Theoretical Limits of Speed and Resolution for Kinodynamic Planning in a Poisson Forest

Choudhury, Sanjiban; Scherer, Sebastian; Bagnell, J. Andrew

doi:10.15607/rss.2015.xi.005

Cited by 4 publications

(3 citation statements)

References 19 publications

(26 reference statements)

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“…Prior work in robotics has established fundamental bounds on performance for particular problems. For example, Karaman and Frazzoli (2012) and Choudhury et al (2015) consider high-speed navigation through an ergodic forest consisting of randomly placed obstacles. Results from percolation theory (Bollobás and Riordan, 2006) are used to establish a critical speed beyond which there does not exist (with probability one) an infinite collision-free trajectory.…”

Section: Domain-specific Performance Boundsmentioning

confidence: 99%

Fundamental limits for sensor-based robot control

Majumdar,

Mei,

Pacelli

2023

The International Journal of Robotics Research

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Our goal is to develop theory and algorithms for establishing fundamental limits on performance imposed by a robot’s sensors for a given task. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano's inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision-making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).

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Section: Domain-specific Performance Boundsmentioning

confidence: 99%

Fundamental limits for sensor-based robot control

Majumdar,

Mei,

Pacelli

2023

The International Journal of Robotics Research

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“…Prior work in robotics has established fundamental bounds on performance for particular problems. For example, [4,5] consider highspeed navigation through an (ergodic) forest consisting of randomly-placed obstacles. Results from percolation theory [6] are used to establish a critical speed beyond which there does not exist (with probability one) an infinite collision-free trajectory.…”

Section: A Related Workmentioning

confidence: 99%

Fundamental Limits for Sensor-Based Robot Control

Majumdar¹,

Pacelli²

2022

Preprint

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Our goal is to develop theory and algorithms for establishing fundamental limits on performance for a given task imposed by a robot's sensors. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).

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“…In [59], they show that a planning algorithm based on state lattices can navigate the robot with limited sensing range. A similar problem is also studied in [60].…”

Section: A Related Workmentioning

confidence: 99%

On Sensing, Agility, and Computation Requirements for a Data-gathering Agile Robotic Vehicle

Ma,

Karaman

2017

Preprint

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We consider a robotic vehicle tasked with gathering information by visiting a set of spatially-distributed data sources, the locations of which are not known a priori, but are discovered on the fly. We assume a first-order robot dynamics involving drift and that the locations of the data sources are Poisson-distributed. In this setting, we characterize the performance of the robot in terms of its sensing, agility, and computation capabilities. More specifically, the robot's performance is characterized in terms of its ability to sense the target locations from a distance, to maneuver quickly, and to perform computations for inference and planning. We also characterize the performance of the robot in terms of the amount and distribution of information that can be acquired at each data source. The following are among our theoretical results: the distribution of the amount of information among the target locations immensely impacts the requirements for sensing targets from a distance; performance increases with increasing maneuvering capability, but with diminishing returns; and the computation requirements increase more rapidly for planning as opposed to inference, with both increasing sensing range and maneuvering ability. We provide computational experiments to validate our theoretical results. Finally, we demonstrate that these results can be utilized in the co-design of sensing, actuation, and computation capabilities of mobile robotic systems for an information-gathering mission. Our proof techniques establish novel connections between the fundamental problems of robotic information-gathering and the last-passage percolation problem of statistical mechanics, which may be of interest on its own right.

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Theoretical Limits of Speed and Resolution for Kinodynamic Planning in a Poisson Forest

Cited by 4 publications

References 19 publications

Fundamental limits for sensor-based robot control

Fundamental limits for sensor-based robot control

Fundamental Limits for Sensor-Based Robot Control

On Sensing, Agility, and Computation Requirements for a Data-gathering Agile Robotic Vehicle

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