once. The P-CIRCA planner seeks to solve planning problems while probabilistically guaranteeing safety. Our domains frequently involve verifying that the probability of failure is below a low threshold (< 0.01). Because the events we sample have such low probabilities, we use Importance sampling (IS) (Hammersley and Handscomb 1964; Clarke and Zuliani 2011) to reduce the number of samples required. However, since we deal with an abstracted model, we cannot bias all paths individually. This prevents IS from achieving a correct bias. To compensate for this drawback we present a concept of DAGification to partially expand our representation and achieve a better bias.

Research paper thumbnail of Front-to-Front Bidirectional Best-First Search Reconsidered

Research paper thumbnail of Rational sensing for an AI planner: a cost-based approach

Task planning involves the construction of plans to accomplish goals and the execution of these p... more Task planning involves the construction of plans to accomplish goals and the execution of these plans in the task environment by an agent. We have developed a planner/executor that can plan to perform sensor operations which allow an agent to gather the information necessary to complete planning and achieve its goals in the face of missing or uncertain environmental information. The problem can be viewed as one of choosing among various sensing policies in order to maximize some reward (a successful plan) or minimize some cost (execution plan length). Determining an optimal policy for a given planning problem consists of computing tradeoffs between domain-specific factors such as sensor reliabilities, the cost of firing sensors, premature action recovery costs, bad data recovery costs, and the cost of human intervention. Some of these costs are determined while others are analytically derived. Exhaustive strategies for this computation become intractable for even a modest degree of environmental uncertainty. A major objective of this research is to suggest computationally feasible ways to solve this problem. Two methods will be presented in two distinct demonstration domains. The first method, static sensor scheduling, involves probabilistically constructing a sensor schedule offline which is used by the planner/executor to minimize expected plan length. The second, dynamic sensor selection, consists of building a directed graph offline and using actual world states as an index into the graph as planning and execution progress. Both algorithms have been implemented and can be shown to be polynomial in both time and space complexity.

Research paper thumbnail of Automated

In multi-agent CIRCA, we extend real-time perfor-mance characteristics to a team of coordinating ... more In multi-agent CIRCA, we extend real-time perfor-mance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illus-trated in Figure 1, individual agents combine the adap-tive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these con-trollers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM’s deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its

Research paper thumbnail of Human Interaction with Autonomous Systems in Complex Environments

Research paper thumbnail of A refinery immobot for abnormal situation management

AAAI'97 Workshop on Robots, Softbots, and …, 1997

Oil re neries literally provide the lifeblood for global economic health, and disruptions to thei... more Oil re neries literally provide the lifeblood for global economic health, and disruptions to their operations have major worldwide impact. We are developing a large-scale semi-autonomous re nery immobot to assist human operators in controlling re neries dur-ing abnormal ...

Research paper thumbnail of Multi-agent mission coordination via negotiation

Working Notes of the AAAI Fall Symposium …, 2001

This paper is intended to give an intuitive overview of the operations of MASA-CIRCA, the Multi-A... more This paper is intended to give an intuitive overview of the operations of MASA-CIRCA, the Multi-Agent Self-Adaptive Cooperative Intelligent Real-Time Control Architecture. While individual CIRCA agents have been under development for some time, we have only recently ...

Research paper thumbnail of Managing Online Self-adaptation in Real-Time Environments

Lecture Notes in Computer Science, 2003

Research paper thumbnail of Projection and Reaction for Decision Support in Refineries: Combining Multiple Theories

Modern decision support systems are forced to deal with perpetual change in their environment: ch... more Modern decision support systems are forced to deal with perpetual change in their environment: change that includes a high degree of uncertainty over the current state of the plant, effects of actions, accuracy of sensor readings, and

Research paper thumbnail of Sensing and deferral in planning: Empirical results

The study described in this report constitutes part of an ongoing research project in the area of... more The study described in this report constitutes part of an ongoing research project in the area of task plan-ning under uncertainty. Traditional approaches to task planning assume that the planner has access to all of

Research paper thumbnail of Other Agents ’ Actions as Asynchronous Events

An individual planning agent does not generally have sufficient computational resources at its di... more An individual planning agent does not generally have sufficient computational resources at its disposal to pro-duce an optimal plan in a complex domain, as delibera-tion itself requires and consumes scarce resources. This problem is further exacerbated in a distributed plan-ning context in which multiple, heterogeneous agents must expend a portion of their resource allotment on communication, negotiation, and shared planning ac-tivities with other cooperative agents. Because other agents can have different temporal grain sizes, plan-ning horizons, deadlines, and access to distinct local information, the delays associated with local delibera-tion and, in turn, shared negotiation are asynchronous, unpredictable, and widely variable. We address this problem using a principled, decision-theoretic approach based on recent advances in Gen-eralized Semi-Markov Decision Processes (GSMDPs). In particular, we use GSMDPs to model agents who develop a continuous-time deliberation policy offline...

Research paper thumbnail of Hybrid Reasoning for Complex Systems

We have recently begun work on extending our least-commitment constraint-based scheduling technol... more We have recently begun work on extending our least-commitment constraint-based scheduling technology to handle more complex dynamical models. The current scheduling process involves a complex interaction between discrete choices (resource assignments, sequencing decisions) , and a continuous temporal model. Discrete choices enforce new constraints on the temporal model. Those constraints may be inconsistent with the current model, thus forcing backtracking in the discrete domain, or if consistent, may serve to constrain choices for discrete variables not yet assigned. The extensions currently underway involve adapting and modifying more complex continuous models. This will permit us to apply the system to such complex problems as crude blending or tank management at a refinery, aircraft mission planning, or spacecraft mission planning and control.

Research paper thumbnail of Plant + Control System + Human: Three's a Crowd (Extended Abstract)

Research paper thumbnail of A Learning Natural Language Parser

A natural language parser is described that analyzes the syntactic structure of an input sentence... more A natural language parser is described that analyzes the syntactic structure of an input sentence in relation to a specified grammar and generates all possible syntax trees of the sentence, along with estimates of the probability of each being the correct parse. The grammar used is based on X-bar theory, and the parsing algorithm is a chart parse – a top-down parser which uses dynamic programming for efficiency in cases where the grammar leads to ambiguities. The parser has a database of the frequency of application of each syntax rule in the grammar as well as a lexicon of known words and their lexical categories and frequency of use in each category. These are used in a probabilistic context-free grammar model to yield the likelihood judgments of the candidate parses and are updated by user feedback, leading to more accurate subsequent estimations.

Research paper thumbnail of Deferring Task Planning in the Tool Box World: Empirical Results

Traditional approaches to task planning assume that the planner has access to all of the world in... more Traditional approaches to task planning assume that the planner has access to all of the world information needed to develop a complete, correct plan which can then be executed in its entirety by an agent. Since this assumption does not typically hold in realistic domains, we have implemented a planner which can plan to perform sensor operations to allow an agent to gather the information necessary to complete planning and achieve its goals in the face of missing or uncertain environmental information. Naturally this approach requires some execution to be interleaved with the planning process. In this report we present the results of a systematic experimental study of this planner's performance under various conditions. The chief difficulty arises when the agent performs actions which interfere with or, in the worst case, preclude the possibility of the achievement of its later goals. We have found that by making intelligent decisions about goal ordering, what to sense, and whe...

Research paper thumbnail of Coordinated Deliberation Management in Multi-Agent CIRCAKurt

Kurt D. Krebsbach Automated Reasoning Group Honeywell Laboratories 3660 Technology Drive Minneapo... more Kurt D. Krebsbach Automated Reasoning Group Honeywell Laboratories 3660 Technology Drive Minneapolis, MN 55418 krebsbac@htc.honeywell.com In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illustrated in Figure 1, individual agents combine the adaptive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these controllers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM's deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its CSM generate plans (controllers) to address those tasks during mission exe...

Research paper thumbnail of Coordinated Deliberation Management in Multi-Agent CIRCA

In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating C... more In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illustrated in Figure 1, individual agents combine the adaptive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these controllers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM’s deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its CSM generate plans (controllers) to address those tasks during mission execution (AMP-to-CSM). CSM Deliberation: The overall team mission is composed of phases, which correspond to modes or time intervals that share ...

Research paper thumbnail of Over-Constrained Scheduling using Dynamic Programming

In this paper, we demonstrate the use of stochastic dynamic programming to solve over-constrained... more In this paper, we demonstrate the use of stochastic dynamic programming to solve over-constrained scheduling problems. In particular, we propose a decision method for efficiently calculating, prior to start of execution, the optimal decision for every possible situation encountered in sequential, predictable, overconstrained scheduling domains. We present our resuits using an example problem from Product Quality Planning.

Research paper thumbnail of Dynamic Sensor Policies

When an agent’s task environment is largely benign and partially predictable (although uncertain)... more When an agent’s task environment is largely benign and partially predictable (although uncertain), and the goals involve accomplishing tasks, we can make the agent more adaptive by planning to acquire unknown or uncertain information during execution of the task. Of course we pay a price for this flexibility. In this paper we dicuss a strategy for measuring this price in a realistic way and reducing it by making rational decisions about how to acquire unknown environmental information with imperfect sensors. Ultimately, we are interested in a generM framework for making optimal sensor decisions which will minimize a cost (or set of costs) we expect to incur by employing sensors. In particular, we propose to generate a tree of possible sensing policies offline (using dynamic programming), cache the optimal sensor decisions at each level, and subsequently use actual world states as indexes into this structure to make a rational sensor choice online. Because no states are discarded in ...

Research paper thumbnail of Iterative-Expansion A

The Florida AI Research Society, 2012

In this paper we describe an improvement to the popular IDA* search algorithm that emphasizes a d... more In this paper we describe an improvement to the popular IDA* search algorithm that emphasizes a different spacefor-time trade-off than previously suggested. In particular, our algorithm, called Iterative-Expansion A* (IEA*), focuses on reducing redundant node expansions within individual depth-first search (DFS) iterations of IDA* by employing a relatively small amount of available memorybounded by the error in the heuristic-to store selected nodes. The additional memory required is exponential not in the solution depth, but only in the difference between the solution depth and the estimated solution depth. A constanttime hash set lookup can then be used to prune entire subtrees as DFS proceeds. Overall, we show 2-to 26-fold time speedups vs. an optimized version of IDA* across several domains, and compare IEA* with several other competing approaches. We also sketch proofs of optimality and completeness for IEA*, and note that IEA* is particularly efficient for solving implicitly-defined general graph search problems.

Research paper thumbnail of Improving Trust Estimates in Planning Domains with Rare Failure Events

National Conference on Artificial Intelligence, Mar 15, 2013

In many planning domains, it is impossible to construct plans that are guaranteed to keep the sys... more In many planning domains, it is impossible to construct plans that are guaranteed to keep the system completely safe. A common approach is to build probabilistic plans that are guaranteed to maintain system with a sufficiently high probability. For many such domains, bounds on system safety cannot be computed analytically, but instead rely on execution sampling coupled with a plan verification techniques. While probabilistic planning with verification can work well, it is not adequate in situations in which some modes of failure are very rare, simply because too many execution traces must be sampled (e.g., 10 12) to ensure that the rare events of interest will occur even once. The P-CIRCA planner seeks to solve planning problems while probabilistically guaranteeing safety. Our domains frequently involve verifying that the probability of failure is below a low threshold (< 0.01). Because the events we sample have such low probabilities, we use Importance sampling (IS) (Hammersley and Handscomb 1964; Clarke and Zuliani 2011) to reduce the number of samples required. However, since we deal with an abstracted model, we cannot bias all paths individually. This prevents IS from achieving a correct bias. To compensate for this drawback we present a concept of DAGification to partially expand our representation and achieve a better bias.

Research paper thumbnail of Front-to-Front Bidirectional Best-First Search Reconsidered

Research paper thumbnail of Rational sensing for an AI planner: a cost-based approach

Task planning involves the construction of plans to accomplish goals and the execution of these p... more Task planning involves the construction of plans to accomplish goals and the execution of these plans in the task environment by an agent. We have developed a planner/executor that can plan to perform sensor operations which allow an agent to gather the information necessary to complete planning and achieve its goals in the face of missing or uncertain environmental information. The problem can be viewed as one of choosing among various sensing policies in order to maximize some reward (a successful plan) or minimize some cost (execution plan length). Determining an optimal policy for a given planning problem consists of computing tradeoffs between domain-specific factors such as sensor reliabilities, the cost of firing sensors, premature action recovery costs, bad data recovery costs, and the cost of human intervention. Some of these costs are determined while others are analytically derived. Exhaustive strategies for this computation become intractable for even a modest degree of environmental uncertainty. A major objective of this research is to suggest computationally feasible ways to solve this problem. Two methods will be presented in two distinct demonstration domains. The first method, static sensor scheduling, involves probabilistically constructing a sensor schedule offline which is used by the planner/executor to minimize expected plan length. The second, dynamic sensor selection, consists of building a directed graph offline and using actual world states as an index into the graph as planning and execution progress. Both algorithms have been implemented and can be shown to be polynomial in both time and space complexity.

Research paper thumbnail of Automated

In multi-agent CIRCA, we extend real-time perfor-mance characteristics to a team of coordinating ... more In multi-agent CIRCA, we extend real-time perfor-mance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illus-trated in Figure 1, individual agents combine the adap-tive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these con-trollers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM’s deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its

Research paper thumbnail of Human Interaction with Autonomous Systems in Complex Environments

Research paper thumbnail of A refinery immobot for abnormal situation management

AAAI'97 Workshop on Robots, Softbots, and …, 1997

Oil re neries literally provide the lifeblood for global economic health, and disruptions to thei... more Oil re neries literally provide the lifeblood for global economic health, and disruptions to their operations have major worldwide impact. We are developing a large-scale semi-autonomous re nery immobot to assist human operators in controlling re neries dur-ing abnormal ...

Research paper thumbnail of Multi-agent mission coordination via negotiation

Working Notes of the AAAI Fall Symposium …, 2001

This paper is intended to give an intuitive overview of the operations of MASA-CIRCA, the Multi-A... more This paper is intended to give an intuitive overview of the operations of MASA-CIRCA, the Multi-Agent Self-Adaptive Cooperative Intelligent Real-Time Control Architecture. While individual CIRCA agents have been under development for some time, we have only recently ...

Research paper thumbnail of Managing Online Self-adaptation in Real-Time Environments

Lecture Notes in Computer Science, 2003

Research paper thumbnail of Projection and Reaction for Decision Support in Refineries: Combining Multiple Theories

Modern decision support systems are forced to deal with perpetual change in their environment: ch... more Modern decision support systems are forced to deal with perpetual change in their environment: change that includes a high degree of uncertainty over the current state of the plant, effects of actions, accuracy of sensor readings, and

Research paper thumbnail of Sensing and deferral in planning: Empirical results

The study described in this report constitutes part of an ongoing research project in the area of... more The study described in this report constitutes part of an ongoing research project in the area of task plan-ning under uncertainty. Traditional approaches to task planning assume that the planner has access to all of

Research paper thumbnail of Other Agents ’ Actions as Asynchronous Events

An individual planning agent does not generally have sufficient computational resources at its di... more An individual planning agent does not generally have sufficient computational resources at its disposal to pro-duce an optimal plan in a complex domain, as delibera-tion itself requires and consumes scarce resources. This problem is further exacerbated in a distributed plan-ning context in which multiple, heterogeneous agents must expend a portion of their resource allotment on communication, negotiation, and shared planning ac-tivities with other cooperative agents. Because other agents can have different temporal grain sizes, plan-ning horizons, deadlines, and access to distinct local information, the delays associated with local delibera-tion and, in turn, shared negotiation are asynchronous, unpredictable, and widely variable. We address this problem using a principled, decision-theoretic approach based on recent advances in Gen-eralized Semi-Markov Decision Processes (GSMDPs). In particular, we use GSMDPs to model agents who develop a continuous-time deliberation policy offline...

Research paper thumbnail of Hybrid Reasoning for Complex Systems

We have recently begun work on extending our least-commitment constraint-based scheduling technol... more We have recently begun work on extending our least-commitment constraint-based scheduling technology to handle more complex dynamical models. The current scheduling process involves a complex interaction between discrete choices (resource assignments, sequencing decisions) , and a continuous temporal model. Discrete choices enforce new constraints on the temporal model. Those constraints may be inconsistent with the current model, thus forcing backtracking in the discrete domain, or if consistent, may serve to constrain choices for discrete variables not yet assigned. The extensions currently underway involve adapting and modifying more complex continuous models. This will permit us to apply the system to such complex problems as crude blending or tank management at a refinery, aircraft mission planning, or spacecraft mission planning and control.

Research paper thumbnail of Plant + Control System + Human: Three's a Crowd (Extended Abstract)

Research paper thumbnail of A Learning Natural Language Parser

A natural language parser is described that analyzes the syntactic structure of an input sentence... more A natural language parser is described that analyzes the syntactic structure of an input sentence in relation to a specified grammar and generates all possible syntax trees of the sentence, along with estimates of the probability of each being the correct parse. The grammar used is based on X-bar theory, and the parsing algorithm is a chart parse – a top-down parser which uses dynamic programming for efficiency in cases where the grammar leads to ambiguities. The parser has a database of the frequency of application of each syntax rule in the grammar as well as a lexicon of known words and their lexical categories and frequency of use in each category. These are used in a probabilistic context-free grammar model to yield the likelihood judgments of the candidate parses and are updated by user feedback, leading to more accurate subsequent estimations.

Research paper thumbnail of Deferring Task Planning in the Tool Box World: Empirical Results

Traditional approaches to task planning assume that the planner has access to all of the world in... more Traditional approaches to task planning assume that the planner has access to all of the world information needed to develop a complete, correct plan which can then be executed in its entirety by an agent. Since this assumption does not typically hold in realistic domains, we have implemented a planner which can plan to perform sensor operations to allow an agent to gather the information necessary to complete planning and achieve its goals in the face of missing or uncertain environmental information. Naturally this approach requires some execution to be interleaved with the planning process. In this report we present the results of a systematic experimental study of this planner's performance under various conditions. The chief difficulty arises when the agent performs actions which interfere with or, in the worst case, preclude the possibility of the achievement of its later goals. We have found that by making intelligent decisions about goal ordering, what to sense, and whe...

Research paper thumbnail of Coordinated Deliberation Management in Multi-Agent CIRCAKurt

Kurt D. Krebsbach Automated Reasoning Group Honeywell Laboratories 3660 Technology Drive Minneapo... more Kurt D. Krebsbach Automated Reasoning Group Honeywell Laboratories 3660 Technology Drive Minneapolis, MN 55418 krebsbac@htc.honeywell.com In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illustrated in Figure 1, individual agents combine the adaptive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these controllers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM's deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its CSM generate plans (controllers) to address those tasks during mission exe...

Research paper thumbnail of Coordinated Deliberation Management in Multi-Agent CIRCA

In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating C... more In multi-agent CIRCA, we extend real-time performance characteristics to a team of coordinating CIRCA agents, each controlling a separate member of a team of unmanned combat air vehicles (UCAVs). As illustrated in Figure 1, individual agents combine the adaptive mission planning (AMP) and automatic controller synthesis (CSM) modules with a plan executive (RTS) that is responsible for reactively executing these controllers. As also shown, CIRCA agents negotiate at all levels of the architecture to coordinate their activities. The focus of this work involves managing the CSM’s deliberation time. The AMP manages this resource in two ways: by determining which tasks to perform through negotiation with other cooperating agents (AMP-to-AMP), and by scheduling time to have its CSM generate plans (controllers) to address those tasks during mission execution (AMP-to-CSM). CSM Deliberation: The overall team mission is composed of phases, which correspond to modes or time intervals that share ...

Research paper thumbnail of Over-Constrained Scheduling using Dynamic Programming

In this paper, we demonstrate the use of stochastic dynamic programming to solve over-constrained... more In this paper, we demonstrate the use of stochastic dynamic programming to solve over-constrained scheduling problems. In particular, we propose a decision method for efficiently calculating, prior to start of execution, the optimal decision for every possible situation encountered in sequential, predictable, overconstrained scheduling domains. We present our resuits using an example problem from Product Quality Planning.

Research paper thumbnail of Dynamic Sensor Policies

When an agent’s task environment is largely benign and partially predictable (although uncertain)... more When an agent’s task environment is largely benign and partially predictable (although uncertain), and the goals involve accomplishing tasks, we can make the agent more adaptive by planning to acquire unknown or uncertain information during execution of the task. Of course we pay a price for this flexibility. In this paper we dicuss a strategy for measuring this price in a realistic way and reducing it by making rational decisions about how to acquire unknown environmental information with imperfect sensors. Ultimately, we are interested in a generM framework for making optimal sensor decisions which will minimize a cost (or set of costs) we expect to incur by employing sensors. In particular, we propose to generate a tree of possible sensing policies offline (using dynamic programming), cache the optimal sensor decisions at each level, and subsequently use actual world states as indexes into this structure to make a rational sensor choice online. Because no states are discarded in ...